Fractions of quantities

The idea

A fraction of a quantity is a part of a whole amount, such as part of a length, a sum of money or a group of objects. The denominator, the bottom number of the fraction, shows how many equal parts the whole is split into. The numerator, the top number, shows how many of those parts you take.

There is a simple two-step method that works every time. First, divide the quantity by the denominator. This gives you the size of just one equal part. Next, multiply that answer by the numerator, to build up the number of parts you need.

If the numerator is 1, you only need the first step. Before you start, check that the quantity divides neatly by the denominator — in most questions it will, and that is a helpful sign that you have chosen the right numbers.

Worked example

Find 3/4 of 28.

1. Divide by the denominator to find one part: 28 ÷ 4 = 7.
2. Multiply by the numerator to take three parts: 7 × 3 = 21.
3. So 3/4 of 28 is 21.

Answer: 21

Watch out

• Dividing by the numerator instead of the denominator — always divide by the bottom number first.
• Stopping after the dividing step when the numerator is bigger than 1 — you still need to multiply.
• Trying to multiply first and divide second with awkward numbers — dividing first keeps the numbers small and tidy.