Transcripts
1. Math intro: find doing mental arithmetic hit help with this course with many different mental arithmetic tricks taken. Look into some I know the answer straight away. Let's take 20 cents of 178 is Easy Way have a number that ends a five way. Wish to find a square that you know the answers going into 20 way. Take our first number. 812 It must weigh. Multiply these two numbers together, and that gives us 72. And since we know the answer is 25 7200 amaze your friends calculator showed him how you could be maths. Some of these match tricks include finding a fraction of any number. Large numbers together heads working out tips in restaurants, techniques using the pen and paper like lattice multiplication on a Japanese style modification. Are you using all these tricks together? You'll be a mental genius
2. Multiply large numbers: Let's say we want to multiply too large numbers. That is less than 100. Here's how we did without using a calculator. Let's pick two round of numbers. Let's go for 92 98. So we wanted times these two numbers together. The first thing we're gonna want today is take our 92 on. We're gonna minus that from hundreds. So it gives us the value of eight. Now, whatever we decide our first number to be, it will always be taken away from 100. Now we take our second number 98 do the same thing. We're gonna mind a stat from hundreds, and that gives us two. We're gonna take these two numbers, this eights and the two we're gonna add them together. This gives us 10. Now, look up previous two numbers. We're gonna take this 10 on minus. It's from 100. So this gives us to value off 90. And something magical just happened here because this is the 1st 2 digits of our answer off 92 times 98 slow cinemas. We started with 18 to. We're going to use them again. This time we're gonna times them together. So eight times tune, as we know, is 16. Now this is where our second bit of magic happens, because that's 16. It's our 2nd 2 digits off our answer. So 92 times 98 equals 9000 and 16. So by just remembering a few simple steps, we can do this complex of multiplication really easily. So for those of you in the back of wasn't listening, let's go over that again. Now this works with any number, but nearer they are 200 the easier it will be to do so. Let's start with 89 94 this time, and that's before we gonna multiply least two together. So get take out 89. I'm honest it from hundreds, and that gives us the value of 11. Then we're gonna do the same thing with 94. We're gonna mindset from hundreds, and that gives us to value of six. Now we get take these two numbers off 11 and six on, we're gonna add them together. So 11 plus six equals 17. Now, we're gonna take our value of 17. I'm gonna minus at from 100 service equals 80 free. So this means the 1st 2 digits off. Our answer is 80 free. Now get the remaining two digits off our answer. We take our 11 and six again. This time we multiply them together to give us a value of 66 and 66 is our final two digits off our answer. So 89 times 94 equals 8366. Now it's your turn. Grab a pen and paper and try this technique out for yourself.
3. Tip at restaurants: So let me go to a restaurant. It's always polite to leave a tip. Well, there's a few ways we can work out how to leave a tip just by using mental arithmetic about needing a calculator. The most common tip is 20% so we're gonna mainly focus on that. But while we're at it also going to show you how to get 10% and 15% from any number easily , let's have a look how we do that. So let's say we go to a restaurant in America on the bill comes to $41.20. Now, how do we work that out in different percentages? So we know how much tip to leave. Let's have a look. But first we take our number 41.2 on we divide it by 10. So we just moved a decimal points. One decimal place till I left. Selous gives us $4.12. Now, this is 10% off 41.2. So already we know what 10% off our bill is now to find 20% which is a standard tip, we take our 4.12 on we double it. We just times it by two. So this simplifies the mass so we can do this calculation in our heads easily. So 4.12 times to its 8.2 full on this is 20% sell a maths involved. To find a standard 20% tip is actually quite simple. Let's have a look at finding a 15% tip. This involves a little bit more fault, but it's not cheap that to find 15% we take our first number are 10% off 41.2, which was 4.12 I mean half it. We divide it by two this time. So this gives us $2.6. Now we simply add that to the 4.12 when we come to 15%. So we take our 10% value, we half it, which gives us 5%. Then we just added back to a 10% value to equal 15% so half of $4.12 $2.6. Let me just add that back to the $4.12 to give us $6. 18 and this is 15% or $41.20. Okay, so say we fly to England on we go to the West End in London for a mill for two because it's Â£132.62. So how do we deal with a free digit bill? Let's have a look. So we take our number. 132.62 I'm divided by 10. An easy way to do that. It's just moved the decimal points one place to the left, so this gives us Â£13.26. Phyllis number is 10% off Â£132.62 pens. So to find 20% of that, we take our Â£13.26 on we double it three times it by two. So this equals Â£26 on 52 pins, and that's our standard 20% tip off. Â£152.62. Now to find 15% off our bill, we take our first value are 10% value, So a 10% of Â£132.62 it's Â£13.26 now we half it. We divided by two on this equals Â£6.60 free. So it's find 15% of our bill. We take this number and we added to our 10% value. The 10% remember is easy to work out because we just moved the decimal place one point until I left. So this means Â£6.60 free, plus Â£13. 62 equals Â£20.25. And this gives us 15% of our bill of Â£102. 62. Okay, let's do one more to make sure we really Now this. We've got off the plane in Bangkok. We jumped in a cab and he's taking us to our hotel now. We didn't agree a price before we got in a cab. So a short journey ended up becoming 864. But but because he's such a nice guy, we decided to give him a 20% tip. This is how we work it out. We take our 860 full, but and we move a decimal 0.1 place to the left. So this makes it 86.4, but which is 10% of the total cap, Johnny. Now to get to 20% we just double it. We times it by two, and this makes it 100 72 bart 720.8. So that is how we easily where account helps give a tip at a restaurant or a cab driver in Bangkok.
4. Math hacks japanese multiplication: you may have heard of Japanese multiplication. It's a technique they used in Japan to teach schoolchildren House do multiplication becoming widely accepted around the world these days. So this is a look at how we actually do it. We're gonna start off with a nice, easy 12 times free. Well, we all know the answer off. This is six. So we can start off using a stick method and see how we can get this value by using this technique. So we started by taking the first number two on. We draw two parallel lines like this in our second value of free. We draw free power lines at 90 degrees to the 1st 2 Then each place that the lines intersect. We count them up like site. So these lines intersect six times, so two times free equals six. Now, this is the basic general concept, but we can use much larger numbers. But before we do, let's have a look at 24 times 32. So we take off first number two on we draw two parallel lines. No off color. Coded this not to make it look childish, which make it easier to see and understand. Our second number is four. So draw four parallel lines on the same direction as the ones before. This represents our first number off 24 two and four. Now, to represent our second number, we draw the lines at 90 degrees. So we draw free lines to represent the free and 32 and two lines to represent, too. The zones could be drawn in any direction. But I find the easiest to draw it this way because then the numbers run in a clockwise fashion around the top off our lines, so it's easier to visualize. Okay, so all we need to do now is count up the intersections between our lines. So we start off from the right hand side on work away, over to the left. So here we have 82 intersections. So our first number is eight. There. We work our way to the left and count up the intersections at the top and also the intersections directly below it. So we count up Poli's on. We come to a value off 16. Now we have two carry the one over to the next column. We're dealing with thousands, hundreds, tens and units, the same as we would do during normal multiplication. So we have two carry the one, so there is only one digit on each column. Once that column is calculated, we move on to our final column far over Onslow left on. We count up these intersections, which gives us six, and then we add one to it from the one we carried over from 16. So let's equals seven. So the answer to 24 times 32 it's 768 now. The reason we draw the lines at 45 degrees, it makes it easy to visualize the columns that each row lives in. So by join these boxes, you can see how we add up each column as we go on. We work from right to left, each time carrying over the remainder into the next column on the left. Okay, so that's multiplying two digits values. But how big can we go with this? Can we do four digits? But the answer is yes. We can do any length of number that we wish. Let's look at 4525 times 3436 How would we do it with a number this large? We start withdrawn outer lines exactly as we did before. So his a quid off lines and by a number of them clockwise starting from the left we can see are some apparent. We have 4000 525 times free 1004 136 in this time. I'm going to draw in the column lines, so it's easier to visualize where each set of numbers lie. So starting from the right, we count up the amount of in sections here, and it comes to 30. So we draw zero on. We carry over the free insulin. Next column for moving over to our next column. Recount all the intersections that appear with inside that column. There is 27 intersections in this column on we add the free remains there that we carried over so altogether we come to 30 so we carried the free at zero. I move on to the next column. So as before, we count up all the intersections and we come to 56 and we had the free remain there so 59 and then we keep moving across the columns doing this until we come up with our final answer, each time moving from right to left, counting the intersections on adding up the remainder. So we eventually come to our answer off. 15,547,000 and 900. So if you're ever in the situation, we need to hear multiply large numbers but don't have a calculator hands. This is one of the quickest and easiest methods that there is. So 4525 times 3436 equals 15 million, 547,900. Now it's your turn. Grab a pen and paper and try this out for yourself. Try out different numbers of different sizes and see how this works, so you get a real feel for doing it. So when the time comes, you know exactly what to do, and you can multiply large numbers easily
5. Multiply large numbers by 11: we're gonna take a look at a trick that we can use to multiply any large number by 11. As we know, the 11 times table is one of the easiest ones to remember. This is great until we start getting into double figures. Once we get into double figures, the results are not the same. So take nine times 11. For example. This is 99 which is easy to remember. But as we get to 12 times 11 132 there's no easy way to visualize this. So here's a quick trick on the help. We can work this out without calculator. Let's start the 1st 1 off with 62 times 11. Now what we do is we take the six under two on which separate them. So the result is going to start with six on end into now, we take those two numbers again and we Adam to each other. So we take the six and the two and we Adam up to equal eight. Now it's just a simple case of in certain. Eight between are six and two, so answer is 682. Let's try again with a different on that. We have 34 times 11 so we do the same thing. We take the free on the full on, we split them apart. Then we add those two numbers together again. So free plus four equals seven. And then we simply drop that seven in between our two values to give us free 174. So 34 times 11 is free, 174. That's a quick, easy way of working out 11 times table as we start approaching larger numbers, right? So let's have a look at what happens when the two numbers we add together become a number larger than 10. So for this example, I'm going to use 84 times 11. So if we take eight on R four on, we separate them as before, and then we add the two together. So eight plus four equals 12. So if we dropped to 12 in between art original digits, we come up with 8124. The only problem lesson is it's wrong. This number is much, much too large value we're expecting. So what we need to do is we need to carry over the one. So as we popped the 12 interest number, you need to carry over the one and add it to the eight. So the answer we are looking for is 924. So 84 times 11 is 924 right? We know this works with a two digit number, but what about a free digit number? Can we still a ploy? The same technique to numbers with more digits? Let's have a look. So let's try 762 times 11. Let's see how this would work. So the same is before we take our first digits on our last digit on, we separate them. Our result will start with seven and end into starting from the right side. We add R six and R two together, which gives us eight. Now we can just pop that into our result as before. Now, if this value is greater knowing we would have to carry over the one as we did with the two digit number, now we continue moving across are some from right to left. So we've added six and two. Now we need to add together the seven under six just gives us an answer off. 13. Since this result is a two digits number, we need to carry over the one as before. So we pop the free into our result carry over the one. Of course, we add that to seven. So our answer is 8382. So 762 times 11 is 8382 on. We can use this technique to multiply any number we like by 11 in our head.
6. Multiply large number Trick 2: this hack is a bit more situational. If the number hasn't even square root, then it's easy to do. But it is possible. If not, let me explain how this works. So let's take the some 64 times 125 now. This is a trick. If we have the first number and double the second, it makes us some a lot easier to visualize what the answer would be. If we have a general idea off our multiplication tables, the answer will jump out at us as we do this calculation. So let's get started. We take our first number 64 on we half it to give us 32. Now we take our second number 125 on we double it. Let's give us 250 then we just do that getting so we take 32 we half it to give us 16 on. We take 250 when we double it. Let's give us 500 Now, The answer toe only sums will remain the same. Now we just keep doing this so we take our 16.5 it to give us eight on our 500 we double it to give us a thousands. Now already, we can see the answer to our some. It jumps out at us eight times 1000 is obviously 8000. So that's the answer. But we can keep going after some is more complicated. So taken 8.5 in it again would give us four on 1000 times to be 2000. So we now have four times 2000 which is again office. It's 8000 but if it's not obvious yet, we can carry on. Going so half in four gives us to doubling 2000 gives US 4000 and now the answer is extremely obvious. It's 8000. So this is how we can simplify a small vacation, some to make it easier to wear accounts. Getting all the way down to two doesn't happen with most numbers. It will only happen if the square root off the first number is, ah, whole number and not a decimal. But we can use it to get down to a lower number on almost all sums to give us a chance to be out to visualize what the answer maybe Let's look a different one another easy one again . This time we're gonna go with 32 times 150 so half of 30 to 1650 times two is free. 100 then half a 16 is eight and 300. Doubled is 600. And then again half of eight is four on day, two times 600 is 1200. Then we get all the way down to two on two times 2400. We can see that. Now we can see what that's gonna look like. That's 4800. So answer is 4800 to the some 32 times 150. So this trick does work with all numbers is just certain numbers that go all the way down to two. But we can always simplify the some, no matter what. So let's have a look at one that only goes down to free. So this time we're gonna do 48 times 50. So we take our 48 we half it, and that gives us 24. There are 50 and we double it to give us 100 now already the summit a lot more simple, and we could probably work out the answer just by looking at this some. But let's keep going. So half in 24 gives us 12 and doubling 100 gives us 200. Now we can see the ants now because 12 times 2 24 So the answer is 2400. But let's keep going a few more steps. Half of 12 gives us six and 200 doubled gives us 400 and then we can go further and say half of six equals free and two times 400 equals 800 so we can keep going and to gets a multiplication table that you're more familiar with. So our answer here is 2400. Okay, so what would happen if we go a bit more complicated? Let's take 88 times 140. And how would this work accounts? So our first step is half of 88 which gives us 44 on 140 doubled, gives us 280 then our next step is half of 44 which is 22 and then double off 280 gives us 560 and then we repeat this to give us 11 times 1120. Now we can't half 11 without going into a decimal place, so half of 11 would be 5.5. And that's gonna make us some difficult to visualize. So we have to finish at this level. But that's not a problem. Remember the last lesson where we times things by 11 easily. We're just gonna do that so we can take us some 11 times 1120 and split the first and last number, as we did in the last lesson. No, he adds, the last two digits off that number two plus zero equals two. Then we take the next two digits, the one under two on. We add them together to give us free. And then finally we take the one on the one at the beginning off. Answer. When we had them scared to give us, too, and using the easy way to multiply by 11 we have come up with the answer. 12,320. So by combining the lessons we've learned over the space of this course. We've come up with a very powerful match system that enables us to mix and match these tricks, to be out to answer a whole range of complex questions. And every time it starts to change the way you look at numbers on the way you approach mathematics.
7. Squared numbers ending in 5: Here's a little trick cupping using for a while. If a number ends in five weaken, square it easily. But first, a rule. The square root of any number that ends in five will always end in 25. So to explain this, let's start with 35 squared. Here's an easy way to work out the square off 35. First of all, we take the first digit, which is a free. Then we add one to it, so it gives us the answer off. Four. Now we take that first digits off free and we times it by four. This consists the answer off 12. So what we do is we take our first digits on. We always add one to it many times this answer again by our fast digits. And this result gives us the 1st 2 units of our answer Now, remembering our rule that square off any number that ends in five will always ends in 25. We simply add 25 to the end of this some sort of square root of 35 1225. Why don't you have practiced this technique a few times? You can do it in your head faster on the calculator. So it's always fun to give a friend a calculator on race them and see if you can beat them . Alright, let's try that again with 55 squared. So as before, we take our first digit of five and we had one to it. This gives us the answer off. Six. Then we take our six on we times that by the first digits off five, so five times six is 30. So we write that down is our answer. So the 1st 2 digits off 55 squared is 30. So since the last two digits off any number that ends in five, that is squared is always equal to 25 R Answer off. 55 Squared is free 1025 so that works with two digit numbers. But what about a free digit number? Well, this works as well, but the mask can get a little bit more difficult, so it might not always be possible to do these calculations in your head as the numbers turn into triple or quadruple digits because at this point, your knowledge off the most filtration tables need to go above 10 but it's still possible, and this very still works with larger numbers. So let's have a look at one. So let's take a look. It's 125 squared now. It's still a reasonably low number, but the maps does get a lot more tricky. So the way it works with large numbers is we separate the follow from the rest of the digits. So we're gonna be working with 12 here. So we take the 12 on. We had one to it to give us 13 no matter the value of the number where you always add one to it. Now we take her answer from this, and we times it by 12. Now, as you can see, the Mass is getting a little bit more tricky as the number gets larger that we're trying to find the square off. Now, for some reason, 12 times 12 has always stuck in my head has 144. So knowing this, I can just add 12 to 144 to get my answer. So 12 times 13 is 156. That means the 1st 3 digits off 125 squared is 156 Now we know this. All that's left to do. It's add 25 to the end of our number, So 125 squared is 15,625 and that is how we found this square off any number that ends in five. As the number gets larger, it does get more complicated, but numbers below 100 is easier and quicker to do and using a calculator.
8. Subtract from 1000: When we subtract numbers from the hundreds, we can normally see what the value is going to be just by looking at some. But women get to thousands. It gets a little bit more complicated to visualize. So here's a handy trick that I've picked up over the years off. How we can do. Listen, our heads. So let's take a look at the some 738 from 1000. So we take our first value off seven on we minus it from nine. We always used nine each time for the 1st 2 digits. I'll explain as we go. So we take the first digit on B minus it from nine equals two. Then we take our second digit of 738 which is free on Reminder, stopped from nine, and that gives us the answer. Six. Then we take our for digit, which is eight. But this time we minus it from 10. The last digits. We always minus from 10. Where is the 1st 2 digits? We minus from knowing so 10 minus eight gives us too. So if you've not worked out yet, our numbers 262 is our answer. Our answer off 1000 minus 738. It's 262. Let's have another look over. Howard done that. So this time let's take a look. It 1000 minus 375. So again we take the first number on B minus it from nine, which gives us six. Then we take the second number on B minus it from seven, which gives us two. Then the third number we minus from 10 which gives us five. The free answers together is Thea answer to our main. Some 1000 minus 375 equals 625. Let's do one more to make sure we've really got this. This time would take 1000 minus 198. So we take our first digits off one from the 198 and we minus it from nine. This gives us eight, and then we take our second digit, which is 99 minus 90 and unfair digit. We always minus from 10. So eight minus 10 equals two. So answer 2000 minus 198 is 802. Okay, so we know we can now minus numbers from 1000 easily. But what if we have a number of more zeros? For example, 10,000. Does this system work with numbers like this? Let's have a look. Let's take a huge some 10 thousands minus 2345. So we started Samos before we take the first digit on we minus it from nine. So our fast digit is to from 2345. We take that to remind us it from nine and equals seven. Then we do the same with the next digits. Free minus nine equals six. Then, for the fair digits we did the same for minus nine equals five. And for the final digits, B minuses from 10 exactly the same way as we do when we're dealing with fountains and not 10 thousands. So there's our answer. It's 7655 now. Once you get used to do in this style of maths in your head, we can eventually move on to numbers that near to 1000 so we can approximate what it's going to be just by looking at the number. So let's take 902 this time. So 486 minus 902. Now, if we minus 902 from 1000 we know it's 98 we can see. Let's just by looking at it so we could lay out to the rest of some as we've done the full taken from a thousands and not 902. So nine minus four is five. Our first digit, our second digits. Eight. So remind us that from nine and it gives us one. And finally, our fair digit is six, and we mindset from 10. So we know that 486 from a thousands is 514. Now that's all remains to be done. Is minus 98 from our value of 514 to give us our answer of 416. Remember, we came to the value of 98 by minus in our largest part of the some by 1000. And then we just subtract that from the final value to give us the answer may seem a bit of a long winded way of getting to this answer. But after a while of doing sums like this, my brain started to work in this direction. So I find it quicker and easier on most of time. I can even do this in my head without calculator.
9. Find fractions of numbers easily: quite often in life. We need to find fractions of numbers, and it's not an easy thing to do. Even with a calculator, for example, with a calculator, we would work the some out like this free apes off 32. To work this out, we would have to convert free apes into a decimal by dividing the free by the eight. And then we were times It's by 32 to arrive at our answer. But there is a much easier way we can do this calculation without a calculator. Let me explain. Let's take the sum to fifth off 25. So the way we're gonna do this is we're gonna take the five. I'm gonna divide 25 by it. So 25 divided by five equals five. Now we get taken to I'm gonna multiply the five by the two, which gives us 10 which is our answer. It's a simple is that Let's have a look at what I'm doing here. I'm just gonna write how that some again to fifth off 25 equal 10. So we take our 25 the number that we're trying to find our fraction off and we divide it. By our denominator, this is the lower part of the fraction. In this case, the five say 25 divided by five, equals five. So I've written a right answer above the number here. So be times are answer by the numerator, which is a top part of the fraction are too here. So two times five equals 10 and this gives us our answer. All right, let's have a look at another one. So let's take chief odes off 30. Free the festival. We take off 30 free and we divide it by free, which is the lower part of our fraction. And this comes to 11. Then all it remains to do is take our 11 and times it by the top part of the fraction the to which gives us an answer of 22. Say you see, finding fractions of whole numbers is really easy with this trick. So let's look at one more. It's list home with the free apes off 64. So we take our denominator of eight Onda. We devise 64 by it to give us the answer off eight, and we can check out answer by doing the opposite so eight times eight is 64. So this is correct. So we take our answer and we times it by the numerator, which is a top hustler. Fraction. So eight times free equals 24. That means the answer off free apes of 64 24 find in fractions of whole numbers is a doddle . When you know the techniques and the best parties, you can do the sums in your head without having to use a calculator or your mobile phone to get the answer.
10. Easy 6 times table: when dealing with six times table. If we have an even number that we wish just times by six, this little trick in save time when trying to work it out. So let's take a look at six times four regarding the four we know, the answer is going to end in the same number. If we times in by an even number. So six times for will end in full and then to find the first digit, we simply take our number four on we half it, so half of four is, too. So our answer is 24. Let's take a look at another one six times eight. So we know the last digit will be eight and then we half it, and that's what the first digit is. So six times eight is 48. So now you know how to do half of the six times table with these
11. Easy 9 times table: There's many different tricks to remember in the nine Times table. Here are two of my favorite ways Let's take a look at nine times five. So we take our five on B minus one from it, and that gives us the first digit off our answer. Now we take this digit on B, minus it from nine, and that is the second part of our answer. So whatever, with times in nine by we minus one from it and that's the first part. And then we minus that number from nine. And that gives us the second digits off the answer. Nine times five is 45. Let's have a look at another one. We're going to do nine times seven this time, so we take our seven on B minus one from it, which gives us six. The latter is the first units off our answer. Then we take six away from nine equals free, so that's the second digit. So the answer to nine times seven is 63 so that works well for small numbers. But what about if we have a large number? Say, for example, nine times 15 when the easy way to approach This is times 15 by 10 which we can do just by simply adding a nought on the end of the answer. And then it's just a simple case of minus in the 15 away from our final answer. So we times the number by 10 and then we mind the city from the answer to give us 135. So nine times 15 is 100 and 35. Okay, so let's do one more to make sure we really have this. It's a nine times 25. We take our 25 on we times it by 10 to give us 250. Then we minus 25 away from 250. And that gives us our answer. So nine times 25 is 225. That's two different tricks to make multiplication by nine Easy
12. Find fractions of numbers easily: quite often in life. We need to find fractions of numbers, and it's not an easy thing to do. Even with a calculator, for example, with a calculator, we would work the some out like this free apes off 32. To work this out, we would have to convert free apes into a decimal by dividing the free by the eight. And then we were times It's by 32 to arrive at our answer. But there is a much easier way we can do this calculation without a calculator. Let me explain. Let's take the sum to fifth off 25. So the way we're gonna do this is we're gonna take the five. I'm gonna divide 25 by it. So 25 divided by five equals five. Now we get taken to I'm gonna multiply the five by the two, which gives us 10 which is our answer. It's a simple is that Let's have a look at what I'm doing here. I'm just gonna write how that some again to fifth off 25 equal 10. So we take our 25 the number that we're trying to find our fraction off and we divide it. By our denominator, this is the lower part of the fraction. In this case, the five say 25 divided by five, equals five. So I've written a right answer above the number here. So be times are answer by the numerator, which is a top part of the fraction are too here. So two times five equals 10 and this gives us our answer. All right, let's have a look at another one. So let's take chief odes off 30. Free the festival. We take off 30 free and we divide it by free, which is the lower part of our fraction. And this comes to 11. Then all it remains to do is take our 11 and times it by the top part of the fraction the to which gives us an answer of 22. Say you see, finding fractions of whole numbers is really easy with this trick. So let's look at one more. It's list home with the free apes off 64. So we take our denominator of eight Onda. We devise 64 by it to give us the answer off eight, and we can check out answer by doing the opposite so eight times eight is 64. So this is correct. So we take our answer and we times it by the numerator, which is a top hustler. Fraction. So eight times free equals 24. That means the answer off free apes of 64 24 find in fractions of whole numbers is a doddle . When you know the techniques and the best parties, you can do the sums in your head without having to use a calculator or your mobile phone to get the answer.
13. Lattice multiplication: lattice multiplication. This one is more a technique used to deal with large numbers off mortification rather than a trick. Let's have a look how this works. Let's take 24 times 41. So this is a two digit number times a two digit number so we can draw a box like this. Now, across the top of the box, we write the 1st 2 digits, so two and four for 24 and down the right hand side, we do the same for the other side off the sun four and one for 41. Now we're going to divide our square boxes up with diagonal lines right now. How this works is we take R four and R four over on the right hand corner on we times 22 together. When we put the answer in the box like this four times four is 16 and we put the one in the top half and the six in the lower half off our box. Then we look at the box below and this is our four times one box. You see how this works? Four times, one is full. So he put zero in the upper part of our box and four in the lower part. And then we move on to our next column. So this has got to at the top and four. So it's two times four. So the answer to two times four is eight. So he put zero in the top past the box on eight in the bottom part. Now, our final bottom left box represents the sum of two times one. So the answer to this is zero to to put a zero, our first number in the top parcel box on to our second number in the lower part. The latter is our lattice field out, and that completes the first stage of this technique. Now, this next stage is how we arrived at our answer 24 times 41. So what we do now is we take each diagonal column like where I've just drawn this arrow and we add up the numbers across that column. So the 1st 1 is easy. This column only has one number in it, and that is four. So the numbers added up in this dark McCollum equal four. So we work from right to left. Adding up the numbers in each Taiko column. So this next column is 60 and two. So six plus zero is six and six. Plus two is eight. So this diagram column added up comes to the answer off. Eight on. We write that below the box. Now we work our way around the box doing the same thing. The next cycle column is one plus eight. So we wrote the answer. Nine. At the end of that column, then we move on to our final top left column on the answer. Here is zero only zero in that diagonal section off that box. So if we read our answer, starting from the top left hand corner in an anti clockwise direction, we come to 0984 and it's the answer to 24 times 41. It's 984 984. So that's the basic self. How lattice multiplication works. Let's look it using a slightly larger number. So we're gonna look at 784 times 97 so we could do the same thing. We go draw a lattice grid, but this time our grid is free squares across and two squares down because our first number is free digits on our second number is two digits. So I'm going to go ahead and write our first number across the top, which is 784 on the second part of our equation are right down the side, which is 97. So put nine and seven going down the side of our boxes. Now we take, each number starts on the top rights box on we multiply. So four times nine is 36. So we put our free in the top parts and are six in the lower part. Then we move on to four times seven, which is 28. So we put it to the top eight bottom, then eight times 9 72 again seven at the top to the bottom, and then eight times seven, which is 56. Then we move up to seven times nine, which is 60 free on seven times seven, which is 49 now, with our lattice filled out, we just add up our numbers in the diagonal columns. So we start with eight. When there is only one number in this column. We just put eights below the next column. We have six plus two plus six, which equals 14 swimming of a double digit answer. We carry the one over to the next dark McCollum, so we write 14 like this. Now, when we add up the numbers in this next darkness column, we also add the one to it. So this next column is free plus two plus five plus nine plus one that comes to 20. So we carry the two when we write zero at the end of this diagram column. So it's next column is seven plus free plus four plus two, which comes to 16. So he wrote the 16 Endless column and carry the one to the final column. Now six plus one is seven, so let's our final number. It's seven. So reading our answer. Anti clockwise starting from the top left, 784 times 97 equals 76 thousands and 48. Right now, Let's get crazy and take this to the extreme and see what sorts of large numbers we can work with. Willis technique. So let's take 12345 times 6789 So our box it needs to be five numbers across on four numbers down. So I pop those numbers along the top. So 1234 and five and down the side 678 and nine. Now let's see how fast I can do this. Five times six is 35 times seven is 35 5 times eight is 40 and five times nine is 45 4 times six is 24 4 times seven is 28 4 times eight is 32 4 times nine is 36 free time. Six is 18 3 times seven is 21 3 times eight is 24 free times nine is 27 2 times six is 12 2 times seven is 14 two times eight is 16 and two times nine is 18 1 time six is 61 time seven is 71 times eighties eight on one times nine is nine. I need to lay down after that, right? That's how lattice grid filled out. Now we just need to add up the diagonal lines to find out what our answer is. The first line is just five, so it adds up to five. Six plus four is 10 and we carried the one over on this line is 22. So we carry the two. Next line is Freddie, So we carry over. The free on this line is 31 again, we carried a free over. Now we keep working on my around, adding up these diagonal columns on we get to our final answer eventually se in a clockwise direction from the top left, we have 83810205 So that means our answer is 83 million, 810,000. 205. And that was a very quick demonstration off house do large numbers with lattice multiplication. Andi An explanation off how lattice multiplication works.
14. Convert between metric and imperial: quite often in life. We find ourselves in a situation where we need to converts between metric and imperial. That's especially true in my career path. As an aerospace engineer, I often work on aircraft designed in America that the drawing shoes, feet and inches on. Other times I'm working on aircraft that was designed in Europe that use the metric system . It's often I find myself in a situation where I need to convert between metric and imperial hits the technical use. Now you will need a calculated these calculations because we're dividing using decimal points, we're gonna start off looking at the most common one. This is dividing millimeters into inches and vice versa, so one inch is equal to 25.4 millimeters. Once we know this the maps, it's easy to combat. Between the two 25.4 millimeters times, one is one inch. So is 25 millimeters to an inch, so one divided by 25.4 equals one millimeter. So say we have 2.5 inches on. We wish to know what that is in metric in millimeters, so we take 2.5 inches on. We times, it's by 25.4. This gives this answer in metric, which in this case is 63.5 millimeters, and to convert from metric to Imperial, we divide by 25.4. So if we take 52 millimeters and we divided by 25 point full converts that into inches. So 52 millimeters, divided by 25.4, equals 2.47 inches. I'm working to free decimal places because that's what the standard engineering units are outside of industry. Centimeters often used, for example, at schools and colleges. So to divide and times centimeters and convert light into inches, we just moved a decimal point. So it divided and time zone by 2.54 So the same calculation again to take 2.5 inches into centimeters. We simply times it by 2.54 and that gives us 6.35 centimeters and to convert from centimeters two inches, weaken, say, 5.2 centimeters divided by 2.5 full, and that equals 2.47 inches. Just by remembering 2.54 we can convert between metric and Imperial with lengths relatively easily for a rough approximation, Weaken times it or divide it by 2.5 for 2.5 or 2.5 is a lot easier to do in our heads without needing a calculator. So if we just need a rough approximation, weaken times, it's or divided by 2.5. Of course, this is no good in industry where accuracy is important. But if you know we think in inches and you wish to convert it into millimeters or centimeters, this is a good way to do it. Okay lets small distances all that large distances. Let's look at kilometers two miles on by sir versa. So the equation we need for miles to kilometers is one mile equals 1.62 kilometers, so we need to remember this number. But, like with millimeters and centimeters, we can just use 1.5 if we need a rough approximation off what this is. This is useful if you're driving in a different country and you're not used to the units of measurements that they use. Okay, let's look at some examples of this five miles times 1.62 that's equal to eight points, one kilometers, Celeste houses that roughly five miles is equal to eight kilometers and then to convert from kilometers two miles, we divide so 10 kilometers divided by R 1.60 that would equal 6.17 miles. Now, instead of remembering all these numbers like 2.54 on 1.62 I've made a conversion chart for you. It's a Pdf file. You can download it and print out. This makes conversion. Ah, whole lot easier this way. You don't have to remember these numbers saying that the last two that we've done its voice to remember these conversions as easily ones that would be using a lot. It's probably just necessary to remember the rough approximations. So, for example, for kilometers, two miles is 1.5 on for metric to Imperial is 25. This is just give you a rough idea so you can work out these distances in your head, right? Let's move on to one more before we wrap up this lesson. Let's look at converting pounds into kilograms, so if we have a look on our charts, we can see that one gram equals North 10.454 kilograms so we can round us up 2.5. Just do a rough calculation in our heads so we can say one gram is almost the equivalent off half a kilogram. But like my examples before, I'm going to show an accurate conversion between pounds and kilograms. So let's take Â£5 to convert this into kilograms. We times it by north 2.454 on this equals 2.27 kilograms. And if we could do list as a rough approximation and use no 0.5 as our conversion number Â£5 would roughly be equal to 1/2 that amount in kilograms, which would be 2.5. Now, if we wish to convert between kilograms and pounds, we just divide by that number instead of times. So 10 kilograms divided by north 100.454 equals just over Â£22. And if we were to do that calculation in our heads by using the point to follow, if instead of North Point for 54 just give us a rough idea. 10 kilograms would have equal to Â£20 so you can see there is a fluctuation. It's not entirely accurate doing in that way, but it's good to give us a rough idea of what the value should be in a pinch. So don't forget to download the PdF in the resources section. So you have a full copy off the conversion charts so you can around these numbers up to do quick conversions in your head. Or you can do actually, as we've done here, by using the exact number given on the charts.
15. Using hands to multiply: So here's a little trick on how we can multiply by 678 or nine just by using our hands. First, we need to put our hands in front of us with palms facing us. Then we have to imagine our fingers and farms are numbered in the same way I have laid out here. So we start with Tenet, our farms, and work our way down to six on our little fingers. As a way to demonstrate this, I will start with eight times eight. Our left hand is the first digits off some on our rights Hand is a second. So we lined up to the two fingers that reference these numbers. Then we count all the fingers that are below, including the two enough some. So we have free fingers on the left hand and free on the right. So this adds up to six. So the first number off our answer is six. Then we count the fingers above these numbers on our left hand and counted the fingers above thes numbers on our right hand. So we have to on the left and two on the right. On we multiply these two numbers together so two times two equals four and that is our second unit off our answer. So eight times eight is 64. Let's take a look at another one. Now this works with 678 and nine times table, but we're going to take a look at seven times eight. So we touch our fingers together, and then we count those fingers and order ones below. So here we have five. So the first digits of answer is five. Then we count up the fingers above this. So I left hands there was free and our rights hands there is too. So free times two is 6 to 7 times eight is 56. And that's how we could do multiplication for 678 and nine times tables just using our hands.
16. Fun with Numbers: fun with numbers. This is a collection of a few games that you can play with numbers that is great to teach Children and also works really well as a way off. Using what we've learned in this course and putting it into practice free off. These little gains has stuck in my head over the years. Let's have a look at them. So here's the 1st 1 I think the number, any number. Now take that number and multiply it by free. Now you need to add 45 that number and then double it. Divide your answer by six. Now take away the original number and you'll be left with the answer off. 15. The answer. It's list will always be 15. Here's another one. Think of a free digit number such as 111222 free, free, free or free digits have to be the same now at those free digits together and divide the result with your original number, the answer will always be 37 and finally one more. I think the number again. It could be any number. Now multiply lattes by free at six. Divide your answer by free. I'm take away the original number. The answer will be to It's always Getting enough is, too, that these fun little games have stuck my head for 80 years, and I just as them on the end of this course as more of a bonus. So I hope you have fun with this.