Ratio and Fractions –

Understanding the link between ratios and fractions is essential for GCSE Maths. Questions that connect the two appear at both Foundation and Higher tier and are tested across AQA, Edexcel and OCR. Many students can work with ratios and fractions separately but struggle when asked to convert between them or find a fractional part from a ratio. This guide makes the connection crystal clear with step-by-step methods, worked examples and practice questions.

What Is the Link Between Ratios and Fractions?

A ratio compares parts to parts. A fraction compares a part to the whole. The key to converting between them is understanding that the total number of parts in a ratio gives you the denominator of the fraction.

Key Formulas

If a ratio is a : b, the total number of parts is a + b.

For a three-part ratio a : b : c, the total is a + b + c, and the fraction for each part uses this total as the denominator.

Going from fractions to ratios

If one quantity is 2/5 of the total, the remaining fraction is 3/5. The ratio is therefore 2 : 3.

Step-by-Step Method

Converting a ratio to fractions

1. Add the parts of the ratio to find the total number of parts.
2. Write each part as a fraction of the total.
3. Simplify the fractions if possible.

Converting fractions to a ratio

1. Express both quantities as fractions of the total with the same denominator.
2. Read off the numerators — these form the ratio.
3. Simplify the ratio if needed.

Finding a fraction of an amount from a ratio

1. Convert the ratio to a fraction (as above).
2. Multiply the fraction by the total amount.

Worked Example 1 — Foundation Level

Question: The ratio of red to blue counters is 3 : 7. What fraction of the counters are red?

Working:

Total parts = 3 + 7 = 10

Fraction of red counters = 3/10

Answer: 3/10 of the counters are red.

Worked Example 2 — Higher Level

Question: In a class, 2/5 of the students are boys. Write the ratio of boys to girls.

Working:

Step 1: Boys = 2/5 of the total.

Step 2: Girls = 1 - 2/5 = 3/5 of the total.

Step 3: Ratio of boys to girls = 2 : 3

Answer: The ratio of boys to girls is 2 : 3.

Worked Example 3 — Exam Style

Question: Money is shared between Amy, Ben and Cara in the ratio 2 : 3 : 5. What fraction of the total does Ben receive? If the total is £450, how much does Ben get?

Working:

Total parts = 2 + 3 + 5 = 10

Fraction for Ben = 3/10

Amount for Ben = 3/10 x £450 = £135

Answer: Ben receives 3/10 of the total, which is £135.

Common Mistakes

• Using a part as the denominator instead of the total. In the ratio 3 : 7, the fraction of red is 3/10, not 3/7. The denominator must be the sum of all parts.
• Forgetting to account for all parts in a three-part ratio. If the ratio is 2 : 3 : 5, the total is 10, not 5 or any pair.
• Mixing up the order. "Ratio of A to B is 4 : 5" means A is 4 parts and B is 5 parts. Reversing them gives the wrong fraction.
• Not converting fractions to a common denominator before forming a ratio. If one quantity is 1/3 and another is 1/4, you must express both with a common denominator (4/12 and 3/12) to get the ratio 4 : 3.

Exam Tips

• Always write down the total number of parts at the start of your working. This earns a method mark and prevents errors.
• When a question says "what fraction," give a fraction. When it says "what proportion," a fraction or decimal is acceptable.
• Check that all your fractions from a ratio add up to 1 (the whole). This is a quick error check.
• On Higher tier, you may need to combine ratio-to-fraction conversion with algebra. Set up the fraction equal to the given information and solve.

Practice Questions

Q1 (Foundation): The ratio of cats to dogs at a shelter is 5 : 3. What fraction of the animals are dogs?

Q2 (Foundation): In a bag of sweets, 3/8 are toffees and the rest are mints. Write the ratio of toffees to mints.

Q3 (Higher): The ratio of adults to children at a concert is 7 : 3. There are 560 people in total. How many children are there?

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Related Topics

• Ratio Basics and Sharing
• Fractions
• Percentage of an Amount
• Ratio Problem Solving in Context

Summary

• A ratio compares parts to parts; a fraction compares a part to the whole.
• For the ratio a : b, the fraction of the first quantity is a / (a + b).
• To convert a fraction to a ratio, find the complementary fraction and write numerators side by side.
• The sum of all ratio fractions must equal 1 (the whole).
• Always use the total number of parts as the denominator when converting ratios to fractions.
• Express fractions with a common denominator before forming a ratio from fractions.