Must Find: Original Value

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Presentation transcript:

Must Find: Original Value Lesson Objective Given: Percentage and New Value Must Find: Original Value Also called: REVERSE PERCENTAGES!

Reverse Percentage Example 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 Who is correct?

Reverse Percentage Problems 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% ! 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.

Reverse Percentage Problems 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 use formula!! New Value = Original Value x Multiplier 0.7 x ? €21 = How can we work out the original price from this?

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? New Value = Original Value x Multiplier 0.7 x ? €21 = €21 ÷ 0.7 = ? original value= €30

Reverse Percentage Problems Whenever you are returning to an original value divide the new value by the multiplier! Find the original values in each of these increase M by 12% and you get 100.8 decrease P by 45% and you get 44

Increase M by 12% and you get 100.8 New Value = 100.8 Multiplier = 100 + 12 = 112%  1.12 New Value = Original Value x Multiplier 100.8 = M x 1.12 100.8 ÷ 1.12 = M M = 90

Decrease P by 45% and you get 44 New Value = 44 Multiplier = 100 - 45 = 55%  0.55 New Value = Original Value x Multiplier 44 = P x 0.55 44 ÷ 0.55 = P P = 80

Classwork/Homework worksheet