Back to National 3

Topic

Fractions

Fractions show equal parts of a whole amount. They are useful for sharing, measuring, recipes, and comparing parts of a group.

Topic explanation

The bottom number of a fraction tells you how many equal parts the whole has been split into. The top number tells you how many of those parts you have.

To find 34 of 32, first divide 32 by 4 to find one quarter. One quarter is 8. Then multiply 8 by 3 to get 24.

Fractions can look different but have the same value. For example, 12, 24, and 48 are equivalent because they each show half of the whole.

Quick methods

Find a fraction of an amount
Divide by the bottom number, then multiply by the top number.
Simplify
Divide the top and bottom by the same number.
Equivalent fractions
Multiply or divide the top and bottom by the same number.
Same denominator
If the bottom numbers match, work with the top numbers.

Worked examples

Example 1

Find 14 of 28.

  1. The bottom number is 4, so split 28 into 4 equal parts.
  2. 28 divided by 4 = 7
  3. One of the four parts is 7.

So: 14 of 28 is 7

Example 2

Find 35 of 40.

  1. Divide by the bottom number first: 40 divided by 5 = 8
  2. That means 15 of 40 is 8.
  3. Multiply by the top number: 8 × 3 = 24

So: 35 of 40 is 24

Example 3

A recipe uses 34 of a 200 g bag of flour. How much flour is used?

  1. Find 14 first: 200 divided by 4 = 50 g.
  2. The recipe needs 3 quarters.
  3. 50 g × 3 = 150 g

So: The recipe uses 150 g of flour.

Practise this topicTake quiz