Finding a Fraction of a Number
Three quarters of 20. Two fifths of 45. Two steps, always in the same order, and the picture makes the order obvious.
The picture
Suppose there are 20 counters and you want three quarters of them.
Quarters means four equal groups. So share the 20 counters into 4 groups, then take 3 of those groups.
That is the whole method, drawn out. The bottom number told you how many groups to make. The top number told you how many groups to take.
Divide then multiply
The rule
Divide by the bottom number. Multiply by the top number.
For 34 of 20: 20 ÷ 4 = 5, then 5 × 3 = 15.
Read the fraction from the bottom up and the steps come out in the right order every time. Cut into 4, take 3.
Why that order
You can multiply first and divide second, and you will get the same answer. 20 × 3 = 60, then 60 ÷ 4 = 15. Both routes are correct.
Dividing first is better for two reasons. The numbers stay small, so mental arithmetic is realistic. And it matches the picture, so a child who forgets the rule can rebuild it by drawing groups.
When dividing first does not work neatly
For 23 of 10, dividing first gives 10 ÷ 3, which is not a whole number. Multiply first instead: 10 × 2 = 20, then 20 ÷ 3, which is 203 or 6 and two thirds. Same answer, less mess.
Worked examples
A unit fraction
- The bottom number is 5, so share 45 into 5 equal groups.
- 45 ÷ 5 = 9, so each group has 9.
- The top number is 1, so take just one group.
- Multiplying by 1 changes nothing, so the answer is 9.
More than one part
- Same first step. 45 ÷ 5 = 9 in each group.
- This time the top number is 2, so take two groups.
- 9 × 2 = 18.
- Sense check: two fifths is a bit less than half, and 18 is a bit less than half of 45. Good.
A money question
- First find the discount. 60 ÷ 3 = 20, so a third of 60 is 20 dollars off.
- The question asks for the new price, not the discount, so keep going.
- 60 − 20 = 40.
- Faster route: taking a third off leaves two thirds. 20 × 2 = 40 gets there in one step.
Where this shows up
This is one of the few school topics a child will genuinely use, so it is worth naming the situations out loud.
- Sales. A third off, a quarter off, half price.
- Recipes. Making three quarters of a recipe that serves 8.
- Sharing. Splitting a bill or a bag of sweets unevenly but fairly.
- Percentages later on. 25 percent is just 14, and 75 percent is 34. A child solid on this topic finds percentages easy.
Common mistakes
1. Dividing by the top number
For 34 of 20, working out 20 ÷ 3. The bottom number is the one that does the sharing, because it says how many equal groups the whole is cut into. Read the fraction from the bottom up.
2. Stopping after the division
Working out 20 ÷ 4 = 5 and writing 5 as the answer to "three quarters of 20". That is one quarter. The second step is not optional unless the top number is 1.
3. Answering the wrong question in word problems
Finding the discount when the question asked for the sale price. Read the last line of the question again before writing the answer. This costs more marks in tests than any arithmetic slip.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
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For parents
Practise this one in shops rather than on paper. Point at a sign that says a third off and ask what the new price is. Real prices, real stakes, and the child gets instant feedback at the till. Ten of those beat a page of exercises.
What to learn next
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