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.
Fractions in ratio problems worksheet — GCSE Foundation
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- 1.In a box of counters the ratio of red counters to blue counters is 4 : 5. What fraction of the counters are blue?
- 2.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.
- 3.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.
- 4.A fruit bowl contains apples, pears and plums in the ratio 3 : 4 : 5. What fraction of the fruit are not plums?
- 5.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.
- 6.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.
- 7.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.
- 8.In a classroom the ratio of boys to girls is 3 : 4. What fraction of the class are boys?
- 9.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.
- 10.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.
- 11.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?
- 12.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.
- 13.A garden has flowers, herbs and vegetables in the ratio 2 : 3 : 4. What fraction of the garden is not vegetables?
- 14.In a choir, 2/9 of the members are boys and the rest are girls. Write down the ratio of girls to boys, in its simplest form.
- 15.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?
Answer key
- (b) 5/9 — Add the parts of the ratio to find how many equal shares make up the whole: 4 + 5 = 9 shares. The blue counters take 5 of those 9 shares, so 5/9 of the counters are blue. 4/9 is the fraction that are red, 4/5 is the ratio copied straight down as a fraction, and 5/4 compares the blue counters with the red counters instead of with the whole box.
- (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.
- (b) 3/10 — Since each bag's ratio has 5 parts and both bags contain the same total number of nuts, imagine each bag has 5 nuts: Bag A has 2 peanuts and Bag B has 1 peanut, so together there are 2 + 1 = 3 peanuts out of a combined 5 + 5 = 10 nuts, giving 3/10. 1/5 comes from using only Bag A's peanuts, 2 out of 10, without adding Bag B's peanuts. 1/10 comes from using only Bag B's peanut, without adding Bag A's peanuts. 3/5 comes from writing the combined peanuts over the number of parts in one bag instead of the combined total number of nuts.
- (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.
- (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.
- (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).
- (d) £120 — Total parts = 5 + 3 = 8, so one part is worth 320 ÷ 8 = 40 pounds. The cake sale is 3 parts, so it raised 3 × 40 = 120 pounds. £200 comes from working out the raffle's share, 5 × 40, instead of the cake sale's share. £40 comes from finding the value of one part but forgetting to multiply by 3. £192 comes from dividing the total by 5 instead of 8 to find the value of one part, 320 ÷ 5 = 64, then multiplying by 3, 3 × 64 = 192.
- (b) 3/7 — Total parts = 3 + 4 = 7. Boys are 3 of the 7 parts, so the fraction is 3/7. 4/7 comes from finding the fraction of girls instead of boys. 3/4 comes from writing the ratio itself as a fraction, without adding the parts to find the total. 7/3 comes from putting the total number of parts over the number of boys instead of the number of boys over the total.
- (a) 1/2 — The ratio 1:2:3 has 1 + 2 + 3 = 6 parts in total. Amir and Bo together receive 1 + 2 = 3 of those parts, so together they receive 3/6 of the £60, which simplifies to 1/2. Using only Amir's single part, 1/6, ignores Bo's share entirely. Adding Bo's and Chen's parts instead of Amir's and Bo's, 2 + 3 = 5, gives 5/6. Comparing Amir and Bo's 3 parts to Chen's 3 parts, rather than to the total of 6 parts, gives 3/3 = 1.
- (b) 4/9 — Method: double the butter part of the ratio, keeping flour the same, find the new total, then write butter's part over the new total. Working: the new ratio is flour : butter = 5 : 4, since butter doubles from 2 to 4. New total = 5 + 4 = 9. Fraction of butter = 4/9. Answer: 4/9. 2/9 comes from forgetting to double the butter part and using the original value 2 over the new total of 9. 4/7 comes from doubling the butter part correctly to 4 but keeping the old total of 7 instead of working out the new total. 2/5 comes from using the original ratio 5:2 directly as butter over flour without doubling anything.
- (b) 3/5 — Method: add all three parts for the total, add together the parts that are not green, then write this over the total. Working: total parts = 4 + 5 + 6 = 15. Not green = 4 + 5 = 9. Fraction = 9/15 = 3/5. Answer: 3/5. 2/5 comes from finding the fraction that IS green (6/15 = 2/5) instead of not green. 4/15 comes from only counting the red baubles as 'not green' and forgetting the gold ones. 9/10 comes from adding only two of the three ratio parts to find the total (4+6=10), missing out the gold part, while still using 9 for the numerator.
- (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.
- (d) 5/9 — Total parts = 2 + 3 + 4 = 9. Flowers and herbs together make up 2 + 3 = 5 parts, so the fraction that is not vegetables is 5/9. 4/9 comes from finding the fraction of vegetables instead of the fraction that is not vegetables. 5/7 comes from leaving flowers out of the total and using only herbs and vegetables, 3 + 4 = 7, as the total. 3/4 comes from writing the ratio of herbs to vegetables directly as a fraction.
- (b) 7:2 — If 2/9 of the choir are boys, the remaining 7/9 must be girls, since the two fractions together make the whole choir. The ratio of girls to boys compares these two parts to each other, giving 7:2. Writing the ratio the wrong way round, boys to girls instead of girls to boys, gives 2:7. Comparing the number of girls to the whole choir instead of to the number of boys gives 7:9. Simply rewriting the given fraction, 2/9, as a ratio without working out how many are girls gives 2:9.
- (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.
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