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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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.