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.
One quantity as a fraction of another worksheet — GCSE Foundation
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- 1.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.
- 2.A bag of potatoes has a mass of 3 kg. A bag of carrots has a mass of 5 kg. Write the mass of the potatoes as a fraction of the mass of the carrots.
- 3.A journey to school takes 12 minutes. A journey to the gym takes 20 minutes. Write the time for the journey to school as a fraction of the time for the journey to the gym, giving your answer in its simplest form.
- 4.There are 84 passengers on a double-decker bus. 35 of the passengers are adults and the rest are children. Write the number of adults as a fraction of the number of children. Give your answer in its simplest form.
- 5.A novel has 312 pages. A comic has 48 pages. Write the number of pages in the novel as a fraction of the number of pages in the comic, giving your answer in its simplest form.
- 6.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.
- 7.A recipe needs 1.2 kg of flour. Dan has 750 g of flour in his cupboard. Write the mass of flour the recipe needs as a fraction of the mass of flour Dan has. Give your answer in its simplest form.
- 8.Sam has £24. Tom has £16. Write the amount of money Sam has as a fraction of the amount of money Tom has, giving your answer in its simplest form.
- 9.A necklace uses 22 blue beads and 8 red beads. Write the number of blue beads as a fraction of the number of red beads. Give your answer as a mixed number in its simplest form.
- 10.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.
- 11.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.
- 12.A tin of beans has a mass of 400 g. A tin of soup has a mass of 500 g. Write the mass of the tin of beans as a fraction of the mass of the tin of soup, giving your answer in its simplest form.
- 13.A charity receives £360 in donations in January and £480 in donations in February. Write the amount received in January as a fraction of the amount received in February, giving your answer in its simplest form.
- 14.A blue ribbon is 45 cm long. A red ribbon is 30 cm long. Write the length of the blue ribbon as a fraction of the length of the red ribbon. Give your answer in its simplest form.
- 15.A coach journey is 372 miles in total. After a stop, the coach has travelled 217 miles. Write the distance still to travel as a fraction of the total journey. Give your answer in its simplest form.
Answer key
- (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.
- (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.
- (d) 3/5 — Put the school journey time over the gym journey time: 12/20. Divide both numbers by their highest common factor, 4: 12÷4 = 3, 20÷4 = 5, giving 3/5. (5/3 comes from writing the times the wrong way round. 2/5 comes from finding the difference in the times, 20 − 12 = 8 minutes, and writing it as a fraction of the gym time, 8/20. 3/8 comes from comparing the school time to the total time for both journeys, 12/32.)
- (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.
- (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.)
- (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.
- (a) 3/2 — Put Sam's amount over Tom's amount: 24/16. Divide both numbers by their highest common factor, 8: 24÷8 = 3, 16÷8 = 2, giving 3/2. (2/3 comes from writing Tom's amount over Sam's amount, the wrong way round. 3/5 comes from comparing Sam's amount to the total amount of money, 24/40, instead of to Tom's amount. 1/2 comes from finding the difference between the amounts, £8, and writing it as a fraction of Tom's amount, 8/16.)
- (d) 2 3/4 — Divide 22 by 8: 8 goes into 22 twice, with a remainder of 6, so 22/8 = 2 and 6/8 left over. Since 6/8 simplifies to 3/4 (dividing both by 2), the blue beads are 2 3/4 of the red beads. 2 5/8 comes from miscalculating the remainder as 22 − 16 = 5 instead of 6. 2 3/11 comes from writing the leftover 6 over the original 22 instead of over the 8, giving 6/22, then simplifying that to 3/11. 1 3/8 comes from halving only the numerator of 22/8 to get 11/8, without halving the denominator too, giving the mixed number 1 3/8.
- (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.)
- (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.
- (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.
- (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) 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) 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.
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