Printable · GCSE Foundation · ages 14-16
One quantity as a fraction of another worksheet — GCSE Foundation
Fifteen questions on "one quantity as a fraction of another" — DfE statement R3. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Answer key: One quantity as a fraction of another worksheet — GCSE Foundation
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- (d) 3/5 — Convert both times to minutes: 2 hours 15 minutes = 135 minutes; 3 hours 45 minutes = 225 minutes. Put the train time over the bus time: 135/225. Divide both numbers by their highest common factor, 45: 135÷45 = 3, 225÷45 = 5, giving 3/5. (5/3 comes from writing the times the wrong way round. 2/5 comes from finding the difference, 225 − 135 = 90 minutes, and writing it as a fraction of the bus time, 90/225. 3/8 comes from comparing the train time to the total time for both journeys, 135/360.)
- (d) 13/10 — First find the selling price: £150 + £45 = £195. Put the selling price over the cost price: 195/150. Divide both numbers by their highest common factor, 15: 195÷15 = 13, 150÷15 = 10, giving 13/10. (10/13 comes from writing the prices the wrong way round. 3/10 is just the profit written as a fraction of the cost price, 45/150, not the selling price. 13/23 comes from comparing the selling price to the combined total of the cost price and the selling price, 195/345.)
- (d) 3/2 — Work out the number of altos: 40% of 30 = 12. The rest are sopranos, so there are 30 − 12 = 18 sopranos. Form the fraction 18/12; both numbers share a factor of 6, so 18 ÷ 6 = 3 and 12 ÷ 6 = 2, giving 3/2. 2/3 comes from writing the fraction the wrong way round, as altos over sopranos (12/18). 3/5 comes from comparing the sopranos with the whole choir (18/30), instead of with the altos. 7/3 comes from miscalculating 30 − 12 as 28 instead of 18, then forming 28/12.
- (d) 5/4 — Work out the number of free seats: 54 − 24 = 30. Form the fraction 30/24; both numbers share a factor of 6, so 30 ÷ 6 = 5 and 24 ÷ 6 = 4, giving 5/4. 4/5 comes from writing the fraction the wrong way round, as reserved over free (24/30). 5/9 comes from comparing the free seats with the total number of seats (30/54), instead of with the reserved seats. 5/6 comes from miscalculating 54 − 24 as 20 instead of 30, then forming 20/24.
- (d) 7/5 — The number of unbroken crayons is 60 − 25 = 35. The comparison is with the broken crayons, so the broken crayons are the denominator: 35/25. Both parts divide by 5: 35 ÷ 5 = 7 and 25 ÷ 5 = 5. The fraction is 7/5, which is greater than 1 because there are more unbroken crayons than broken ones.
- (a) 3/5 — The quantity being described goes on the top of the fraction and the quantity it is compared with goes on the bottom. Here the potatoes are written as a fraction of the carrots, so the mass of the potatoes is the numerator and the mass of the carrots is the denominator. Both masses are already in kilograms, so no conversion is needed. This gives 3/5, and since 3 and 5 share no common factor it is already in its simplest form.
- (b) 13/2 — Put the number of pages in the novel over the number of pages in the comic: 312/48. Divide both numbers by their highest common factor, 24: 312÷24 = 13, 48÷24 = 2, giving 13/2. (2/13 comes from writing the page counts the wrong way round. 11/2 comes from finding the difference in the page counts, 312 − 48 = 264, and writing it as a fraction of the comic's page count, 264/48. 13/15 comes from comparing the novel's page count to the total number of pages in both books, 312/360.)
- (a) 35/32 — Work out each weekly total first. Last week: 5 × 7 = 35 hours. This week: 4 × 8 = 32 hours. Last week's total is being written as a fraction of this week's total, so last week goes on the top and this week goes on the bottom, giving 35/32. The two totals share no common factor, so the fraction cannot be cancelled. It is greater than 1, which says that Priya worked more hours last week than this week.
- (d) 3/16 — Convert 4 kg to grams: 4 kg = 4000 g. Form the fraction 750/4000. Both numbers share a factor of 250, so 750 ÷ 250 = 3 and 4000 ÷ 250 = 16, giving 3/16. 16/3 comes from writing the fraction the wrong way round, as 4000/750. 15/8 comes from converting 4 kg using ×100 instead of ×1000, treating it as 400 g, then simplifying 750/400. 3/20 comes from dividing 750 by 250 correctly to get 3, but dividing 4000 by 200 instead of 250, giving 3/20.
- (b) 3/10 — Work out the empty space: 500 − 350 = 150 litres. Form the fraction 150/500; both numbers share a factor of 50, so 150 ÷ 50 = 3 and 500 ÷ 50 = 10, giving 3/10. 7/10 comes from writing the fraction of the tank that is full (350/500), instead of the empty space. 1/2 comes from miscalculating 500 − 350 as 250 instead of 150. 3/7 comes from comparing the empty space with the water held (150/350), instead of with the tank's total capacity.
- (d) 7/3 — The film's length is being described, so it goes on the top, and the documentary's length goes on the bottom: 105/45. The highest common factor of 105 and 45 is 15, so divide both parts by it: 105 ÷ 15 = 7 and 45 ÷ 15 = 3. The fraction is 7/3. Because the film is longer than the documentary the fraction is greater than 1, which is exactly what a top-heavy fraction records.
- (a) 12/5 — If A is 5/12 of B, then B is the reciprocal of that fraction times A: flip 5/12 to get 12/5, so B is 12/5 of A. 5/12 comes from keeping the same fraction without flipping it, treating the relationship as if it works the same way in both directions. 7/12 comes from computing 1 − 5/12 = 7/12, which is not how a fraction reverses. 12/7 comes from subtracting 5 from 12 to get 7, and writing 12 over that, instead of swapping the numerator and denominator of 5/12.
- (d) 7/3 — Put the kettle's energy over the toaster's energy: 2.1/0.9. Multiply both numbers by 10 to clear the decimals: 21/9. Divide both by their highest common factor, 3: 21÷3 = 7, 9÷3 = 3, giving 7/3. (3/7 comes from writing the energy values the wrong way round. 4/3 comes from finding the difference, 2.1 − 0.9 = 1.2 kWh, and writing it as a fraction of the toaster's energy, 1.2/0.9. 7/10 comes from comparing the kettle's energy to the total energy used by both appliances, 2.1/3.0.)
- (d) 8/5 — Two masses can only be compared once they are in the same unit. Since 1 kg is 1000 g, the recipe needs 1200 g. The recipe's mass is being written as a fraction of Dan's mass, so 1200 goes on the top and 750 on the bottom, giving 1200/750. The highest common factor of the two is 150: 1200 ÷ 150 = 8 and 750 ÷ 150 = 5. The fraction is 8/5, which is greater than 1 because the recipe needs more flour than Dan has.
- (a) 2/3 — Put the laptop bag's mass over the school bag's mass: 2.4/3.6. Multiply both numbers by 10 to clear the decimals: 24/36. Divide both by their highest common factor, 12: 24÷12 = 2, 36÷12 = 3, giving 2/3. (3/2 comes from writing the masses the wrong way round. 1/3 comes from finding the difference in the masses, 3.6 − 2.4 = 1.2 kg, and writing it as a fraction of the school bag's mass, 1.2/3.6. 2/5 comes from comparing the laptop bag's mass to the total mass of both bags, 2.4/6.)
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