Ratio, Proportion & Rates of Change
№ 173Sheet № 173 · Foundation + Higher · AQA · Edexcel · OCR
Simplifying Ratios –
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.
§Key definitions
Question:
Simplify the ratio 24 : 36.
Q1 (Foundation):
Simplify 45 : 60.
Q2 (Foundation):
Write 0.4 : 1.2 as a ratio in its simplest form.
Q3 (Higher):
Write the ratio ⅖ : ⅗ in the form 1 : n.
§Formulas to memorise
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)
Worked example
Simplify the ratio 24 : 36.
Working: HCF of 24 and 36 is 12. 24 ÷ 12 = 2 36 ÷ 12 = 3
⚠ 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.
MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/simplifying-ratios