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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- (a) 3/8 — Convert 2 hours to minutes: 2 hours = 120 minutes. Form the fraction 45/120. Both numbers share a factor of 15, so 45 ÷ 15 = 3 and 120 ÷ 15 = 8, giving 3/8. 8/3 comes from writing the fraction the wrong way round, as 120/45. 9/40 comes from converting 2 hours using ×100 instead of ×60, treating it as 200 minutes, then simplifying 45/200. 45/2 comes from not converting the hours to minutes at all, and writing 45 over 2.
- (d) 4/7 — Put the tomato plant's height over the sunflower's height: 80/140. Divide both numbers by their highest common factor, 20: 80÷20 = 4, 140÷20 = 7, giving 4/7. (7/4 comes from writing the heights the wrong way round. 3/7 comes from finding the difference in the heights, 140 − 80 = 60 cm, and writing it as a fraction of the sunflower's height, 60/140. 4/11 comes from comparing the tomato plant's height to the total height of both plants, 80/220.)
- (b) 4/5 — Write the mass of the beans over the mass of the soup: 400/500. Divide the top and bottom by 100 to get 4/5. Choosing 5/4 comes from writing the soup's mass over the beans' mass, the wrong way round. Choosing 1/5 comes from finding the difference in mass (500 − 400 = 100) and writing that over the mass of the soup, instead of using the mass of the beans. Choosing 5/9 comes from writing the mass of the soup over the total mass of both tins (500 out of 900), instead of over the mass of the beans.
- (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.
- (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.
- (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) 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.
- (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) 10/7 — Put Saturday's distance over Sunday's distance: 17.5/12.25. Multiply both numbers by 100 to clear the decimals: 1750/1225. Divide both by their highest common factor, 175: 1750÷175 = 10, 1225÷175 = 7, giving 10/7. (7/10 comes from writing the distances the wrong way round. 3/7 comes from finding the difference, 17.5 − 12.25 = 5.25 km, and writing it as a fraction of Sunday's distance, 5.25/12.25. 10/17 comes from comparing Saturday's distance to the total distance ridden, 17.5/29.75.)
- (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.
- (a) 3/4 — Write January's total over February's total: 360/480. Both numbers share a factor of 120, so dividing top and bottom by 120 gives 3/4. Choosing 4/3 comes from writing February's amount over January's amount, the wrong way round. Choosing 1/4 comes from finding the difference between the two months (480 − 360 = 120) and writing it over February's amount, instead of using January's amount. Choosing 3/7 comes from writing January's amount over the total received across both months (360 out of 840), instead of over February's amount alone.
- (a) 3/2 — Find each average speed: car = 180 ÷ 3 = 60 mph; lorry = 160 ÷ 4 = 40 mph. Put the car's speed over the lorry's speed: 60/40. Divide both numbers by their highest common factor, 20: 60÷20 = 3, 40÷20 = 2, giving 3/2. (2/3 comes from writing the speeds the wrong way round. 9/8 comes from comparing the distances travelled, 180/160, without working out the speeds. 3/4 comes from comparing the times taken, 3/4, instead of the speeds.)
- (c) 5/7 — First find the number of children: 84 − 35 = 49. The question compares the adults with the children, not with everyone on the bus, so the denominator is 49 and the numerator is 35, giving 35/49. Both parts divide by 7: 35 ÷ 7 = 5 and 49 ÷ 7 = 7. In its simplest form the fraction is 5/7.
- (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.)
- (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.)
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