Printable · GCSE Foundation · ages 14-16
Fractions in ratio problems worksheet — GCSE Foundation
Fifteen questions on "fractions in ratio problems" — DfE statement N11. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
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Fractions in ratio problems worksheet — GCSE Foundation
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- 1.In a fruit basket the ratio of bananas to oranges is 2 : 5. What fraction of the fruit are oranges?
- 2.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?
- 3.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.
- 4.A fruit bowl contains apples, pears and plums in the ratio 3 : 4 : 5. What fraction of the fruit are not plums?
- 5.In a photo album the ratio of colour photos to black-and-white photos is 9 : 4. Work out the number of black-and-white photos as a fraction of the number of colour photos.
- 6.In a fruit crate the ratio of oranges to lemons is 5 : 6. What fraction of the fruit in the crate are lemons?
- 7.In a chess club, 3/8 of the members are girls and the rest are boys. Write down the ratio of girls to boys.
- 8.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?
- 9.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.
- 10.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?
- 11.In a car park the ratio of vans to cars is 2 : 7. Work out the number of vans as a fraction of the number of cars.
- 12.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.
- 13.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.
- 14.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.
- 15.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?
Answer key
- (d) 5/7 — Add the parts of the ratio to find the total: 2 + 5 = 7. Oranges are 5 of those 7 parts, so the fraction of the fruit that are oranges is 5/7. 2/7 comes from finding the fraction of bananas instead of oranges. 5/2 comes from writing the ratio itself as a fraction, without adding the parts to find the total. 7/5 comes from putting the total number of parts over the number of oranges instead of the number of oranges over the total.
- (b) 2/5 — The statement compares girls with boys, so girls : boys = 2 : 3. The club is therefore 2 + 3 = 5 equal shares and the girls take 2 of them, so 2/5 of the members are girls. 2/3 repeats the part-to-part fraction the question gives, 3/5 is the fraction that are boys, and 1/3 comes from treating 2/3 as a fraction of the whole club and taking what is left.
- (c) 1/3 — Method: find non-fiction's fraction of the whole, then multiply by the fraction of non-fiction that is history. Working: total parts = 4 + 5 = 9, so non-fiction is 5/9 of all books. History books are 3/5 of the non-fiction books: 3/5 × 5/9 = 15/45 = 1/3. Answer: 1/3. 3/5 comes from giving the fraction of non-fiction books that are history, without relating it to all the books at the fair. 5/9 comes from stopping after finding the fraction of all books that are non-fiction, without finding the history books within that. 4/15 comes from multiplying 3/5 by the fraction that is fiction (4/9) instead of the fraction that is non-fiction (5/9).
- (c) 7/12 — Add all three parts to find the number of equal shares: 3 + 4 + 5 = 12. The fruit that are not plums are the apples and the pears together, which is 3 + 4 = 7 shares, so 7/12 of the fruit are not plums. 7/24 comes from adding 3/12 and 4/12 by adding the denominators as well as the numerators, 5/12 is the fraction that are plums, and 7/5 compares the other fruit with the plums instead of with the whole bowl.
- (a) 4/9 — Method: write the number of parts for the photos being compared over the number of parts for the photos they are being compared to. Working: black-and-white photos are 4 parts and colour photos are 9 parts, so black-and-white photos as a fraction of colour photos is 4/9. Answer: 4/9. 9/4 comes from writing the ratio the wrong way round, comparing colour to black-and-white instead of black-and-white to colour. 4/13 comes from comparing black-and-white photos to the total number of photos (4+9=13) instead of to the colour photos. 9/13 comes from comparing colour photos to the total number of photos instead of black-and-white to colour.
- (a) 6/11 — Method: add the parts of the ratio to find the total, then write the required part over the total. Working: 5 + 6 = 11 parts in total; lemons make up 6 of the 11 parts, so the fraction of lemons is 6/11, which is already in its simplest form. Answer: 6/11. 5/11 comes from finding the fraction of oranges instead of lemons. 5/6 comes from writing the ratio of oranges to lemons directly as a fraction instead of comparing lemons to the total. 6/5 comes from writing the ratio of lemons to oranges directly as a fraction instead of comparing lemons to the total.
- (c) 3 : 5 — The club is 8 equal shares and the girls take 3 of them, so the boys take 8 − 3 = 5 shares. A ratio compares one part with the other part, so girls : boys = 3 : 5. Writing 3 : 8 compares the girls with the whole club rather than with the boys, 5 : 3 puts the two parts in the wrong order, and 8 : 3 compares the whole club with the girls.
- (a) 1/4 — First find the fraction of the people who are children: the pool is 3 + 5 = 8 equal shares and the children take 5, so the children are 5/8 of the people. The boys are 2/5 of that, and 'of' means multiply: 2/5 × 5/8 = 10/40 = 1/4. Answering 2/5 gives the boys as a fraction of the children only, 3/20 multiplies by the adults' fraction 3/8 instead of the children's, and 3/5 is the fraction of the children who are girls.
- (b) 4 m — Blue fabric is 3 parts and this equals 1.5 m, so one part is 1.5 ÷ 3 = 0.5 m. Yellow fabric is 5 parts, so it is 5 × 0.5 = 2.5 m. The total length is 1.5 + 2.5 = 4 m. 2.5 m is the length of yellow fabric only, without adding the blue fabric back in. 1.5 m is just the given length of blue fabric, with the yellow fabric never worked out. 2.4 m comes from swapping the ratio, treating blue as 5 parts and yellow as 3 parts, giving one part as 1.5 ÷ 5 = 0.3 m and yellow as 3 × 0.3 = 0.9 m, then adding 1.5 + 0.9 = 2.4.
- (a) 3/13 — Vegetables are 9 of the 9 + 4 = 13 parts, so vegetables are 9/13 of the plot. Potatoes are a third of the vegetable section, so potatoes are 1/3 of 9/13, which is 9/39, simplifying to 3/13, of the whole plot. 9/13 comes from stopping after finding the fraction of the plot that is vegetables, without taking the further third for potatoes. 1/3 gives the fraction of the vegetable section that is potatoes, not the fraction of the whole plot. 4/39 comes from taking a third of the flowers' fraction, 4/13, instead of the vegetables' fraction.
- (b) 2/7 — The comparison asked for is part with part, not part with whole, so the number of cars goes on the bottom. The ratio gives 2 shares of vans for every 7 shares of cars, so the vans are 2/7 of the cars. 2/9 uses the 9 shares in the whole car park as the denominator, 7/2 compares the cars with the vans, and 7/9 is the fraction of the vehicles that are cars.
- (b) 1 : 2 — 2/5 of 50 is 20, so there are 20 red counters and 50 − 20 = 30 blue counters. Taking 5 red counters out leaves 15 red and 30 blue, so red : blue = 15 : 30. Dividing both parts by 15 gives 1 : 2. 2 : 3 is the ratio before any counters are removed, 2 : 1 has the two parts the wrong way round, and 4 : 5 comes from taking the 5 counters out of the blue instead of the red.
- (c) 3:4 — The jacket costs 3/7 of £84, which is 3 × (84 ÷ 7) = 3 × 12 = £36. The bag then costs the rest of the money, £84 − £36 = £48. The ratio of the jacket to the bag is 36:48, which simplifies to 3:4. Writing the fraction spent on the jacket, 3/7, directly as the ratio, without working out that the bag's share is the remaining 4/7, gives 3:7. Giving the ratio the wrong way round, bag to jacket instead of jacket to bag, gives 4:3. Assuming the jacket and bag cost the same, ignoring the fraction given, gives 1:1.
- (a) 3/5 — The question compares the rock albums directly with the pop albums, so write the rock part over the pop part: 3/5. 5/3 comes from writing the ratio the wrong way round, comparing pop with rock instead of rock with pop. 3/8 comes from comparing the rock albums with the total number of albums, 3 + 5 = 8, instead of with the pop albums. 5/8 comes from comparing the pop albums with the total number of albums instead of the rock albums with the pop albums.
- (d) 3/10 — Total parts = 7 + 3 = 10. Gold beads are 3 of those 10 parts, so the fraction is 3/10. 7/10 comes from finding the fraction of red beads instead of gold beads. 7/3 comes from writing the ratio itself as a fraction, without adding the parts to find the total. 3/7 comes from comparing gold beads with red beads instead of with the total number of beads.
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