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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- (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) 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.)
- (a) 18/25 — First find the new number of rose bushes: 90 × 1.2 = 108 (a 20% increase multiplies by 1.2). Then write 108 over 150 and divide top and bottom by 6 to get 18/25. Choosing 3/5 comes from using the original 90 rose bushes without applying the 20% increase (90/150 = 3/5). Choosing 25/18 comes from writing the number of lavender bushes over the new number of rose bushes, the wrong way round. Choosing 3/25 comes from multiplying 90 by 0.2 instead of 1.2, finding only the increase (18) rather than the new total, then writing 18/150 = 3/25.
- (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) 7/5 — 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) 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.
- (a) 5/12 — Work out the distance still to travel: 372 − 217 = 155 miles. Form the fraction 155/372; both numbers share a factor of 31, so 155 ÷ 31 = 5 and 372 ÷ 31 = 12, giving 5/12. 7/12 comes from writing the distance already travelled as the fraction of the journey (217/372 = 7/12), instead of the distance still to travel. 145/372 comes from miscalculating 372 − 217 as 145 instead of 155. 5/7 comes from comparing the remaining distance with the distance already travelled (155/217 = 5/7), instead of with the total journey.
- (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.)
- (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) 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.
- (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.
- (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.)
- (d) 3/2 — The length of the blue ribbon goes on the top and the length of the red ribbon goes on the bottom, giving 45/30. Both parts divide by 15: 45 ÷ 15 = 3 on the top, and 30 ÷ 15 = 2 on the bottom. So the fraction is 3/2. It is greater than 1 because the blue ribbon is longer than the red one, and a fraction of one quantity compared with another is allowed to be top-heavy.
- (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) 4/3 — Work out the number of bananas: 3/4 of 16 = 12. Form the fraction 16/12 (apples over bananas); both numbers share a factor of 4, so 16 ÷ 4 = 4 and 12 ÷ 4 = 3, giving 4/3. 3/4 comes from giving the fraction that was already stated in the question (bananas as a fraction of apples), instead of inverting it. 4/1 comes from reading '3/4 of the apples' as 'the apples reduced by 3/4', giving only 4 bananas, then 16/4 = 4. 4/7 comes from comparing the apples with the total number of pieces of fruit (16/28), instead of with the bananas alone.
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