Year 10 Foundation · Work with fractions
Find a fraction of an amount
Learn how to find and change amounts by a fraction, work back to the whole, swap between mixed numbers and improper fractions, and add, subtract, multiply and divide fractions to solve problems.
Definition
A fraction describes equal parts of a whole: the denominator says how many equal parts the whole is split into, and the numerator says how many of those parts you have. At GCSE you calculate with fractions directly: taking a fraction of an amount, adjusting an amount up or down, working back from a part to the whole, and doing arithmetic with the fractions themselves. The idea underneath all of it is the size of one part: divide by the denominator and you know what one part is worth.
Why Do I Have to Learn This?
Fractions describe parts of a whole, like half a pizza or a quarter of an hour. They are everywhere in cooking, telling the time and sharing fairly.
Key Rules:
- 1. To find a fraction of an amount, divide by the denominator and multiply by the numerator: 35 of 40 is 40 ÷ 5 = 8, then 8 x 3 = 24.
Remember:
- •Divide by the bottom, times by the top; match the denominators before adding or subtracting; flip the second fraction to divide.
Don’t Forget...
- •Adding numerators and denominators straight across: 12 + 13 = 25. Halves and thirds are parts of different sizes, so their counts cannot be added directly; rewritten as sixths, 36 + 26 = 56, and 25 is smaller than the 12 you started with.
- •Dividing by the numerator instead of the denominator when finding a fraction of an amount. The denominator is the number of equal parts, so it is the number you divide by: 35 of 40 starts with 40 ÷ 5 = 8, not 40 ÷ 3.
- •Taking the fraction of the given amount when asked to work back to the whole. If 23 of a number is 18, then 18 already represents two parts: one part is 18 ÷ 2 = 9 and the whole is 9 x 3 = 27, whereas 23 of 18 gives 12, which is smaller than the number you started with.
Denominator
The bottom number of a fraction: how many equal parts the whole is split into.
In 34 the denominator is 4.
Worked Example:
A jacket costs £60. In a sale the price is reduced by 14. Work out the sale price.
Find 14 of £60: divide by the denominator, 60 ÷ 4 = 15.
The numerator is 1, so there is nothing more to multiply: the reduction is £15.
Decrease the original amount by the reduction: 60 - 15 = 45.
Answer: £45
Why It Works:
Dividing an amount by the denominator splits it into that many equal parts, so the result is the value of one part, and multiplying by the numerator counts the parts you want; working back to the whole runs the same two steps in reverse. A common denominator is needed before adding because only parts of the same size can be counted together, and rewriting a fraction by multiplying top and bottom by the same number leaves its value unchanged. Dividing by a fraction asks how many of it fit into the first, and flipping the second fraction turns that question into a multiplication with the same answer.
Another Example:
Work out 23 + 34, giving your answer as a mixed number.
The denominators 3 and 4 are different, so rewrite both fractions over 12, their lowest common denominator.
23 = 812 and 34 = 912, multiplying top and bottom of each by the same number.
Add the numerators: 812 + 912 = 1712.
1712 is more than one whole: 1212 makes 1, leaving 512.
Answer: 1 and 512
Animated Example:
Free Find a fraction of an amount Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Before this: Fractions (Year 9)
Let’s Practise the Concept
Step 1 of 3
Put the fraction on the line
Tap where 2/5 belongs between 0 and 1.
Tap the line where 2/5 belongs.