Fractions of quantities

The idea

Finding a fraction of a quantity means sharing that quantity into equal parts and taking some of them. The denominator (the bottom number) tells you how many equal parts to share into. The numerator (the top number) tells you how many of those parts to take.

The reliable method has two steps. First divide the quantity by the denominator to find the size of one part. Then multiply that result by the numerator to find the size of the parts you need. If the numerator is 1, the first step alone is the answer.

Some questions add a second step. You might be asked what is left after a fraction has been used, spent or eaten. Work out the fraction first, then subtract it from the starting quantity. Read the question carefully to see whether it wants the part you found, or the part that remains.

Worked example

Find 5/6 of 42.

1. Divide by the denominator to find one part: 42 ÷ 6 = 7.
2. Multiply by the numerator to take five parts: 7 × 5 = 35.
3. So 5/6 of 42 is 35.

Answer: 35

Watch out

• Dividing by the numerator and multiplying by the denominator — the order matters: divide by the bottom number first.
• Forgetting the second step in remainder questions — after finding the fraction, subtract it if the question asks what is left.
• Multiplying the quantity by both numbers without dividing — always share into equal parts first.