Ratio and fractions

Objective. Move between part-to-part ratios and fractions of a whole.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Ratio and fractions describe the same proportional relationship in two different forms, and converting between them means focusing on parts of the whole rather than parts of each other. If a ratio is a:b, the whole is split into (a + b) parts, so the fraction of the whole for the first quantity is a/(a+b). For a ratio of 3:5, the whole has 8 parts, so the first quantity is 3/8 of the total and the second is 5/8. Always add the ratio parts first to find the whole before writing any fraction.

Worked example

A ratio of red to blue counters is 2:7. What fraction of the counters are blue?

1 $Add the ratio parts to find the whole: 2 + 7 = 9$
2 $The blue part of the ratio is 7$
3 $Write blue as a fraction of the whole: 7/9$
4 $The fraction of blue counters is 7/9$

Answer: 7/9

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Common mistake. Pupils often write the fraction using only one part of the ratio as the denominator, turning 3:5 into 3/5 of the whole instead of 3/8. Always add both parts of the ratio to get the correct denominator for the whole.

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