Multi-Part Ratio Practice Test Worksheets
Multi-part ratio questions test whether you can turn a word problem into parts, find the value of one part, and use that value to answer several related questions. The same ratio can answer totals, single parts, combined parts, and differences.
For students who know basic ratios, but lose marks when a total has to be split across three or more parts.
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What Do Multi-Part Ratio Questions Look Like?
Multi-part ratio questions test whether you can turn a word problem into parts, find the value of one part, and use that value to answer several related questions. Students are given a ratio connecting three or more quantities and a specific clue—such as a single part, a total, or a difference—to find unknown amounts. Here is a worked example.
Start from One Named Part
Question: Three friends share prize money in the ratio Alice:Ben:Clara = 2:1:8. If Alice receives £12, how much does Clara receive?
Worked Method
Step 1: Alice has 2 ratio parts. £12 ÷ 2 = £6, so one part is £6.
Step 2: Clara has 8 parts. 8 × £6 = £48.
Tip: Always divide by the ratio part attached to the amount you were given, not by the total number of parts.
Rules to Help You Solve Multi-Part Ratio Questions
To solve multi-part ratio questions like the example above, determine what one ratio part is worth and apply it to each question.
🧮 Rule 1: Add parts for a total
If a total amount is given, add every ratio part first, then divide the total by that sum.
Example: Ratio 2:5:3 has 10 parts. If the total is 40, one part is 40 ÷ 10 = 4.
🎯 Rule 2: Use the named part as the anchor
If one category amount is given, divide by that category's ratio number to find one part.
Example: If 45 blue beads match 5 parts, one part is 45 ÷ 5 = 9.
➕ Rule 3: Combine parts when the question combines groups
When two categories are given together, add their ratio parts before dividing.
Example: Red and green counters are 4 + 7 = 11 parts. If together they make 88, one part is 8.
↔️ Rule 4: Find the gap between two parts
Subtract the smaller ratio number from the larger to find the gap in parts. To find an actual difference, multiply this gap by the value of one part. If the difference is given, divide it by the gap to find one part.
Finding a difference: Science:history books = 7:4 gives a gap of 3 parts. If one part is 6 books, the difference is 3 × 6 = 18 books.
Using a given difference: If there are 18 more science books, one part is 18 ÷ (7 − 4) = 6 books.
Two More Worked Examples
Here are two more examples showing how to work from a given total or from a difference between parts.
Start from the Total
Question: A concrete mix uses cement:sand:gravel in the ratio 1:7:5. The builder needs 78 kg of concrete in total. How many kg of gravel should be used?
Worked Method
Step 1: Add the ratio parts: 1 + 7 + 5 = 13 parts.
Step 2: Find one part: 78 ÷ 13 = 6 kg.
Step 3: Gravel is 5 parts, so 5 × 6 = 30 kg.
Tip: When the total is given, add all the ratio parts before dividing.
Start from a Difference
Question: A concrete mix uses cement:sand:gravel in the ratio 1:7:5 by weight. The mix contains 24 kg more sand than cement. How many kg of gravel are needed?
Worked Method
Step 1: Sand has 7 parts and cement has 1 part. Their difference is 7 − 1 = 6 parts.
Step 2: Those 6 parts weigh 24 kg, so one part is 24 ÷ 6 = 4 kg.
Step 3: Gravel has 5 parts, so 5 × 4 = 20 kg.
Answer: 20 kg of gravel.
Tip: The 24 kg is the difference between sand and cement, so divide by their 6-part gap. The 13-part total is not the amount given. This is a separate mix from the previous example, so calculate one part again.
