1. © T Madas Finding the amount before a Percentage Change

2. © T Madas The value of a painting went up by 25% and is now valued at £400. What was its value before the increase? The answer IS NOT £400 less 25%, WHY? If you increase £300 by 25% you get i.e. £300 £375 Why doesn’t a decrease by 25% get balanced by an increase of 25%? How do we solve a problem like this?

3. © T Madas Value Before 400 x 1.25 £320 400 ÷ 1.25 The value of a painting went up by 25% and is now valued at £400. What was its value before the increase?

4. © T Madas An item costs £282 after V.A.T at 17.5%. What is its price before V.A.T? This formal equation set up shows why this method works but it is not strictly required b £240 x 1.175 ÷ 1.175 £282

5. © T Madas An item costs £93.50 after a 15% discount. What did it cost before the discount? b £110 x 0.85 ÷ 0.85 £93.50

6. © T Madas Find the number which was increased by 12% to give 420. b 375 x 1.12 ÷ 1.12 420

7. © T Madas Find the number which was decreased by 17% to give 415. b 500 x 0.83 ÷ 0.83 415

8. © T Madas Finding the amount before a percentage increase or decrease: Take the final amount and divide it by the appropriate percentage multiplier Find the number that was increased by 30% to give 520 520 ÷ 1.3 = 400 Find the number that was decreased by 30% to give 420 420 ÷ 0.7 = 600 Finding the amount after a percentage increase or decrease: Take the original amount and multiply it, by the appropriate percentage multiplier Increase 500 by 15% 500 x 1.15 = 575 Decrease 700 by 11% 700 x 0.89 = 623 Percentage Multiplier Summary

9. Practice on finding the amount before a Percentage Change using a calculator

10. © T Madas What number was increased by 10% to give 121? 110 Amounts Before Percentage Changes What number was increased by 15% to give 184? 160 What number was increased by 12% to give 252? 225 What number was increased by 27% to give 406.4? 320 What number was decreased by 10% to give 468? 520 What number was decreased by 25% to give 273? 364 What number was decreased by 40% to give 252? 420 What number was decreased by 11% to give 534? 600

11. © T Madas What number was increased by 12% to give 140? 125 What number was decreased by 12% to give 484? 550 What number was increased by 17.5% to give 282? 240 What number was decreased by 17.5% to give 660? 800 What number was increased by 5.5% to give 147.7? 140 What number was decreased by 5.5% to give 1701? 1800 What number was increased by 1% to give 343.4? 340 What number was decreased by 1% to give 742.5? 750 Amounts Before Percentage Changes

12. © T Madas 110% of a number is 121. What is the number? 110 115% of a number is 184. What is the number? 160 112% of a number is 252. What is the number? 225 127% of a number is 406.4. What is the number? 320 90% of a number is 468. What is the number? 520 75% of a number is 273. What is the number? 364 60% of a number is 252. What is the number? 420 89% of a number is 534. What is the number? 600 Amounts Before Percentage Changes

13. © T Madas 112% of a number is 140. What is the number? 125 88% of a number is 484. What is the number? 550 117.5% of a number is 282. What is the number? 240 87.5% of a number is 700. What is the number? 800 105.5% of a number is 147.7. What is the number? 140 94.5% of a number is 1701. What is the number? 1800 101% of a number is 343.4. What is the number? 340 99% of a number is 742.5. What is the number? 750 Amounts Before Percentage Changes

14. © T Madas Test on finding the amount before a Percentage Change using a calculator

15. © T Madas What number was increased by 10% to give 121? 110 Amounts Before Percentage Changes What number was increased by 15% to give 184? 160 What number was increased by 12% to give 252? 225 What number was increased by 27% to give 406.4? 320 What number was decreased by 10% to give 468? 520 What number was decreased by 25% to give 273? 364 What number was decreased by 40% to give 252? 420 What number was decreased by 11% to give 534? 600

16. © T Madas What number was increased by 12% to give 140? 125 What number was decreased by 12% to give 484? 550 What number was increased by 17.5% to give 282? 240 What number was decreased by 17.5% to give 660? 800 What number was increased by 5.5% to give 147.7? 140 What number was decreased by 5.5% to give 1701? 1800 What number was increased by 1% to give 343.4? 340 What number was decreased by 1% to give 742.5? 750 Amounts Before Percentage Changes

17. © T Madas 110% of a number is 121. What is the number? 110 115% of a number is 184. What is the number? 160 112% of a number is 252. What is the number? 225 127% of a number is 406.4. What is the number? 320 90% of a number is 468. What is the number? 520 75% of a number is 273. What is the number? 364 60% of a number is 252. What is the number? 420 89% of a number is 534. What is the number? 600 Amounts Before Percentage Changes

18. © T Madas 112% of a number is 140. What is the number? 125 88% of a number is 484. What is the number? 550 117.5% of a number is 282. What is the number? 240 87.5% of a number is 700. What is the number? 800 105.5% of a number is 147.7. What is the number? 140 94.5% of a number is 1701. What is the number? 1800 101% of a number is 343.4. What is the number? 340 99% of a number is 742.5. What is the number? 750 Amounts Before Percentage Changes

19. © T Madas