Multi-Part Ratio Practice
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.
The Rules Every Multi-Part Ratio Question Uses
The key move is to find what one ratio part is worth. Once you know the unit value, every part of the question becomes a short multiplication.
🧮 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
For "how many more" questions, first find the gap in the ratio. Then multiply that gap by the value of one part.
Example: 7 science book parts - 4 history book parts = 3 parts. If one part is 6 books, the gap is 3 × 6 = 18 books.
How to Solve Multi-Part Ratio Questions
Three useful moves: anchor on a named part, divide a total into parts, and use differences between parts carefully.
1. 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.
2. 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.
3. Difference Does Not Mean Total
Question: A stationery box has red:blue:green pencils in the ratio 4:7:2. There are 65 pencils in total. How many more blue pencils are there than green pencils?
Worked Method
Step 1: Add all parts: 4 + 7 + 2 = 13.
Step 2: Find one part: 65 ÷ 13 = 5 pencils.
Step 3: Blue pencils minus green pencils is 7 - 2 = 5 parts.
Step 4: 5 parts × 5 pencils per part = 25 pencils.
The trap: The question asks for the difference between two categories, not the number of blue pencils.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Multi-Part Ratio pack contains 90 core problems across 3 printable test sets. Each problem has 3 sub-questions, giving 270 ratio calculations covering totals, named parts, combined parts, and differences.
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