✓ Revise Right course
To simplify a ratio, divide every part by the highest common factor. A ratio is a comparison of two or more quantities, written in the form a:b. Free notes.
Simplifying and Interpreting Ratios is part of Ratio and Proportion Fundamentals in GCSE AQA Higher Maths.
3 min
Reading time
23
Lessons in this topic
GCSE AQA Higher
Pathway
Reviewed by Revise Right
Content review
To simplify a ratio, divide every part by the highest common factor. A ratio is a comparison of two or more quantities, written in the form a:b. Free notes.
AQA GCSE Maths mock draft, 26–31 Oct. Draft coverage: Maths Paper 1 (Higher tier). Reviewed for an original-practice sitting; check student availability before registering. Marking and results will follow later, after separate approval. Eligible new accounts receive a five-day Pro trial when signup email verification completes. Previous trials keep their original expiry. After expiry, new papers need Pro unless you have an explicitly confirmed free sitting offer for this event. That offer adds no Pro time or AI learning. Saved attempts and released results remain readable. No card or automatic charge.
Use this lesson to stay inside Ratio and Proportion Fundamentals while connecting the detail back to the wider Ratio, proportion and rates of change topic.
Read the core explanations from Simplifying and Interpreting Ratios before testing yourself from memory.
Imagine you're making orange squash. The bottle says 'mix 1 part squash with 4 parts water'. That's a ratio — 1:4. It tells you the relationship between the amounts.
Ratios appear everywhere in real life. Recipe ingredients, paint mixing, currency exchange rates, and even your phone screen dimensions all use ratios. Understanding them helps you scale recipes up or down, work out fair shares, and solve proportion problems.
The key insight is this: ratios show relationships, not actual amounts. A 1:4 ratio could mean 1ml to 4ml, or 100ml to 400ml — the relationship stays the same.
Ratios use the colon symbol (:) to separate the parts. The ratio 6:9 means 'for every 6 of the first quantity, there are 9 of the second'. But this isn't in its simplest form.
To simplify ratios, we find the highest common factor (HCF) of all the numbers and divide each part by it. This is like cancelling fractions — we're removing common factors to make the numbers as small as possible.
For 6:9, both numbers divide by 3. So 6÷3 = 2 and 9÷3 = 3, giving us 2:3. This is the simplest form because 2 and 3 have no common factors except 1.
Worked example: Simplifying the Ratio 12:18:24
Write 12:18:24 in its simplest form
Answer: 2:3:4
Just like equivalent fractions, ratios can look different but represent the same relationship. The ratio 1:2 is equivalent to 2:4, 3:6, 10:20, and so on.
We create equivalent ratios by multiplying or dividing all parts by the same number. This is crucial for solving ratio problems where you know the total or one part of the ratio.
Think of it like scaling a recipe. If a recipe for 2 people uses ingredients in the ratio 1:3, then for 6 people you'd multiply everything by 3, giving 3:9. The relationship stays the same.
Worked example: Finding Missing Values in Ratios
If the ratio of cats to dogs is 3:5, and there are 15 cats, how many dogs are there?
Answer: 25 dogs
Now you've seen the key methods, let's practise them. Remember the two main skills: simplifying ratios using the HCF, and finding equivalent ratios using scale factors.
For simplification problems, always find the HCF first. For missing value problems, find what one part was multiplied by, then apply that to all parts.
Students often make predictable errors with ratios. The most common mistake is not simplifying fully — stopping when there are still common factors left.
Another trap is mixing up the order. If the question asks for 'the ratio of boys to girls' and you calculate girls to boys, you'll lose marks even if your numbers are correct.
In exam questions, always check your final ratio by seeing if the parts have any common factors. If they do, you haven't finished simplifying.
Worked example: Avoiding the 'Incomplete Simplification' Trap
A student simplified 24:36:48 and got 12:18:24. What went wrong?
Answer: The student didn't find the HCF correctly. The fully simplified ratio is 2:3:4.
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-25.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
To simplify a ratio, divide every part by the highest common factor. For 6:9 the HCF is 3, giving 2:3, and for 12:18:24 the HCF is 6, giving 2:3:4.
A ratio is a comparison of two or more quantities, written in the form a:b. A squash bottle that says mix 1 part squash with 4 parts water gives the ratio 1:4, which could mean 1 ml to 4 ml or 100 ml to 400 ml.
Equivalent ratios represent the same proportional relationship and are made by multiplying or dividing all parts by the same number. For example, 1:2 is equivalent to 2:4, 3:6 and 10:20.
A missing value in a ratio is found by working out the scale factor from the known part, then applying it to the other part. If the ratio of cats to dogs is 3:5 and there are 15 cats, the scale factor is 15 ÷ 3 = 5, so there are 5 × 5 = 25 dogs.
A ratio is fully simplified when the parts have no common factors other than 1. Dividing 24:36:48 by 2 gives 12:18:24, which can still be simplified; dividing by the HCF of 12 gives 2:3:4.
12:18:24 simplifies to 2:3:4. The HCF of 12, 18 and 24 is 6, found from 12 = 2² × 3, 18 = 2 × 3² and 24 = 2³ × 3, and dividing each part by 6 gives 2, 3 and 4.
6:9 simplifies to 2:3, because both numbers divide by their HCF of 3: 6 ÷ 3 = 2 and 9 ÷ 3 = 3. This is the simplest form because 2 and 3 have no common factors except 1.
24:36:48 simplifies to 2:3:4 by dividing every part by the HCF of 12. Dividing by only 2 gives 12:18:24, which is not fully simplified, a common mistake.
The order of a ratio matters: the ratio of boys to girls is not the same as girls to boys. Writing the parts in the wrong order loses marks even when the numbers are correct.
A ratio shows a relationship, not actual amounts. A 1:4 ratio of squash to water could mean 1 ml to 4 ml or 100 ml to 400 ml, because the relationship stays the same.
A ratio is simplified with prime factors by writing each part in prime factors and taking the lowest power of each common prime to get the HCF. For 12:18:24, the common factors 2¹ and 3¹ give HCF = 6, and dividing gives 2:3:4.