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Lesson Objective

Lesson Objective. By the end of the lesson you should be able to go backwards through percentage problems to find the starting value. Reverse Percentage Problems. example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale?.

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Lesson Objective

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  1. Lesson Objective • By the end of the lesson you should be able to go backwards through percentage problems to find the starting value.

  2. Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? Pupil A works out the answer as £27.30 Pupil B works out the answer as £30 Which one is correct?

  3. Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? Pupil B is correct. But why? What has pupil A done wrong? Pupil A has made the mistake of increasing £21 by 30% to undo the decrease of 30% from the original price. The problem with this is the 30% taken off the original price was not 30% of £21 but 30% of whatever the original price was.

  4. 0.7 x original price = £21 Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? This problem can be made much simpler if we think of it as multipliers. This is still a percentage decrease problem (why?), what multiplier should we use? How can we work out the original price from this?

  5. Reverse Percentage Problems example 1– a shop has a sale with 30% off everything. A jumper costs £21 in the sale. How much did it cost before the sale? This problem can be made much simpler if we think of it as multipliers. This is still a percentage decrease problem (why?), what multiplier should we use? 0.7 x original price = £21 ÷ original price = £30

  6. Reverse Percentage Problems Whenever you are returning to an original value in a percentage problem you must remember to divide by the multiplier! • example 2 – find the missing values in each of these. • 35% of N is 24.5 • increase M by 12% and you get 100.8 • decrease P by 45% and you get 44 N=24.5 ÷ 0.35 = 70 M=100.8 ÷ 1.12 = 90 P=44 ÷ 0.55 = 80

  7. Reverse Percentage Problems • Your turn. On your worksheet use straight lines to join question numbers to their answers • Some lines go over others • All lines are either vertical or horizontal

  8. Reverse Percentage Problems 100. 984 after a 23% increase 984 ÷ 1.23 = 800 so join 100 to 800

  9. Reverse Percentage Problems 800. 5% is 16 16 ÷ 0.05 = 320 Join 800 to 320

  10. Reverse Percentage Problems 320 is a dead end Choose another question number (bold numbers are good starting points) Keep going until the maze is complete

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