1. Solving Reverse Fraction Problems
Mathematics
Solving Reverse Fraction Problems

2. Lesson Objectives The aim of this powerpoint is to help you…
to find the original value when you have been given the increased or decreased value
to revise dividing by fractions

3. Reversing Fractional Changes
You MUST use ‘method 2’ of fractional change
Writing this method as a formula we have…
New fraction × Original quantity = Changed Quantity
To work backwards to find the original quantity we must do the opposite…
Changed Quantity ÷ New fraction = Original quantity
You will need to remember the method for dividing by fractions!

4. Example 1
In a sale, all the prices are marked down by 3 10 If the sale price of some jeans is £56, what was their original price? 1 – 3 10  £56 ÷ 7 10 
× original = £56
56 1 × =
56×10
1×7
560 7 = 
560 ÷ 7 =
£80

5. Reversing Fractional Changes
Watch out for the increase or decrease being quoted rather than the new value.
Writing this as a formula we have…
Fraction × Original quantity = Increase or decrease
To work backwards to find the original quantity we must do the opposite…
Increase or Decrease ÷ Fraction = Original quantity
You will still need to remember the method for dividing by fractions!

6. Example 2
Rosemary’s weekly wage increases by 2 5 This equates to an increase of £40. What did she originally earn each week? 2 5 × original = £40 £40 ÷ 2 5 
40 1 × =
40×5
1×2
200 2 = 
200 ÷ 2 =
£100

7. Quick Practice A Increase 36 by 4 9 B Decrease 50 by 3 10
C A hat usually costs £36.99.
In a sale a third is knocked off the price.
What is the dale price of the hat?
D Sarah earns £7.50 per hour.
If this increases by 2 5 , what is her new hourly
rate of pay?
Work out your answers before clicking on to the next slide.

8. Answers A 4 9 of 36 = B 1 – 3 10  C 1 – 1 3  D 1 + 2 5 
(36 ÷ 9) x 4 = 16 
= 52
Using Method 1
Using Method 2…
of 50 =
(50 ÷ 10) x 7 = 35
2 3 of =
(36.99 ÷ 3) x 2 =
£24.66
7 5 of =
(7.5 ÷ 5) x 7 =
£10.50

9. What next?
Print out the notes called Frac10. Read them and make sure you answer any questions
If you need more practice, try the worksheet called RevFrac-S1.xlsx.
You have now completed all the work in the Fractions Module, though you will come across FDP conversions in the Percentages module.
Please attempt the Fractions Assessment.