4.3 Fractions of amounts
Fractions of amounts can be found by using your division and multiplication skills. To work out a fraction of any amount you first divide your amount by the number on the bottom of the fraction – the denominator. This gives you 1 part.
You then multiply that answer by the number on the top of the fraction – the numerator.
It is worth noting here that if the number on the top of the fraction is 1, multiplying the answer will not change it so there is no need for this step. Take a look at the examples below.
Example: Divide by the denominator
Method
To find of 90 we do 90 ÷ 5 = 18.
Since the number on the top of our fraction is 1, we do not need to multiply 18 by 1 as it will not change the answer.
So of 90 = 18.
Example: Multiply by the numerator
Method
To find of 42 we do 42 ÷ 7 = 6.
This means that of 42 = 6.
Since you want of 42, we then do 6 × 4 = 24.
So of 42 = 24.
Let’s go back to the jacket that used to cost £80 but is now in the sale with 2/5 off. How do you find out how much it costs? Firstly, you need to find 2/5 of 80. To calculate this you do:
- £80 ÷ 5 = £16 and then £16 × 2 = £32
This means that you save £32 on the price of the jacket. To find out how much you pay you then need to do £80 − £32 = £48.
Activity 8: Comparing fractions of amounts
You are looking to buy house insurance and want to get the best deal. Put the following offers in order, from cheapest to most expensive, after the discount has been applied.
| Company A | Company B | Company C |
|---|---|---|
£120 per year | £147 per year | £104 per year |
Special Offer: 1/3 off!
| Special Offer: 2/7 off!
| Special Offer: 1/4 off!
|
Answer
Company C is cheapest:
- 1/4 of £104 = £104 ÷ 4 = £26 discount
- £104 − £26 = £78
Company A is second cheapest:
- 1/3 of £120 = £120 ÷ 3 = £40 discount
- £120 − £40 = £80
Company B is most expensive:
- 2/7 of £147 = £147 ÷ 7 × 2 = £42 discount
- £147 − £42 = £105
Discounts and special offers are not always advertised using fractions. Sometimes, you will see adverts with 10% off or 15% off. Another common area where we see percentages in everyday life would be when companies apply VAT at 20% to items or when a restaurant adds a 12.5% service charge. The next section looks at what percentages are, and how to calculate them.
Summary
In this section you have:
- learned how to express a quantity of an amount in the form of a fraction
- learned how to, and practised, simplifying fractions
- revised your knowledge on finding basic fractions of amounts and progressed to finding more complex fractions of amounts.