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# Non-unitary fractions of amounts
- URL: https://www.esheets.io/non-unitary-fractions-of-amounts/
- Published: 2026-04-05T15:54:10.000Z
- Updated: 2026-07-09T18:51:33.000Z
- Author: Richard Linnington
- Tags: Maths, Number

Non-unitary fractions of amounts help us find several equal parts of a quantity, such as three quarters of 20 or five sixths of 18\. This is useful in everyday life when working out portions, discounts, recipes, and shared amounts. [Jump to the questions](#practise-now)

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## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise non-unitary fractions of amounts with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Dividing the amount by the denominator.
- Multiplying by the numerator.
- Finding more than one equal part of the whole.
- Checking the answer is a sensible fraction of the amount.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

## Topic guide

### What this worksheet practises

This worksheet focuses on finding non-unitary fractions of amounts (fractions where the top number is greater than 1, like 3/4 or 2/5). This is a vital everyday skill for calculating discounts, sharing money, or adjusting recipes.

### Key method

The golden rule for finding a fraction of an amount is: **Divide by the bottom, multiply by the top.**

- Look at the denominator (the bottom number) of the fraction. This tells you how many pieces the whole amount is being chopped into. Divide your amount by this number.
- This first calculation gives you the value of just *one* slice (a unitary fraction).
- Now look at the numerator (the top number). This tells you how many of those slices you actually need.
- Multiply your "one slice" answer by the top number to find the final total.

### Worked example

**Find 3/5 of £40.**

Step 1: Divide by the bottom number (5) to find the value of one fifth.

40 ÷ 5 = 8.

So, 1/5 of the money is £8.

Step 2: Multiply by the top number (3) because we want three fifths.

8 × 3 = 24.

The final answer is £24.

### Common mistakes to avoid

The most common mistake is performing the operations backwards: multiplying the amount by the bottom number and dividing by the top. This results in mathematically nonsensical answers. Always remember the logical process: chop it up first (divide), then collect the pieces you need (multiply).

### Things to remember

If you are finding a proper fraction (like 3/4) of a number, your final answer must always be smaller than the number you started with. If you calculate 3/4 of 40 and your answer is larger than 40, you have definitely done the operations in reverse.