Simplifying Ratios – GCSE Maths Revision Guide

Simplifying ratios is a core GCSE skill that underpins almost every ratio and proportion question. A simplified ratio uses the smallest possible whole numbers, making it easier to work with in context problems.

What Is Simplifying Ratios?

Simplifying a ratio means dividing all parts of the ratio by their highest common factor (HCF) until no further simplification is possible. The result is an equivalent ratio in its simplest form.

For example, 12 : 18 simplifies to 2 : 3 because the HCF of 12 and 18 is 6. When ratios involve decimals, you first multiply to remove the decimal places. When ratios involve fractions, you multiply each part by the lowest common denominator.

The form 1 : n is useful for comparing rates. To convert any ratio a : b into 1 : n, divide both sides by a.

Ratios appear throughout GCSE Maths — in recipes, map scales, sharing problems, and probability — so fluency in simplifying is essential.

Key Formulas

To simplify a : b, divide both parts by HCF(a, b)

To convert to 1 : n form, divide both parts by the first number: 1 : (b ÷ a)

Step-by-Step Method

If the ratio contains decimals, multiply all parts by 10 (or 100) to make them whole numbers.
If the ratio contains fractions, multiply all parts by the lowest common denominator.
Find the HCF of all parts and divide each part by it.
If asked for the 1 : n form, divide every part by the first number.

Worked Example 1 — Foundation Level

Question: Simplify the ratio 24 : 36.

Working: HCF of 24 and 36 is 12. 24 ÷ 12 = 2 36 ÷ 12 = 3

Answer: 2 : 3

Worked Example 2 — Higher Level

Question: Write the ratio 0.6 : 1.5 in the form 1 : n.

Working: Multiply both by 10: 6 : 15 Simplify by dividing by 3: 2 : 5 Convert to 1 : n by dividing both by 2: 1 : 2.5

Answer: 1 : 2.5

Worked Example 3 — Exam Style

Question: Write the ratio ¾ : ½ in its simplest form.

Working: LCD of 4 and 2 is 4. ¾ × 4 = 3 ½ × 4 = 2

Answer: 3 : 2

Common Mistakes

Not fully simplifying. If you divide by a common factor that is not the HCF, you may need to simplify again. Always check whether the parts still share a common factor.
Leaving decimals in a simplified ratio. A ratio in its simplest form should use whole numbers (unless the question asks for 1 : n form, where a decimal is acceptable).
Getting the order wrong. Ratios are order-dependent — 3 : 5 is not the same as 5 : 3. Match the order to what the question specifies.
Mixing up units. If the parts are in different units (e.g., 2 m and 50 cm), convert to the same unit first before simplifying.

Exam Tips

Always convert to the same units before simplifying if the quantities are measured differently.
If the question says "simplest form," you need whole numbers with no common factor.
If it says "1 : n," you divide everything by the first part and can leave a decimal.
Three-part ratios (a : b : c) work the same way — find the HCF of all three parts.
Show each step of simplification clearly — dividing by 2, then by 3, etc. — to earn method marks even if you do not reach the simplest form in one step.

Practice Questions

Q1 (Foundation): Simplify 45 : 60.

Answer: HCF = 15. 45 ÷ 15 = 3, 60 ÷ 15 = 4. The ratio is 3 : 4.

Q2 (Foundation): Write 0.4 : 1.2 as a ratio in its simplest form.

Answer: Multiply by 10: 4 : 12. HCF = 4. Simplified: 1 : 3.

Q3 (Higher): Write the ratio ⅖ : ⅗ in the form 1 : n.

Answer: Multiply by 5: 2 : 3. Divide by 2: 1 : 1.5.

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Summary

Simplify a ratio by dividing all parts by their HCF.
Remove decimals by multiplying by 10, 100, etc., before simplifying.
Remove fractions by multiplying by the lowest common denominator.
The 1 : n form is found by dividing all parts by the value of the first part.
Always convert to the same units before comparing or simplifying.
Three-part ratios follow the same process — find the HCF of all three values and divide.

Simplifying Ratios –