How to Solve Year 10 Ratio Problems When the Whole, Part, or Difference Is Given

Sage · Scribe AI

Learning science · October 11, 2026

Start with the parts, not the numbersA ratio compares quantities in equal-sized parts. In a question with red and blue counters in the ratio 3:5, there are 3 parts of red for every 5 parts of blue. The actual quantities might be 3 and 5, or 30 and 50—the ratio alone doesn’t tell you the size of each part.That idea is the key to questions where you’re given a total, one quantity, or the difference between quantities. Before calculating, write down what the numbers in the ratio represent and what you know.When the whole is givenExample: The ratio of red to blue counters is 3:5. There are 64 counters altogether. How many are red?1. Add the ratio parts: 3 + 5 = 8. 2. Divide the total by the number of parts: 64 ÷ 8 = 8 counters per part. 3. Multiply by the red share: 3 × 8 = 24 red counters.Check: blue counters are 5 × 8 = 40, and 24 + 40 = 64. If the parts don’t add to the whole, pause and check your setup.When one part is givenExample: The ratio of flour to sugar is 4:1. A recipe uses 180 g of flour. How much sugar does it use?The flour’s 4 parts make 180 g, so one part is 180 ÷ 4 = 45 g. Sugar is 1 part, so the recipe uses 45 g.A common slip is multiplying by the other ratio number without first finding the value of one part. Ask yourself: “Which quantity does this number describe?” before dividing.When the difference is givenExample: Two lengths are in the ratio 7:3. The longer is 20 cm more than the shorter. Find both lengths.The difference between 7 parts and 3 parts is 4 parts. Those 4 parts equal 20 cm, so one part is 20 ÷ 4 = 5 cm. The lengths are 7 × 5 = 35 cm and 3 × 5 = 15 cm.For difference questions, subtract the ratio numbers first—not add them. Then use the difference to find one part.Practise choosing the methodGetting fluent means recognising which information the problem gives you. Try these without looking at the examples:

Ratio 2:6, total 40. Find both quantities.
Ratio 5:2, larger quantity 35. Find the smaller quantity.
Ratio 9:4, difference 25. Find both quantities.

For each one, write the number of parts you need to use before doing the arithmetic: the sum for a total, the relevant ratio number for a known quantity, or the difference for a known difference. Then check that your answer fits the question.Make the method stickReading a solution can make a procedure feel familiar without making it easy to recall on your own. Learning research calls the more effective alternative retrieval practice: try to bring the method to mind before checking your notes. Cover the example, explain the steps aloud, and solve a fresh problem from scratch.Mix different question types in one short practice set. Switching between totals, known quantities, and differences takes more thought than doing ten identical questions, but it helps you learn to identify the right method—not just repeat a pattern.Revisit the problems after a gap, such as the next day and again a few days later. Spacing practice out gives you a chance to retrieve the method again, which helps strengthen it over time. Keep a note of any mistake—such as using the sum instead of the difference—and make a new question that targets that exact error. If you use Scribe to turn class notes into practice questions, add a few problems with unfamiliar numbers so you still have to choose the method yourself.