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11+ Fractions of Amounts: Questions and Worked Answers
Learn to find fractions of amounts, calculate what remains and work backwards to the whole, with three examples and six original practice questions.
Finding a fraction of an amount means splitting the whole into equal parts and choosing some of those parts. For example, three fifths of a collection means that the collection has been divided into five equal groups and you want three groups.
This lesson moves from finding a part to finding what remains and working backwards. Suggested difficulty: foundation to intermediate, with a final stretch question. These are editorial estimates, not an exam-board grading. You should already be comfortable with multiplication and division. Try the questions without a calculator, keeping your working on paper.
The examples and practice questions are original learning resources, not official past-paper questions. Check your target school’s current exam information before treating any topic list as its syllabus.
What do the numerator and denominator tell you?
In 3/5, the denominator is 5: it tells you how many equal parts make the whole. The numerator is 3: it tells you how many of those parts you need. The fraction describes the relationship between the selected part and the whole; it is not the number of objects by itself.
Imagine 35 counters arranged in five equal groups. Each group contains seven counters. Three groups contain 21 counters. Drawing five equal boxes and writing seven in each is a useful way to see why the calculation works.
The method: find one part, then the required parts
To find a/b of an amount, divide the amount by b, then multiply by a. Finding one part first keeps the numbers manageable. Write the units beside your final answer: a fraction of a length is a length, while a fraction of a group of children is a number of children.
You can also multiply first and divide afterwards, but an intermediate calculation may be larger. Choose an order you can carry out accurately. When the fraction is less than one, your answer should be less than the original positive amount. This quick estimate catches many slips.
Does the question ask for the part or the remainder?
Words such as left, remaining and unused tell you to take another step. If 2/7 of some money is spent, 5/7 remains. You can find the money spent and subtract it from the total, or calculate 5/7 directly. Both methods should give the same answer.
Keep track of the whole. Half of the remaining money is not necessarily half of the original money. For a problem with several stages, write down the new amount after each stage before calculating its next fraction.
Working backwards from a fraction
If you know that 3/8 of a collection is 27, the 27 belongs to three parts, not eight. Divide 27 by 3 to get one part, then multiply by 8 to rebuild the whole. You are reversing the forward calculation.
After finding the whole, use the original fraction on your answer. If it does not reproduce the amount given in the question, inspect which number of parts you divided by.
How to use the practice
Attempt all six questions before opening the answers. Questions 1 and 2 practise direct calculations; 3 asks for a remainder; 4 reverses the method; 5 compares amounts; and 6 changes the whole halfway through.
For each mistake, decide whether you misunderstood the fraction, chose the wrong whole or made an arithmetic slip. Explain the corrected method aloud, then try a similar calculation with different numbers. One small practice set cannot establish exam readiness.
Worked examples
Example 1: Find 3/7 of 84.
- Seven equal parts make 84, so one part is 84 ÷ 7 = 12.
- Three parts are 12 × 3 = 36.
- Check: 3/7 is less than a half, and 36 is less than half of 84.
Answer: 36
Example 2: A ribbon is 96 cm long. Maya uses 5/8 of it. How much ribbon remains?
- One eighth is 96 ÷ 8 = 12 cm.
- Five eighths is 12 × 5 = 60 cm, so Maya uses 60 cm.
- Subtract the used length: 96 − 60 = 36 cm.
- Alternative: the remaining 3/8 is 12 × 3 = 36 cm.
Answer: 36 cm
Example 3: Three fifths of a box of pencils is 42 pencils. How many pencils are in the full box?
- The 42 pencils represent three equal parts.
- One part is 42 ÷ 3 = 14 pencils.
- The whole has five parts: 14 × 5 = 70 pencils.
- Check: 70 ÷ 5 × 3 = 42.
Answer: 70 pencils
Common mistakes to avoid
- Dividing by the numerator when finding a fraction of a known whole. First divide by the denominator to find one equal part.
- Stopping after finding one part. A numerator greater than one means you need several parts.
- Giving the amount used when the question asks how much remains. Reread the final sentence.
- Using the original whole after the question says “of the remainder”. Write down the remainder first.
- Assuming every fraction must make an amount smaller. That check applies to positive fractions less than one; an improper fraction can make it larger.
Try it yourself
Write down your working before opening each answer. If you make a mistake, check the explanation and try the question again.
1. Find 2/9 of 72.
Show answer and explanation for question 1
Answer: 16
One ninth is 72 ÷ 9 = 8. Two ninths is 8 × 2 = 16.
2. Find 7/10 of £130.
Show answer and explanation for question 2
Answer: £91
One tenth is £13. Seven tenths is 7 × £13 = £91. Keep the pounds unit.
3. A tray holds 56 seedlings. A gardener plants 3/8 of them. How many are still on the tray?
Show answer and explanation for question 3
Answer: 35 seedlings
One eighth is 7, so 3/8 is 21 seedlings planted. The remaining number is 56 − 21 = 35. Alternatively, calculate the remaining 5/8.
4. Four sevenths of a number is 36. What is the number?
Show answer and explanation for question 4
Answer: 63
Four parts equal 36, so one part is 36 ÷ 4 = 9. Seven parts equal 9 × 7 = 63.
5. Which is greater: 3/4 of 44 or 5/6 of 42? By how much?
Show answer and explanation for question 5
Answer: 5/6 of 42 is greater by 2.
44 ÷ 4 × 3 = 33. Separately, 42 ÷ 6 × 5 = 35. Compare the amounts, not just the fractions: 35 − 33 = 2.
6. Stretch: A club has 90 stickers. It gives away 2/5 of them, then uses 1/3 of the remaining stickers on posters. How many stickers are left?
Show answer and explanation for question 6
Answer: 36 stickers
First it gives away 90 ÷ 5 × 2 = 36, leaving 54. It then uses 54 ÷ 3 = 18, leaving 54 − 18 = 36. The second fraction acts on 54, not 90.
Sources and context
The questions and worked examples on this page are original practice material, not official past-paper questions. Exam requirements vary by school and entry year.