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11+ Fractions Questions & Answers

Fractions turn up all over 11+ Maths papers, both on their own and hidden inside word problems. Here are ten exam-style questions with worked answers that show the quickest reliable method for each.

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What fractions questions come up in the 11+?

Expect four main types: finding a fraction of an amount, spotting equivalent fractions and simplifying, adding or subtracting fractions with different denominators, and ordering or comparing fractions. Harder papers mix these into word problems, for example working out what is left after two steps.

One idea unlocks most of them: to compare, add or subtract fractions, first make the bottom numbers (the denominators) the same.

Try the 10 questions below. Tap a question to reveal the worked answer.

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1. What is 5/8 of 72?
  • A) 40
  • B) 45
  • C) 48
  • D) 54
Answer: B) 45. Divide by the bottom number to find one eighth: 72 ÷ 8 = 9. Then multiply by the top number: 9 × 5 = 45. 'Divide by the bottom, times by the top' works for a fraction of any amount.
2. Which fraction is equivalent to 3/4?
  • A) 6/9
  • B) 9/12
  • C) 12/15
  • D) 8/10
Answer: B) 9/12. Multiplying the top and bottom by the same number doesn't change a fraction's value. 3 × 3 = 9 and 4 × 3 = 12, so 3/4 = 9/12. Simplifying the others shows they're different: 6/9 = 2/3, 12/15 = 4/5 and 8/10 = 4/5.
3. Work out 2/3 + 1/4.
  • A) 3/7
  • B) 11/12
  • C) 3/12
  • D) 5/6
Answer: B) 11/12. You can't add fractions until the denominators match. The smallest number both 3 and 4 go into is 12, so 2/3 = 8/12 and 1/4 = 3/12. Now add the tops: 8 + 3 = 11, giving 11/12. The answer 3/7 comes from adding the tops and the bottoms, which is a very common mistake.
4. Which of these fractions is the largest?
  • A) 3/5
  • B) 5/8
  • C) 7/10
  • D) 2/3
Answer: C) 7/10. Change each one into a decimal so they can be compared fairly: 3/5 = 0.6, 5/8 = 0.625, 7/10 = 0.7 and 2/3 is about 0.667. The largest is 0.7, which is 7/10.
5. Write 20/32 in its simplest form.
  • A) 5/16
  • B) 5/8
  • C) 4/6
  • D) 2/3
Answer: B) 5/8. Find the highest common factor of 20 and 32, which is 4. Divide the top AND the bottom by it: 20 ÷ 4 = 5 and 32 ÷ 4 = 8, giving 5/8. Always divide both numbers by the same amount; 5/16 comes from dividing the top by 4 but the bottom only by 2.
6. Sam has £36. He spends 1/4 of it on a book, then spends 1/3 of the money he has left on lunch. How much money does he have left now?
  • A) £12
  • B) £15
  • C) £18
  • D) £21
Answer: C) £18. Work in two steps and read carefully: the second fraction is of the money LEFT, not of the original £36. A quarter of £36 is £9, which leaves £27. A third of £27 is £9, which leaves £27 − £9 = £18.
7. A class has 30 children. 2/5 of them walk to school. How many children do not walk to school?
  • A) 12
  • B) 15
  • C) 18
  • D) 20
Answer: C) 18. First find how many walk: 30 ÷ 5 = 6, and 6 × 2 = 12. The question asks how many do NOT walk, so subtract: 30 − 12 = 18. You could also spot that 3/5 don't walk: 6 × 3 = 18.
8. Work out 3/4 − 1/6.
  • A) 2/10
  • B) 7/12
  • C) 1/2
  • D) 5/12
Answer: B) 7/12. Make the denominators the same first. 12 is the smallest number that both 4 and 6 divide into, so 3/4 = 9/12 and 1/6 = 2/12. Subtract the tops: 9 − 2 = 7, so the answer is 7/12.
9. If 3/5 of a number is 24, what is the number?
  • A) 14.4
  • B) 35
  • C) 40
  • D) 45
Answer: C) 40. If three fifths make 24, one fifth is 24 ÷ 3 = 8. The whole number is five fifths, so it is 8 × 5 = 40. Check it: 3/5 of 40 is 40 ÷ 5 × 3 = 24.
10. Write 17/5 as a mixed number.
  • A) 3 2/5
  • B) 2 3/5
  • C) 3 1/5
  • D) 4 2/5
Answer: A) 3 2/5. Divide the top by the bottom: 17 ÷ 5 = 3 remainder 2. That's 3 whole ones with 2 fifths left over, so 17/5 = 3 2/5.

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