Reverse Percentages – Calculator – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

I invested some money in the bank and got 20% interest. At the end of the year I had $360. How much did I put in the bank? × 1.2 100% 120% ? $300 $360 ÷ 1.2

I invested some money in the bank and got 40% interest. At the end of the year I had $630. How much did I put in the bank? × 1.4 100% 140% ? $450 $630 ÷ 1.4

I invested some money in the bank and got 45% interest. At the end of the year I had $652.50. How much did I put in the bank? × 1.45 100% 145% ? $450 $652.50 ÷ 1.45

This year oil increased by 15% to $109.25 per barrel. How much did a barrel cost at the start of the year? × 1.15 100% 115% ? $95 $109.25 ÷ 1.15

This year oil increased by 7.5% to $97 per barrel. How much did a barrel cost at the start of the year? × 1.075 100% 107.5% $90.23 ? $97 2 d.p. Why? ÷ 1.075

Oil was $65 after a 40% increase. What was its original price? Example: Oil went up 20% and cost $48. How much was it before the increase? A T-shirt was $28 after a 15% tax. What was its original price? × 1.2 100% 120% ? $48 A dress was $65 after a 12.5% increase. What was its original price? ÷ 1.2 Petrol increased to $145.35 after a 7.4% tax. What was its original price?

Answers Oil was $65 after a 40% increase. What was its original price? Example: $46.43 Oil went up 20% and cost $48. How much was it before the increase? A T-shirt was $28 after a 15% tax. What was its original price? × 1.2 $24.35 100% 120% ? $48 A dress was $65 after a 12.5% increase. What was its original price? ÷ 1.2 $57.78 Answers Petrol increased to $145.35 after a 7.4% tax. What was its original price? $135.34

A pair of jeans were 30% off and cost $42. How much were they before the sale? × 0.7 100% 70% ? $60 $42 SALE! ÷ 0.7

A pair of jeans were 40% off and cost $54. How much were they before the sale? × 0.6 100% 60% ? $90 $54 SALE! ÷ 0.6

A pair of shoes were 24% off and cost $38. How much were they before the sale? × 0.76 100% 76% ? $50 $38 SALE! ÷ 0.76

A pair of shoes were 8% off and cost $74. How much were they before the sale? × 0.92 100% 92% $80.43 ? $74 SALE! ÷ 0.92

A pair of shoes were 7.8% off and cost $64. How much were they before the sale? × 0.922 100% 92.2% $69.41 ? $64 SALE! ÷ 0.922

Answers 40% off! Now $36! 24% off! Now $26! 9% off! Now $43! Find the original prices for these goods. 40% off! Now $36! Example: A pair of shoes were $78 in the 30% off sale. How much were they before the decrease? × 0.7 100% 70% ? $78 24% off! Now $26! ÷ 0.7 9% off! Now $43! Answers 7.25% off! Now $73!

Answers 40% off! Now $36! Were $60 24% off! Now $26! Was $34.21 Find the original prices for these goods. 40% off! Now $36! Example: A pair of shoes were $78 in the 30% off sale. How much were they before the decrease? Were $60 × 0.7 100% 70% ? $78 24% off! Now $26! ÷ 0.7 Was $34.21 9% off! Now $43! Answers 7.25% off! Now $73! Were $47.25 Was $78.71

Oil was $65 after a 30% increase. Original price = ? Oil went up 20% and cost $48. How much was it before the increase? A T-shirt was 60% off and cost $54. How much was it before the sale? × 1.2 × 0.4 100% 120% 100% 40% ? $48 ? $54 ÷ 1.2 ÷ 0.4 Oil was $65 after a 30% increase. Original price = ? A T-shirt was $42 with 30% off. Original price = ? Oil was $78 after a 44% increase. Original price = ? A T-shirt was $43 with 24% off. Original price = ? Oil was $92 after a 7% increase. Original price = ? A T-shirt was $35 with 8% off. Original price = ?

Answers Oil was $65 after a 30% increase. Original price = $50 Oil went up 20% and cost $48. How much was it before the increase? A T-shirt was 60% off and cost $54. How much was it before the sale? × 1.2 × 0.4 100% 120% 100% 40% ? $48 ? $54 ÷ 1.2 ÷ 0.4 Answers Oil was $65 after a 30% increase. Original price = $50 A T-shirt was $42 with 30% off. Original price = $60 Oil was $78 after a 44% increase. Original price = $54.17 A T-shirt was $43 with 24% off. Original price = $56.58 Oil was $92 after a 7% increase. Original price = $85.98 A T-shirt was $35 with 8% off. Original price = $38.04

¼ PAGE 1) A T-shirt is sold with a 20% discount. It is sold for $67. What was its original price? 2) There is 24% off a pair of shoes in the shop. It now costs $65. What was its original price? 3) After a tax of 22%, a car sells for $9800. What was its original price? A shop sells milk for $2.50 a litre. This includes a tax of 27%. How much is a litre of milk without tax? A gallon of oil is taxed 18% by the government. One garage gives a 25% discount and sells a gallon for $4.67. What was its original price?

¼ PAGE Answers 1) A T-shirt is sold with a 20% discount. It is sold for $67. What was its original price? $83.75 2) There is 24% off a pair of shoes in the shop. It now costs $65. What was its original price? $85.53 3) After a tax of 22%, a car sells for $9800. What was its original price? $8032.79 A shop sells milk for $2.50 a litre. This includes a tax of 27%. How much is a litre of milk without tax? $1.97 A gallon of oil is taxed 18% by the government. One garage gives a 25% discount and sells a gallon for $4.67. What was its original price? $5.28

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