Transcripts
1. Basic math intro 11:10:18: welcome to quickly mastering basic math, where together we will be learning math from scratch. I know math can be one of the most frustrating topics in school and in life. That's because we're never taught the basic steps of math that really help us learn and more importantly, understand every math topic with ease. Math is like building a house or a structure where the foundation is the most important thing built because it helps the house for structure stay up and the strength of the foundation also determines how long the house stays up for. And that's what I would like to help you with. A very good and strong math foundation that will help you build on top of it and let you move on to more advanced math topics with ease, such as pre algebra, algebra and geometry. To name a few way will achieve this by me, teaching some amazing math tricks that will have you solving problems like you never thought you were capable of. And that's because, just like you are with someone who struggled with Matt as well and out of my personal frustration and after failing math and numerous times when I was in school. I develop some strategies that will help you get ahead and Matt, like you never thought possible. The best part is we will accomplish this together any matter of a few minutes a day because I've taken each topic in basic math and broken down into a few minute videos, which will help you understand any math topic quickly and effectively. In this class, we will be covering the most important fundamental math concepts that will help you in everyday life, such as audition subtraction, multiplication, division, fractions, decimals and much more. So stop letting math frustrate you and let me show you how good you can become at math. Let's get started.
2. Adding 1 & 2 digit numbers: in this first section, we're going to start things off with addition, where we will be adding one into a digit numbers. By the end of this section, you will be very confident. With addition, there won't be any addition problems you won't be able to solve. I recommend you get a few sheets of paper and pencil and write out the problems with me as I present them to you, because it will be the very best way you'll be able to absorb the material. If at any time you miss something or don't understand something I say or do you could always rewind the video or send me an email and I'd be happy to help you. Let's get started far. First problem. We will be adding two plus four. Now I'm going to assume you may have never done addition or you have in practice for a long time. So let's briefly explore the concept of addition. So what does it mean when you're trying to add two things together, which, in our case, it's two plus four? But it could be two pencils plus four pencils or two cars plus four cars. I'm going to count with pencils, so make things more visual for you. So when you see two plus four, you're basically being asked if you have two pencils and four pencils, how many do you have all together or in total? So you start with your first number and begin toe added by one one to then you move on to your next set of numbers or, in this case, pencils. Three, four, five six. So, in total, we have six pencils. So the answer to our problem two plus four equals six. Now that we have solved our first problem, let's get in the habit of writing all our problems all vertically on top of one another. Because when we start adding two at three digit numbers and will help to solve them much easier as you'll see any moment, I just want to make a quick point that whether the problem is right now vertically on top of one another like this or ran out horizontally like so, nothing changes to plus four equals six. Now let's move on to the next problem. Four plus three again. Most of the time you'll be given the problem in this format. But as I mentioned before. Let's place it on top of one another, like so because it makes it easier to solve when we have several digits, as we did before with the pencils. I want to repeat that so you can see how addition works visually, but you can use your fingers to count or anything else that helps you. The great thing about practicing is that with time you'll be able to do it very easily. You won't need to count with your fingers. You just need to practice as we will in this course by solving a lot of problems. So again, let's bring out our pencils for first number. We have four, so let's count up to four. You can use your fingers to count, or you can do as I did when I was younger. I would draw circles on my paper, but to help you see things a little better, I'll use my pencils. So let's count one to three four. Now let's move on to our next numbers. And since we have counted up to four, all we need to do is keep adding one to our four. So now let's just think for a second. What comes after four. The number five. So we just count up from four. Since we're adding three more, so that's continue adding one to our 43 more times five six seven. Your total answer is now seven, since you had three more pencils to count. In addition, you're basically just taking your first Paul of things. It can be pencils, your fingers or circles on your paper and added with second pile or set of numbers. Now let's move on to our next problem, where we will be using slightly bigger numbers. Nine plus six. Now you could come with your fingers or draw circles on your paper. I use my pencils so you can see it visually and understand it better. So let's count our first set of numbers. Nine one to three four five six seven a nine. Now let's at our second set of numbers, 6 to 9 to get our answer. Since we're already at nine, we start from the next number after nine, which is 10 and count up from there. So let's continue. 10 11 12 13 14 15. Our total is 15. Great. If you're still not getting the hang of this. It's OK. You just have to keep practicing with me and you'll see how good you become for next problem. We're gonna ease our way into adding a one digit number with a two digit number. No, I don't want this to scary, because the way I'll show you is gonna make things very easy. No matter how many numbers you're adding so far. Next problem. Let's add 11 plus four. Now we can continue using our pencils to count or use our fingers, as you may be doing. But as you start to add bigger numbers, it takes a lot of time to use your fingers or objects like pencils. So I want to show you how you can easily solve problems with bigger numbers with ease. The way you solve such a problem is working your way from the right to the left. Another thing you need to keep in mind is that when you are adding a bigger and a smaller number, you want to place the bigger number on top, and the smaller number on the bottom also noticed that since we have a double digit number on the top and a single digit number on the bottom. You need to always push or move the number all the way to the right. I line it up with the furthest number to the right, which in this case the smaller number is four. So we place it all the way to the right under the one, and you'll see that as we solve more problems. If at this point there is anything you don't understand, just keep working with me, and I'll assure you it will make sense. So now how do we go about solving this problem? Well, we can go about it in two ways. One way is you can count from the number 11 by starting at 11 and simply adding four, which will give you the answer a second way. You can do it, and this is the way I recommend is by adding the numbers from the right toe. The left, as I mentioned earlier. So let's take a look at how we can do that. First, you want to ask yourself what is one plus four, which is much easier than trying to figure out what is 11 plus four. And if you're trying to use your fingers it's much easier to add one plus four. So let's solve this problem. One plus four equals. If use your fingers or count objects, you'll see that you arrive at five. Now, is this where we're going? From the right to the left? We move on to the second column, and in our second column we have a number one, but nothing on the bottom to add to the one. We carry the one down and put it next to our five, and we get our answer to the problem off 11 plus four, which is 15. Great. If you've done everything I've shown you so far, you should be very proud of yourself. You're doing great. We're making good progress for next problem. We'll be looking at 21 plus seven. I know the numbers are starting to look bigger, but please don't let that scare you with the technique we learned, no matter how large the numbers become, will still be able to solve our problems with ease, just as we did before. We will be working from the right column toe the left column. So let's look at the right column and start solving this problem. We have one plus seven, which, if you add the one to the seven, you get eight another. We have solved our first column. We'll work our way to the left column and saw our second column. And as we've seen before, if in the second column there isn't a number below, you simply carry the number down. And when we carry our two down, we get 28 which is the answer to our problem. 21 plus seven. Great. Now let's move on to our next problem because I want you to get the hang of this so we'll be working on a lot of problems so you can get good practice for next problem. We're gonna be looking at 51 plus five again. Don't let the big numbers intimidate you. The way in which we have been solving our problems helps us add numbers, no matter how big they are. So let's start solving this problem by looking at the right column one plus five. You can use your fingers or you can do it in your head, which is going to give us six. Now we move on to the next column on the left as is, there is no number under the five. We carry it down and get our total, which is 56. Great. Now let's try something slightly different for next problem, and this is a problem that is very important that you understand what's going on. We're gonna take a look at 13 plus eight, and as we've done before, we will be adding the right column first, then moving on to the left column. So first, let's add eight plus three, which gives us 11 if you start counting from eight and at three. Now, if you've noticed in all our other problems, when we added two numbers, we always got a single digit number as the answer, and now we have a double digit number, which is 11. But this is not the right thing to do. The basic rule is that when you're adding up to numbers in this format, if you get a single digit number, you put that single digit number down here, as we've been doing in all our previous problems. But if you get two digits like we get here when we add three plus eight, you will have to do something a little bit different, which is called carrying the number two The following Column. So let's see how that stunned again. Let's do three plus eight, which is going to give us 11. But instead of writing the 11 down here, we're going toe on Lee, right? The number on the right side of the two digit number and the number on the left will come appear to the left column, where we will add it with the number on the left column. And if this is a bit confusing, please don't worry. We will be practicing this a lot, so you will understand exactly what's going on. Just make sure to keep falling along with me, and you'll see how easy this becomes. So now that we have added three plus eight and got her answer of 11 and carried are one, we can now add our numbers on the left side, which is simply going to be one plus one. And the answer to that is going to be, too, and we finally get our answer off 21. Great. Let's build on what we just learned and move on to our next problem, which is going to be similar So for our next problem, let's take a look at 37 plus four. As we've been doing before, let's add the right side first, then move on to the left. So on the right, we have seven plus four, which is going to give us 11. But as we have seen before, when we get a double digit answer, we carry the number on the left and place it on top of the left column. And then we simply add the left column, which is one plus three, which is going to give us four, and we get the answer to our problem. 37 plus four equals 41. Great. You'll see that as we do more of thes problems, you'll start to get better at them for next problem. Let's look at 65 plus nine. Don't let the bigger numbers scare you because the same rules apply. So the first thing we want to do is at the right side, which is five plus mine. If you count them from nine and at five, you'll get 14. So you leave the number four since it's on the right and carry the one on top of the six. Now we move on to the left side of the problem. Since we have solved the right side and on the left we have one plus six, which is going to give a seven. If you count the from six and at one and we get the total of 74 now for next problem, we're going to change things up a bit. And I don't want the extra numbers too scary or intimidate you because the same techniques still applies. So for a next problem, we're gonna have our first double digit plus that will did your problem, which is going to be 15 plus 12. And as we've seen before in our previous problems, the same rules still apply. We still start on the right side and then move on to the left side. Great. So let's get started. First, we want to solve five plus two, which, if you count the from five and at two, you get seven. Now we simply just move on to the left column and add one plus one, which gives us two and we get the assets were problem 15 plus 12 equals 27 break, just in case you're getting a bit confused or unsure of what's going on. Let's do a few more problems so you can get the hang of this so far. Next problem. Let's take a look at slightly bigger numbers. 45 plus 35 as we've been doing before. First, let's start on the right side by adding five plus five, which is going to give us 10. And as we've seen before, when we're adding two numbers on the right side and we get a double digit answer like ton, we simply leave the number on the right side, which is zero and carry the one. Now we move on to the next column and solve it. So first, let's do one plus four, which is going to give us five. And then we take our five and add it with the next number under, which is three. So five plus three equals eight, and we put that next to our zero down here. How we get our total answer off 80. At this point, you should be very proud of yourself. We have covered. I learned a lot so far. Let's just do one more of these problems so you can get the hang of this and we can move on to our next edition topic, where we will continue to learn amazing things for next problem. Let's take a look at 53 plus 38. First, let's solve the right side like we've been doing. So three plus eight is going to give us 11. And of course, we leave the number closest to the right and carry our number on the left. No, we do one plus five, which is going to give a six. And then we do six plus three, which is going to give us nine. And we put that next to our one, and we have the total of 91. Great. I hope you've been following along with me. And remember, if there is anything you didn't understand or very big confused with anything, we went over a recommend the rewatched the video or rewind the parts your a bit unclear on . And if that doesn't help, you can always email me and I will try my best to do anything I can to help you. I appreciate you watching this video, and on the next lecture we will do a small quiz of five problems just to practice the things we learned in this video
3. Adding 3 & 4 digit numbers: Hey, everyone, welcome back In this video we will be building on top of what we learned in our previous lecture by using some of the skills that we learned and learning a few more, which will only help you become better at math. All that I ask is that you stay with me and follow along on every problem that I do. And if at any moment there is something you don't understand, that's okay, you can rewind the video and watch as many times as you need. And if that doesn't help, you can send me an email. And I will do my very best to assist you because being able to put these videos together and help you is very important to me. And I just love doing it. So I appreciate you watching this course. Let's go ahead and learn a few more things in this video will be learning how to add three and four digit numbers. In our previous lecture, we added single digit numbers and double digit numbers, and we got through it very well. So let's continue and let's not let more digits intimidate or scare us. Let's just keep in mind that the same rules apply and not very much changes. So let's get started. For our first problem, we're gonna be looking at 112 plus 10. I know your first thought when looking at this problem might be the fact that for the first time we have a three digit number, so it must be a bit harder. But it really is not just as we did before. We work our way from the right column to the left column and add our numbers step by step. Let's take a look at how we can do that. Let's go to our first column on the right and add two plus zero, which is going to give us two, since zero has no value and represents nothing. Next we go to the next column on the left, where we have one plus one, which is going to give us, too. As I'm sure you probably guessed Fry last step to solve this problem and get her answer, we go to the next column on the left, where we only have a one. And as you seem before, when we have a number by itself like this, we just carry it down and we finally get our answer, which is 122. So, as you can see, not much changes whether you're adding two digit numbers or you're adding three digit numbers. So let's continue practicing, because that's how you will become better and better at math for next problem. We're gonna be looking at 346 plus 123 and again, I know we're starting to see bigger and bigger numbers, but the rules are still the same, so let's see how we can solve this. First we start in the right column where we have six plus three. If you count up from six and add one to it three times, you will arrive at nine. Great. Now we simply move on to our next column on the left, where we have four plus two, which, if you count up from four and add to you get six now we finally move on one more time to our last column on the left, where we have three plus one, which gives us four, and we have our final answer, which is 469 by now. You can see that no matter how many numbers year, adding the same rules still apply for next problem. Let's look at 154 plus 375 just as we did before. Let's start on the right column and work our way to the left as we solve our problems. So for our first column, we have four plus five, which is going to give us nine if you count up from four and add one to your four five times. Now, we move on to our next column on the left, where we have five plus seven and in this column we're gonna have to do as we did before. When we add two numbers on, we get a double digit response. So let's see how we can do that. Five plus seven is going to give us 12. We leave the number closest to the right, which lines up with the number we're adding, and we carry the number on the left to the top of the Left column. Now we move on to our last column, where we add one plus one, which will give us two. And then we moved down two plus three, which will give us five. And we placed that down here and we get our final answer, which is 529. Great. I know that might be a lot to take in, but don't worry. We're gonna be doing a few more problems like this so you can understand exactly what's going on and be able to solve any addition problems that you encounter for next problem. Let's add 415 plus 197. As we've been doing, we're going to come to the first column on the right and add five plus seven, which, if you count the from five and add 1257 times, you'll get 12. And as we've seen before, when you have a double digit answer and you have more numbers to add, you leave the number on the right, which in this case is too. Do you carry the one and place it on top of the next column on the left, where you will add it with the numbers below it. So first, let's add one plus one, which is going to give us, too. But that's not our final answer. We still have this nine, which we need to add to our to so nine plus two is going to give us 11. And as we've just seen, we carry our number on the left, which in this case is the blue one and leave the number on the right. Now we move on to our next a last column on the left, where we first want to add one plus four, which is going to give us five. And to get our final answer, we add five plus one, which is going to give a six. And we get our final answer, which is 612. Great. Let's just do one more problem like this on will conclude this section in addition, by adding four digit numbers. So for our next problem, let's add 925 plus 254. The first thing we want to do is add five plus four, which is going to give us nine no number to carry. So we move on to our next column, where we have two plus five, which is going to give us seven, and then we move on to our last column on the left, where we have nine plus two, which is going to give us 11. There are no more numbers to add, so we just place are 11 here and we have our final answer of 1000 179. Great. We've made so much progress, you should be very proud of yourself. And I hope you're starting to see that math is not hard. I know you may be saying to yourself, We're just doing addition, so it's easy, but I can assure you every single topic that we cover in this course is going to be just as easy. All I ask is that you follow along and just keep a positive mind and know that these skills are very obtainable all that. It takes a bit of practice, which will keep doing for our next problem. We're going to start to add our 1st 4 digit number and keep in mind not much changes. Same rules apply. All you'll see is just one more digit for next problem. Let's take a look at 2345 plus 113 just as we've been doing all along, we're gonna first come to our first column on the right, where we have five plus three, which is going to give us eight. If you add 1 to 53 times. And as you've probably guessed next, we simply move on to the next column on the left and we add four plus one, which is going to give us five. Now we move on to our next column and add three plus one, which is going to give us four. And for I last step, we move on one more time to the left, where we have to by itself and as we've seen before, when we have a digit by yourself at the end, we just carry it down and we reach our final answer, which is 2458. As you can see, not much changes whether we add two digit numbers or we add four digit numbers. But let's take a look at what happens when we're adding four digit numbers and we have to carry a number to the next column for our next problem. Let's take a look at 4739 plus 2716. The first thing you want to do is come to the right column, where we have nine plus six, which is going to give us 15. We leave the five in its place and we carry the one toe the next column. Next, we simply move to our next column, where we first want to add one plus three that will give us four. Then we add four plus one, which is going to give us five. Next, we move on to our next column, where we have seven plus seven, which is going to give us 14. As you might have guessed, you leave the number on the right, which is four, and we carry the one toe the next column. Next we move on to our last column and we first ad one plus four, which is going to give us five. And for our last step, we add five plus two, which is going to give us seven, and we finally have our final answer, which is 7455. Far last problem. We're gonna be adding 1931 plus 9517. First, let's go to our first column on the right, where we have one plus seven, which is going to give us eight. Next, we move onto the next column, where we have three plus one, which is going to give us four. Then we move on one more time to the left or we have nine plus five, which is going to give us 14. We leave the for in its place and we carry the one and move on to the next and last column , and we first add one plus one, which is going to give us, too. And fry final and last up. We add two plus nine, which is going to give us 11. And we have our answer, which is 11,448. Great. This concludes this section. In addition, in our next section, we're going to be looking at subtraction where we're going to start by just subtracting single digit numbers than double digit numbers. Three digit numbers on finally four digit numbers. I look forward to seeing you there
4. Subtracting 1 & 2 digit numbers: Hey, everyone, welcome to this section. Also traction In our previous section, we learned all about addition, where we added 12 three and four digit numbers. In this section, we will be exploring the topic of subtraction, which is the opposite of addition, and you'll see that as we go through the many problems we will be solving, we're going to start by subtracting one in two digit numbers, followed by subtracting three and four digit numbers so that you can have a good understanding of subtraction and be able to solve any problems you may encounter. If at any moment there is something you don't understand or you have any questions, you can always re watch the video. Or you can send me an email, and I'd be glad to assist you to the best of my abilities. Let's get started by learning how to subtract one and two digit numbers for our first problem. Let's take a look at four minus two. Now this is what is referred to US attraction. Instead of adding these two numbers together and seeing how much we have in total, we want to find the difference by subtracting and just as we did in our previous section. In addition, where I use my pencils to show you visually politician works. I want to use them again here to show you how subtraction works. So for our first set of numbers, we have four and we want to subtract two or take away too. So we simply subtract two pencils or we take away two pencils on. It gives us our final answer, which is to I know that was a bit fast. I just wanted to give you a quick demonstration of what happens when you hear someone say, minus or take away. But don't worry. In this section, we're gonna be doing plenty of problems so that you can understand exactly what's going on for our next problem. Let's take a look at seven minus four. Again, let's bring seven pencils out so that you can understand visually what's happening when you subtract four from seven. Here we have seven pencils and we want to take away for so we simply count four one to three four, and then we simply count what's left. And that's our answer, which is three for a next problem. Let's take a look at 16 minus five. I'm sure you notice we weren't from subtracting single digit numbers to now our first double digit number. But don't let that worry you. The same rule still apply. Things only change slightly, which, if you've seen the previous section. In addition, you already know what those changes are. But if you don't, it's OK. You'll learn them now. So let's see how we solve this problem. The first thing we want to do is work from the right column to the left. So let's go to our first column on the right, where we have six minus five. I want to show you visually what it looks like with my pencil so you can fully understand what it means to subtract, which simply makes to take away or eliminate. So here we have six pencils and we want to subtract five. We simply count or take away five pencils to get our answer. So let's count one to three four five. The five we just counted is what we take away, and what we have left is our answer, which is one. Now we move to our next column on the left, where we only have a one, and when we have a single digit by itself at the end of a problem, you simply carry it down and we get our final answer, which is 11. We're making great progress so far. Let's continue for next problem. Let's take a look at 20 minus seven. If you notice here in the right column for the first time, we have a smaller number on top, which is zero and a bigger number on the bottom, which is seven in our last section. In addition, we learned that you can just add thes two numbers and get your total. But in subtraction, it's different. You have to do what's called borrowing. Borrowing is when you simply borrow from the next column to the left, which in this case, it's the two and combine it with the number on the right, which in this case is zero. So let's see how we can solve this, just as we did and every problem we previously solved, we come to the right column and say, zero minus seven. We can't do that because seven is bigger and you can't subtract a bigger number from a smaller number, so we come to the next column on the left, where we had the number two we borrow from are to where we immediately put a line over it so that we know it's no longer a two. And we put a one right next to us so that we know that we have a one. If that's a bit confusing, please don't worry. We'll be doing this several times so that you understand exactly what we are doing when we borrow so another we borrowed one from our to. We can now place that one here. Next of the number in our first column, which is zero and it becomes a 10 and now we can say 10 minus seven is going to equal three for a last step. We move on to the column on the right, where we have one by itself and we can just carry it down and we get our final answer, which is 13. I know that maybe a bit too taken at once, but let's do another problem so that you can get the hang of this and understand exactly what's going on for next problem. Let's take a look at 31 minus 23. The first thing we want to do is come to the column on the right, as we did in our last problem, and say one minus three. You can't subtract a smaller number from a bigger number, so we do the following. We come to the column on the left, where we have a three and borrow one immediately. You want to place a line over the number you are borrowing from, so you can be aware that it no longer has its original value. And since we only need to borrow one are three becomes a two since three minus one is to and the one we borrowed go. So the first column on the right, where it's needed and are one becomes an 11. And now we say 11 minus three. I'm going to illustrate this with little circle so you can pause the video if you like and count them and you see that when you take away three from 11 you get eight. Now we go to our next column, where we have Tu minus two, which is going to give us zero, and our final answer is eight for next problem. Let's take a look at 94 minus 68. The numbers are starting to get a little bigger, but don't let that worry you. The same rules still apply. So just as we did in previous problem, let's come to our first column on the right. Where we have for minus eight. Four is smaller than eight. And as we said before, you can't subtract a smaller number from a bigger number. So we have to borrow from our nine in the next column. We want to put a line over it on. Since we only need to borrow one, it becomes an eight and the one we borrowed. We place it in front of our four, and it becomes 14. Now we can say 14 minus eight, which is going to give us six for last step. To solve this problem. We move on to our next column, where we have eight minus six, which is going to give us, too. And we have our final answer, which is 26. Great. This is going to conclude this video on subtracting one and two digit numbers in our next video. We're going to subtract three and four digit numbers. I look forward to seeing you there
5. Subtracting 3 & 4 digit numbers: Hey, everyone, welcome back. In our last video, we subtracted one in two digit numbers and in this video will be subtracting three or four digit numbers. Don't let more digits worry you. Not much changes. Remember the same rules apply. And if there is anything you don't understand or need help with, remember, I'm here to help you. You can just send me a message, and I'll be glad to help. Far. First problem. Let's start with something easy. 215 minus 12. The first thing we want to do is come to the first column on the right, just as we've been doing in previous problems where we have five minus two. I want to use my blue circles to illustrate the subtraction and so you can see how we arrive at our answer. So five minus two is going to give us three. Next, we move on to the next column on the left, where we have one minus one, which is going to give a zero. Since anything mine, it's itself is going to equal zero because it cancels itself. Oh, next we move on one more time to the left, where we have to buy itself, and we simply carried down because any number that remains by itself at the end of the problem is just going to carry itself down. Great. As you can see, not much changes when you subtract the more digits the same rules still apply. But just for practice sake, let's keep doing a few more problems because practices how you become good at math for next problem. Let's take a look at 527 minus 163. The first thing we want to do is come to the column on the right, where we have seven minus three, which is going to give us for when we take away the three. Next, we move on to the column on the left, where we have Tu minus six and as we've seen before in subtraction, when you have a larger number on the bottom and a smaller number on top, we have to borrow from the next number on the left. So we put a line over our five and it becomes a four, and since we borrowed one are a two becomes a 12. Great. Now we can say 12 minus six is going to give us six. Now we move on to our next column on the left, where we have for minus one, which is going to give us three for our next problem. Let's take a look at 4847 minus 435. As I'm sure you know, by now, the first step was solving a problem is coming to our first column on the right, where we have seven minus five, which is going to give us, too. Next, we move on to our next column on the left, where we have four minus three, which is going to give us one. Next, we move on again to the left, where we have eight minus four, which is going to give us four. And for last step. We have four by itself, so we just carry it down. Great. Let's do one more of these problems so you can get the hang of it and we can move on to our next topic for next problem. Let's take a look at 8619 minus 1245. The first thing we want to do is come to the first column on the right, as we've been doing in all our previous problems, where we have nine minus five, which is going to give us four. Next, we move on to our next column on the left, where we have one minus four, as you seem before, when we have a smaller number on the top and a bigger number on the bottom, we have to borrow from the next column on the left, which in this case is our six. Immediately, we want to put a line over our six, so we know it no longer holds its value and it becomes a five and our one becomes an 11. Now we can say 11 minus four equals seven. Next we move again to the to the left, where we have five minus two, which is going to give us three. And for a life step, we move one more time to the left, where we have a minus one, which is going to give us seven. I hope you feel very proud of yourself. We've covered a lot so far and practice on a lot of problems, and yet to come or a lot of amazing things you learn if you stick with me and keep watching the course in our next section will be introducing you to multiplication by giving you a detailed explanation of what is multiplication and why it's important to know how to multiply, followed by us going over the multiplication table and best of yet, doing a lot of multiplication problems. So practice and become better at math. I appreciate you watching this video. I look forward to seeing you in the very next section.
6. Intro into Multiplication: Hey, everyone, I'm not. He made it to this section of the course where we will be learning all about multiplication to recap. So far, we've covered addition and also subtraction. Or maybe you just decided to skip those sections because all you needed was some practice on multiplication, which is completely fine. When I started creating this course, I created each section as a stand alone section so you can browse whatever topic you need the most helping. But just in case you do need a refresher in addition or subtraction to snow, those sections are available to you and will definitely give you the help you need. And if you have any questions about anything, you can just some your message and I would be glad to help. So what will we be learning in this section? Exactly? First, I would like to give you an introduction to multiplication where I will explain the concept of multiplication, why it's important and how it's useful. Then I will break down the multiplication table for you entirely followed by us doing a good amount of multiplication problem so that you can have a good understanding of how to multiply. Great We have a lot of good things to cover, so let's get started. Your first question right from the start is probably what is multiplication? Multiplication is simply a shortcut for addition. You're probably wondering, why do I need a shortcut when I could just add? And that's a great question. Well, when you're dealing with small numbers is great account and use addition. But when you started dealing with larger numbers, multiplication always say's that they and in this section we will see how and why Multiplication is so beneficial. So let's see a visual example of how multiplication is a shortcut for addition. Let's say you have three circles on. We're going to add three more circles, plus again three circles. So in total we have three groups of three, and from the previous problems we worked in the previous section, I'm sure you know how to add the's three groups. But just as a refresher, let's see how it was done. And this is where you'll see the comparison between addition and multiplication. And just as I said a moment ago, it's a shortcut for addition. So let's add these three groups three plus three is going to give a six and we have three and to add to our six. So let's bring it down and we add three plus six, which is going to give us nine. And if that's a bit confusing, you can simply pause the video and count the blue circles one by one, and you'll see we have a total of nine. So that was a long way to find out how much we have in total through addition. But now let's see how multiplication is the shortcut. For addition, we have three groups of three, so a multiplication, we say three times three, which is going to give us nine Great. Any time you see multiplication, you can break it down into addition. But that would take up a lot of time. But in this section will continue to practice multiplication. So you master multiplying. So let's look at another example with smaller numbers so you can have a better understanding of what's going on. So let's say we have three groups of two or as we would say in multiplication three times to, because we have three sets of two circles, but it can be pencils, cars, bikes or even numbers. So let's break it down as we did before so you can see what occurs when we multiply. So here we can see we have three sets of two. Let's add our first to which is going to give us four. Then we bring down our remaining, to which we added what are four and is going to give us a total of six, which is the same as using our multiplication shortcut and say three, which represents the number of groups or sets one to three times two, which is what the groups are made off, which is going to equal six. I want you to keep in mind that in multiplication, it doesn't matter if you say three times two or two times three. The answer is still the same. Six. Great. I know that maybe a lot to take in, and if you don't fully understand what's going on, please bear with me and keep watching. I can assure you that after all the practice will be doing, you understand what multiplication is and you'll be able to solve any multiplication problem. Next will be going over the multiplication table, which is going to give you a good foundation and help you understand the whole concept of multiplication. But first, let me give you three main rules there. Get to know one. Multiply the first rule is anything multiplied by zero equals zero. In other words, when you multiply any number against general, your answer is going to be zero. For example, zero times two equals zero because there are zero groups or sets of numbers. So zero times 100 equals zero and zero times 54 equals zero. Rule number two Anything multiplied by one equals the same number. You're multiplying one by. So, for example, one times two is, too, because we have one set of two. So therefore, your answer is to another example. One times 267 equals 267. One times 389 is going to equal 389 Great. And for our last rule before we conclude this video is anything multiplied by 11. Is that number twice up to nine, and we'll see exactly what this means when we get to the Levins timetable. But for now, let's see a few examples so 11 times three equals 33 11 times five equals 55 and 11 times seven equals 77. I know this may be a lot to take in, but I can assure you, if you continue watching and working with me, you will become very good a multiplication, especially after we learned our multiplication tables, which is going to start next, so I look forward to seeing you there.
7. 1's Time Table: Hey, everyone, welcome back. For the rest of this section, we will be breaking down the multiplication table, starting at one and ending at 12. The multiplication table is very important. One learning how to multiply. The strategy I used when I was learning how to multiply was using flash cards by putting the answer on one side and the problem on the other. Or you can write them out and recite them so you can recall them instantly. Both techniques can work which ever way you decide to learn them. Just know that your multiplication table will help you tremendously in math and also in life because you were constantly needing to multiply, add, subtract, divide. And best of all, math is one of the best exercises for your mind. In this video, we're going to start with the ones times table, and the way I want to present it to you is by showing you the problem, followed by showing you what the problem looks like visually with my blue circles. So if you're unsure what the answer is, you can pause the video and count the circles. So, for example, one times one equals one, so we only have one circle because the circle represents our answer. And remember from the previous video when we talked about the multiplication rules. Anything times one is a number. You aren't more supplying one by so one times two equals two, one times three equals three, one times four equals four, one times five equals five, one times six equals six, one times seven equals seven, one times eight equals eight, one times nine equals nine, one times 10 equals ton. One terms 11 equals 11 one times 12 equals 12. That concludes this video on the Ones Times table. In our next video, we're going to be looking at the two times table.
8. 2's Time Table: in this video, we're gonna be taking a look at the tools Times table. So two times one is to two times two is four, two times three is six, two times for is eight. Two times five is ton, two ton. Six is 12. Two times seven is 14 turns a 16 two times nine 18 two times 10 20 two times 11 22 two times 12 24. That concludes this video on the twos, times table. In our next video, we're gonna be taking a look at the three times table.
9. 3's Time Table: in this video, we're gonna be taking a look at the three times table. So three times One is three, three times to six three times three nine three times four 12 three times five 15 three times six 18. Three times seven 21. Three times eight 24. Three times nine 27. Three times 10 30 three times 11 33. Three times 12 36 This concludes the threes times table. In our next video, we're going to be taking a look at the Forest Times table.
10. 4's Time Table: in this video, we're gonna be taking a look at the forced Times table four times one four four times two A four times three 12 four times for 16 four times five 20 four times six 24 four times seven 28 four times eight 32 Four times nine 36 four times ton 40 four times 11 44 Four times 12 48 That concludes the forced times table In our next video, we're gonna be taken to look at the five times table.
11. 5's Time Table: in this video, we're gonna take a look at the five times table. Five times one five five times, two ton, five times three 15 five times four 20 five times five 25 five times six 30 five times seven 35 five times eight 40 five times nine 45 five times 10 50 five times 11 55 five times 12 60 This concludes the five times table In our next video, we're going to take a look at the six times table.
12. 6's Time Table: in this video, we're gonna be taking a look at the six times table six times one six six times, too 12 six times three 18 six times four 24 six times five 30 six times six 36 six times seven 42 Six times eight 48 Six times nine 54 Six times 10 60 six times 11 66. Six times 12 72 That concludes this video on the six times table. On our next video, we're gonna take a look at the Service Times table.
13. 7's Time Table: in this video, we're gonna take a look at the suddenness. Times Table seven times one seven seven times two 14 seven times three 21 seven times four 28 seven times five 35 seven times six 42 seven times seven 49 seven times eight 56 seven times nine 63 seven times 10 70 seven times 11 77 seven times 12 84 That concludes his video on the seven times table. In our next video, we're going to be taking a look at the Ace Times table.
14. 8's Time Table: in this video, we're gonna take a look at the eight times table eight times one A eight times two 16 eight times three 24 eight times four 32 A times five 40 eight times six 48 eight times seven 56 A. Times eight 64 eight times nine 72 eight times 10 80 eight times 11 88 eight times 12 96 That concludes this video on the eight times table. In our next video, we're gonna be taking a look at the nice Times table.
15. 9's Time Table: in this video, we're gonna be taking a look at the nice. Times Table nine times one nine nine times two 18 nine times three 27 nine times for 36 nine times five 45 nine times six 54 nine times seven 63 nine times eight 72 nine times nine 81 nine times 10 90 nine times 11 99 nine times 12 108 That concludes this video on the nice times table In our next video, we're going to be taking a look at the tons Times table.
16. 10's Time Table: in this video, we're gonna be taking a look at the tense. Times table 10 times one ton, 10 times, too 20 10 times three 30 10 times four 40 10 times five 50 10 times six 60 10 times seven 70 10 times eight Andy 10 times nine 90 10 times 10 100 10 times 11 110 10 times 12 120 That concludes this video on the tense times table. In our next video, we're going to look at the Levis Times table.
17. 11's Time Table: in this video, we're going to be taking a look at the Levins. Times Table 11 times one 11 11 times two 22 11 times three 33 11 times four 44 11 times five 55 11 times six 66 11 times seven 77 11 times eight 88 11 times nine 99 11 times 10 110 11 times 11 121 11 times 12 132 That concludes this video on The Levins Times table. In our next video, we're gonna be looking at the 12 Times table.
18. 12's Time Table: in this video, we're gonna be taking a look at the 12 times table. 12 times one 12 12 times two 24 12 times three 36 12 times four 48 12 times five 60 12 times six 72 12 times seven 84 12 times A 96 12 times nine 108 12 times 10 120 12 times 11 132 12 times 12 144 That concludes this video on the 12 times table. In our next video, we're going to take all that we learned in our times table and put it to practice by doing a lot of multiplication problems. I look forward to seeing you there.
19. Multiplication Practice Problems: Hey, everyone, I'm not He made it to this last video before we conclude the multiplication section. So far we've covered the concept of multiplication and we also broke down the entire multiplication table, which I honestly beg you to learn Well, because it will help you tremendously. It is not necessary that you know how to multiply large numbers like 20 times 45 because no one expects you to know how to multiply such numbers. However, it is important that you can multiply single digit numbers. And that's why the multiplication table is very useful and important that you learn it well , if you don't know the multiplication table yet, I want to continue watching this video where we will be solving a lot of multiplication problems. That's okay. I encourage you to keep watching because your mind will pick up on a lot of things that will help you become better at multiplication. But just keep in mind that knowing your multiplication table will help you solve multiplication problems with ease. For our first problem, let's start with something simple four times two. If you know your multiplication table, you know the answer is eight. But let's take a moment and see how we arrived at eight. And what does it mean when we multiply when we say four times two. That means we have four groups of two, which is represented by our blue circles, so you can see what that looks like. And if we add all of our twos, we arrive at eight. What in reverse? We also have two groups of four, which also gives us eight. Let's try another problem and break it down so you can see what's really occurring when we multiply for next problem. Let's take a look at six times three. So again, what does it mean when we say six times three. We simply mean we have six groups of three, which looks like this, or it can be three times six where we have three groups of six, and that gives us 18. You can take the time and pause the video and count the circles I you see. In both cases we have 18. You're probably wondering, why do we need to multiply when we can just break the group's down and simply add? And that's a great question. But as you see in a moment when we started to multiply multiple numbers. It is much faster and easier to multiply than adding, I just want to break down one more problem for you like this so you can fully understand what's occurring when we multiply. Pharmanex problem. Let's solve seven times four. So, just as we seem previously, when we say times, it means we have seven groups off. Four. It can be bikes, pencils, cars or even blue circles. Or we can say four times seven, which looks like this. And if you know your four or seven times table, you know we arrive at 28. Great. Now let's look at a problem which we'll show you. Why multiplying as useful. Let's solve 20 times seven. And please don't let the bigger numbers scare or intimidate you. The rules I'm going to show you will help you to multiply any numbers as long as you know your times table and place them on top of one another, like we'll be doing in the many examples to come. So how do we solve this? Just as we do? In addition, we start on the right column and multiply our 1st 2 numbers in this case, it's zero and seven. Earlier we said anything multiplied by 00 So zero times seven is going to give us zero. Now, this is where solving an addition problem and a multiplication problem start to defer instead of carrying our last number down, which is to we have the multiply it by seven to get our answer. So seven times two is going to give us 14 and our final answer is 140. And yes, you can break this down into groups and cow, and also add the groups like with it previously with our blue circles. But that will take you forever. If you simply know your times table and you know anything multiplied by zero gives you zero and seven times to gives you 14. You have your answer in less than 10 seconds. If you're still in a bit confused on how toe solve multiplication problems like this, please don't worry. We're gonna be doing a ton of multiplication problems in this video to help you master multiplication. So for our next problem, let's look at 11 times four, just as we've seen in our previous problem, we want to come to the first column on the right. Well, we have one times four, which is going to give us four. Next, we simply multiply across where we have four times. One which a gun gives us four and our final answer is 44. Great. That was pretty easy far. Next problem. Let's take a look at 53 times nine. So, just as we did before, the first thing we want to do is come to the first column on the right, where we have three times nine, which is going to give us 27. And just like in addition, we leave the number on the right in its place, which is the seven, and we carry the number on the left, which is the to next. We do just as we did before, when we must apply across five times nine and then we add our two so whatever we get wound multiply five times nine, which is going to give us 45 plus. The two on top is 47 our final answer is 477. Great now for next problem. Let's I had one more digit to make things a bit more challenging and see how we can solve it. So for our next problem, let's ticket look at 24 times 12 the first thing we want to do is come to the first column on the right, where we have four times two, and that's going to give us eight. Next. We want to. Most apply across to times to where we'll get four now. This is where I really want you to pay attention. Another. We have finish multiplying all our numbers on top with our 1st 2 we move on to the next number on the bottom one and won't supply all the numbers on top and place them under our first answer. That might be a bit confusing, so let's do it a few times. So you see what I mean? So when we move on to our one, we first want to place a zero under the first answer we got. When we multiply our numbers on the top by two, then we want to multiply our one, which is our second number on the bottom by all the numbers on top. But we want to start with the furthest one. So the right, which In this case, it's four, so four times one is four. So we placed that for next to our zero, and then we simply multiply two terms, one which is going to give us, too. And we place that next to our four. And as you can see, after we multiply all our numbers, we have two rolls of numbers. The first role is from our to, and the second row is from our one. And to get our final answer, we simply add these numbers. And if you watched the section, In addition, adding these numbers should be no problem. So eight plus zero is eight. Next four plus four equals eight and far lost that we simply carry the two down, since there's no more numbers to add, and our final answer is 288. Great. Let's keep doing a few more of these multiplication problems so you can get the hang of what's going on when we multiply for next problem. Let's take a look at 43 times 23 just as we did in our last problem. We want to come to the first column on the right, where we have three times three, which is going to give us mine. Next we multiply our three across with the number on top, which is four. So for a time, story is going to give us 12. Next, we move on to our next number on the bottom, which is, too, and we do the same as we did with our three, where we multiplied it by three on top than across with our four. And it's the same in every multiplication problem. After there's no more numbers on top, we move on to our next number on the bottom and multiply by all the numbers on top. But first you always want to place your zero on the year first answer. And after you have your zero now we multiply our to buy all the numbers on top, so two times three gives us six. Next we multiply four times two, which equals eight. And for our last step so we can get our final answer. We add these two rolls of numbers so nine plus zero equals mine. Next two plus six equals eight, and finally, one plus eight equals nine, and we have our final answer, which is 989. Great for next problem. Let's take a look at 71 times 39. The first thing we want to do has come to the first column on the right, where we have nine times one which is going to give us mine. Next, we want to multiply our night across with our seven. So nine times seven is going to give us 63. Next, we move on to our next digit on the bottom and multiply all the numbers on top. But first we want to place a zero under our first answer. Then we multiply. So three times one is going to give us three, and we place that three next to our 1st 0 Then we have three times seven, which is going to give us 21 we place that 21 next to our three. And next we simply add these two rows of numbers and then we get our final answer. So let's add. First, we come to the first column on the right, where we have nine plus zero, which is going to give us nine. Next, we have three plus three, which is going to give us six. Then we move on to our next column on the left, where we have six plus one, which is going to give us seven. And for our final step, we have a two at the end by itself, which we simply carried down. And our final answer is going to be 2769. Great for next problem. Let's take a look at 132 times 11 just as we did in our last problem. We come to the first column on the right, where we have one times two, which is going to give us, too. Next we multiply are won by the next number on the top. So one times three is going to give us three. Next we multiply are won by the last number on top, which is one. So one times one is going to be one Great. We're now finish multiplying our first number on the bottom by all the numbers on the top. So next we move on to our second number on the bottom and do the same thing. But first, let's place a zero under our first answer, like we did in our last problem, so that when we add things later, it comes out right. Now that we have our zero, we can multiply. So one times two is going to give us too, and we place that to next to our zero. Next we multiply one times three, which is going to give us three. Next we multiply one times one, which is going to give us one. Now that we have done all our multiplication, we simply had to get our final answer. So let's see how we get that. So let's go to our first column where we have two plus zero, which is going to give us, too. Next, we move on to the column on the left, where we have three plus two, which is going to give us five. Next we move on to left again, where we have one plus Torri, which is going to give us four. And for our last step, we have a one by myself, which we can just carry down, and we get our final answer, which is 1400 and 52. I really hope you're starting to get the hang of solving multiplication problems, but just In case you would like a little more practice, let's do one nice problem. And just remember, you can always rewind the video and watch the areas that youthful you're unclear off. That's the benefit of having a course like this, that you can watch it over and over until you understand it. So for our next problem, let's take a look at 654 times 37 the first thing we want to do. A sculpture of the first column on the right, where we have four times seven, which is going to give us 28. We leave the number on the right and we carry the number on the left, which is to next We multiply seven times five, which is going to give us 35. Plus. The two on top is 37 now. We carry the three on the left and we leave the seven in its place, and now we multiply seven times six, which is going to give us 42 plus three is going to give us 45. Great. Now we move on to our next number on the bottom three. But before we multiply, we place a zero under our first answer. Now we multiply the re times for which is going to give us 12 and we place that 12 Next war zero We carry the one and not we multiply three times five, which is going to give us 15 plus one on top is 16. We carry the one and leave the six in this place. Next we multiply three times six, which is going to give us 18 plus one on top is 19. Great. Next we simply add these two rules of numbers and we get our final answer. Celestia, how we get that done. A plus zero is going to give us eight. Seven plus two is going to give us nine five plus six is going to give us 11. We carry the one on the left. I leave the one on the right in its place. Next we have for plus nine, which is 13 plus one. I was 14. We carry our one for last step and one plus one is two and we have our final answer. 24,198. Great! That concludes this section on multiplication. We covered a lot in this video. But if by any chance there was a part that you don't understand, I encourage you to rewind the video and re watch a gun. And if that doesn't help at any moment, you can send me email and I'll be glad to hope you as much as I can in our next section will be getting an introduction into the vision. I look forward to seeing you there.
20. Intro Into Division : Hey, welcome back to this section of easily learning basic math where we'll be learning all about the vision. The vision is one of those topics in math that a lot of people have a hard time learning and understanding. But I gonna sure you that with examples and techniques that I've come up with, you'll be able to solve any division problem. All I ask is that you will follow along with me, just as we did in previous sections. In this video, I'll be giving you an introduction to the vision. Then we'll be taking a look at the vision with remain there, followed by dividing 12 and three digit numbers so you can get some great practice at dividing. So what is Division vision is the opposite of multiplication sort of house attraction is the opposite of addition. So or not, it's understand division and do well at solving division problems. I encourage you to learn your multiplication well, which we covered in the last section. We have some amazing things to cover, so let's get started, just as we did in our previous section, where we learned all about multiplication and the concept of why it's important and useful to be able to multiply. I want to start here by explaining the concept of division. So let's look at a basic problem. Eight. Divided by two. What does this really mean? When you hear divide or you see this problem given to you another way, The problem will be given to you is like this and you'll see as we get into more division problems, why it's better. It's always right and solve your problems like this. So let's see what this means. So basically we're taking eight and we're dividing it by two. I want to give you a visual example of what this really means. Here we have April circles, which represents our eight, and you're being asked, how many groups of two can you divide into? Eight. So let's see how many groups of two are in eight. So we just basically count by two and divided from the rest of the group. Here we have our 1st 2 so this place is green line here to divide that, let's count two more and again divide that let's do the same thing again and count two more and divide that and at end. We have to left, which is already divided into its own group. And this is what you're basically being asked when you see a divided by two. How many groups of two and eight. Now that we have all our group separated, we simply count the groups and get our answer. So let's count how many groups of two We have one tool three four, and the answer is for great. I know that maybe a lot to take in, but no worries. I'm going to break down a few more of these problems so you can see what occurs when we divide. So for our next problem, let's take a look at nine divided by three again, Let's look at what it means when we're asked to divide. And just as we did a moment ago, I wanna visually show you what occurs when we divide. So let's bring up blue circles back so you could better understand what's occurring when we divide. So when were asked what is nine divided by? Three were being asked how many groups of three can you divide nine by and this is where we will see how multiplication relates to division But first, let's see how many times we can divide nine by three. So let's count groups off three and divide them on so we don't have any more groups of three. So here we have our 1st 3 and let's count three again and divide that. And at the end, we can see we have a group of three already separated. And just as we've seen in previous problems, once we have our group separated, we count how many groups we have and the total amount of groups is our answer. So let's count one to three, and our answer is three. Great. And just as I mentioned a few seconds ago, let's see how this relates to multiplication. If you know your multiplication and you know what to numbers multiplied by each other, gives you nine helps you determine what nine divided by three years, for example, three times three gives you nine. So that basically tells you that three groups of three gives you nine, and that helps you determine that nine divided by three is three. That might be a little bit confusing, but as we do more and more problems and make more connections, you'll see how multiplication and division, really as we get into more problems, you'll see you can solve simple division problems by knowing what numbers multiplied by each other gives you your answer for next problem. Let's think you look at 10 divided by five. Let's bring out our blue circles again so you can see what occurs when we divide. As I said a moment ago when you know what to numbers most supplied by each other, give you the bigger number in the division problem. You can get your answer very fast. So what's The number is multiplied by each other. Gives us tons. Well, if you know your multiplication table, you know that five times two gives you ton automatically that tells you to Groups of five gives you turn so in turn and divided by five gives you two groups because it takes two groups of five to give you 10. I know that maybe a lot to take in, but as we do more problems, you'll begin to see more connections and solve problems with ease. But just in case you're still learning in multiple occassion table and happened to run into some division problems, you could still break down the problem by groups as we did with our blue circles. So let's see how we can get that done. So here we have 10 circles and all at which one to determine how many groups of five and 10 . So we count five and divide them, and then we count five more. And since we have no more blue circles to make groups, we count our groups to determine our answer. So let's come home. Any groups? One to. We have two groups. So our answer is to great. I really hope you're starting to get the hang of division. But just in case you're not, don't worry, we're still gonna be doing many, many more problems for next problem. Let's take a look at six divided by two. And as I mentioned at the beginning of this video, let's start by writing out our problems like this because it's much easier to solve. So let's see how we can solve this problem, just as we did at the beginning of our last problem. We want to see how we can arrive at the answer by calculating two times whatever number gives a six so If you know your tools Times table, you know that two times three gives us six. So our answer is three, and we place that appear on top of the little house, and it's that simple. That's why I say that knowing your Times table really helps you solve your division problems with ease. So remember to learn your multiplication table well, for next problem. Let's take a look at 12 divided by three. The first thing you want to ask yourself is three times what number gives me 12. If you know your three times table, you know that three times for gives you 12. So our answer is four, and I'll quickly show you with our blue circles. There are four groups of three and 12 so here we have our 12 blue circles. So let's count groups of three one to three four, and we see that we have four groups of three and 12. It's our answer. Is four great far. Next problem. We're gonna take division a bit further so you can better understand division problems. So let's take a look at 16 divided by four. And as you may have guessed, it's always better to write all your division problems in this format, and you'll see why in a moment. But I just want to clarify that whatever you're dividing into goes inside this little house in this case are 16 and whatever you're dividing by those outside of the little house in this case, our four. Now that we have our problem right now, the first question you want to ask yourself is four times what number gives us 16. If you know you're forced times, table your arrive at the answer immediately. But if you don't, it's OK. You can start at the very beginning of your forced times table and work your way up and see how close you can get toe 16 or at 16. Exactly. So let's see how we can get that done. Four times. One is four, four times two. It's a we're still not a 16. So we want to continue, so we get as close as possible or we arrive at the number exactly, So let's continue four times three is going to give us 12. Next, let's take a look at four times for, which gives us 16 and that's what we're looking for. great, and we place that for on top of our little house, and we want to make sure it's on top of our six, and not just anywhere up here. And as we divide more digits, you'll see why knowing where to place your number. It's important, and just in case you want to really make sure you have the right answer and it may not seem important right now, but as we get into more advanced division problems, you'll see why. This is another important step to make. And it's a simple step. All you have to do is a little bit of multiplication and a little bit of subtraction. So the first thing you want to ask yourself is, Once you have your final answer on top, which is four, you multiply it with the number you are dividing by, which is also for so four times for is 16. We take the 16 and we place it under the number we are dividing into, which is also 16. And now we simply subtract 16 minus 16 so six minus six zero and one minus 10 and here we see we have no remainder, and that tells us that we divided our numbers evenly, and you're probably wondering, what is the point of doing this last step? But as we get into more problems, you'll see that sometimes you'll have remained there, and you'll start to see that in our next video, where we will start dividing problems with remain there. But for now, let's look at one more problem so you can better understand how to divide a problem completely. And then we can move on to our next section and division, which is going to be dividing problems with remainder. For next problem. Let's take a look at 20 divided by five. And just as we did before, we want to write out our problem like this. Now that we have our problem ran now in the correct format, the first thing you want to ask yourself is what multiplied by five gives us 20. So let's see how we can get there. If you know your multiplication, you'll know the answer immediately. But just in case you're still learning them and need more practice, you can start at the beginning of the five times table and work your way up until you get to the number 20 or as close as possible. So let's multiply in order to solve this problem. Five times one equals five, five times two equals ton, five times three equals 15 five times four equals 20. Great. And that's the number we're looking for. So now we know that for is our answer. Because we arrived at 20 and we want to place that for appear. And just as we did in previous problems, we want to check our answer in order to make sure that we have the correct answer by asking ourselves again. Four times five gives us 20 and we placed that number under original 20 on far last step we subtract So zero minus zero is going to give us zero. Tu minus two is going to give us zero and we have a remainder of zero, which tells us we divided the number even. And the four is the correct answer. This concludes this video on intro into division in our next video will be doing more division problems. And the only thing that changes is that we will have a remainder. I look forward to seeing you there
21. Dividing with a remainder: Hey, everyone, welcome back. In our last video, we learned how to divide, which is one of the most important topics in math. In this video, we're going to be going over some problems that are very similar to what we learned before . The only difference is that in this video we're gonna be learning what to do when we're dividing and we have a remainder. Great. Let's get started. What before we do. I just want you to keep in mind that this is going to be very easy and there's not much more you have to know in order to solve these problems. Let's get started with something simple. Nine. Divided by four Just as we've seen in our previous video, we want to write out the problem like this and you'll see why, as we start dividing bigger and bigger numbers, why this format is better. Just as before, when we were solving aren't division problems, the first question you want to ask yourself is four times what number is going to give me nine or mes closest possible to the number nine. So let's start at the beginning of our forced times table and work our way up, so four times one is going to give us four. Remember, we're trying to go all the way up to nine or as close as possible, so we want to continue till we get there. So four times two is eight. We're still not at nine. So let's try one more time. Four times three is going to give us 12. But that's too much. So we have a bit of a problem because four times two equals eight and that's not enough because we want nine. But at the same time, for times three is 12 which is too much. So we have to do the following. In this case, we have to ask ourselves, How many times can four go into nine without surpassing the number nine? And as we've seen a moment ago when we were doing our force Times table in order to determine four times what number it gets his closest to nine We saw that four times two gives us eight. So our answer is to for girls into 92 times great. But there is one more step we have to do in order to check that this is the correct answer . And if there's a remainder or not. So we do, just as we did at the end of our previous video, we checked with multiplication as attraction by asking ourselves two times for equals eight . We place that eight under our nine and we subtract nine minus eight equals one, and this tells us we have a remainder of one. And before, we always had a remainder of zero down here. So we left it alone, since zero has no value. But since we now have a one, we simply write our final answer like this up here, next to our to we add a small are that stands for remainder, and we put the one after. So our answer is to remain there one, and to take it a step forward, I would like to quickly bring back our blue circles so I can visually show you what's going on. So here we have nine circles, and as we learned before, when we say nine divided by four, we want to find out how many groups of four and nine. So let's count for and at this green line to divide our first group. And let's count for more and at another green line. And as you can see, we have two groups of four and a remainder of one at the end. I know that maybe a lot to take in, but that's one of the many benefits of a course like this. You can rewind and watch it a few times, helping you understand things better each time. Plus, we will be doing a few more problems like this in order to help you better understand dividing with they remain there for next problem. Let's take a look at 13 divided by two again. The first thing we need to ask ourselves is two times what number is going to give me 13 or get me as close as possible to 13 without surpassing or going over the number 13. If you're still learning your times table, the best way to approach this is by starting at the beginning of the twos times table and working your way up. So let's do that two times one equals two, two times two equals four, two times three equals six. And as you can see as we go up in our times table, the closer we get to 13. So let's continue two times for equals. Eight, two times five equals 10 two times six equals 12 almost 13 but still not quite there. So let's try once more. Two times seven equals 14. And as you can see, we surpassed the number 13. So we go back to the nearest multiple of two. That gets us the closest to 13 which is two times six, which gives this 12. So our answer is six on far final step in order to see if there's any remainder, we check our problem by saying six times too equals 12. We placed our 12 under our 13 and we subtract 13 minus 12. So three minus two equals one and one minus 10 and we have a remainder of one. So we put our small are that stands for remainder at the top with our six, and we place our one after the are, since that's our remained there. Great. As you can see once you practice solving any type of problem a few times, whether it's addition, subtraction, multiplication or division, it just becomes easier and easier after you do it a few times, and it's the same with any type of problem in math. So let's reinforce what we just learned by doing one more problem before we move on to our next video, which is where we will be looking at a lot of practice problems in division. So far less problem. Let's take a look at 27 divided by seven again. The first question you want to ask yourself is seven times what number is going to give me 27 or get me as close as possible to the number 27. So let's start at the beginning of our sevens times table and work our way up seven times. One is going to give us seven. Seven times two is going to give us 14. Seven times three is 21. We're closer to 27 but not quite there. So let's try once more. Seven times four equals 27 as we can see seven times for us too much because it surpasses 27. So let's go back to the next closest multiple, which is three, and we want to place that up top and now we check to see if there is any remainder by saying three times seven is 21. We placed on number under our 27 on we subtract. So seven minus one equals six. Next Tu minus two equals zero and we have our final answer, which is three remain there. Six. Great. This concludes his video on division with remainder in. Our next video will be doing a lot of division problems so you can get the hang of dividing 23 and four digit numbers. So let's see how we can get that done. See you there.
22. Division Problems: Hey, everyone, welcome back. In our last video, we learned how to solve division problems with a remainder. By now, you should be fairly comfortable solving division problems. But just in case you're not in this video and in the next one will be solving a few more problems in order to reinforce your knowledge on division and also show you what occurs when you divide bigger numbers. So I encourage you to watch this video and the next one in order to fully grasp with the concept of division entirely for our first problem. Let's take a look at 42 divided by two, and the first thing we want to do is rewrite the problem in this format, and in this video, you'll start to see why it's much better to write it out like this. And what we're basically doing here is trying to divide to into 42 in this problem, we're going approach things differently as opposing the previous problems. We saw it because I don't know, right off the top of my head, how many times to can go into 42 or what times to was going to give me 42 or as close as possible to 42. So instead of looking at 42 we want to look at the first number we are dividing into, which is four. I say How many times can to go into four or you can say two times what gives me four? Since it's easier to reach than two times what gives me 42 so two times two is me for so our answer is to then we do as we did before. Two times two is four. We place that for under the four we just divided into and then we subtract. But we only want to subtract The left column since is the number we divided into, so four minus four is going to give us zero. Then we ask ourselves, How many times can to go into zero since zero has no value, you can't divide into it or create groups of two. So we do the following. We bring down our two next to the four and we place in next to our zero, and now we can ask ourselves to goes into two once. So we placed that up here and then we say one times two equals two, and we place that so under are so down here and we subtract again in order to see if there's a remainder or if it's divided evenly. So two a minus two equals zero, and our final answer is 21. Since we have a remainder of general great, I know that might be more than we did in previous problems, but just trust me and stay with me here. We're gonna do enough problems where you'll get the hang of it, and as you do it, more and more will become more clear and therefore easier so far. Next problem. Let's take a look at 47 divided by three, just as we did in our last problem. Instead of trying to figure out what times three gives us 47 we want to look at the first digit of 47 which is four. And ask ourselves, How many times can three going to four? The answer is one, since three times one is three and if we try to go further it so let's say three times to it's six, so we have to go with one, says three times. One is three and it's closer to four and we placed that on top of our forces were trying to figure out How many times can three go into four? Next we ask ourselves. One times three equals three. We place that under our four since we divided into four and we subtract four minus three, which is going to give us one. Next we acts ourselves. How many times does one go into three? We can make groups of three from the number one, so we bring down the next number. We haven't divided by which is seven and we combine it with one which is going to make it 17. And now we say three goals in 17. We can break it down several ways as we've seen before, or we can look at our threes times table and see that three times five is 15 and that's pretty much as close as we can get to 17. So we take our five and we place it appear on top and we ask ourselves five times three is 15. We place that 15 down here under our 17 and we subtract seven minus five is going to give us too one minus one zero and we have a remainder of to. It's Our final answer is 15 remainder two. Great. Before we move on to our next problem, I want to show you a little trick that can help you find out quickly if you have the right answer when you divide and this is called checking your answer. So let's take a look at how we can get this done. And this is another example of how multiplication and division relate, because in order to check if your answer is correct, you have to multiply your answer, which in this case is 15 by the number you are dividing by, which is three. So let's multiply three times five this 15 We live the five and carry the one, then three times one is three plus the one we carried four on we get 45. But remember, we have a remainder off to. So we added to our 45 and we get 47 which is what we were originally dividing by. And that right there tells you 15 remained. There, too, is the correct answer. I know you might have never seen this or haven't seen this in a while, so you might be a bit confused. But it's OK because we will be solving a few more problems. I will help you better understand how to make all these steps and always get the right answer. So let's move on to our next problem, which is going to be 64 divided by four. And just as we did before and our last problem, instead of looking at the whole number of 64 trying to see how many groups off. Four, we can divide 64 into or what times four gives the 64. Let's look at the first digit of 64 which is six and divided by four. Asking how many times does four go into six. Four is almost as large as six, so we can assume it goes in one time and we placed I one on top of our six. Next we ask ourselves one times four. It's four and we placed at four under, are six and we subtract. Six minus four is going to give us, too. Then we ask ourselves, four goes into two. How many times we can't do that? So we bring our next number down, which is four, and now we have 24. Now we can see how many times does four go into 24 six times. So we placed that on top and now we say six times four, which is going to give us 24. And then we placed that down here under our 24 as attract 24 minus 24 is going to give us zero on. Our final answer is 16. And just as we did before, let's check this answer to see if we have to correct answer or if we divide it correctly by multiplying. So the way we tracked things, we want to take our answer, which is 16 and multiply by the number we were divided by, which is four. So 16 times four six times four is going to give us 24 carry the two. Then we have four times one, which is four plus two, is six and we get 64 which was what we originally divided by. And we see our answer is correct. Great for next problem. Before we conclude this video, let's look at 92 divided by 23. The first question we want to ask ourselves in this case is what times 23 is going to give me 92 since we can't go about this problem like the previous ones, because the numbers don't allow us. So let's start at the beginning of our 20 threes times table and work our way up. So 23 times one is going to give us 23 23 times to is going to give us 46. 23 times three is going to give us 69. 23 times four is going to give us 92. 90 two is what we're looking for. So we know that four times 23 helps us arrive at 92. So let's place that for on top. And next we ask ourselves four times 23 which is going to give us 92. We placed at 92 under our 92 which is being used to be divided into, and we subtract 90 to minus 92 which is going to give us zero, and we have no remain there. Now let's check this answer. And for this last problem, I want to do things differently. I want to sort of leave it to you as a test so you can figure it out by rewinding the video and seeing how you check your answer to make sure you have the right answer. And if you have any questions, you can always post a discussion or semi email, and I'd be glad to help you in our next video. We will be concluding that the vision section by looking a few more things that I would like to show you in the vision and then you'll be fully prepared to divide any problem that ever comes your weight. I appreciate you watching this course, and I look forward to seeing you in the next video. Thank you.
23. Dividing 4 Digit Numbers: Hey, everyone, welcome to our last video in this section where we will be doing two more division problems . And I wanted to do these last two problems to show you what happens when the number you are dividing by is bigger than the number you are dividing into. So let's get right into it far. First problem will be dividing 509 by 25 and immediately we can see that 25 goes into 52 times. So we place that too. On top of our zero telling us we divided our 50. So all we have left is that nine at the end. Next we ask ourselves two times 25 gives us 50. We place that 50 under the 50 we divided by and we subtract 50 minus 50 is going to give us zero. Next we ask ourselves, 25 goes into zero. How many times we can't do that because zero has no value and you can make groups of 25 from zero. So we do as we did in our previous video and we bring down the next number we're dividing by. Since we already divided 50 by 25 are we have left is nine. So we bring down nine and now we ask ourselves 25 goes into nine. How many times we can't do that? Because we can't make groups of 25 out of nine. And as we've seen before, when we have something remaining at the end of the problem, it becomes the remainder. But in this case, the nine, it's part of the whole number, so we just can't make it a remain there. So we have to do the following. We ask ourselves 25 girls into 90 times. We pleased as zero on top next door to and now we do as we did before. Zero times 25 is going to give a zero and we placed as zero under our nine as attract NY minus zero is going to give us nine and now are nine becomes our remainder. So our final answer is 20. Remain there. Nine. Andi to make sure we have the correct answer. Let's check this, as we did before in our previous video, and the way we are going to do this is by multiplying 20 which is our final answer by 25 which is what we're dividing by. So let's see how we can get that done. Five times zero is zero five times two. It's ton. Next, we place our zero as a placeholder and continue two times zero is zero. So times two, it's four and we have 100 plus 400 which gives us 500. Now we have 500. And remember, we have a remainder of nine. So we add the 500 with our nine. And that gives us 500 mine, which is what we're looking for since that's the number we were dividing by. And that tells us 20 remainder nine is the correct answer. Great. And for our last problem before we conclude division, we're gonna take a look at 6000 800 divided by 34. The first thing we want to do is ask ourselves How many times can 34 go into 68? 34 times two 68. So our answer is to next two times 34 68. We placed at 68 under the 68 we are dividing into on. We subtract 68 minus 68 is going to give us zero. And in our next step we will see what we encountered in our last problem where we say 34 goes into zero. How many times we can't do that. So we bring down the next number we are dividing by, which is zero as C 34 goes into zero zero times. So we place that of top and now we say zero times 34 zero. We placed as zero under the zero. We just divided by as a track zero minus zero, which is going to give us zero. And as we seem before, 34 can't go into zero. So we bring down the following digit. We're dividing by zero and say 34 goes into 00 times and we placed at zero on top and we get our final answer, which is 200 because we have no more than just to divide by. But just to make sure we have the right answer, let's check this as we checked all our division problems in the past by multiplying our final answer 200 so four times zero equals zero four times zero equals zero four times two equals eight. Next we place a zero as a placeholder and move on to our three three times in a row. Zero three times zero is zero again three times to it's six, and now we add 100 plus 6000 which we can see will clearly give us 6800. And that matches the number we're dividing into. So that tells us that our final answer is 200. This concludes this section in the vision. If you have any questions, remember to rewind the video and watch it again. And if you still have trouble posted discussion or a semi in email, and I'd be glad to help you in our next section, we're going to start looking at fractions. Fractions is one of those topics and math that a lot of people struggle with, but I've put together some great examples and explanations toe hope you fully understand fractions and be able to solve any fraction problems you come across. So I want to thank you for watching this course, and I look forward to seeing you in the next section
24. Simplifying fractions part 1: Hey, everyone, welcome to this section of easily learning basic math where we will be learning one of the most important topics and math fractions. Fractions is one of those topics in math that most people find difficult and intimidating. And maybe it's due to the fact that it just doesn't appear as regular numbers the same way other math topics are presented. Or maybe it's just you never had someone teach you from a student's point of view. And that's one of the main reasons why was inspired to create this course. Because just like you, I struggled in math when I was in school. But through hard work and endless hours of studying and experimenting, I became great at math, and that's what I want to share with you. So I want you to keep this in mind. I never forget this, and it will become more and more obvious to you as you watch this course. Math is not hard. All it takes is practice and learning the right steps. And that's what I'll be showing you in this section with fractions. How to solve any fraction problems, step by step and never worry about not being able to solve one again. So what will we be learning in this section? First, I would like to start things from scratch the same way I doing each section of this course , and it's by explaining and showing you visually. What are fractions at? What is the use of fractions? Then we will be learning how to add subtract fractions, followed by finding the common denominator. Then we will be multiplying fractions. And to conclude this section, we will be dividing a few fraction problems. Great, we have some amazing things to learn, so let's get right to it. So it is a fraction the best way I can help you visualize what fractions are I want to use as an example, something we all enjoy eating pizza. I want you to visualize this big circle as a pizza pie. And let's say, for example, you order an entire pizza pie for you and your friends. When the pizza arrives at your door, you have an entire pizza or one whole pizza. So let's say, for example, you take one slices, you're hungry. You no longer have a whole pizza. You have what's now called a fraction of the pizza pie. And that's basically what fractures represent. Something that's less than one could be. Pizza numbers, money, etcetera. Let's go back to our pizza and say One of your friends takes a slice of the pizza and now it looks like this. I'm sure you've heard before the word half, which means you have one whole thing. You break it into two pieces and one piece is taken and you're left with half that's was represented here by our pizza pie 1/2 on the left, which is the red. The other half is eaten, which represented by the green. And the way you write this in a fraction or mathematical terms is like this. The bottom number, which is two, represents how many pieces you have in total, which we can clearly see. We have to have. So we have to. In total, the number on top represents how many pieces we have left. Remember, you had a slice and your friend had a slice, which was half the pizza. So that means we have half left. And this line here basically lets you know you have a fraction or you're dealing with a fraction. So this basically means one hash in this case, half a pizza. Now let's look at another example. Let's see again. We have our whole pizza pie. We said it on the table, and no one has taken any slices. Let's say we want to divide it evenly among you and your three friends. Since you watch the division section of this course and can divide very well, you figure you all can have a slice. So you decided to just cut the piece into four slices. Let's see what that looks like. If we count the slices, we can clearly see we have for in total. And remember a few seconds ago, I said the bottom number of a fraction represents how much in total in this case, how many slices in total and the top represents how many slices you have left. Let's say out of politeness, you decide to give your best friend the first slice of the pizza. What would that look like? Let's say we gave him the green slice. Now he has what is called 1/4 of the pie, which are mathematical terms, is called 1/4 and a great example of this, which will help you understand this better is a comparison between a dollar bill and 4/4. Let's see what that looks like for a second. Let's say, for example, you have a dollar. I'm sure you know $1 can also be represented by 4/4. And let's say you go to the store and buy some candy for 1/4 or 25 cents, just like the pizza. This is 1/4 of a dollar or 1/4 of a dollar, the same as the pizza. I hope with this example, you go start to see the usefulness of knowing your fractions and how it can be applied. Another. We have looked at two fractions, 1/2 which we can see here, and 1/4 which we can see here. And the reason I bring these two fractions back is to show you that 1/2 is actually bigger than 1/4 and you may be asking yourself how when four is larger than two. But if you look at the pieces, you'll see half is bigger than 1/4. And just to show you another example, let's bring back our dollar and 4/4 just to show you that 1/4 which is 1/4 is smaller than 1/2 which is 2/4 great. Let's look at the slightly different Let's bring back our pizza pie. And let's say you and your friends ate half of the pie, which is represented by the green half. And let's say from that half, you and your friends break it into another half again. What would that look like? As you can see here you took one slice, which is the Greenpeace, and your friend took a slice, which is the blue piece. At the beginning, we had four slices, but now toe have been eaten, so we took two pieces out of four pieces. So this fraction is 2/4. And the reason I show you this example is because it's very important that you understand that even though 1/2 and 2/4 look different, they are in fact the same. Let's look at the picture for a second. The pizza on the left. We cut in half and you can see I have have highlighted. And when I highlight the other pie 2/4 you can see despite the other half being split in two because you had a slice and your friend had a slice. It's still the same size. And to prove this to you, we're gonna do something. You'll be acid. Do one solving fraction problems, and that's called simplifying the steak. Away our pizza for a second and just focus on the numbers. Here we have our fractions, which are equal, but to make sure they're equal, we want to simplify them. And simplifying fractions is sort of like balancing them out, also known as reducing them to their simplest form. The way we simplify them is by looking at the fraction we want to reduce, which in this case is 2/4 in order to see if, in fact, that is the same as 1/2. And the way we do that is by dividing, which we covered in great detail in the last section. So let's say we want to divide 2/4 by two at the top and two at the bottom as well. So two divided by two is one, since anything divided by itself is one and four, divided by two, it's too, so notice what we've done. We took the 2/4 and divided the top and the bottom by the same thing and we arrived at different fraction, which is 1/2 and there is really nothing else. We can divide the top in the bottom to make it any simpler. So we basically just reduced this fraction toe, a soloist term also known as simplifying. And we'll see many examples like this as we get deeper into this section. Simplification is what we will make the main focus of this for his video, because it will help you tremendously when solving fractions. So let's look at a few more examples. I want to do the following. I'm going to draw a few more pies, and I want you to try and think of what it will look like in terms of a fraction. So let's say, for example, we have something that looks like this that's once again bring back our pizza pie. The only difference now is we have divided it or cut it into more pieces. And as we learn before, we already know that the bottom number of a fraction represents how many we have in total, and the top represents how many pieces we have taken. So if we have taken one slice from the pie. What is this fraction? The first question you want to ask yourself is how many pieces were taken, and the second question is how many pieces are left. We have one slice that was taken, and the bottom is how many pieces we have left, which, if we count the slices, we see we have six total pieces. So we call this Fraction 1/6 which tells you you don't have a hope. I you have 1/6 of a pie was translate toe one out of six. Great. Let's look at another example Here we have the same six pieces we have before, so we know the bottom number ISS six, because the bottom number of a fraction represents how many pieces we have in total. But let's say this time we take three pieces instead of one. What is this fraction? This fraction is 3/6 which also equals to 1/2 and you may ask yourself how and as we learned before on as you will be asked many times, we're solving fraction problems. We have to reduce it to a simplest form or simplify it, and the way we simplify is by simply dividing the top by the same number as we divide the bottom. So let's divide the top by three. Hand the bottom by three. So three divided by three is one and six. Divided by three is too great. And here we can see that 3/6 is in fact the same as 1/2. When we reduce the fraction toe a simplest form, this video is starting to become quite lengthy. So I want to stop here and continue simplifying a few more fraction that the very next video I want to thank you for watching and I'll see you in the very next video.
25. Simplifying fractions part 2: Hey, everyone, welcome to Part Two of simplifying fractions in this video. I want to pick up right where we left off in our last video, where we started learning about what are fractions and how to reduce them to their simplest form, just as we've seen before. Let's bring back our pizza pie and keep looking at fractions and simplifying them, which will help you when adding, subtracting, multiplying and dividing fractions. For our first example, let's look at our pizza pie again. And this time let's say a few more people have joined this. So we divide the pie into more pieces. Eight to be exact, and we're going to give out one piece of the pie. How would that fracture look? So we know we have a total of eight. And remember, we said the number we have in total is the bottom number, so the number would take away is the top number. So how would that look? In a fraction, it will look like this, it at the bottom and one on the top, which we say is 1/8. And the next question you want to ask yourself is, Can you reduce this fraction and the answer is no, because you can't divide the top in the bottom by anything great. So let's take a look at another example. Here we have our a slices of pizza again, and this time we're going to give two slices away instead of one. What would this fraction look like? If you guess 2/8 you're correct. The bottom number is how many slices we have in total, and the top is how many slices were taken, which is to our last fraction 1/8. We couldn't simplify it because it was already at its simplest form, and, you know, when it's at its simplest form, you can't divide the top in the bottom by the same number. But in this case into eighths, we can divide the top in the bottom by the same number and simplified toe. A simplest form. We just have to determine what number is, And as you do more and more fraction problems, it will become easier to find the number which you can divide the top in the bottom by. In this case, that number is two. So two divided by two is one and eight. Divided by two is four, which gives us 1/4. And as we seem before, we already know what 1/4 looks like. For next example, Let's look at our A slices again, and this time we're going to give out one more slice out of the eight. And as I'm sure you can guess by now, that's going to give us 3/8. And you can simply ask yourself, Can I simplify this fraction any more than it is? And the answer is no, because there is no number you can divide both three and eight by, so the fraction is already at a simplest form. Next, let's look at our last pizza example where we're going to give away yet another slice, which is going to bring us to 4/8. And you want to ask yourself, Can I simplify this fraction more than it already is? And the answer is yes. And at this case we're going to divide the top in the bottom by four. So let's divide. Four. Divided by four is one and eight. Divided by four is to. So as you can see, 4/8 is equal to 1/2 and let's see that visually so you can see that it's actually the same thing. And as you can see, if we look at the two examples closely, 4/8 and 1/2 are, in fact equal. This is going to conclude this video on simplifying fractions. I hope you are able to understand the concept of simplifying fractions. If, by any chance you had any trouble, you can feel free toe. Send me a message and I'd be glad to help you. In the next video. We're going to start adding fractions. I look forward to seeing you there.
26. Adding fractions: Hey, everyone, welcome back. I hope you're started to get the hang of fractions. So far in this video, we will be learning how to add fractions. If you didn't watch the previous video where I introduced the concept of what is a fraction , please do so. It will make the things we will learn in this video much easier to understand. Just as we've seen in our lives video. I want to bring back our pizza pie, or I least a circle that resembles a pizza pie cut in half, which in a fraction looks like this. Now let's say right next to our first half, we have a second pie with different toppings. But there is only 1/2 remaining and we want to add these two halfs. What will we have? Will have one hope. I You're probably wondering, how can 1/2 and another half give us one whole number? And that's what I want to show you. Remember, we learned in our last video the bottom number of a fraction represents how many we have in total, and the top number is how many pieces or slices we have. But these two numbers have a special name, which I want to quickly introduce you to. The correct name for the top number of a fraction is numerator, and the bottom number of a fraction is called the nominator. And from this point on, I'll start referring to the top and bottom number by the correct name so that you can become familiar with them and start using them yourself before we start adding fractions. There is just one rule you need to know, and this rule applies both toe adding fractions and subtracting fractions. The rule is that the nominators off the fractions must be equal. In other words, they need to be the same. So in this first problem we have both won half plus 1/2 and we can clearly see that the denominator is the same, which is too, so we can add these two fractions with no problem. So one thing I recommend is first bringing over your denominator. Like so since all we have to do is at the top number, also known as the numerator, and the same applies once attracting fractions. If the denominator is the same, all you have to do is add or subtract the numerator you're probably wondering what happens when the denominator is different. I will cover that a bit later in this section, when we cover finding the common denominator. Since we determined we have the same denominator, we can simply add these to enumerators, so one plus one equals two. And as we learned before, when we cover simplifying fractions, we can simplify this fraction. All we need to do is divide as we've done before when simplifying fractions. And I'll give you a little hit here any time you saw a fraction problem and you have a fraction liked over to like we have here. When we simplify this fraction, it means one, because if we divide to by itself, it gives us one. And it's important. You understand that even though we've been talking about fractions and I've been giving you examples of pizza because most likely you've always seen it sliced up into a fraction. Fractions are a form of division or another way to divide. So, for example, when we have 1/2 which is basically 1/2, it's the same as saying so divided into one. But since we can't make groups of two out of one. We have to solve it in the form of a fraction. And that's what we just covered. 1/2 plus 1/2 equals one hole. Great. Let's look at another example problem, which will only help you understand things better for next problem. Let's take a look at 1/4 plus 1/4. The first thing we want to do is what we did in our last problem. Let's bring over the denominator since is the same and makes it simple. Now all that's left is adding the norm aerators. So one plus one gives us, too, and that gives us a final answer of 2/4. Great. Every time you solve a fraction problem, you want to ask yourself, Can I reduce this fraction? And in the case of 2/4 yes, you can. So let's see how we can do that. Remember that when we want to simplify a fraction, we want to divide the numerator and the denominator by the same number. So in the case of 2/4 we can divide the top and the bottom by two. So two divided by two is going to give us one and four. Divided by two is going to give us too great. Now we simplify to fourth to its lowest terms, and that gives us 1/2. And if you look at the picture quickly, highlight how to Fourths is the same as 1/2. Great for next problem. Let's take a look at 36 plus three six, and the first thing we want to look at is if the denominators are the same and you'll see why when we get to find in the common denominator. But in this case, since they are in fact the same, we could just bring it over. And all that is left is adding the numerator, which is three plus three, is going to give us six, and that's going to give us 6/6. And as we mentioned before, when we have a fraction like this, where the numerator and the denominator is the same, it's the same as one hole. I hope you're starting to get the hang of adding fractions with same denominator. In our next video, we're going to take a look at a few practice problems to help reinforce what we learned in this video. I want to thank you for watching, and I look forward to seeing you there
27. Subtracting fraction: Hey, everyone, welcome back in our Lives video. We learned how to add fractions In this video. We will learn how to subtract fractions, and it's very similar to adding fractions. The only difference is that instead of adding your subtracting, so let's take a look at how that's done. For our first problem, let's take a look at 4/8 minus 2/8 just as we learned in the last section, when we have the same denominator weaken, simply bring it over like so and then proceed to subtract the numerator. So now that we have our denominator over, we simply subtract four minus two, which will give us, too. And our final answer is 2/8 and also, as we learned in our Lives video. Every time we solve a fraction problem, we want to ask ourselves, Can we simplify this fraction? And in this case, yes, we can, because we can divide the numerator and denominator by the same number, which is to so so divided by two is going to give us one and eight. Divided by two is going to give us four. Great, so this tells you 2/8 is the same as 1/4 for next problem. Let's take a look at 6/8 minus 1/8. And, as we've learned when adding and subtracting fractions with the same denominator, want to bring over our denominator on? Now? We subjects attract our norm aerators. So six minus one is going to give us five, and that gives us 5/8. And now we ask ourselves, Can we reduce or simplify this fraction any further? And the answer is no, because there is no number that we can divide the top in the bottom number by that can help us achieve that. So that's look at one more problem before we move on to our practice problems. For next problem. Let's take a look at 36 minus 26 And just as we learned before, let's bring over our denominator Since is the same, which will simply lead us to subtracting are numerator. So three minus two is going to give us one, and our final answer is 1/6. This fraction is already in the simplest form, so there's nothing else we can do to it. Great. This conclusion is video on subtracting fractions. In our next video, we will be doing a few practice subtraction problems in order to reinforce what we learned . So I want to thank you for watching, and I look forward to seeing you there.
28. Adding fraction problems: everyone welcome back in our last video, we learned how to add fractions in this video. We're gonna pick up right back where we left off and add a few more fractions, which will only help. You better understand adding fractions for our first problem. Let's take a look at 7/10 plus 3/10. First, let's bring over. Our denominator says they are the same, which will leave us with our two numerator is which we simply add. So seven blistery is going to give us 10 and that gives us a fraction of 10/10. I would learn that our previous video that when we have a fraction with the same number on top and the same number on the bottom, it can be simplified as one hole. So our final answer is one for next problem. Let's take a look at 2/7 plus 4/7. First, let's bring over our denominator, which is seven, and then we simply add our numerator, which is two plus four, and that gives us six, and our final answer is 6/7 or 6/7. There is no number. We can divide the top in the bottom by so this fraction is at its simplest terms. For next problem. Let's take a look at 12 overs. 24 plus 6/24. And just as we did before, let's bring over our denominator and then proceeds at our numerator. So 12 plus six is going to give us 18 and that gives us 18/24. Great, and this is a fraction weaken. Definitely reduce. So let's see how we can do that. Remember one reducing a fraction. You always want to divide the top and the bottom number by the same digit. And in the case of 18/24 the greatest comment factor or the number weekend used to simplify this fraction is six, which we will divide both the numerator and the denominator. By so 18 divided by six is going to give us three on 24 Divided by three is going to give us four, and that gives us our final answer of 3/4. Great. This is going to conclude this video in our next video. We're going to start learning how to subtract. Fractions is very similar to adding fractions. The only difference is we subtract. I want to thank you for watching this video, and I look forward to seeing you in the next video
29. Subtracting fraction problems: Hey, everyone, welcome back in our lives video. We learned how to subtract fractions in this video will be picking up right where we left off and continue subtracting a few more fraction problems in order to reinforce what we learned so far. First problem. Lisicki, Look at 4/10 minus 1/10 just as we learned before. When we have the same denominator, we want to bring it over so that all we have to do is just add or subtract the numerator. So let's bring over our denominator than subtract. Okay, now that we have our denominator in place, all that's left this for minus one, which is going to give us three tense and this fraction is at his lowest terms, so we can't reduce it any further. So let's move on to our next problem, which is going to be 6/14 minus 5/14. The first thing we want to do is bring over the denominator, which is 14 and that leaves us, was just needed toe. Subtract the numerator, so six minus five is going to give us one, and that gives us our final answer of 1/14 and I'm sure you can guess by now that when you have a fraction with the numerator of one, you can't really reduce any further. So let's look at one last problem before we move on to finding the common denominator for less problem. Let's take a look at 12/24 minus four over 24 and the first thing we want to do is bring over our denominator, since it doesn't require any math and then we can focus on subtracted the numerator. So 12 minus four is going to give us eight, and that gives us 8/24 and I would check if we can reduce this fraction. And indeed we can, because both eight and 24 are divisible by eight. So eight divided by eight is going to give us one and 24 divided by eight is going to give us three. So that tells us 8/24 is the same. S 1/3 Great, this concludes, is video on subtracting fractions. In our next video, we're going to start talking about finding the common denominator, which is one of the most important concepts when dealing with fractions. So I highly recommend watching it. I want to thank you for watching this video, and I look forward to seeing you in the next one.
30. Finding the Common Denominator: Hey, everyone, welcome back in our Lives video, we saw some practice problems subtracting fractions in this video, we're going to cover a very important topic when dealing with fractions. That's finding the common denominator. Finding the common denominator basically means when you're trying to add or subtract two fractions with different denominators, you have to make sure both are the same. Remember in our previous video, we said that when adding or subtracting fractions, the denominators must be equal. In this video, we're gonna look at what happens when we're trying to solve fractions with different denominators. Hence the name finding the common denominator For our first example, let's take a look at 1/2 plus 1/4 as I'm sure you can see in this first example are the nominators are different, so we have to find the common denominator so that we can add these fractions. And the way that we do that is by changing the fractions of it and will helps us change the fractions in order to solve them is a bit of multiplication, remember, was simplifying fractions. We have to divide the top number, the numerator, but the same number we divide the bottom number. The denominator? Well, the same applies when finding the common denominator. But instead of dividing the top and bottom number, we're going to be multiplying. So let's see how we can get that done. And one little tip is when deciding which fraction you want to convert. You want to look at the fraction with the smallest denominator, which in this case is 1/2 has the smallest denominator, even though the fraction is bigger, that the nominator by itself is smaller, and that may be a bit confusing. But as we do a few more of thes problems, you'll start to understand these more and more. So remember we said a second ago to find the common denominator. We want to multiply the top and bottom by the same thing in order to make our denominators equal. So the way we confined the common denominator is by asking ourselves, what number can I multiply two by two? Give me four and make my denominators equal, And the answer is to because two times two is four, so let's move are 1/4 to the side for a bit so we can find the common denominator. And let's multiply. So one times two is going to give us too, and two times two is going to give us four. Great. Now we can see we have found our common denominator by multiplying the top in the bottom number by the same thing. And now that our denominators are the same, we can add. So let's do that. And as we've seen before in our previous video, when adding fractions, we want to bring over our denominator, which is going to leave us with the last step, adding our numerator. So two plus one is going to give us three, and that gives us our final answer off 3/4. And this fraction is at a simplest term, so we can't reduce it any further. Let's look at another example for next problem. Let's take a look at 2/3 plus to sixth. And as we learned in the last problem, we want a first look at the fraction with the smallest denominator in this case, the three and 2/3. And once we have the fraction, we want to change or multiply the top in the bottom in order to find the common denominator , Then we want to find the number that can best help us get there. So we want to ask ourselves, What can we multiply? Three by that can help us get to six. And the answer is to because two times three is six And remember, we want to multiply the top in the bottom by the same number. So two times two is going to give us four and the Re times two is going to give us six. And that's going to give us a fraction off 46 And now that we have the same denominators, we can add our two fractions. So let's bring over our six first. Then we add our numerator. So four plus two is going to give us six, and that gives us a final answer of 6/6. I remember in our previous videos, when we were adding and subtracting fractions, we said that when we have a fraction that the numerator and the denominator are the same, we can simplify as one hole. Great far Next problem. Let's take a look at 2/4 minus 3/8 and just as before, we want to look at the fraction with the smallest denominator in this case, the four into fourths. Next, we want to ask ourselves, What number can I multiply four by to give me eight? And this is another case where no, your multiplication helps. The answer is to because four times two is going to give us eight. So remember infractions, whatever you multiply the bottom by, you also have to multiply the top by. So let's multiply. Two times two is going to give us four and four times two is going to give us eight, and that gives us a new fraction off 4/8. Now we can subtract. So let's bring over Art the nominator, since they are the same and don't require any math. Next, let's subtract for minus three, which is going to give us one, and that gives us our final answer off 1/8. And this fraction is at its simplest form so we can move on to the next. This next problem, I really needed to pay attention because it's a bit tricky, so let's see how we can solve 2/3 minus 1/2. So right from the beginning, we can see that nothing we can multiply two by gives us three and vice versa. Nothing we can multiply three by will give us, too. So in this case you have to multiply both fractions instead of one. And a little trick I learned when dealing with this type of fractions is multiplying each fraction by the other fractions denominator. Let's see what that means. So here we have 2/3 and we want to multiply the top in the bottom by the other fractions denominator, which is, too. So let's do that two times two is going to give us four and three times two is going to give us six. So are no Fraction is for six and next. We want to do the same with the other fraction, because the denominators are equal yet. So now let's modify our other fraction by multiplying the top in the bottom by three. So one times three is going to give us three and two times three is going to give us six, and now we have 36 and now we dis attract are two fractions. So first, let's do as we did before bringing over our denominator and the last step we subtract the numerator so four minus three is going to give us one, and that gives us our final answer of 16 I know that's a lot of steps. But as you practice solving more and more fraction problems, these steps will become easier. Let's look at one more problem before concluding this video for next problem. Let's look at 3/4 minus 1/3. This problem is similar to the last. If we look at our denominators and try to determine how we can make them equal, we see that there is no number we can multiply for by. That will give us three, and there is no number we can multiply three by that will give us for and again, I want you to remember this little tip. When you encounter a problem like this, you just have to multiply each fraction by the other fractions. Denominator. So 3/4 we've multiplied by three and we won't supply 1/3 by four. Let's see what that will give us. Let's first solve 3/4 so three times three is going to give us nine and four times three is going to give us 12 and that's going to give us 9/12. Next. Let's modify 1/3. So one times four is going to give us four and three times four is going to give us 12 and that's going to give us for over 12. And now that we have equal denominators, we can subtract are fractions. So first, let's bring over our denominator 12 and the last step. Subtract are numerator. So nine minus four is going to give us five, and that gives us our final answer off. 5/12. Great. I hope you're starting to get the hang of finding the common denominator and adding and subtracting fractions. We're going to conclude this video here. I want to thank you for watching. And if you have any questions, please send me an email and I'd be glad to help you. In our next video. We're going to be looking at multiplying fractions, which in my opinion, is easier than adding fractions. So once again, thank you for watching. And I'll see you in the next video
31. Multiplying fractions: Hey, everyone, welcome back. In our last video, we learned about finding the common denominator in this video. We will be learning about multiplying fractions. I know solving fractions can be a little tricky due to how they appear and saying We're gonna be multiplying. That may worry you, but I can assure you that if you know how to multiply multiplying fractions, it's even easier than adding them. Let's see why. Let's say we have a whole pie, and it's not really a fraction because we haven't broken it up into pieces. Because, remember, we said a fraction is basically a home number broken into pieces, which we covered in the first video of this section. So let's say we want a more supply. Our hope I buy a fraction of a pie, for example, 1/2. One thing our lights explain is that when you multiply fraction by whole number, you have to convert the whole number into a fraction. But before we do that, let's see what happens when we won't supply one whole by 1/2. Remember, in multiplication, anything multiplied by one is that was your multiplying that number or in this case, half of a number, so half times one is going to be half. I know that must be a bit confusing, but as we work through more problems and multiply our fractions more, you'll see why. So let's go over again what we just did. But instead of using our pictures, let's look at the numbers I mentioned a second ago. Went multiplying. A fraction and a whole number. You have to convert the whole number into a fraction. So how would we convert one into a fraction? All we have to do is put a line under it and at a one as a denominator. Because remember, in our previous videos, when we were simplifying fractions, we said, Anything divided by itself. It's one, and this is where you'll see why. Cause they're multiplying. Fractions is easier than adding them. Because no matter what the denominator or numerator is, all you have to do is multiply across. Let's see what I mean by solving this fraction. So the first thing you want to do when multiplying fractions is you first, Multiply your to enumerators like so one times one is going to give us one, Then we simply multiply are the nominators. So one times two is going to give us, too. And now you can see no matter what numbers you have, we're multiplying fractions. You just multiply across. For next example, let's do something similar to our first Let's multiply, too times half, just as we did before, we learned that when multiplying a whole number by half, we have to convert the whole number into a fraction. And the way we do that is by simply adding a line under our whole number, then placing a one as a denominator as we did before. Next we just multiply across our to enumerators so times one is going to give us, too. And next we do the same with our denominators. So one times two is going to give us, too, and that gives us 2/2. And as we learned before, when we were simplifying fractions, we learned that when you're numerator and denominator are the same, it's the same as one hole, or you can simplify it as one hole. Next, let's take a look at 3/5 times 3/3 in this problem. Since we already have two fractions, all we need to do is multiply across and we want to start with our two numerator. So three times three is going to give us nine. Next we multiply our to enumerators. So five times three is going to give us 15. And that's going to give us a fraction off. 9/15 on when we saw a fraction. Remember, we always want to check if we can simplify the fraction toe its simplest form, and in this case, yes, we can. Let's see how we can do that. Remember, we learned that when simplifying a fraction, we want to divide the numerator and the denominator by the same number. And in the case of 9/15 that number is three. So nine divided by three is going to give us three and 15. Divided by three is going to give us five, and our final answer is 3/5. Great far. Nick's problem. Let's take a look at 56 times 1/4. The first thing we want to do is multiply our numerator so five times one is going to give us five. Next we want to multiply are the nominators. So six times four is going to give us 24 and that gives us a final answer off 5/24. And this fraction is in the simplest terms, so we can't reduce it any further. So let's move on to our next problem for next problem. Let's multiply 4/7 times 4/5. First, we want to multiply our top numbers so four times four is going to give us 16. Next we multiply art the nominator. So seven times five is going to give us 35 and last, we want to ask ourselves, Can we simplify this fraction any further? And the answer is no, because no number can be divided both by 16 and 35 to make this fraction simpler. So therefore, the final answer is 16/35 and that's going to conclude this video on multiplying fractions . And our next video will be closing out this section with learning how to divide fractions, which is very similar to multiplying them. So I want to thank you for watching this, and I look forward to seeing you in the next one
32. Dividing fractions: Hey, everyone, welcome back in our Lives video, we learned about multiplying fractions In this video. We will be concluding this section by learning how to divide fractions, which is very similar to multiplying them. Funny thing about dividing fractions is that no division is required and I'll show you why . Far first problem. Let's take a look at 26 divided by 1/3 in this fraction were clearly being asked to divide , which in our mind should appear like this as one big fraction. But when you encounter a problem that requires you to divide, all that you simply have to do is switch your second fraction in this case, 1/3 to 3/1 and the division sign into a multiplication sign. Then we simply just multiply like we did in our Lives video, where we learned how to multiply fractions and just in case you're a bit confused. Original Fraction was 1/3 and we changed it by making the numerator that the nominator and the denominator the numerator. Now let's multiply two times three is going to give us six and six times one is going to give us six as well, and that's going to give us 6/6. And as we learned before, we have a fraction that the numerator and the denominator are the same. We can simplify as one hole, so one is our final answer, and it's that easy to divide fractions if you know how to multiply. Well, dividing fractions is a breeze. Let's look at another example 3/5 divided by 2/3. So remember, the first thing we want to do is switch our second fraction 2/3 by flipping the numerator with the denominator like so and also the division sign with a multiplication sign and you can see. Now we have to over three. After we switched around the numerator with the denominator. Now you multiply across like we would multiply any fraction. So three times three is going to give us nine and five times two is going to give us 10. This fraction cannot be reduced any further, so let's move on to our next problem for next problem. Let's take a look at 1/6 divided by 1/2. The first thing we want to do is, as we did before, switch our second fraction numbers, which is 1/2 to to over one. So let's see what that looks like. Great. Next we simply multiply. So one times two is going to give us, too. And then we multiply. Are the nominators six times. One is going to give us six, and that gives us a fraction off to over six. And this fraction is a fraction we can simplify by dividing the top in the bottom number by to so so divided by two is going to give us one and six. Divided by two is going to give us three in. Our final answer is 1/3 great for our final problem. Let's take a look at 8/11 divided by 7/8. Just as before, we want to flip our second Fraction 7/8. Let's see what that looks like that's going to give us 8/7, and now we multiply. So eight times eight is going to give us 64 and for a last step 11 times seven is going to give us 77. And that gives us a final answer off 64/77. And that's gonna conclude this video on dividing fractions and also on the section on fractions. I hope after this section you're starting to understand fractions and how to solve them. I want to thank you for watching this video. And if you have any questions about dividing fractions or any other questions regarding other sections off this course, police send me a message and I'll be glad to help you Thanks.
33. Decimal Place Value: Hey, everyone, welcome back In this section we will be learning about decimals. In the previous section, we learned all about fractions. How to add, subtract, multiply and divide. Fractions in this section will be learning all about decimals, also referred to as a decimal place value. First, I will start by explaining the concept the decimal place value, which will further help you understand how to add, subtract, multiply and divide decimals. Let's imagine for a second that we have the number three and four. You may ask yourself what is between the numbers three and four. Let's draw a line to better, Illusory and visualize what is between the numbers three and four. Specifically, the answer is 3.5, which can also be represented as 3.5. The point is what tells you it's a decibel number. So now you know any time you see a number with a dot that tells you it's a decimal number, the number after the dot to the right of the decimal point. In this case five tells you how close it is to the next number, which is four. And in this case, 3.5 or 3.5 is between three and four. And if you look at the number line, you can see that it falls right in between the two numbers. It's a better understand how we arrive. At 3.5, we count as follows from left to right 3.1, 3.2, 3.3, 3.4 3.5, which we already have, then 3.6, 3.7, 3.8, 3.9 and 3.10 is basically the next number, which is four, So we don't write it. This is the case for all in numbers, whether it's between three and four, 101 a one or simply one and two. And as a quick side note, I want to point out that the number after the decimal point, which in this case is five, is referred to as the 10th place. And as you have more numbers beyond the decimal point, they have different names, and we're going to get into that and just a second. But first I want to go back to our number line so that I can show you, just as we had numbers living between other numbers like 3.5 being between three and four and 3.1 all the way to 3.9 toe arrive to our next number, which was four in the number line above. The same thing occurs when you look between our decimal numbers. Let's take a look at 3.2 and 3.3 so you can see what I mean. Let's draw another number, line and place 3.2 on the left because that's where we will start counting and 3.3 on the right and we start counting just as we did before. But instead of the being 3.3 like it was before on the number line above, we add another number next to which gives us another decimal police and we start at one which makes the number next to 3.23 point 21 and we continue counting Up 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 and then we arrive at 3.3 and you can keep repeating this process over and over and go deeper into the decimal place value. Which brings me back to where we were before when I said the first number after the decimal is the 10th place. And when we had another digit, the next decimal place number is the 100th place. If we had yet another number like 3.244 the last number would be referred to as the 1000th place to make sure you understand what I mean. Let's take a look at the number three point 244 again. So the first number after the decimal point is to which is the 10th place. The next number to the right after the two is four, which is the 100th place, and the next number to the right is the thousands place. At this point you may be ask yourself what is the point of these numbers after the decimal point? What these numbers tell you is how close you are to the next hole number, which is just like a fraction, and you'll start to see what I mean by this as we start to add and subtract fractions, which we will start on our next video On our next video, we will start adding subtracting and multiplying decimal numbers so that you can further understand what we've been talking about in this video. I look forward to seeing you there.
34. Adding, Subtracting and Multiplying decimal numbers: Hey, everyone, welcome back. In our last video, we learned what decimal place value is in this video. We're going to expand them when we started learning on our lives video and start adding subtracting and multiplying numbers with decimals far first problem. We have 3.2 plus 4.1 before we start adding I want to say that adding, subtracting and multiplying decimals is the same as adding subtracting and multiplying numbers as we didn't earlier sections. So if you need to refresh your memory on how to do those things, it would be a great idea to pause the video, go back to the sections where you feel you may need more. Practice this and come back. When you feel ready, it will help you understand, adding, subtracting and multiplying decimals with ease. Before we start adding our decimal numbers, let's do as we did it before and place them on top of one another vertically so that we could make adding much easier. When you place them on top of one another, you want to make sure you align your decimals just as we did before. We want to start adding from the right column two plus one is going to give us three. Three plus four is going to give us seven and for a last step to determine are no decimal number. We simply bring down our decimal point toe where it originally waas, and that gives us a final value of 7.3 for next problem. Let's take a look at 8.4 plus 5.9. Let's align our numbers vertically so we can add easier and we add, just as we did before, four plus nine is going to give us 13. We've right down the three below and we carry the one. Now we add eight Plus five is going to give us 13 plus one, which we carried over is going to give us 14. And for our last step, we just bring down our decimal point, and that gives us a final value off 14.3 for our next problem. Let's take a look at 12.1 plus 1.8, let's add one plus eight equals nine. Then we move on to our next column and we add two plus one is going to give us three and we're left with one which we bring down and are last, that we simply bring down two decimal point, which is going to give us 13.9 as our final answer. Let's switch things up a bit now and subtract, which is very similar toe, adding decimals. The only difference is we subtract, but the same concept of lining apart decimal point and bringing out the decimal point after we subtract still applies. Let's subtract 7.9 minus 2.4, and we start with our right column. Nine minus four is going to give us five. We moved to the next column and we continue subtracting seven to minus two is going to give us five. And for our last step, we just simply bring down the decimal point, and that gives us a final value of 5.5. Let's try another problem, because that's how math becomes easier. It's by practicing and doing problems. The more you practice and solve problems, the easier and better you get, and eventually you won't even have to think much to solve a problem. You'll just see the answer. Let's continue with our next problem. 16.7 minus 3.5 seven minus five is going to give us, too. We moved to our next column and subtract six minus three is going to give us three. We have one left, so we simply bring it down. And for a last step, we bring down the decimal point and get our value, which is 13.2. As you can see whether we add or subtract decimal numbers, it's very similar you add or subtract your numbers and then simply bring down your decimal point to get your final answer. Let's switch gears a bit and start multiplying decimal numbers. Just as we learned in the multiplication section, we multiply numbers. The same applies when multiplying decimals. The only difference is when we place our decimal point and you'll see what I mean after we most supply our first decimal numbers, which is going to be 5.3 times 1.7. When multiplying decimal numbers, you can line up your numbers vertically, as we've done before when multiplying numbers. Unlike adding as attracting decimals where you have to align your decimal point when multiplying, you don't have to worry about lining up your decimal point. All you have to do is a liar, numbers correctly and ignore the decimal point until you multiply your numbers. One. Steve multiplied your numbers. You can easily determine where to place your decimal point by counting, and I'll show you after we multiply. So let's multiply. Three times seven is going to give us 21. We write down the one and carry the two. Next, we multiply across seven times five is going to give us 35. Plus two of that we carried over is going to give us 37. Next would place are zero, and now we multiply. One times three is going to give us three. And for last multiplication step, we multiply. One times five is going to give us five. Now we add to get our final answer. Zero plus one is going to give us one seven plus three is going to give us 10. We write down the zero and carry the one three plus five is going to give us eight plus. The one that we carried over is going to give us nine, and that gives us a final answer of nine No. One and for a last step to determine where we place our decimal point. We simply look up at the number. We were multiplying by 5.3 times, 1.7, and we simply count everything to the right of the decimal point in this case, three and seven, and we count one to we have two numbers beyond our decimal points. So now all we have to do is go down to our final answer, and from the right to the left, we count the month of numbers we had beyond our decimal point. And since we said we had to, we count two spaces one to, and we place our decimal point, and that gives us a final answer off 9.1 I know that might be a become fusing if it was your first time multiplying decimal numbers. So let's try a few more problems. You can get the hang of it foreign mixed problem. Let's take a look at 15.2 times 4.8. Let's line up our decimal numbers and multiply eight times two is going to give us 16. We write down the six and carry the one. Next we multiply eight times five, which is going to give US 40 plus. The one we carried over gives us 41. We write down the one and carry the four. Next we multiply eight times. One is eight plus. The four is going to give us 12. Now we move on to our four and first let's place our zero and start multiplying by four. Four times two is going to give us eight. Next four times five is going to get us 20. We write down the zero and carry that too. Next four times one is going to give us four plus two is going to get the six. No, we add to get our final answer, six plus zero is going to give us six eight plus one is going to give us nine two plus zero is going to give us too. And finally, six plus one is going to give us seven for our final step. In order to determine where we place our decimal point, we count all the numbers beyond the decimal point one to we have to. So we count from the right to the left and place our decimal point one to and we write down our decimal point and that gives us a final answer of 72.96. As you can see when multiplying decimal numbers, we multiply as we wouldn't want. Apply any numbers. And after we multiply, we count the numbers beyond the decimal point and go down to the number that resulted from the multiplication and count from the right to the left of the number of spaces that we counted when counting how many numbers we have beyond the decimal point and we place our decimal point. Let's try one more problem just so you can really get the hang of multiplying decimal numbers far. Next problem. Let's multiply 3.11 times 6.9 this place our numbers on top of one another so we can multiply easier. Let's start by multiplying nine times. One is going to give us nine next nine times one again, and that's going to give us nine. Next nine times three is going to give us 27. Now we move on to our six and multiply, But first, let's place our zero and now we multiply six times. One is going to give us six. Next we multiply six times won again and that's going to give us six again. And finally six times three, which is going to give us 18. And now we add to get our final answer, nine plus zero is going to give us nine. Next nine plus six is going to give us 15 right down the five and carry the one seven plus six is going to give us 13 plus. The when we carried over is going to give us 14. We're right down the four and carry the one next two. Plus A is going to give us 10 plus one We carried over is going to give us 11. We write down one and carry one, and finally we add the one which is carried over, plus one is going to get us to, and we have our final answer. Now that we have our final answer, all we need to do is determine where to place our decimal point. So we simply look at our original decimal numbers, which we multiplied and count the numbers that are beyond the decimal point. As you can see, we have three. So that tells us we need to count three spaces from the right to the left. Let's count just to make sure one to three. And now we look down at our final answer and count three spaces from the right to the left , one to three and place our decimal point. And that gives us a final answer off 21.459 I know that can be a big confusing this your first time multiplying decimal numbers. But that's the beauty of having a course like this. You gonna re watch the video and go with me step by step and learned the steps and be able to multiply. And a decimal number that concludes this video on adding, subtracting and multiplying decimal numbers. In our next video, we will learn how to divide decimal numbers. I look forward to seeing you there.
35. Dividing decimal numbers: Hey, everyone, welcome back. In our last video, we learned Tato, add, subtract and multiplied decimal numbers. In this video, we're going to learn how to divide decimal numbers. If you washed earlier sections of this course where we were learning how to divide. Dividing decimal numbers isn't that much harder. There are only a few more steps required to solve a problem, which she will learn in this video Far first problem. Let's divide 4.37 by two. The first thing you want to do when dividing eight decimal number is you want to place a decimal point on top of the line wherever it is located and the decimal number you are dividing. And that's important to do first. Because as you divide, you want to write around the decimal point and you wanted to be fixed. So let's divide. And just as we learned before, one dividing how many times can to go into four. The answer is to so we write that number on top of the line and next we ask two times two is going to give us four and we're right that forward down and we subtract. Four minus four is going to give us zero. Next we ask to goes into zero and they can't because zero is less than two. So we do as we did before we bring down the next number where dividing, which is three. And now we ask to goes into 31 time and we write that one on top. Then we multiply. One times two is two and we subtract that two from three three minus two is one. And as we did before, two goes into one. And it can't because when a smaller so we bring down the next number we're dividing in this case seven. And now we ask ourselves, how many times can to go into 17? The answer is eight because eight times two is 16. I went right that 16 down here after we multiply eight times two and now we subtract 17 minus 16 is one. Next we ask again, as we have before. How many times can to go into one? And the answer is zero, since one is smaller than two and this is where dividing decimals can get a little tricky, because when we had a number we couldn't divide into, we looked at the number were dividing and brought down one of its digits, as we did with three and seven. As you can see in this case, we don't have any more numbers. So we simply at a zero at the end of the number, we're dividing like so and then we bring it down. Now we can ask How many times can to go into 10. The answer is five. We write that, and now we multiply five times to which is 10. We'll write that down and subtract 10 minus 10 0 and now we don't have anything else to divide. So we're done, and we've have a final answer off 2.185 If that was a big confusing for you, it's okay. We're gonna work on a few more problems, which will help you understand dividing decimals better, because that's what learning is all about. At first, you might not understand, but through familiarity and trying over and over, you become better and better and understand any problem you attempt to solve for next problem. Let's take a look at 10.75 divided by five, the first thing we need to do is place our decimal point on top of the line so that we know where to place our numbers and let's start dividing five goes into 10 two times. So we placed that too, on top. And now we multiply. Two times five is going to give us 10. Now we subtract 10 minus 10 is going to give us zero. Next we ask, How many times can five go into zero? It can't because there was smaller and we can't divide five by nothing. So we do as we did before and we bring down the next digit from the number we're dividing, which in this case is seven. Now we ask, how many times can five go into seven and the answer is one. So we write that one on top and we multiply one times five, which is going to give us five. And we placed at five under the seven as subtract seven of minus five is going to give us too. Next we ask, how many times can five go into too? And it can't because tourism honor. So we need to do as we did before and bring down the next number we're dividing. So we bring down the next number, which is five. And now we ask, How many times can five go into 25? And the answer is five. Now we multiply five times five is going to give us 25. Next we subtract 25 minus 25 which is going to give us zero, and that gives us a final answer off 2.15. I hope you're starting to see that dividing decimal numbers is very similar to dividing any numbers. The only difference is you have to place your decimal point above the line and make sure you add a zero toe. The number you're dividing if you need to. For next problem, let's divide 9.64 by 0.3. This is the first time we're dividing two decimal numbers, and all you have to do when you're dividing two decimal numbers is move the decimal 20.1 place to the right. So, for example, let's look at 0.3. All we need to do as I stated before is move one decimal place to the right, and that gives us the number three and weaken. Just rewrite that as number three, but before you start dividing, you have to remember that since you moved the decimal 0.1 police to the right, on the number you are dividing by, you have to do the same for the number you're dividing into. In this case, 9.64 becomes 96.4 when we moved the decimal one place to the right and now we can divide first, let's place our decimal above the line. And now we can divide three goes into 93 times we write the three on top and we multiply three times three is going to give us nine. We write that down and we subtract nine minus nine is going to give us zero. Next we check. How many times can three going to zero and it can't. So we bring down a digit. Now we have six and we check How many times can three go into six? The answer is to so we write that on top and now we multiply two times three is going to give us six and we write that down and subtract six minutes six is going to give us zero. We know three can't be divided by zero. So we bring down a digit and we check how many times three goes into four. The answer is one. So we write that on top and multiply one times three is going to give us three. So we write that down and subtract four minus three is going to give us one. Now we check. How many times can three goingto one as we learn before it can go into one? Because it's smaller. So we add a zero to the end of the number we're dividing and bring it down. That gives us 10. We know 10 is bigger than three. So now we can divide three goes into 10 3 times. So we write that on top and now we multiply three times three is going to give us nine, and now we subtract 10 minus nine is going to give us one, and now we check if we can divide and we know we can't because one is smaller than three. So we had a zero to the end of the number we're dividing and bring it down, just as we did before. I want to highlight an important point here where we come to a loop, which simply means something is repeating itself over and over. Think of an infinite loop, and that's exactly what we have here. Before we said that we have one which we couldn't divide by three. So we added a zero to the end of the number we were dividing by, which gave us 10 and allowed us to divide it by three, which we placed on top and next multiplied three times three, which gave us nine. And we wrote that down to subtract by 10 which again gave us one, which would just repeat when we try to divide one into three and we can. So we add a several to the end and will keep repeating this over and over. And when that occurs, we simply look at our final answer and place a line on top of the last number that keeps repeating itself. If you'd like, you can keep adding a zero to the end and continue dividing three by 10 and you'll see you'll keep getting three. That's what this line above the three indicates that the number will just keep repeating itself. That's going to conclude this video on dividing decimals. If that was a big confusing. I highly recommend watching the video at least two or three more times and working out the problems with me, and you'll start to get the hang of it. If you have any questions, please don't have to take to ask, and I'll be glad to help. Thank you for watching.