3 Minute Maths - Percentages

1. Introduction: hello and welcome to three minute maths percentages. This set of lessons will have you mastering percentages in no time. But don't think they have to work through the whole course in one go. This course is perfect for the student who only has a few minutes to spare each day. I've set out each lesson so that they could be completed in short bursts. Whenever you find yourself with a moment of freedom before you start this course, let me share with you an extremely handy learning tip that helped me to progress quickly and effectively in learning anything. When most people start studying for anything, they tend to spend the first day or two studying for hours and hours and get through loads of work. However, very quickly this begins to dwindle. You might feel like spending hours studying maths, which is great, but you want that feeling of motivation to continue. However, your motivation won't continue. If you actually spend hours studying, limit your city time to just three minute chunks and you'll start to notice that three things begin to happen. Firstly, your maintain your enthusiasm. If you want to learn anything, you have to maintain enthusiasm or else you won't want to continue. If you limit your study time to just three minutes, you'll keep maths fresh and exciting and you'll be eager to learn. If you spend hours studying very quickly, you'll get bored with maths and it'll turn into a chore. Secondly, you'll study more consistently. It's much better to study for just three minutes once a day than study for three hours once a week. A spare three minutes is relatively easy to find, even in the most hectic schedules. If you make sure you complete at least 13 minutes recession every day, it will quickly become a habit that you'll do without thinking. It's much easier to fit in a daily three minute habit than a weekly one hour have it. And so, by doing this, you will become a much more consistent loner. And consistency is the key to success. Thirdly, your remember things better. This is my favorite reason as to why you should limit your study to just three minute chunks. If you study something for just three minutes every day, your trick your brain into memorizing the information more quickly than if it were to see the information for hours each day. It will think I see this information every day, so it must be important, but I don't see it for very long, so I better hold on. Twitter make into a memory fast. You'll be amazed at how much more easily things tend to stay in your brain if you limit yourself to just three minutes a day, so three minutes is the key. Do a three minute study session and then give yourself at least half an hour before you do another three minutes. You should aim to do at least 13 minute drunk every day, any more than that is a bonus. But one is just fine. So work through the course on completely exercises and you'll be amazed at how much you've learned. 2. Lesson 1 (Finding 10% by dividing by 10): finding 10% off a number if you asked to find 10% of something we have to do is divide it by 10. So to find 10% off £50 all you have to do is 50 divided by 10 and you get £5. What would be 10% off? £70? Well, £70 divided by 10 is £7 sir. 10% of £70 is £7. But how do you divide by 10? Now, I have written this course, assuming that you don't know anything at all about maths. So I'll try and explain anything that might not be obvious to divide any number by 10. If the number ends in a zero, all you have to do is remove the zero. So what is 10% off? £120? Well, 120 ends in a zero. So to divide it by 10 we just remove the zero and you get £12. So 10% of £120 is £12. See if you can work out these. What would be 10% off? £60? £6 10% off £90 £9 what would be 10% off? £200 £20? And so you just remove 102 divided by 10. What would be 10% off? £300? £30? What would be 10% off? £20? £2? What would be 10% off? £500? £50? What would be 10% off? £7000? £700? And so you just take off one of the zeros and you're left with £700. What would be 10% off? £3000? £300? And so it doesn't matter. How many zeros are number ends in. If you're dividing it by 10 all you have to do is take off one of the zeros. What would be 10% off? £10 £1 Onda. What would be 10% off? £80 £8 3. Lesson 2 (Dividing by 10 with numbers that don't end in a zero): We've just learned that if you want to find 10% of something or you have to do is divided by 10. And then we also learned that if a number ends in zero, to divide it by 10 or you have to do is remove the zero. But what about if you had to find 10% off something like £62? Well, £62 doesn't end in a zero. And if you have a number that doesn't have a zero on the end to divide it by 10 you can't just take this year off. What you have to do instead is imagine there is a decimal point on the end of the number, and then just move the decimal 0.0.1 place to the left. So is 62 divided by 10. Well, imagine a decimal point on the end of 62 then move it. One place to the left, and you get 6.2 6.2 in terms of money is £6.20. So what would be 10% off? £84? Well, imagine there's death more point on the end, off 84 or 84 point on then move it. One place to the left and you get 8.4 in money. 8.4 is £8.40. The reason for this is that with money, you always need to numbers after the decimal point. So if you only have one number after the decimal point, you need to add another zero to the end. And that's why we get £8.40. So see if you can work out the following what would be 10% off? £168? £16? 80. So you imagine a decimal point on the end on move it one place to the left and you get 16.8 onda. Obviously, when it's money, you need to numbers after the decimal point, so we make it £16. 80. What would be 10% off? £34 £3? 40. What would be 10% off? £105 £10.50. And so it doesn't matter how many numbers you have. You just put a decimal point on the end and then move it one place to the left, and so we get 10.5. And then if it's money. You have to put two numbers after the decimal point so you can add a zero if you only have one number on that makes £10. 50. What would be 10% off? £96? £9? 60. What would be 10% off? £13 £1.30 4. Lesson 3 (Dividing decimals by 10): we know now that to find 10% of a number, you just divide it by 10. And we also know that if a number ends in the zero to divide it by 10 you just take away one of the zeros. If it doesn't ended in a zero, then you imagine a decimal point on the end and you move it one place to the left. So what would be 10% of £978? £97? 80. So you imagine a decimal point on the end 978 point, and then you move it one place to the left, so you get 97.8 on because it's money. You have to add an extra zero to the end so that there's two numbers after the decimal point and you get £97. 80. What would be 10% of £99? £9.90 10% off. £29. £2.90. What would be 10% of £145? £14. 50. What would be 10% of £74? £7? 40. But what about if you have to work out something like 10% off £20. 40. Well, because there's already a decimal point in this number, you can just move it one place to the left. So 20.40 or £20.40 divided by 10 gets you 2.0 for zero. However, with money, you can only have two numbers after the decimal point. And so we have 30 for zero. So you take off the last number, which is a zero. So we get £2 on four p. So what would be 10% off? £163? 20. So we divide 163.20 by 10 by moving the decimal 0.1 place to the left, so we get 16.3 to 0. But because it's money, we have to get rid off. The third number after the decimal point and so 10% off £163.20 is £16.32 What would be 10% off £54.30 £5.43 10% off £19.80 £1.98 10% off. £734.90. £73. 49 5. Lesson 4 (Dividing by 10 with decimals less than 10): We've just learned that if you have to find 10% off a number that has a decimal point in it , then you can simply move their small 0.1 place to the left when you divide by 10. Andi, if you're dealing with money, then you can only have two numbers after the decimal point. So what would be 10% off? £54.20 £5. 42. 10% off. £52.40 £5. 24 What would be 10% off? £61.60 £6. 16 What would be 10% off? £28.70 £2.87 10% off. £355.50 £35.55 10% off £36.20 £3. 62 What would be 10% off? £10.40 p. £1.4. So to find 10% of any number, you simply divide it by 10. You have to be a little bit careful if you have to find 10% off numbers. Less than 10 for example, 10% off £4. 20 just like before, because there's already a decimal point in this number, you can just move it one place to the left, but when you move it to the left, you want out of numbers. What you have to do is put a zero at the start when you move the decimal point, so 4.20 divided by 10 is point for 20 But because you've run out of numbers, you can write 0.4 to 0, then, because it's money, you get rid of the zero from the end on you end up with 0.42 or 42 p. So what would be 10% off? £3.20? So all you do is move the point one place the left, so 3.20 divided by 10 gives you 0.3 to 0. But you have to put a zero at the start because you've run out of numbers on because it's money. You can only have two numbers after the decimal point, and so 10% off £3. 20 is 32 p, or £0.32. What would be 10% off? £4.30. 43 peat 6. Lesson 5 (Dividing by 10 with whole numbers less than 10): what would be 10% off £6? 90 If you move the decimal 0.1 place to the left, you get 0.690 You have to put a zero in front of that, and you get 0.690 on because it's money. Then you can take the last year away because you can only have two numbers after the decimal point, and that gives you 69 p. What would be 10% of £1.20 12 p. 10% off. £4.90. 49 p. 10% off £2.30. 23 p 10% off £3.90. 39 p. And just to explain in case you're wondering, you can write 39 p as £0.39 or just US 39 b and so there are always two ways to write it. What would be 10% off? £6.40. 64 p. 10% Off £9.90 99 p What would be 10% off? £3.40. 34 p On what would be 10% off. £8.80. 88 p. Similarly, if you have a number less than 10 like £4 which doesn't have any pennies. Then there's an extra bit to remember when you divide it by 10 to find 10% of it. Whenever there isn't a decimal point in a number, just put one on the very end and then move it one space to the left when you divide by 10. So to work out, 10% off £4 you need to do for divided by 10. And you can just put a decimal point on the end to get four point, and you move it as more 0.1 place to the left. That gives you 0.4 or 0.4 once you put it, zero in front of it. And because it's money, you have to make sure there are two numbers after the decimal point. So instead of 20.0.4, you can say 0.40 which gives you in terms of money, 40 p. So what would be 10% off? £7? Seven divided by 10 is 0.7 on because it's money. You put a zero on the end of it, and you get £0.70 p, or just 70 P what would be 10% off £3. 30 p. 10% OFF £7. 70 p What will be 10% off £9 90 p 7. Lesson 6 (Dividing pennies by 10): What would be 10% off £2. 20 p. 10% of £1. 10 p. 10% Off £8 80 p What would be 10% of £5 50 p What would be 10% off? £4 40 p What would be 10% off? £6 60 p Now finally, if you have a number less than £1 identifying 10% of it, you move the decimal point to the left, just like normal. For example, if you had to find 10% off 30 p well, first you imagine 30 ps decimal and it's 0.30 to divide it by 10. You move the decimal 100.1 place to the left and you get 0.30 And again, you can put a zero in front of that so you get 0.30 because it's money you take off the last zero from the end on you get 0.3 which is three p. So 10% of 30 p is three p. What will be 10% off 60 p? Well, another way of saying 60 p is 0.60 You move. The decimal place wants to the left, which gives you 0.6 which is six p. So 10% of 60 p is six p. What would be 10% off 70 p. Seven p. 10% of 20 to be 10% of 10 p. One p What would be 10% off 60 p. Six p What would be 10% off 90 p. Nine p What would be 10% off? 30 p. Three p. 10% off 80 p. Eight p What would be 10% off 40 p. Four p What would be 10% off 50 p. Five p. So we now know to find 10% of any number you simply divided by 10 Andi to divide a number by 10. If it ends in a zero, you remove the zero. If it doesn't end in a zero, you imagine a decimal point on the end and move it one place to the left. If there's a number that already has a decimal point, well, then just move it one place to the left. If you're dealing with money, then you always remember that you can only have two numbers after the decimal point, so if you have any more than two numbers, then you have to get rid of some. 8. Lesson 7 (Finding 20% of a number): Let's practice finding 10% with a mixed variety of different numbers. What would be 10% off? £500. £50? What would be 10% off? £600. £60? What would be 10% off? £720. £72? What would be 10% off? £1250. £125? What would be 10% off? £62. 50 £6. 25 What would be 10%? Off? £89. 60 £8. 96 What will be 10% off? £4.20. 42 p. What would be 10% off? £6.80. 68 p. What would be 10% off? £51.60 £5.16. What would be 10% off? £180? £18 Finding 20% off a number. Finding 20% of any number is quite simple. If you know how to find 10% 20 is double 10. So to find 20% of a number, you start by finding 10% and then just double it. For example, to find 20% off £50 you start by finding 10% of £50 which is £5 on, then double it to get £10. What would be 20% off? £70? Well, you start by finding 10% off £70 which is £7. Could you just take the zero off and then you double it to get £14? So 20% off £70 is £14. What would be 20% off? £62? 10% of £62 is £6.20 and so you double it to get £12. 40. What would be 20% off? £84? £16? 80 Because 10% is a pound. 40 double is £16. 18 What would be 20% off? £168 £33.60 10% over £168 is £16.80 on you double it to get £33.60 9. Lesson 8 (Practise finding 20% of a number): We've just learned that if you want to find 20% off, any number or you have to do is start by finding 10% and then do it. So what would be 20% off? £54? 30 £10? 86 Because 10% off £54.30 is £5.43 and you double it to get £10. 86. What will be 20% off? £500? £100? What would be 20% of £600? £120? What would be 20% off? £720. £144. What would be 20% off? £1250. £250 because 10% is 100 and £25. Because you just take off the zero and then you double it to get £250. What would be 20% off? £62? 50 Well, 10% is £6.25 you double it to get £12. 50. What would be 20% off? £89.60 while 10% is £8.96. And if you double £8.96 you get £17. 92. What would be 20% off? £4? 20. 84 p. What will be 20% off? £6.80 £1.36 because 10% is 68 p. And if you double 68 p, you get £1. 36. What would be 20% off? £51.60 £10. 32 on what will be 20% of £180 £36. 10. Lesson 9 (Finding 5% of a number): finding 5% of a number. We now know how to find 10% of a number, which you do just by dividing by 10. And we also know how to find 20% of a number, which you do by finding 10% on, then doubling it to find 5% of a number. You start by finding 10% and then you just have it because five is half of 10. For example, to find 5% off £50 you start by finding 10 person, which is £5 and then half of that is £2.50. What would be 5% off? £70? Well, you start by finding 10% which is £7 and half of that is £3. 50. See if you can work out how to find 5% off £120. £6 because 10% is £12 on behalf of that is £6. What will be 5% off £62 £3.10 because 10% is £6.20.5 of that is £3.10. What would be 5% off? £84 £4.20 Because 10% is £8.40 on behalf of £8. 40 is £4. 20. What would be 5% off? £168. £8. 40 because 10% is £16.80 and you have that to get £8. 40. What would be 5% off? £20? 40 p. £1 to pee. 10% is £2 for P and so half of that is £1 to pee. What would be 5% of £163.20 £8. 16 Because 10% is £16.32 and half of that is £8.16. What would be 5% off? £54? 80 £2. 74. This is because 10% is £5.48 and then half of that is £2.74. If you struggle to have £5.48 in your head, then don't worry, because it is quite a hard thing to do. But what I try and do is split anything that looks tricky into smaller chunks. So instead of having £5.48 in my head, I have £5 which I know is £2.50 and then I have 48 p, which is 24 p. £2.50 ad, 24 p is £2.74. And so it's easier to do it if you split up into two little chunks rather than trying toe have £5.48 in your head. 11. Lesson 10 (Practise finding 5% of a number): to find 5% off any number. You start by finding 10% and then you have it. So what would be 5% off? £500 £25? What would be 5% of £600 £30? What would be 5% of £720 £36 on this might be another one of those ones. That's quite tricky. Too hard in your head because 10% off £720 is £72 usually when there's an odd number involved, that's when it makes it a little bit tricky. Toe Harvin your head. And so the seven makes it a little bit trickier. But again, what I do is split it into two smaller chunks, and so half off £70 is £35 half of £2 is £1. So he's 35 1 is 36. And don't worry about doing it that way, because eventually you'll get quicker right doing it so they're splitting up into two different chunks. It seems like it's a longer route toe take toe workout half of a number. If you do it often enough. Eventually, it's become such a quick reflex for you that you'll be out to do it almost without thinking . So what would be 5% off? £1250? £62? 50 because 10% is £125. Andi. If you split this open to two chunks, then you could say what's half off? £120 which is £60 on what's half off. £5.2 pounds 50 60 plus £2.50 is £62. 50. What would be 5% off? £62.16. £3. 13 Because 10% is £6.26 half of £6. 26 is £3. 13. What will be 5% off? £89.60 £4. 48 So 10% off £89. 60 is £8.96. And if you have that well again, you've got the nine, which makes it a little bit tricky. But half of £8 is £4 then you've got the 96 p. While I would split this into two chunks. Half of 90 p is 45 on behalf of six p is three. So 45 at three is 48. £4. 48 What would be 5% off? £4.20. 21 p, because 10% is 42 p and half of force to pee is 21 p. 12. Lesson 11 (Finding 1% of a number): what would be 5% off £6.80. 34 p. What would be 5% off? £51.60 £2? 58 because 10% is £5.16 and you can split this into two chunks. Toe Harv It half of £5 is £2.50 on half of 16 p is eight p. So £2. 58 What would be 5% of £180 £9? So we now know to find 10% of any number, you divide it by 10 to find 20%. When you start with finding 10% on, did you do it? And to find 5% you start by finding 10% and you have it. Well, let's look now at how to find 1% off any number to find 1% of a number. You simply divide it by 100 for example, 1% off £50 is 50 p because 50 divided by 100 is no 1000.5 on. In terms of money, no 0.5 is 50 p to divide any number by 100. You imagine that there's a decimal point on the end of the number. Andi, you move it to places to the left. So what would be 1% off? £70? Well, if you imagine that there's a decimal point on the end off 70 and you move it to places to the left, you get 0.70 Andi in money. This is 70. So 1% off £70 is 70 p. What would be 1% off? £120? £1? 20 Because you imagine that was decimal point on the end of 120 you move it to places to the left to get 1.20 or £1.20 what would be 1% off? £62? 62 p. What would be 1% off? £84? 84 p. What would be 1% off? £168 £1.68 13. Lesson 12 (Practise finding 1% of a number): We've just learnt that if you want to find 1% off any number, you divide it by 100. So what would be 1% off? £24? 24 p. What would be 1% off? £163 £1. 63. What would be 1%? Off? £54? 54 p. What would be 1%? Off? £500? £5? What would be 1% off? £600? £6? What would be 1% off? £720. £7. 20. What would be 1% off? £1250 £12. 50. What will be 1% off £62 62 p. What would be 1%? Off £89? 89 p. What would be 1% off? £40? 40 p. What would be 1% off? £51? 51 p. And finally, what would be 1% off? £180. £1. 80. What about if you had to find 1% off a number like £3. When you divide £3 by 100 you imagine a decimal point on the end on move it to places to the left. When you move a decimal point and you're not of numbers, remember to always put zeros where there are no numbers. Therefore, three divided by 100. Well, imagine moving the decimal point once and then twice to the left. You have to fill in the gaps with zeros, so you get 0.3 which is three p. What would be 1% off? £5? Well, if you divide five by 100 you get 0.5 which in money is five p. What would be 1% off? £8? Eight. P. 1% of £6. Six p What would be 1% off? £1? One p What will be 1% off? £9? Nine p or what would be 1% off? £4 four p 14. Lesson 13 (Finding 2% of a number): finding 2% of a number. Looking at the patterns that we've been using to find 10% 20% 5% on now, 1% you might be able to work out. How to find 2% of any number we have to do is start by finding 1% and then double it, since two is double one, for example, to find 2% off £50 you start by finding 1% so you divide it by 100 you get 50 p. Then you double it to get £1 so 2% or £50 is £1. What would be 2% off £70 If you do 70 divided by 100 to find 1% you get 70 p and then you double it to get £1.40. So it's even work out. How to find 2% off £120 £2.40 because 1% is £1.20 on double, £1.20 years to pounds. 40 What will be 2% off? £62 £1.24 because 1% is 62 p and if you double 62 p you get £1.24 what would be 2% off? £84 £1.68 because 1% is 84 p On double 84 p is £1.68. What would be 2% off? £168. £3. 36 because 1% is £1.68 you double that to get £3. 36. What will be 2% off? £24. 48 p. What would be 2% off? £163 £3.26. 2% off £54 £1.8 p. What would be 2% off? £500? £10 Because 1% is £5 on double. That gives you £10. 15. Lesson 14 (Finding 50% of a number): what would be 2% off £600 £12? What would be 2% off? £720 £14. 40. What would be 2% off? £1250? £25 because 1% is £12. 50 on double £12. 50. Gives you £25. What is 2% off? £62 £1. 24 What is 2% off? £89 £1.78. 2% off £4 AP because 1% is four p on double four is eight. What's 2% off? £6 12 p. What is 2% off? £51 £1.2 p. What is 2% off? £180 £3.60. Now let's have a look at finding 50% off a number. 50% is probably the easiest percentage to find because all you have to do is have the number. For example, to find 50% off £30 you just have £30 you get £15 so 50% is the same as half of something. So what would be 50% off £70 £35 because half off 70 is 35. So see if you can work out what 50% off, £120 is £60 50% off £62 £31. What is 50% off? £84 £42. What is 50% off £168 £84. What is 50% off £20.40 p £10.20 p 16. Lesson 15 (Practise finding 50% of a number): so to find 50% off any number or you have to do is have it. So what will be 50% off? £163? 20. £81. 60. What would be 50% off? £54? 18. £27. 40. What would be 50% of £500? £250. 50% of £600. £300. What would be 50% off? £720. £360. What would be 50% off? £1250. £625. What would be 50% off £62. 60. £31. 30. What would be 50% off? £89.60. £44.80 50% off. £4.20 £2. 10. What would be 50% off? £6? 80 £3. 40. What would be 50% off? £51.60. £25. 80. What would be 50% off? £180 £90. So to find 50% of any number or you have to do is have it 17. Lesson 16 (Finding 25% of a number): finding 25% of a number. Once you know how to find 50% of something, finding 25% is really simple. Or we have to do is find 50% and then have it again because 25 is half off. 15. So basically what you're doing is finding 1/4 of it. For example, to find 25% off £50 you have it and then have it again. Half off £50 is £25. Andi, half off £25 is £12.15. So 25% off £50 is £12. 15. What would be 25% off? £70? Well half of 70 is 35 on behalf of 35 is 17.5 in money. That £17.50. So 25% of £70 is £17. 50 What would be 25% off? £120. £30. What will be 25% off? £62 £15.50 25% of £84 £21! What will be 25% of £168 £42 25% off £20. 40 p. £5. 10. What would be 25% off. £163.20. £40.80 25% Off £54.80 £13. 70 What would be 25% off? £500. £125 25% off £600. £150. What would be 25% off £72 £180. What would be 25% off? £1250. £312. 50. What will be 25% off £62. 60 £15. 65 What would be 25% off? £89. 60 p. £22.40 p. 18. Lesson 17 (Finding any percentage of any number): in the last lesson, we learned that if you want to find 25% of a number, you simply have it and then have it again or find 1/4 of it. So what would be 25% off? £4.20 £1.5 p. What will be 25% off? £6? 80 £1? 70 What would be 25% off? £51? 60 £12.90 And finally, what would be 25% off? £180? £45? Now we've learned how to find 10% which we do by dividing by 10 20% which you can do by doubling 10% 5% which you can do by Harding, 10% 1% which you can do by dividing the number by 100 2% which you confined by doubling 1% 50% which you confined by harming the number and then 25% which had confined by Harding, 50%. But what about if you want to find things like 30% or 60% or 85%? Well, what we can do is use the percentages that we've used so far and put them together to find any other percentage. For example, how do we find 30%? Well, there are a couple of ways to do this. You could find 10% sometimes it by three, or you could find 10% on, then 20% and have them together. How would we find 60%? Well, you could find 10% and then multiply it by six. Or you could find 20% and then multiply it by three. How would you find 85%? Well, you could start by finding 10% on multiplying it by eight to get 80 and then you could find 5%. Andi added on to the 80%. Or how could you find 16%? Well, you can find 10% 5% on 1% and if you add them all together, you get 16%. Or you could find 2% on multiply it by eight. So there are many ways to find different percentages of numbers. All you have to do is use the percentages that we've learned how to find so far on. Put them together 19. Lesson 18 (Ways to find different percentages): you confined or the percentages by adding together the percentages that we know how to find . So how would you find 13%? You could find 10% 2% on 1%. Another together. How would you find 6% of a number? You could find 5% and 1% on Adam together. Or you could find 2% and multiply it by three. How would you find 3% of a number? You could find 2% on 1% and of them together. Or you could find 1% and multiply it by three. How would you find 15% of a number? You can find 10% on 5% and of them together, or you confined 5% and multiply it by three. What would be a way off finding 35% for number? You could find 10% 20% and 5% and Adam together. Or you could find 10%. Multiply it by three to get 30% and then add 5% on to the end. What would be a way off finding 40% of a number? You could find 20% of it. Andi. Multiply it by two, or you could find 10% of it and multiply it by four. What would be a way of finding 18% of the number you could find 10% 5% 2% on 1% and add them all together to make 18%. Or you could find 2% on multiply it by nine. What would be a way off finding 99% of a number if you find 1% then you can subtract that because 100% take away. 1% leaves you with 99%. How could you find 70% of a number? You could find 50% on 20% and then add them together. What would be a way off finding 9% of a number if you find 10% and 1% then you can subtract the 1% from the 10% which leaves you with 9%. So there are many different ways that you can find different percentages off any number you can use. Whichever method you find easiest 20. Lesson 19 (Practise finding any percentage of any number): So now you know how you would go about working out different percentages. Now let's have a go at actually doing them. So what would be 30% off? £500? Well, 10% off. £500 is £50 and if you multiply it by three to get 30% you get £150. What is 60% off? £250 50% off £250 is 100 and £25 on 10% is £25. If we add those together, you get £150. What would be 85% off? £610? What you could do is find 15% and subtract it from 100% because that will leave you with 85%. So to find 15%. What we could do is find 5% and multiply it by three 5% off. £610 is £30 on 50 p. Multiply that by three and you get £91.50 so £610 take away £91. 50 is £518. 50. What will be 16% off? £320? 10% is fair to £2. 5% is £16.1 percent is £3. 20. If we add all those three together 32 plus 16 plus £3.20 you get £51. 20. What would be 13% off? £412. 10% is £41.20 and 1% is £4.12. So if you multiply that by three, you get £12.36 £41.20 plus £12.36 is £53.56. 21. Lesson 20 (Practise finding any percentage of any number): How would you find 6% off £805 where he could start by finding 5% Onda, adding 1% to it? 5% off £805 is £40.25. 1% is £8.5. And if we add them together, you get £48. 30. What will be 3% off? £60? 1% is 60 p on 60 p. Times three is £1. 80 What would be 17% off £25? We could find 10% 5% and 2% and add them together. 10% is £2. 50 5% is half of that, which is £1.25 on day. 2% is 50 p. £2.50 plus £1.25 plus 50 p is £4.25 What would be 15.5% off £800? The 8000.5 is half of 1% so you can find 1% and have it. We could find 5% multiply it by three and then add on half a percent. 5% is £40 times by three is £120 and then to find half of a percent. We start by finding 1% which is £8 half of that is four. So 120 plus four is £124. What would be 20.5% off? £500? Well, you confined 20% on men half a percent and add them together, 20% off. 500 is 100 and half a percent. Well, if you find 1% which is £5 half that is £2.50 100 plus £2.50 is £102.50. 22. Lesson 21 (Using a calculator): using a calculator. If you have a particularly tricky percentage to work out, then you could reach for your calculator. ANDI There are a couple of really easy ways that you can use your calculator toe workout percentages. The first method is to use the percent button. Now. If your calculator has a percent button, then it's easy. If you had to find out what 30% off £500 waas, all you do is type 500 times 30% and then press equals and you'll get the answer. How would you work out? 60% off, £250 on a calculator, you would type in 250 times 60% and you get £150. The second method is to use decimals. This method can be used if you have a calculator that doesn't have a percent button or we have to do is turn the percent into a decimal. All percentages can be turned into a decimal less than one. For example, 30% can be written as 0.3 or 20% can be written as 0.2. All you have to do is divide the percent by 100 you'll get a decimal. Once you have the decimal, all you have to do is multiply it by the number and you'll find the percentage. For example, if you wanted to find 20% off 50 what you can do is turn 20% into 0.2 and times it by 50 50 times 0.2 is 10 which is the answer. You just need to be able to put the percentage as a decimal. So what would be 13% as a decimal? No 0.13 22% as a decimal no 0.22 8% as a decimal 0.8 say just divided by 100 19% as a decimal 0.19 5.2% as a decimal 0.52 And then once you have the decimal, all you have to do is multiply it by any number to find that percentage, for example, to work out 85% off 610 you start by converting 85% into a decimal, which is no 850.85 and then you multiply that by 610 610 times. No 6100.85 is £518. 50. What would be 16% off? £320? Well, 16 as a decimal is no 160.16 So £320 times 0.16 is £51.20. 23. Lesson 22 (Practise using a calculator to find percentages of numbers): We've just learned that one way to find a percentage on a calculator is to type in the number times by the percent and use the percent button. Another way is to turn the percentage into a decimal. So, for example, if you have to find 15.5% off £800 either you could type in 800 times 15.5 and then press the percent button. Or you can turn 15.5 into a decimal, which is no 0.155 on times that by 100 800 times 0.155 is £124. Both methods work just as well on the second method is really only there if your calculated doesn't have a percent button usual calculator to work out the following equations. What would be 15.5% off? £800. £124 20.5% off. £500. £102.50 30% off £600. £180 80% off. £130 £104. What would be 17% off £80 £13. 60. What would be 14.3% off? £900? £128. 70. What would be 8.21% off £1000 £82.10. 90.2% off £40 £36. And AP, what would be 83% off? £70 £58. 10. And finally, what would be 10.6% off? £50? £5? 30. And so you can do that in two ways. Either you can type in 50 times 10.6% impress equals. Or, if your calculator doesn't have a percent button, turned 10.6% into a decimal, which is 0.106 And then you type in 50 times 0.106 and then it gives you £5.30 p. 24. Lesson 23 (Let's practise): Now let's have a go at doing some mixed questions on all sorts of different percentages. These next few videos are going to be full off practice questions for you to have a girl. You don't have to do them all in one go. What you should do is try and do one video every so often just to keep on top of it. All this is because if you do all the questions in one go, you're not really doing any improvements in your brain past the 1st 3 or four questions. All that will happen is your race through them on work out a pattern as to how to answer them without even thinking. What you want to do, however, is save some of the questions for a later date. Then, after a week or so, go back through Onda. Answer a few more questions to check. You can still do it a few weeks after that and go back and answer a few more questions and then about a month after that, do the same again, and that's the next few questions. This way of doing things is much more beneficial. It will elongate the learning process on turn everything into long term memories. It also means that you won't ever have to revise very hard if you're doing math exams by the time the exams. Com, you'll have covered every topic little and often, so you'll know how to do everything easily without having to revise Lodin lose. So what would be 5% of 80? Well, 10% of 80 is 8.5 of that is for what would be 12% off 150 10% of 150 is 15. Andi to get the 2% If we start by finding 1% which is 1.5 weaken, double it to make three. 15 plus three is 18. So the answer is 18. What would be 85% off 900 toe work This question out, I would find 15% of 900 hons. Subtract it because if you do, 100% take away 15% you get 85% so 15% of 900 well find 10% which is 90 and 5% which is 45 90 at 45 135 and then all you have to do is 900. Take away 135 which is 765. What would be 60% off? 250. You could find 50% on 10%. Another together, 50% off 250 is 125 on 10% of 250 is 25 125. AD 25 is 150. 25. Lesson 24 (Let's practise): what would be 15% off, 90 10% is nine and 5% is 4.5. If you add nine and 4.5 together you get 13.5. What would be 23% off? 300 10% off 300 is 30. So we double that to get 20%. That makes 60 and then 1% of 300 is three. If you times that by three you get 9 60 plus nine is 69. What would 85% off? 650 b well again. For this one, I would find 15% on subtracted because 100% take away, 15% leave you with 85%. So 10% of 650 is 65 Onda 5% is 32.5. If you add 65 32.5, you get 97.5, 650 take away 97.5 is 552.5. What would be 99% off 700 If you find 1% then you can take it away because 100% take away 1% leaves you with 99%. So 1% off. 700 is seven on 700 take away. Seven is 693. What would be 14% off 75 while 10% off 75 is 7.5. Andi to find 4% we confined 1% which is north 10.75 and multiply it by four. So no 0.75 times four is three. If we add them together, then you get 7.5 plus three, which is 10.5. What would be 17% off? 350? Well, you can find 10% 5% and then 2%. So 10% of 350 is 35. 5% is half of that, which is 17.5 on then. 2% is seven because 1% is 3.5 and we double it to get seven 35 plus 17.5 per seven is 59.5 26. Lesson 25 (Let's practise): what would be 16% off 200 So 10% off 200 is 20 5% is 10 and then 1% is too. So 20 plus templates to makes 32. What would be 80% of 180? I would find 20% and then subtracted because 100% take away, 20% leaves you with 80%. So 10% of 180 is 18 which means 20% is 36 180 Take away. 36 is 144. What would be 9% off? 130. I would find 10% and then find 1% and subtract it from the 10%. 10% is 13 on 1% is 1.3 so 13 take away. 1.3 is 11.7. What would be 90% off? 125 If you find 10% then you can subtract it. So 10% of 125 is 12.5 and then 125 take away. 12.5 is 112.5. What would be 50% off 67. So 50% is just half and half of 67 is 33.5. What would be 25% off? 53 to find 25%. You can just have it on behalf again. So half off 53 is 26 point 5.5 off 26.5 is 13.25 What would be 34% off? 140. We confined 30% and then 4%. So 30% We confined by finding 10% 10% of 100 and 40 is 14. If you multiply that by three, we get 42 and then 4% weaken Dubai finding 1% and then multiplying it by four. 1% is 1.4. If you multiply that by four, we get 5.6. So 42 plus 5.6 is 47.6 27. Lesson 26 (Let's practise): what would 75% off 200 b. I would find 25% because what you can do then is subtract that from 100% and it will leave you with 75%. So to find 25% we just quarter the number. 1/4 of 200 is 15 and 200 take away. 50 is 150. What would be 62% off? 390. I would find 60% and then 2%. So to find 60% of 390 you confined 10% and multiply it by six. 10% is 39 on 39 times six is 234. Sorry. Had to wait it out and then to find 2% we confined 1% which is 3.9 on doing it, which gives you 7.8 and then 234 plus 7.8 is 241.8. It was a tricky one. How would you find 81% off? 45 You can find 80% and then 1% so 10% off 45 is 4.5. If you multiply that by eight, you get 36 then 1% is 0.45 So the answer is 36.45 What would be 99% off 60 if you find 1% and subtract it for that will leave you with 99%. So 1% of 60 is no 600.6 and then 60. Take away 0 00.6 is 59.4. What would be 12% off? 45 10% off 45 is 4.5 and then 1% is 0.45 If we double that, we get 0.9 on day 4.5 plus 0.9 is 5.4. What would be 10% off? 14 one point full? 28. Lesson 27 (Let's practise): what would be 30% off? 50 10% or 50 years? Five. And if you multiply that by three, you get 15. What would 40% off? 230 B. 10% of 230 is 23 and if you multiply that by four, you get 92. What would be 21% off? 350 10% of 350 is 35 so we double that to get 70 and then 1% is 3.5. So the answer is 73.5. What were 20% off? 350 B 10% is 35 on we double that to get 70 what would be 80% off? 230 If you find 10% which is 23 double that, we get 20% which is 46. And you can subtract that from 230 because that will leave you with 80%. So 230 take away. 46 is 184. What would be 87% off 1200? I would find 13% because it seems like an easy percentage to find on subtracted from 100. So to find 13% we confined 10% and 3%. 10% is 120 on day. 3% is 12 times three, which is 3600 and 20 had 36 is 156. And so we just do 1200. Take away 156 which leaves you with 1000 and 44. What would be 55% off? 1230 50% is 615 and then 5% is 61.5 615 at 61.5 is 676.5. 29. Lesson 28 (Let's practise): what would be 65% off? 3450 you could find 50% 10% and then 5% another more together. So 50% off 3450 is 1725. 10% is 345 and then 5% is half of that, which is 172.5. If you add 1725 close 345 plus 172.5, you get 2242.5. What would be 45% off? 4500 If you find 50% you can then subtract from that 5%. So 50% of 4500 is 2250 to find 5%. We can just divide that by 10 and so 2250 divided by 10 is 225 and then we do 2250 Take away 225 which is 2000 and 25. What would be 90% of 7000. If you find 10% and then subtract it, it will leave you with 90%. So 10% of 7000 is 700. And then we do 7000. Take away 700 which is 6300. What would be 98% off? 2340 if we find 2% then we can subtract that to get 98%. So 1% off 2340 is 23.4. If you do all that, you get 46.8 and then 2340 take away. 46.8 is 2293.2. What would be 22% off? 340 10% is 34 double that is 68. That's the 20% on then to find 2% weaken Double 3.4, which is 6.8 and so 68 plus 6.8 is 74.8 30. Lesson 29 (Let's practise): what would be 11% off 1230 10% off 1230 is 123 and then 1% is 12.3, 123 at 12.3 is 135.3. What would be 30% of 150 10% is 15 multiplied by three is 45. What will be 30% off? 2450 10% off 2450 is 245. And if you multiply that by three, you get 735. What would be 40% off? 5630 10% is 563 multiplied by Full gives you 2252. What would be 89% off? 230 for this one. I would find 11% on subtracted from 100% to leave you with 89%. So 10% is 23 on 1% is 2.3 23 at 2.3 is 25.3 which, if you subtract from 230 leaves you with 204.7. What would be 12% off? 250 10% is 25 on day, 2%. We confined by finding 1% which is 2.5 and doubling it, which gives you five, so 25 plus five is 30. 31. Lesson 30 (Let's practise): what would be 34% off 560 you can find 30% on add it to 4%. So 10% of 560 is 56. And if you multiply that by three, you get 168. 1% is 5.6. Andi, 5.6 times four, is 22.4, 22.4 plus 168 is 190.4. What would be 72% off? 640 If you find 10% which is 64 Onda, multiply it by a seven. That gives you 448 which is 70% and then to find 2%. We just find 1% which is 6.4 on double it to get 12.8. If we add them together, you get 460.8. What would be 68% off? 455? I would find 70% and then take away 2%. So to find 70% weaken do 45.5 times seven, which gives us some 318.5 and then to find 2%. Then you can find 1% which is 4.55 If you double 4.55 you get 9.1 and then 318.5. Take away 9.1 leave you with 309.4. What would be 30% off 23. 10% of 23 is 2.3 times three to give you 30% is 6.9. What would be 20% off? 674. 10% off 674 is 67.4 times by two is 134.8. 32. Lesson 31 (Let's practise): what would be 80% off, 560 if you find 20% and subtract it, then you'll be left with 80% 10% of 560 years. 56 double that is 112 and then 560 take away. 112 is 448. What would be 15% off? 230 10% is 23 and 5% is half of 23 which is 11.5. 23 at 11.5 is 34.5. What would be 1% of 150 150 divided by 100 is 1.5. What is 3% off? 25. You can start by finding 1% which is no 0.25 and then you can multiply that by three. To get no 30.75 What would be 8% off? 245 if you find 10% and then subtract 2% then you'll get 8%. So 10% off. 245 is 24.5 and 2% is well you start by finding 1% which is 2.45 on double it to get 4.9 on 24.5. Take away 4.9 leaves you with 19.6. What is 2% off? 6789. You can start by finding 1% which is 67.89 and you could double that to get 135.78 What is 9% off? 350 If you find 10% which is 35 on subtract 1% which is 3.5 you're left with 31.5. 33. Lesson 32 (Let's practise): what would be 5% off 135. If you start by finding 10% which is 13.5, you can have that to get 5% which gives you 6.75 What would be 4% off 34 If you get 1% by dividing by 100 you get 0.34 which you can, then times by four to get 1.36 what would be 14% off? 57 you can find 10% which is 5.7, and then add it to 4%. So to get 4% you can find 1% which is 0.57 on multiply it by four. Is there a 0.57 times four is 2.28 and 2.28 plus 5.7 is 7.98 What would be 24% off 78? I would find 25% and then take away 1%. So to find 25% you just have to find 1/4 on 1/4 of 78 is 19.5 and then 19.5. Take away 1% while 1% off 78 is 0.78 So 19.5 takeaways air 0.78 is 18.72 What would be 25% off 59. 1/4 of 59 is 14.75 What would be 8% off? 56 you can find 1% which is 0.56 and multiply it by eight to get 4.48 And finally, what is 40% off? 790 You can find 10% which is 79 on multiply it by four to get 316. 34. Lesson 33 (Increasing a number by a percentage): percentage increase. Now you know how to find percentages of numbers. You can use that knowledge to carry out percentage increases. For example, how would you increase £300 by 20%? Well, you start by finding 20% off £300 which you can do by finding 10% and then doubling it. So 300 divided by 10 is 30 and 30. Doubled is 60 so 20% off £3.60 pounds and then you just added on £300 plus £60 is £360 . See if you can increase £60 by 15% so you start by finding 15% off £60 which you can do by finding 10% which is £6 then 5% which is £3 adding them together. £6 at £3 is £9 and then you add it on to £60 so £60 plus £9 is £69 so to increase £60 by 15% it becomes £69. You can use this method toe add V A T to a price that doesn't include it. For example, if you went to a shop and so you could buy a kitchen sink for £360 excluding VAT. That means they haven't added the V a T it in the U. K V A. T is 20% on did you added on. So what would be the full price of the sink, including the 80 if it's £360 excluding the 80 20% off, £360 is £72 on day, £360 plus £72 is £432 so the price, including the 80 would be £432. What about this question? If a population of a city increased in size by 2% from one year to the next, what would be the population in 2019 if it was 180,000 in 2000 and 18? Well, you start by finding 2% of 180,000 which is 3600. Then you add that onto the original population, so 180,000 plus 3600 is 183,600. How about this? In 2015 House was worth £250,000. Three years later, the value of the house had increased by 12%. What was the new value of the house in 2018? 12% off, 250,000 is 30,000. Because if you find 10% which is 25,000 and 2% which is 5000 and Adam together, it gives you 30,000 and then £250,000 plus £30,000 is £280,000 which is the answer. 35. Lesson 34 (Increasing a number by a percentage): you see if you can work out the answer to this question. A cat weighed 3.6 kilograms in January on By December, its weight had increased by 15%. What was the new weight off the cat? So 15% off 3.6 kilograms is nor 0.54 kilograms. And then, if you take 3.6 kilograms on add nor 0.54 you get 4.14 kilograms. And so to get the 15% if you find 10% which is 0.36 on 5% which is half of that 0.18 And Adam together 0.36 at 0.18 is 0.54 What about this question? Somebody bought a painting in 1950 for £25. Then, 68 years later, they sold it at an auction. The painting sold for 120,000% more than the original purchase price. How much did it? Cell phone? For this question, you need to work out 120,000% off £25. You can find percentages that are larger than 100% in the same way as finding percentage is lower than 100%. So to find 100 and 20,000% of something, just find 1% and then multiply it by 120,000. So 1% of £25 is 25 p 25 p times 120,000 is 30,000. So we take £30,000 add it to the original £25 you get 30,000 and £25 which is the answer . On Thursday, the temperature in London was 20% warmer than it was on Wednesday. If it was 20 degrees Celsius on Wednesday, what was the temperature on Thursday? You need to find 20% off 20 degrees Celsius, so 10% of 20 is too, which means 20% off 20 is four degree Celsius, then 20 degrees Celsius plus four degrees Celsius is 24 degrees Celsius, so the temperature on Thursday was 24 degrees Celsius. 36. Lesson 35 (Increasing a number by a percentage): see if you can work out the answer to this question. A family of mice had 30 members. A few years later, the number of mice and the family had increased by 70%. How many mice were now in the family? You have to find 70% of 30 so 10% of 30 is three on day. Three times seven is 21. So 70% of 30 is 21 then 30 plus 21 makes 51. So 51 mice were in the family. Increase £750 by 25%. You need to find 25% of £750 by quartering it or Harding is and then having it again on Do you get £187? 50 and then you add it on. So £750 plus £187.50 is £937. 50 increase 5400 by 12% to find 12% off. 5400. You confined 10% which is 540 and then find 2% which is 108 and so 12% of 5400 is 648. If you add it onto the 5400 you get 6000 and 48 increase £9000 by 54% to find 54% off £9000. You confined 50% and then 4% so 50% is just half, which is £4500 on. To find 4% you can find 1% which is 90 and times it by four to get £360. So £4500 plus 360 is 4000 £860. Then you add it on to £9000 to get £13,860. 37. Lesson 36 (Increasing a number by a percentage on a calculator): How would you increase 12 by 40%? 40% of 12 You confined by finding 10% and then multiplying it by four. So 12 divided by 10 is 1.2 times four is 4.8 and then 12 plus 4.8 is 16.8. How would you increase £10 by 35% 35% off £10 is £3.50 and then £10 plus £3. 50 is £13.50 percentage increases on a calculator. There are three very easy ways to increase a number by a certain percentage on a calculator . Method one is to use the plus on the percent buttons. This method is very easy to use. For example, if you want to increase £80 by 23% all you have to type in is 80 plus 23% and empress equals and you'll get the answer 98.4, which in money is £98.40 and so the carpet does it all for you. How would you increase £180 by 70%? You were type in 180 plus 70% and Then when you press equals, you'll get £306 which is the answer. Method two is using just the percent Borden. This method is a little less easy to use, but still very simple. Andi. It's good to understand this method, even if you never use it. We used this method when finding percentages of numbers. For example, if you wanted to find 30% off 50 you simply typed in 50 times 30%. And then when you press equals, you get the answer. 15. When you're increasing in number by a certain percentage, however, you want to include the original number on, then add the extra bit to it. For example, if he wants to increase 50 by 30% you would need to have 50 and then add the 30% to it. If you typed in 50 times 100% on a calculator and press equals, you'll get the answer 50. And that's because 100% of 50 is 50 obviously. So if you want to increase £50 by 30% what you need to do is type 50 times 130% and you'll get 65 This is because 130% off 50 is 65 since 100% of 50 is 50 on 30% of 50 is 15 on then 50 plus 15 is 65. 38. Lesson 37 (Increasing a number by a percentage on a calculator): If you want to increase 120 by 10% then basically you're going to be finding 110% of 120. So you type into a calculator or 120 times 110% and you'll get 132 which is correct. So how would you increase £70 by 40% on a calculator? Using this second method, you would need to find 140% off £70 by typing into a calculator 70 times 140% and then press equals and you'll get 98. The third method is to use decimals. This method can be used if you have a calculator that doesn't have a percent. Borten we have to do is turn the percent into a decimal. We already know how to do this from earlier on with normal percentages. So remember we said things like 30% as a decimal is 0.3. Well, if you want to increase by 30% you would use the decimal 1.3. Instead, all percentages can be turned into a decimal less than one. So we had 30% was 0.3 20%. 0.2 or percentage increases will be a decimal bigger than one. This is because the one stand for the 100% and the number after the decimal stand for the percentage increase. It's the same idea is the first method where you had to write a percentage increase off 30% as 130% while 130% as a decimal is 1.3. So if you want to increase £50 by 20% you were type into a calculator 50 times 1.2 and you would get 60. This is because 50 times one is 50 on 50 times air 500.2 is 10 and so 50 plus 10 is 60. How would you increase £70 by 40% on a cockatoo? Using this third method, you would need to find 140% off £70 by typing into a calculator 70 times 1.4 and you'll get 98. Using a calculator is handy if you have to do a particularly tricky percentage increase. You can even use it to find percentage increases that include decimals. For example, if you wanted to increase £200 by 34.5% well, let's look at the three different methods on how you would do this on a calculator. Method one is to type in 200 plus 34.5% and you get 269. This is the easiest method on public, the one you would use most often. Method two is to type in 200 times, 134.5% on again. You'll get 269 when you press equals the third method. To use the decimals, you have to type in 200 times 1.345 and then you will get 269. The percentage, 34.5% as a decimal, is 0.345 and so when it's a percentage increase, it becomes 1.345 39. Lesson 38 (Increasing a number by a percentage on a calculator): use a calculator toe workout. The following percentage increases using whichever method you prefer, so increase £800 by 15.5% £924. So we the ikan type in 800 plus 15.5%. You could type in 800 times 115.5%. Or you can type in 800 times 1.115 Andi. You'll get the same answer for all three of those increased £500 by 20.5% £602.50. And so we the you can type in 500 plus 20.5%. You could type in 500 times 120.5%. Or you could type in 500 times 1.205 and you'll get 602.5. All of them, which and money is £602. 50. Increase £600 by 30% £780 so you can either type in 600 plus 30% 600 times 130% or 600 times 1.3 increase £130 by 80%. £234 is there Either you can type in 130 plus 80% 130 times 180% or 130 times 1.8. Increase £80 by 17%. £93. 60. So either you can type in 80 plus 17% 80 times 117% or 80 times 1.17 and you'll get the same answer. £93.60 increase £900 by 14.3% 1000 and £28. 70. So we do. You can type in 900 plus 14.3%. You could type in 900 times 114.3% or you can type in 900 times 1.143 40. Lesson 39 (Decreasing a number by a percentage): increased £1000 by 8.21% 1000 and £82. 10. So either you can type in 1000 plus 8.21% you could type in 1000 times 108.21%. Or you can type in 1000 times 1.8 to 1. No matter which way you use, you will get 1000 and £82. 10. Increase £40 by 90.2%. £76.8 p so you can either type in 40 close 90.2% 40 times 190.2% or 40 times 1.902 Increase £70 by 83% £128. 10. So you can either type in 70 plus 83% 70 times 183% or 70 times 1.83 Increase £50 by 10.6% . £55.30 so you can either type in 50 plus 10.6% 50 times 110.6% or 50 times 1.106 percentage decrease. Now you know how to increase the number by a percentage. You can also very easily decrease the number by a percentage. All you have to do is find the percentage and then subtract it from the original number. For example, how would you decrease £300 by 20%? Well, you would start by finding 20% off 300 which you can do by finding 10% and then doubling it . So 10% of 300 is 30 on double. That is 60 and then you subtract it, so £300 take away. £60 is £240. See if you can decrease £60 by 15%. To find 15% of £60 you confined 10% which is £6 on then 5% which is £3. Another together £6 plus £3 is £9 and then you can subtract it from 60. So £60 take away. £9 is £51 41. Lesson 40 (Decreasing a number by a percentage): see if you can answer this percentage decrease question. If a TV was originally £400 then there was a 20% sale on what would be the new price off the TV, you simply need to decrease £400 by 20%. So 20% off £400 is £80 on £400. Take weigh £80 is £320. If a population of a city decreased in size by 2% from one year to the next. What would be the population in 2019 if it was 180,000 in 2018 2% off, 180,000 is 3600 and 180,000 take away, 3600 is 176,400. In 2015 a call was worth £25,000. Three years later, the value of the car had decreased by 35%. What was the new value off the car in 2018 35% off. 25,000 is 8750 and then £25,000 take away £8750 is £16,250. A cat weighed 4.2 kilograms in January on by December, its weight had decreased by 15%. What was the new weight off the cat, 15% off 4.2 kilograms is 0.63 kilograms and then 4.2 kilograms. Take away 0.63 kilograms is 3.57 kilograms. Somebody bought a computer in 2010 for £2500 but then when they sold it eight years later , the computers value had dropped by 85%. How much was it now, with 85% off, 2500 is 2000 125. So £2500 take away. £2125 leaves you with £375 42. Lesson 41 (Decreasing a number by a percentage): on Thursday, the temperature in London was 20% cooler than it was on the Wednesday if it was 20 degrees Celsius on Wednesday. What was the temperature on Thursday? 20% off, 20 degrees Celsius is four degrees Celsius and then 20 take away for equals 16 degrees Celsius. A family off elephants had 30 members. A few years later, the number of elephants in the family had decreased by 30%. How many elephants were now in the family? 30% off, 30 is nine and then 30. Take away nine is 21 so the answer is 21. Elephants decrease £750 by 25% 25% off. 750 is £187. 50 and then £750. Take away 108 £7. 50 is £562. 50 decrease 5400 by 12% 12% off. 5400 is 648 and then 5400. Take away. 648 is 4752. Decrease £9000 by 54% 54% off £9000 is £4860 and then £9000. Take away £4860 is £4140. 43. Lesson 42 (Decreasing a number by a percentage on a calculator): decrease 12 by 40% 40% off 12 is 4.8 and then 12. Take away. 4.8 is 7.2. Decreased £10 by 35% 35% off £10 is £3.50 and then £10. Take away £3. 50 is £6.50 percentage decreases on a calculator. There are two very easy ways to decrease the number by a certain percentage on a calculator . The first method is to use the minus button on the percent bottom on the calculator. This method is the same as the increasing percentages Method one, except you use the take away sign instead of the ad sign. For example, if you want to decrease £80 by 23% all you have to type in is 80. Take away 23% on when you press equals, you'll get the answer. 61.6, which in money is £61.60. How would you decrease £180 by 70%? You'll just type in 180. Take away 70% on when you press equals, you'll get £54. The second method is toe workout. What's missing? This method can be used if you have a calculator that doesn't have a percent. Bottom we have to do is work out what percentage off the number is left want you decreased it. For example, if you want to decrease £50 by 20% well, once you've taken off the 20% you'll be left with 80%. This means you simply to find 80% or 50. You can do this however you like, either by typing in 50 times 80% or 50 times 0.8 on you'll get 40 which is the correct answer. How would you decrease £70 by 40% on a calculator? Using the second method, you'll need to find what is left after you subtract 40% and that would be 60% since 100% take away 40% equal 60%. And then you just need to find 60% off £70 by typing into a calculator 70 times 0.6 or 70 times 60% and you'll get 42 which is £42 44. Lesson 43 (Decreasing a number by a percentage on a calculator): use a calculator toe workout. The following percentage decreases using whichever method you prefer. How would you decrease £800 by 15.5%? You can either type in 800. Take away 15.5% or you could subtract 15.5 from 100 get 84.5 and then do 84.5% off. 800 you'll get 676. Decreased £500 by 20.5% £397.50 decrease £600 by 30% £420 Decrease. £130 by 80% £26 Decrease. £80 by 17% £66.40 Decrease £900 by 14.3% £771.30 Decreased £1000 by 8.21% £917.90 decrease £40 by 90.2% £54.12 decrease £70 by 83% £11.90 decrease £50 by 10.6% £44.70 45. Lesson 44 (Simple interest and compound interest): simple interest and compound interest. If you put some money into an account that accumulated interest, then it would go up. But the amount that it would go up by would depend on two things firstly and obviously, what the interest raters. And secondly, whether it's simple interest or compound interest, the phrase interest rate means what percentage increase is applied, usually once a year. For example, if you put £200 into an account that had a 2% a P R, which means annual percentage rate, then every year you would get a 2% increase. 2% of £200 is £4 so after one year you would have £204. Simple interest means that they based the interest on the original amount of money you had . For example, if you put £200 into an account with 5% a PR simple interest, here's what would happen over five years. So the original amount was £200. After one year, you have £200 plus 5% off £200 which is £10 you end up with £210 after two years. You have £210 plus 5% off the original amount, which was £200 which is £10 and you add that on to get £220. After three years, it's £220 plus 5% of £200 which gives you £230. After four years, you have £230 plus 5% of £200 which makes £240. And after five years, it's £240 plus 5% of £200 which gives you £250. So that's simply interest. Compound interest means that they based the interest on whatever is in the account at the end of each year. For example, if you put £200 into an account with 5% a PR compound interest, here's what would happen over five years. So the original amount is £200. After one year, you get £200 plus 5% of £200 which makes £210. After two years, you have £210 plus 5% off £210 because the percent increase is based on whatever is in the account at that time. So 5% of £210 is £10. 15. So you add that on and you get £220. 50 after three years, £220.50 plus 5% off £220. 50 well, 5% of £220.50 is actually £11 on and 2.5 p. But usually they around a talk to say, you'll get £11.3 p. If you add £11.3 p onto £220.50 then you get £231. 53. After four years, you have £231.53 plus 5% off, £231.53 5% off £231. 53 is actually 11.5765 but they'll round it up, so you get £11. 58. If you add that on, you get £243.11 and then finally, after five years you have £243.11 plus 5% of £243.11 and 5% of £243. 11 is 12.1555 but they're round it up to 12.16 which is £12. 16. You add £12.16 to £243.11 and you get £255.27 p. And so compound interest is based on whatever's in the account at that time, where a simple interest is based only on the very original amount. So you can see that you can make more money with compound interest than with simple interest. After five years, simple interest you made £250 but after five years of compound interest, you made £255. 27 That's £5.27 more 46. Lesson 45 (Simple interest and compound interest): see if you can answer these questions on interest rates. How much money would you have after two years if you put £5000 into an account with 7% a PR simple interest, so the original amount is £5000. After one year, you have £5000 plus 7% of £5000. Well, 7% of £5000 is £350 so you add the tone and you get £5350. After two years, you have £5350 plus 7% of £5000 which makes £5700. How much money would you have after two years? If you put £5000 into an account with 7% a PR compound interest after one year, it will be the same as the previous question. You have £5000 for a 7% of £5000 which is £350 that makes you £5350. However, after two years now you have £5350 plus 7% off £5350. 7% of £5350 is £374. 50 So you add that own and you get £5724. 50. How much money would you have after three years if you put £20,000 into an account with 10% a PR simple interest? After one year, you have £20,000 plus 10% of £20,000 which is £2000 that makes you £22,000. After two years, you have £22,000 plus 10% of £20,000 which makes you £24,000. And after three years you have £24,000 plus 10% off £20,000 on. That makes you a total of £26,000. But how much money would you have after three years? If you put £20,000 into an account with 10% a PR compound interest after one year, it'll be the same as the previous question. £20,000 plus 10% of £20,000 makes 22,000 bombs after two years. However, now you have £22,000 plus 10% off £22,000. Well, £22,000 divided by 10 is 2200. And if you add that on, you get £24,200. After three years, you have £24,200 plus 10% off £24,200 which is 2420. If you add that on, you get £26,620. 47. Lesson 46 (Compound interest formula): simple interest is easy to work out, even over many, many years, because all you have to do is at the same amount each time. For example, if you put £800 in an account at 4% a PR simple interest, you know you will get £32 every year because 4% of £800 is there to do pounds. So even after 50 years, you know how much you will have £32 per year times 50 years is £1600 plus the original £800 makes £2400. Compound interest is a little trickier to work out over long periods because you don't add the same amount each time it's based on. However, much is in the account at the end of each year. For example, if you wanted to work out the previous question using compound interest, you would have to work out every year for 50 years, and it would take forever. However, the wonderful thing about maths is a thing called a formula in months, there are always patterns to things, so you can usually find ways of working even the most impossible things out easily. We can make things called formula, which we can use to work out tricky calculations. The formula for working out compound interest is this. The end amount equals the original amount times increasing percentage to the power of how many years Or we can write it like this. A equals p R to the power of Team A is the end amount. That's how much you'll end up with P is the original or the principal amount are is the interest rate and T is the number of years the interest rate has to be written as a decimal with a one in front of it, like we saw when we learned how to increase a number by a percent is using a calculator. So here's how we would use it to work out this question. If you put £800 in an account at 4% a PR compound interest, how much would you have after 50 years when we use the equation a equals P R T. So let's look at what we have and then put the numbers into the equation. So P is the original amount, which is £800 are is the interest rate where it's 4%. So we write our as 1.4 because it's an increasing interest and T is the number of years where that's 50. So in a calculator you will type in 800 times 1.4 to the power off 50. If you type this into a calculator, you'll get £5685.35 p. 48. Lesson 47 (Interest questions): We've just seen that the formula for working out the compound interest over a number of years is a equals p r to the power of T, where a is the end amount P is the original or principal amount are is the interest rate and T is the number of years. The little T is a power. And if you're not sure how to type to the power of T on your calculator, look for the button that either looks like this X to the power of why. Or it might look like this little arrow pointing upwards. You press the button before typing the number of years. So for 1.4 to the power of 50 you were type either 1.4 the little X Y button and then 50 or you were type in 1.0 for the little arrow button and then 50. See if you can use a calculator to work out the following You start with £1500 on. Do you put it into an account with 3% a PR simple interest for 20 years? How much would you have after 20 years? 3% off £1500 is £45 on. Because it's over 20 years, you times that by 20 and add it on to the original amount. So 45 times 20 is £900 then £1500 plus £900 is £2400. For this next question, you'll need the compound interest formula. You start with £1500 you put it into an account with 3% a PR compound interest for 20 years. How much would you have after 20 years? So if you use the formula, you have 1500 times 1.3 to the power of 20 which will give you £2709.17 p. In actual fact, the number you'll get on a calculator is 2709.1668520041 etcetera. But because this is money, you can round it up to 17 which is 17 b 49. Lesson 48 (Interest questions): If you start with £52,000 on you, put it into an account with 15% a PR simple interest for five years. How much would you have after five years? 15% off. £52,000 is £7800. If you multiply that by five, you get £39,000 £39,000 plus the original £52,000 makes £91,000. You start with £52,000 you put it into an account with 15% a PR compound interest for five years. How much would you have after five years? So you would have to use the formula on type into a calculator. P r to the power of T P is the original amount £52,000 times the interest rate 1.15 to the power off the number of years, which is five. So 52,000 times 1.15 to the power of five equals £104,590 on 57 p. If you start with £2 million you put it into an account with 8% a P r simple interest. 15 years? How much money would you have after 15 years? 8% off. £2 million is £160,000. If you multiply that by 15 because it's 15 years, that makes £2,400,000. Add that to the original amount and you get £4,400,000 or 4.4 million. If you start with £2 million on this time, you put it into an account with 8% a P r compound interest for 15 years. How much money would you have after 15 years? Well, if you use the formula, your type in two million times 1.8 to the power off 15 and you'll get £6,344,338.23 p so you can see make a lot more money using compound interest rates than simple interest rates . 50. Lesson 49 (Reverse percentages): reverse percentages. A reverse percentage is when you have to work backwards to work out what the original price of something waas after it was increased or decreased. For example, if there was a TV in a sale that said 50% off and the sale price was £300 you would know that the original price would be £600. This is because £300 is what was left when 50% was taken off. And so you just do it. But when the sale prices are a little less simple, it gets a little bit trickier. A car was £8000 in a 20% sale. What was the original price? Well, to work this out, we need to go backwards if you imagine the original price is £100 and then they decreased it by 20%. What is left? Well, 80% Because 100% take away, 20% is 80%. This means that £8000 is equal to 80% so we just need to get back to 100%. We can't simply find 20% of this because this isn't the original amount. You can only find 20% off the original amount to add on to the 80% a trick that always works, no matter what the percentage is, is to divide by the new percent and then multiply by 100 to get us back to 100%. Dividing by the new percent gives you 1% and then multiplying by 100 gets you back to 100% . So if 80% equals £8000 we just need to divide by 80 to get 1%. So £8000 divided by 80 is £100. So 1% is £100. We can now just multiply by 100 to get back to 100% £100. Times 100 is £10,000. So the original price of the car before the sale was £10,000. You can always do a check to make sure you got it right. 20% off. £10,000 is £2000 on When you do 10,000 take away 2000 you get £8000 which was the sale price of the car. So we got it right. So just remember that dividing by the new percentage and then multiplying by 100 always works to find the original price of something. Let's try another. A T shirt is on sale. The new price is £17.50 and it's in a 30% sale. What was the original price when if the price of the T shirt was reduced by 30% then 70% is what is left over. So the £17.50 is actually 70% off the original amount. We just have to divide by 70 and then multiply by 100 to find the original price. £17.50 divided by 70 is 25 p 25 p. Times 100 is £25. So the original price of the T shirt was £25 on. We can always do a quick check to make sure we got it right. If the T shirt was reduced by 30% What we need to find 30% of £25 10% of £25 is £2.50 times by three. To get 30% is £7.50 £25. Take away £7. 50 is £17.50 which was the sale price. So we got it right 51. Lesson 50 (Reverse percentages): if the price of a bag of bananas was increased by 15%. £23. 45. What was the price of the back of bananas originally? Well, this time the price went up by 15% instead of down, so the new price is actually 115%. This means we have to divide by 115 to get back to 1% and then multiply by 100 to get the original price, which is 100% so. £3.45 divided by 115 is three p. You might do that in a calculator, then three p times 100 is £3 so the original price of the bananas was £3. Again, we can always check that. So if the bananas were increased by 15% we need to find 15% off. £3 10% off. £3 is 30 p, and half of that is 15 p, which is 5%. Add them together and you get 45 p £3 plus 45 p is £3.45 which is what the bag off bananas was increased to. So we got it right. Let's try and do some practice questions now. If a car was reduced by 20% to £7200 what was its price? Originally, £7200 is 80% because if the price was reduced by 20% than 80% is left over. So £7200 divided by 80 is £90 which is 1%. Then we multiply that by 100 90 times. 100 gives us £9000 so the original price was £9000 and you can check it if you want by finding 20% off £9000 which is £1800. 9000 take away. 1800 is £7200. If a houses value increased by 10% and its new price was £275,000 what was its value originally? Well, because the price of the house was increased by 10%. That means that the new price is 110% off the original, so £275,000 is equal to 110%. If we divide by 110 we can get 1%. So 275,000 divided by 110 gives you 2500. And then we multiplied by 100 2500 times. 100 gives you £250,000 which was the original price off the house. 52. Lesson 51 (Reverse percentages): a pair of curtains were in a sale that said 30% off if the new price was £210. How much were the curtains? Originally, 100% take away, 30% leaves you with 70% so £210 equals 70% and then £210 divided by 17 equals £3 £3 times 100 is £300 so the curtains were originally £300. Tom went to a market on bartered with the cellar of a coat. He managed to get the coat for £18 which was 10% less than it was originally priced At how much was the coat? Originally, 100% take away. 10% is 90%. So he got the coat for 90% off. Its original value, which means £18 equals 90%. £18. Divided by 90 is 20 p, so 20 p is 1% and then 20 p, multiplied by 100 is £20 so the coat originally cost £20. Julia bought a painting and sold it two years later. For £500 she made 25% more than she originally paid for it. How much did Julia pay for the painting? Originally 100% plus 25% is 125% which means £500 is equal to 125% off. The original price £500 divided by 125 is £4 and then £4 times 100 is £400.