Sheet № 228 · Foundation + Higher · AQA · Edexcel · OCR
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 r
§Key definitions
Question:
The ratio of red to blue counters is 3 : 7. What fraction of the counters are red?
Answer:
3/10 of the counters are red.
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?
§Formulas to memorise
Fraction of the first quantity = a / (a + b)
Fraction of the second quantity = b / (a + b)
Add the parts — of the ratio to find the total number of parts.
Write each part as a fraction — of the total.
Simplify — the fractions if possible.
Express both quantities as fractions — of the total with the same denominator.
Read off the numerators — these form the ratio.
Simplify — the ratio if needed.
Worked example
The ratio of red to blue counters is 3 : 7. What fraction of the counters are red?
Working:
⚠ 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.