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Divide by the bottom, multiply by the top — and the same in reverse.
Question 1 of 12
Niamh has given away 4/5 of her marbles, which is 40 of them. How many marbles did she have to start with?
This works backwards from the part to the whole. If 40 is 4/5, then 1/5 is 40 ÷ 4 = 10. The whole is 5 of those: 10 × 5 = 50. Checking forwards: 4/5 of 50 is 40, which is what the question said. Multiplying 40 by 5 straight away gives 200 and skips the step that matters. Find one part first. Getting to the unit fraction is the move that makes every reverse question work.
The answer is C. This works backwards from the part to the whole. If 40 is 4/5, then 1/5 is 40 ÷ 4 = 10. The whole is 5 of those: 10 × 5 = 50. Checking forwards: 4/5 of 50 is 40, which is what the question said. Multiplying 40 by 5 straight away gives 200 and skips the step that matters. Find one part first. Getting to the unit fraction is the move that makes every reverse question work.
Martha has given away 2/3 of her beads, which is 42 of them. How many beads did she have to start with?
This works backwards from the part to the whole. If 42 is 2/3, then 1/3 is 42 ÷ 2 = 21. The whole is 3 of those: 21 × 3 = 63. Checking forwards: 2/3 of 63 is 42, which is what the question said. Multiplying 42 by 3 straight away gives 126 and skips the step that matters. Always check by going forwards again. A reverse question that does not check out has gone wrong somewhere.
The answer is D. This works backwards from the part to the whole. If 42 is 2/3, then 1/3 is 42 ÷ 2 = 21. The whole is 3 of those: 21 × 3 = 63. Checking forwards: 2/3 of 63 is 42, which is what the question said. Multiplying 42 by 3 straight away gives 126 and skips the step that matters. Always check by going forwards again. A reverse question that does not check out has gone wrong somewhere.
Omar has given away 1/5 of her marbles, which is 29 of them. How many marbles did she have to start with?
This works backwards from the part to the whole. If 29 is 1/5, then 1/5 is 29 ÷ 1 = 29. The whole is 5 of those: 29 × 5 = 145. Checking forwards: 1/5 of 145 is 29, which is what the question said. Multiplying 29 by 5 straight away gives 145 and skips the step that matters. The answer must be bigger than the part you were given, since the part is only a fraction of it.
The answer is B. This works backwards from the part to the whole. If 29 is 1/5, then 1/5 is 29 ÷ 1 = 29. The whole is 5 of those: 29 × 5 = 145. Checking forwards: 1/5 of 145 is 29, which is what the question said. Multiplying 29 by 5 straight away gives 145 and skips the step that matters. The answer must be bigger than the part you were given, since the part is only a fraction of it.
Jack has given away 5/8 of her marbles, which is 70 of them. How many marbles did she have to start with?
This works backwards from the part to the whole. If 70 is 5/8, then 1/8 is 70 ÷ 5 = 14. The whole is 8 of those: 14 × 8 = 112. Checking forwards: 5/8 of 112 is 70, which is what the question said. Multiplying 70 by 8 straight away gives 560 and skips the step that matters. The answer must be bigger than the part you were given, since the part is only a fraction of it.
The answer is C. This works backwards from the part to the whole. If 70 is 5/8, then 1/8 is 70 ÷ 5 = 14. The whole is 8 of those: 14 × 8 = 112. Checking forwards: 5/8 of 112 is 70, which is what the question said. Multiplying 70 by 8 straight away gives 560 and skips the step that matters. The answer must be bigger than the part you were given, since the part is only a fraction of it.
What is 1/5 of 100?
Divide by the bottom, then multiply by the top. 100 ÷ 5 = 20, which is 1/5 of the amount. 1 of those is 20 × 1 = 20. Stopping after the division is the commonest slip: 20 would be the answer if the question had asked for 1/5. Bottom first, then top. Dividing before multiplying keeps the numbers small enough to do in your head.
The answer is B. Divide by the bottom, then multiply by the top. 100 ÷ 5 = 20, which is 1/5 of the amount. 1 of those is 20 × 1 = 20. Stopping after the division is the commonest slip: 20 would be the answer if the question had asked for 1/5. Bottom first, then top. Dividing before multiplying keeps the numbers small enough to do in your head.
Rosie has given away 1/8 of her conkers, which is 7 of them. How many conkers did she have to start with?
This works backwards from the part to the whole. If 7 is 1/8, then 1/8 is 7 ÷ 1 = 7. The whole is 8 of those: 7 × 8 = 56. Checking forwards: 1/8 of 56 is 7, which is what the question said. Multiplying 7 by 8 straight away gives 56 and skips the step that matters. Always check by going forwards again. A reverse question that does not check out has gone wrong somewhere.
The answer is C. This works backwards from the part to the whole. If 7 is 1/8, then 1/8 is 7 ÷ 1 = 7. The whole is 8 of those: 7 × 8 = 56. Checking forwards: 1/8 of 56 is 7, which is what the question said. Multiplying 7 by 8 straight away gives 56 and skips the step that matters. Always check by going forwards again. A reverse question that does not check out has gone wrong somewhere.
Alfie has given away 3/4 of her stickers, which is 21 of them. How many stickers did she have to start with?
This works backwards from the part to the whole. If 21 is 3/4, then 1/4 is 21 ÷ 3 = 7. The whole is 4 of those: 7 × 4 = 28. Checking forwards: 3/4 of 28 is 21, which is what the question said. Multiplying 21 by 4 straight away gives 84 and skips the step that matters. Find one part first. Getting to the unit fraction is the move that makes every reverse question work.
The answer is D. This works backwards from the part to the whole. If 21 is 3/4, then 1/4 is 21 ÷ 3 = 7. The whole is 4 of those: 7 × 4 = 28. Checking forwards: 3/4 of 28 is 21, which is what the question said. Multiplying 21 by 4 straight away gives 84 and skips the step that matters. Find one part first. Getting to the unit fraction is the move that makes every reverse question work.
What is 1/5 of 225?
Divide by the bottom, then multiply by the top. 225 ÷ 5 = 45, which is 1/5 of the amount. 1 of those is 45 × 1 = 45. Stopping after the division is the commonest slip: 45 would be the answer if the question had asked for 1/5. Check the size: more than half the fraction should give more than half the amount.
The answer is D. Divide by the bottom, then multiply by the top. 225 ÷ 5 = 45, which is 1/5 of the amount. 1 of those is 45 × 1 = 45. Stopping after the division is the commonest slip: 45 would be the answer if the question had asked for 1/5. Check the size: more than half the fraction should give more than half the amount.
Sophie has given away 3/4 of her trading cards, which is 27 of them. How many trading cards did she have to start with?
This works backwards from the part to the whole. If 27 is 3/4, then 1/4 is 27 ÷ 3 = 9. The whole is 4 of those: 9 × 4 = 36. Checking forwards: 3/4 of 36 is 27, which is what the question said. Multiplying 27 by 4 straight away gives 108 and skips the step that matters. The answer must be bigger than the part you were given, since the part is only a fraction of it.
The answer is B. This works backwards from the part to the whole. If 27 is 3/4, then 1/4 is 27 ÷ 3 = 9. The whole is 4 of those: 9 × 4 = 36. Checking forwards: 3/4 of 36 is 27, which is what the question said. Multiplying 27 by 4 straight away gives 108 and skips the step that matters. The answer must be bigger than the part you were given, since the part is only a fraction of it.
Rosie has given away 3/8 of her beads, which is 66 of them. How many beads did she have to start with?
This works backwards from the part to the whole. If 66 is 3/8, then 1/8 is 66 ÷ 3 = 22. The whole is 8 of those: 22 × 8 = 176. Checking forwards: 3/8 of 176 is 66, which is what the question said. Multiplying 66 by 8 straight away gives 528 and skips the step that matters. Find one part first. Getting to the unit fraction is the move that makes every reverse question work.
The answer is D. This works backwards from the part to the whole. If 66 is 3/8, then 1/8 is 66 ÷ 3 = 22. The whole is 8 of those: 22 × 8 = 176. Checking forwards: 3/8 of 176 is 66, which is what the question said. Multiplying 66 by 8 straight away gives 528 and skips the step that matters. Find one part first. Getting to the unit fraction is the move that makes every reverse question work.
What is 2/5 of 220?
Divide by the bottom, then multiply by the top. 220 ÷ 5 = 44, which is 1/5 of the amount. 2 of those is 44 × 2 = 88. Stopping after the division is the commonest slip: 44 would be the answer if the question had asked for 1/5. Bottom first, then top. Dividing before multiplying keeps the numbers small enough to do in your head.
The answer is D. Divide by the bottom, then multiply by the top. 220 ÷ 5 = 44, which is 1/5 of the amount. 2 of those is 44 × 2 = 88. Stopping after the division is the commonest slip: 44 would be the answer if the question had asked for 1/5. Bottom first, then top. Dividing before multiplying keeps the numbers small enough to do in your head.
What is 2/3 of 120?
Divide by the bottom, then multiply by the top. 120 ÷ 3 = 40, which is 1/3 of the amount. 2 of those is 40 × 2 = 80. Stopping after the division is the commonest slip: 40 would be the answer if the question had asked for 1/3. Bottom first, then top. Dividing before multiplying keeps the numbers small enough to do in your head.
The answer is D. Divide by the bottom, then multiply by the top. 120 ÷ 3 = 40, which is 1/3 of the amount. 2 of those is 40 × 2 = 80. Stopping after the division is the commonest slip: 40 would be the answer if the question had asked for 1/3. Bottom first, then top. Dividing before multiplying keeps the numbers small enough to do in your head.
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