Non-unitary fractions of amounts
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
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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 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.