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

2. 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?

3. 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.

4. 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 ?
€ =
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?
New Value = Original Value x Multiplier
0.7 x ?
€ =
€21
÷ 0.7
= ?
original value= €30

6. 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

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

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

9. Classwork/Homework worksheet