GCSE MATHS • HIGHER TIER

Simplifying Ratio Made Simple

Use the Highest Common Factor to reduce ratios to their simplest equivalent form.

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Simplifying Ratio in Four Moves

1

Identify

Identify every part of the ratio.

2

Find the HCF

Find the Highest Common Factor of all ratio parts.

3

Divide

Divide every part by the same HCF.

4

Check

Check that the ratio cannot be simplified any further.

What You’ll Learn

Understand Ratios

Know how ratios compare two or more quantities.

Find the HCF

Use common factors to identify the largest number that divides every part.

Simplify Two-Part Ratios

Reduce ratios such as 8:12 to their simplest form.

Simplify Three-Part Ratios

Apply the same method to ratios such as 30:45:60.

Connect Ratios and Fractions

Understand how ratio parts can represent fractions of a total.

Key Rules

Use the Same Divisor

Divide every part of the ratio by the same number.

Use the HCF

Divide by the Highest Common Factor to simplify the ratio fully.

Include Every Part

For a three-part ratio, find the HCF of all three values.

Keep the Original Order

Do not change the order of the ratio parts.

Worked Proof: Simplifying Ratio

Step-by-Step Method

  • 1. Identify every part of the ratio.
  • 2. Find the Highest Common Factor of all the ratio parts.
  • 3. Divide every part by the same HCF.
  • 4. Keep the ratio parts in their original order.
  • 5. Check that the ratio cannot be simplified further.

More Worked Examples

1

Question: Simplify 8:12

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12
HCF = 4
8 ÷ 4 = 2
12 ÷ 4 = 3
Answer : 2:3

2

Question: Simplify 15:25

HCF = 5

15 ÷ 5 = 3
25 ÷ 5 = 5
Answer : 3:5

3

Question: Simplify 18:24

HCF = 6

18 ÷ 6 = 3
24 ÷ 6 = 4
Answer : 3:4

4

Question: Simplify 30:45:60

HCF = 15

30 ÷ 15 = 2
45 ÷ 15 = 3
60 ÷ 15 = 4
Answer : 2:3:4
  • Common GCSE Mistakes
  • Same divisor: Divide every part of the ratio by the same number.
  • HCF: Use the Highest Common Factor so the ratio is fully simplified.
  • Ratio vs fraction: Do not confuse a ratio comparison with a fraction of a whole.
  • Final check: Make sure no common factor greater than 1 remains.
  • Exam Tips
  • Find the HCF of all parts before dividing.
  • Show the division applied to every ratio part.
  • For three-part ratios, include all three values when finding the HCF.
  • Keep the order of the ratio parts unchanged.
  • Check whether your final ratio can be simplified again.
  • Use factors and prime-number skills to find the HCF efficiently.

Skills Used in Simplifying Ratio

Ratios

Highest Common Factor

Factors and Multiples

Prime Numbers

Division

Equivalent Ratios

Fractions

Percentages

Proportion

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Frequently Asked Questions

A ratio compares two or more quantities.

A simplified ratio represents the same relationship using smaller numbers, making it easier to understand and compare.

Find the HCF of all parts, divide every part by it, then check that no further simplification is possible.

Yes. The source states that three-part ratios use the same method as two-part ratios.

For a ratio such as 2:3, there are 5 total parts, so the quantities represent 2/5 and 3/5 of the total.

The source recommends factors, multiples, prime numbers, fractions, percentages and proportion-related topics.