Simplifying Ratios - AQA - GCSE Maths Revision - BBC Bitesize - BBC

In this guide

1. Revise
2. Test

Pages

1. What is a ratio?
2. Simplifying ratios
3. Simplifying more difficult ratios
4. Dividing in a given ratio
5. Finding unknown ratios
6. Scale factors

Simplifying ratios

Click to explore updated revision resources for GCSE Maths: Simplyifying ratios, with step-by-step slideshows, quizzes, practice exam questions, and more!

Ratios can be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided any more.

Example

Simplify \(6:12\).

Divide both numbers by 2:

\(6:12 = 3:6\)

Divide both numbers by 3:

\(3:6 = 1:2\)

A quick way of doing this in just one step is to divide by the highest common factor of all the numbers in the ratio. In this example, the highest common factor of 6 and 12 is 6. Dividing each number by the HCF:

\(6:12 = 1:2\)

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Previous imageNext imageSlide 1 of 7, 6 red:12 yellow, A ratio of 6:12 with 6 red coloured counters and 12 yellow coloured counters spread out horizontallyEnd of image gallery

Question

Simplify these ratios fully:

1. \(4:6\)
2. \(9:12\)
3. \(5:10:15\)

Show answer

1. Divide both numbers by 2: \(4:6 = 2:3\)
2. Divide both numbers by 3: \(9:12 = 3:4\)
3. Divide all numbers by 5: \(5:10:15 = 1:2:3\)

Next pageSimplifying more difficult ratiosPrevious pageWhat is a ratio?

More guides on this topic

• NEW: Equivalent ratios and simplifying ratios
• NEW: Ratio and fractions, and sharing in a ratio
• NEW: Scale drawings and maps
• NEW: Percentages of an amount
• NEW: Percentage change
• NEW: Repeated percentage change, interest and exponential change
• NEW: Working with proportion
• NEW: Equations of direct and inverse proportion
• Percentages - AQA
• Direct and inverse proportion - AQA

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