Calculating a Percentage Multiplier Demonstration This resource provides

Calculating a Percentage Multiplier – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

Using decimals to find a percentage of a quantity. 300% = 80 × 3 80 80 200% = 80 × 2 80 100% = 80 × 1 80 50% = 80 × 0. 5 40 80 80

Using decimals to find a percentage of a quantity. 100% = 90 × 1 90 50% = 90 × 0. 5 45 75% = 90 × 0. 75 67. 5 27% = 90 × 0. 27 24. 3

Use a decimal to calculate these percentages of quantities. 100% = 70 × 1 100% = 270 × 1 70 270 50% = 70 × 0. 5 75% = 270 × 0. 75 45 202. 5 20% = 70 × 0. 2 32% = 270 × 0. 32 14 86. 4 90% = 70 × 0. 9 63 35% of 70 = 24. 5 67% = 270 × 0. 67 180. 9 12. 5% of 270 = 33. 75

Increasing & Decreasing using a Decimal Multiplier 1. 2 Increase 90 by 20% 1 0. 2 100% 20% 90 × (1 + 0. 2) = 90 × 1. 2 = 108 0. 7 1 Decrease 90 by 30% 100% 30% 0. 3 90 × (1 − 0. 3) = 90 × 0. 7 = 63

Increasing & Decreasing using a Decimal Multiplier 1. 45 Increase 140 by 45% 1 0. 45 100% 45% 140 × (1 + 0. 45) = 140 × 1. 45 = 203 0. 85 1 Decrease 140 by 15% 100% 15% 0. 15 140 × (1 − 0. 15) = 140 × 0. 85 = 119

Increasing & Decreasing using a Decimal Multiplier a) Increase 180 by 40% 252 d) Decrease 240 by 30% 168 b) Increase 230 by 35% 310. 5 e) Decrease 510 by 45% 280. 5 c) Increase 110 by 27% 139. 7 f) Decrease 330 by 19% 267. 3

Using a percentage multiplier Increase 250 by 20% + 100% = 1. 0 + 020% = 0. 20 120% = 1. 20 250 × 1. 20 = 300

Using a percentage multiplier Your Turn Increase 250 by 20% + 100% = 1. 0 Increase 320 by 40% + + 100% = 1. 0 + 020% = 0. 20 040% = 0. 40 120% = 1. 20 140% = 1. 40 250 × 1. 20 = 300 320 × 1. 40 = 448

Using a percentage multiplier Increase 280 by 15% + 100% = 1. 0 + 015% = 0. 15 115% = 1. 15 280 × 1. 15 = 322

Using a percentage multiplier Your Turn Increase 280 by 15% + 100% = 1. 0 Increase 340 by 35% + + 100% = 1. 0 + 015% = 0. 15 035% = 0. 35 115% = 1. 15 135% = 1. 35 280 × 1. 15 = 322 340 × 1. 35 = 459

Using a percentage multiplier Increase 310 by 22% + 100% = 1. 0 022% = 0. 22 122% = 1. 22 310 × 1. 22 = 378. 2 +

Using a percentage multiplier Your Turn Increase 310 by 22% + 100% = 1. 0 Increase 260 by 17% + + 100% = 1. 0 022% = 0. 22 017% = 0. 17 122% = 1. 22 117% = 1. 17 310 × 1. 22 = 378. 2 260 × 1. 17 = 304. 2 +

Using a percentage multiplier Increase 230 by 16. 5% + 100% = 1. 0 15. 5% = 0. 165 116. 5% = 1. 165 230 × 1. 165 = 267. 95 +

Using a percentage multiplier Your Turn Increase 230 by 16. 5% + 100% = 1. 0 Increase 170 by 21. 5% + + 100% = 1. 0 15. 5% = 0. 165 21. 5% = 0. 215 116. 5% = 1. 165 121. 5% = 1. 215 230 × 1. 165 = 267. 95 170 × 1. 215 = 206. 55 +

Using a percentage multiplier Increase 150 by 6. 3% + 100% = 1. 0 06. 3% = 0. 063 106. 3% = 1. 063 150 × 1. 063 = 159. 45 +

Using a percentage multiplier Your Turn Increase 150 by 6. 3% + 100% = 1. 0 Increase 230 by 3. 7% + + 100% = 1. 0 06. 3% = 0. 063 03. 7% = 0. 037 106. 3% = 1. 063 103. 7% = 1. 037 150 × 1. 063 = 159. 45 230 × 1. 037 = 238. 51 +

Using a percentage multiplier Your Turn Increase 310 by 22% + 100% = 1. 0 022% = 0. 22 122% = 1. 22 310 × 1. 22 = 378. 2 A) Increase 340 by 20% + B) Increase 250 by 60% C) Increase 410 by 15% D) Increase 330 by 45% E) Increase £ 5. 40 by 32% F) Increase 823 g by 7% G) Increase 78 cm by 12. 5% H) Increase 763 ml by 3. 5%

Using a percentage multiplier Your Turn Increase 310 by 22% + 100% = 1. 0 022% = 0. 22 122% = 1. 22 310 × 1. 22 = 378. 2 + A) Increase 340 by 20% 408 B) Increase 250 by 60% 400 C) Increase 410 by 15% 471. 5 D) Increase 330 by 45% 478. 5 E) Increase £ 5. 40 by 32% £ 7. 13 F) Increase 823 g by 7% 880. 61 g G) Increase 78 cm by 12. 5% 87. 75 cm H) Increase 763 ml by 3. 5% 789. 705 ml

Using a percentage multiplier Decrease 240 by 30% − 100% = 1. 0 − 030% = 0. 3 70% = 0. 7 240 × 0. 7 = 168

Using a percentage multiplier Your Turn Decrease 240 by 30% − 100% = 1. 0 Decrease 180 by 40% − − 100% = 1. 0 030% = 0. 3 040% = 0. 4 70% = 0. 7 60% = 0. 6 240 × 0. 7 = 168 180 × 0. 6 = − 108

Using a percentage multiplier Decrease 130 by 15% − 100% = 1. 0 015% = 0. 15 85% = 0. 85 130 × 0. 85 = 110. 5 −

Using a percentage multiplier Your Turn Decrease 130 by 15% − 100% = 1. 0 Decrease 190 by 35% − − 100% = 1. 0 015% = 0. 15 035% = 0. 35 85% = 0. 85 65% = 0. 65 130 × 0. 85 = 110. 5 190 × 0. 65 = 123. 5 −

Using a percentage multiplier Decrease 270 by 17. 5% − 100% = 1. 0 017. 5% = 0. 175 82. 5% = 0. 825 270 × 0. 825 = 222. 75 −

Using a percentage multiplier Your Turn Decrease 270 by 17. 5% − 100% = 1. 0 Decrease 320 by 16. 5% − − 100% = 1. 0 017. 5% = 0. 175 016. 5% = 0. 165 82. 5% = 0. 825 83. 5% = 0. 835 270 × 0. 825 = 222. 75 320 × 0. 835 = 267. 2 −

Using a percentage multiplier Decrease 140 by 7. 5% − 100% = 1. 0 07. 5% = 0. 075 92. 5% = 0. 925 140 × 0. 925 = 129. 5 −

Using a percentage multiplier Your Turn Decrease 140 by 7. 5% − 100% = 1. 0 Decrease 220 by 3. 5% − − 100% = 1. 0 07. 5% = 0. 075 03. 5% = 0. 035 92. 5% = 0. 925 96. 5% = 0. 965 140 × 0. 925 = 129. 5 220 × 0. 965 = 212. 3 −

Using a percentage multiplier Your Turn Decrease 130 by 15% − 100% = 1. 0 015% = 0. 15 85% = 0. 85 130 × 0. 85 = 110. 5 A) Decrease 280 by 30% − B) Decrease 360 by 70% C) Decrease 430 by 25% D) Decrease 270 by 15% E) Decrease £ 4. 40 by 27% F) Decrease 671 g by 6% G) Decrease 48 cm by 11. 5% H) Decrease 621 ml by 2. 5%

Using a percentage multiplier Your Turn Decrease 130 by 15% − 100% = 1. 0 015% = 0. 15 85% = 0. 85 130 × 0. 85 = 110. 5 − A) Decrease 280 by 30% 196 B) Decrease 360 by 70% 108 C) Decrease 430 by 25% 322. 5 D) Decrease 270 by 15% 229. 5 E) Decrease £ 4. 40 by 27% £ 3. 21 F) Decrease 671 g by 6% 630. 74 g G) Decrease 48 cm by 11. 5% 42. 48 cm H) Decrease 621 ml by 2. 5% 605. 475 ml

What happens when someone invests in a business? I’ve got an idea that’ll make millions! Hmmmm…. People can make more money by giving money to businesses. They hope the business uses the money to grow & increase their income. +1% If the business does get bigger they will give the money back, plus interest. +8% +120%! But! What if the business is not successful? − 3% The investors can lose their money! − 14% − 100%!

Banks make safe investments & give their customers a small interest rate. You can invest in many companies on the stock market. This can be much riskier! 2% per annum 15% loss! in one year

I invested $300 and got 120% back! Wow! $60! Is Sally correct? Original +100% +20%

I invested $500 and lost 200%! Is this possible? We can’t eat 200% of something & things in a shop can’t cost 200% less. A 100% decrease means everything is gone! But, if we can use negative numbers, we can lose over 100%. A company can make negative profit – they are spending money to just keep going!

Invested 1 Year Interest $ @ End of Year $500 50% $750 $400 25% $500 $550 20% $660 $300 15% $345 $480 35% $648 $600 41% $846 $260 85% $481 $600 0. 5% $603 $1400 2. 5% $1435 $120 1. 25% $121. 50 $80 97. 75% $158. 20

Invested Loss! $ @ End of Year $600 50% $300 $800 25% $600 $250 20% $200 $500 15% $425 $160 35% $104 $400 41% $236 $580 85% $87 $800 0. 5% $796 $1200 2. 5% $1170 $160 1. 25% $158 $50 97. 75% $1. 13 (1. 125)

Invested Profit / Loss! $ @ End of Year $600 +50% $900 $800 +25% $1000 $250 +20% $300 $500 +15% $575 $300 +41% $423 $460 +36% $625. 60 $260 − 10% $234 $600 − 25% $450 $1400 − 60% $560 $120 − 75% $30 $140 − 82% $25. 20 $120 − 97. 5% $3

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk