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Home / Practice / Maths
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.
What is 3/4 of 28?
Divide by the bottom, then multiply by the top. 28 ÷ 4 = 7, which is 1/4 of the amount. 3 of those is 7 × 3 = 21. Stopping after the division is the commonest slip: 7 would be the answer if the question had asked for 1/4. Check the size: more than half the fraction should give more than half the amount.
The answer is A. Divide by the bottom, then multiply by the top. 28 ÷ 4 = 7, which is 1/4 of the amount. 3 of those is 7 × 3 = 21. Stopping after the division is the commonest slip: 7 would be the answer if the question had asked for 1/4. Check the size: more than half the fraction should give more than half the amount.
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.
Rhys has given away 3/8 of her conkers, which is 75 of them. How many conkers did she have to start with?
This works backwards from the part to the whole. If 75 is 3/8, then 1/8 is 75 ÷ 3 = 25. The whole is 8 of those: 25 × 8 = 200. Checking forwards: 3/8 of 200 is 75, which is what the question said. Multiplying 75 by 8 straight away gives 600 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 75 is 3/8, then 1/8 is 75 ÷ 3 = 25. The whole is 8 of those: 25 × 8 = 200. Checking forwards: 3/8 of 200 is 75, which is what the question said. Multiplying 75 by 8 straight away gives 600 and skips the step that matters. Find one part first. Getting to the unit fraction is the move that makes every reverse question work.
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 7/10 of 230?
Divide by the bottom, then multiply by the top. 230 ÷ 10 = 23, which is 1/10 of the amount. 7 of those is 23 × 7 = 161. Stopping after the division is the commonest slip: 23 would be the answer if the question had asked for 1/10. The word "of" is an instruction to multiply, even when it does not look like one.
The answer is A. Divide by the bottom, then multiply by the top. 230 ÷ 10 = 23, which is 1/10 of the amount. 7 of those is 23 × 7 = 161. Stopping after the division is the commonest slip: 23 would be the answer if the question had asked for 1/10. The word "of" is an instruction to multiply, even when it does not look like one.
What is 2/5 of 105?
Divide by the bottom, then multiply by the top. 105 ÷ 5 = 21, which is 1/5 of the amount. 2 of those is 21 × 2 = 42. Stopping after the division is the commonest slip: 21 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. 105 ÷ 5 = 21, which is 1/5 of the amount. 2 of those is 21 × 2 = 42. Stopping after the division is the commonest slip: 21 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 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.
Oliver has given away 1/6 of her marbles, which is 8 of them. How many marbles did she have to start with?
This works backwards from the part to the whole. If 8 is 1/6, then 1/6 is 8 ÷ 1 = 8. The whole is 6 of those: 8 × 6 = 48. Checking forwards: 1/6 of 48 is 8, which is what the question said. Multiplying 8 by 6 straight away gives 48 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 A. This works backwards from the part to the whole. If 8 is 1/6, then 1/6 is 8 ÷ 1 = 8. The whole is 6 of those: 8 × 6 = 48. Checking forwards: 1/6 of 48 is 8, which is what the question said. Multiplying 8 by 6 straight away gives 48 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 5/8 of 264?
Divide by the bottom, then multiply by the top. 264 ÷ 8 = 33, which is 1/8 of the amount. 5 of those is 33 × 5 = 165. Stopping after the division is the commonest slip: 33 would be the answer if the question had asked for 1/8. 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. 264 ÷ 8 = 33, which is 1/8 of the amount. 5 of those is 33 × 5 = 165. Stopping after the division is the commonest slip: 33 would be the answer if the question had asked for 1/8. Bottom first, then top. Dividing before multiplying keeps the numbers small enough to do in your head.
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