Combined Ratio and Fraction Problems
Combined ratio and fraction problems are multi-step 11+ questions that mix both skills in a single problem, such as sharing a total in a ratio after a fraction has already been removed, or splitting one ratio share further using a fraction. They test whether a pupil can move fluently between fraction and ratio representations and complete each step in the correct order, which is where most marks are lost.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole problem before starting any calculation, and identify which operation happens first: the fraction step or the ratio step.
- Where a fraction of an amount is found first, calculate that amount, then treat the result as the new total for the ratio step, or the other way round if the ratio comes first.
- Convert a ratio part into a fraction of the whole by writing that part over the sum of all the parts, to move fluently between the two forms.
- Keep every intermediate amount clearly labelled, such as 'amount after step 1', so it is not confused with the final answer.
- Work through each step in order, using the result of the previous step as the input to the next, rather than trying to combine everything into a single calculation.
- Check your final answer against the original total: your combined amounts should always add back up to the whole you started with.
Worked example
A charity raises 900 pounds. 2/3 of the money is spent on equipment, and the rest is shared between two projects in the ratio 3 : 2. How much does each project receive?
- Find the amount spent on equipment: 2/3 x 900 = 600 pounds.
- Find the amount left to share between the two projects: 900 - 600 = 300 pounds.
- Find the total number of parts in the ratio: 3 + 2 = 5 parts.
- Find the value of one part: 300 / 5 = 60 pounds.
- Find each project's share: 3 x 60 = 180 pounds and 2 x 60 = 120 pounds.
Practice questions
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Q1A bag contains 60 marbles. 1/4 of them are red, and the rest are shared between blue and green marbles in the ratio 2 : 3. How many green marbles are there?Show answer
Answer: 27 (red = 15, remaining 45 split into 5 parts of 9, green = 3 x 9 = 27)
Q2A total of 180 pounds is shared in the ratio 1 : 5 between Zara and a savings fund. Zara then spends 1/3 of her share. How much does Zara have left?Show answer
Answer: 20 pounds (Zara's share = 30, and 30 - 1/3 x 30 = 30 - 10 = 20)
Q3In a class of 30 pupils, 3/5 walk to school. Of the pupils who do not walk, the ratio who cycle to those who are driven is 1 : 3. How many pupils are driven to school?Show answer
Answer: 9 (walkers = 18, remaining 12 split into 4 parts of 3, driven = 3 x 3 = 9)
Q4A recipe makes 900 g of dough, split in the ratio 5 : 4 between a loaf and a batch of rolls. The rolls are then divided into pieces, each weighing 1/8 of the rolls' total dough. How many roll pieces are made?Show answer
Answer: 8 pieces (rolls = 4/9 x 900 = 400 g, each piece = 1/8 x 400 = 50 g, and 400 / 50 = 8)
Q5A journey of 320 km is split into two parts in the ratio 3 : 5. Given that 1/4 of the shorter part is on a motorway, how many km of the journey are on a motorway?Show answer
Answer: 30 km (one part = 40, shorter part = 3 x 40 = 120, and 1/4 x 120 = 30)
Q6True or False: to find 2/5 of a ratio share, you first work out the share as a number, then find the fraction of that number.Show answer
Answer: True
Q7Explain why it is important to identify which step, the fraction or the ratio, happens first in a combined ratio and fraction problem.Show answer
Answer: Doing the steps in the wrong order applies the fraction or ratio to the wrong amount and gives a different, incorrect total; the amount left after a fraction has been removed is not the same as the original total, so any ratio step that follows must use the correct, updated amount.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A youth club has 84 members. 3/7 of the members are girls, and the rest are boys. The boys are split into two teams in the ratio 3 : 5. How many boys are in the larger team?
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A vineyard harvests 1200 kg of grapes. 1/3 of the grapes are used to make juice, and the rest are shared between two wineries in the ratio 5 : 3. (a) Work out how many kg of grapes are used to make juice. (b) Work out how many kg of grapes are left to share between the wineries. (c) Work out how many kg of grapes each winery receives.
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Free printable worksheet
Want more practice on paper? Download the combined ratio and fraction problems worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 46 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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