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Multiply straight across; divide by making the pieces smaller.
Question 1 of 12
Work out 4/7 × 11.
Multiplying by a whole number means taking that many of the fraction: 11 lots of 4/7. Only the top is multiplied — 4 × 11 = 44 — because the pieces do not change size, there are simply more of them. That gives 44/7, which is 6 2/7 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. Convert to a mixed number at the end if the top ends up larger than the bottom.
The answer is A. Multiplying by a whole number means taking that many of the fraction: 11 lots of 4/7. Only the top is multiplied — 4 × 11 = 44 — because the pieces do not change size, there are simply more of them. That gives 44/7, which is 6 2/7 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. Convert to a mixed number at the end if the top ends up larger than the bottom.
Work out 5/6 × 1/4. Give your answer in its simplest form.
Multiplying two fractions is the one case where you simply multiply straight across: 5 × 1 = 5 on the top, 6 × 4 = 24 on the bottom, giving 5/24. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 5/6 of 1/4 is this same calculation. Cancel before multiplying if you can. It keeps the numbers small and the simplifying is then already done.
The answer is C. Multiplying two fractions is the one case where you simply multiply straight across: 5 × 1 = 5 on the top, 6 × 4 = 24 on the bottom, giving 5/24. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 5/6 of 1/4 is this same calculation. Cancel before multiplying if you can. It keeps the numbers small and the simplifying is then already done.
Work out 1/4 ÷ 3.
Dividing by 3 means splitting 1/4 into 3 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 3, so the bottom is multiplied: 4 × 3 = 12, giving 1/12. Multiplying the top instead would make the answer bigger, which cannot be right for a division. Dividing by 2 is the same as halving, and halving a fraction is doubling its bottom. The same idea scales up.
The answer is D. Dividing by 3 means splitting 1/4 into 3 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 3, so the bottom is multiplied: 4 × 3 = 12, giving 1/12. Multiplying the top instead would make the answer bigger, which cannot be right for a division. Dividing by 2 is the same as halving, and halving a fraction is doubling its bottom. The same idea scales up.
Work out 4/5 × 5/8. Give your answer in its simplest form.
Multiplying two fractions is the one case where you simply multiply straight across: 4 × 5 = 20 on the top, 5 × 8 = 40 on the bottom, giving 20/40, which simplifies to 1/2. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 4/5 of 5/8 is this same calculation. Multiplying two fractions that are each less than one always gives something smaller than both. It is a good check.
The answer is B. Multiplying two fractions is the one case where you simply multiply straight across: 4 × 5 = 20 on the top, 5 × 8 = 40 on the bottom, giving 20/40, which simplifies to 1/2. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 4/5 of 5/8 is this same calculation. Multiplying two fractions that are each less than one always gives something smaller than both. It is a good check.
Work out 4/5 × 1/5. Give your answer in its simplest form.
Multiplying two fractions is the one case where you simply multiply straight across: 4 × 1 = 4 on the top, 5 × 5 = 25 on the bottom, giving 4/25. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 4/5 of 1/5 is this same calculation. Cancel before multiplying if you can. It keeps the numbers small and the simplifying is then already done.
The answer is B. Multiplying two fractions is the one case where you simply multiply straight across: 4 × 1 = 4 on the top, 5 × 5 = 25 on the bottom, giving 4/25. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 4/5 of 1/5 is this same calculation. Cancel before multiplying if you can. It keeps the numbers small and the simplifying is then already done.
Work out 1/8 × 9.
Multiplying by a whole number means taking that many of the fraction: 9 lots of 1/8. Only the top is multiplied — 1 × 9 = 9 — because the pieces do not change size, there are simply more of them. That gives 9/8, which is 1 1/8 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. Convert to a mixed number at the end if the top ends up larger than the bottom.
The answer is A. Multiplying by a whole number means taking that many of the fraction: 9 lots of 1/8. Only the top is multiplied — 1 × 9 = 9 — because the pieces do not change size, there are simply more of them. That gives 9/8, which is 1 1/8 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. Convert to a mixed number at the end if the top ends up larger than the bottom.
Work out 3/5 × 1/8. Give your answer in its simplest form.
Multiplying two fractions is the one case where you simply multiply straight across: 3 × 1 = 3 on the top, 5 × 8 = 40 on the bottom, giving 3/40. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 3/5 of 1/8 is this same calculation. "Of" means multiply. Half of a quarter is a half times a quarter.
The answer is A. Multiplying two fractions is the one case where you simply multiply straight across: 3 × 1 = 3 on the top, 5 × 8 = 40 on the bottom, giving 3/40. No common denominator is needed — that is only for adding and subtracting, and looking for one here wastes time. The word "of" means the same thing: 3/5 of 1/8 is this same calculation. "Of" means multiply. Half of a quarter is a half times a quarter.
Work out 5/8 × 3.
Multiplying by a whole number means taking that many of the fraction: 3 lots of 5/8. Only the top is multiplied — 5 × 3 = 15 — because the pieces do not change size, there are simply more of them. That gives 15/8, which is 1 7/8 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. Multiplying by a whole number makes a fraction bigger. If your answer shrank, something went wrong.
The answer is B. Multiplying by a whole number means taking that many of the fraction: 3 lots of 5/8. Only the top is multiplied — 5 × 3 = 15 — because the pieces do not change size, there are simply more of them. That gives 15/8, which is 1 7/8 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. Multiplying by a whole number makes a fraction bigger. If your answer shrank, something went wrong.
Work out 2/5 ÷ 2.
Dividing by 2 means splitting 2/5 into 2 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 2, so the bottom is multiplied: 5 × 2 = 10, giving 2/10, which simplifies to 1/5. Multiplying the top instead would make the answer bigger, which cannot be right for a division. Dividing a fraction by a whole number makes it smaller. Check your answer against that before moving on.
The answer is B. Dividing by 2 means splitting 2/5 into 2 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 2, so the bottom is multiplied: 5 × 2 = 10, giving 2/10, which simplifies to 1/5. Multiplying the top instead would make the answer bigger, which cannot be right for a division. Dividing a fraction by a whole number makes it smaller. Check your answer against that before moving on.
Work out 1/7 × 9.
Multiplying by a whole number means taking that many of the fraction: 9 lots of 1/7. Only the top is multiplied — 1 × 9 = 9 — because the pieces do not change size, there are simply more of them. That gives 9/7, which is 1 2/7 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. The denominator stays put. The size of each piece has not changed.
The answer is D. Multiplying by a whole number means taking that many of the fraction: 9 lots of 1/7. Only the top is multiplied — 1 × 9 = 9 — because the pieces do not change size, there are simply more of them. That gives 9/7, which is 1 2/7 as a mixed number. Multiplying the bottom as well is the usual error, and it makes the answer smaller rather than bigger. The denominator stays put. The size of each piece has not changed.
Work out 2/3 ÷ 3.
Dividing by 3 means splitting 2/3 into 3 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 3, so the bottom is multiplied: 3 × 3 = 9, giving 2/9. Multiplying the top instead would make the answer bigger, which cannot be right for a division. More pieces means smaller pieces, so the denominator is the one that grows.
The answer is B. Dividing by 3 means splitting 2/3 into 3 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 3, so the bottom is multiplied: 3 × 3 = 9, giving 2/9. Multiplying the top instead would make the answer bigger, which cannot be right for a division. More pieces means smaller pieces, so the denominator is the one that grows.
Work out 2/3 ÷ 2.
Dividing by 2 means splitting 2/3 into 2 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 2, so the bottom is multiplied: 3 × 2 = 6, giving 2/6, which simplifies to 1/3. Multiplying the top instead would make the answer bigger, which cannot be right for a division. Dividing by 2 is the same as halving, and halving a fraction is doubling its bottom. The same idea scales up.
The answer is C. Dividing by 2 means splitting 2/3 into 2 equal parts, so the answer must be smaller than the fraction you started with. Each piece gets cut into 2, so the bottom is multiplied: 3 × 2 = 6, giving 2/6, which simplifies to 1/3. Multiplying the top instead would make the answer bigger, which cannot be right for a division. Dividing by 2 is the same as halving, and halving a fraction is doubling its bottom. The same idea scales up.
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