Simplifying ratios
Click to explore updated revision resources for GCSE Maths: Simplifying ratios, with step-by-step slideshows, quizzes, practice exam questions, and more!
A relationship between two quantities. can be fully simplified just like fractions. To A fraction is simplified when there are no more common factors shared by the numerator and denominator. For example, the fraction 8/10 simplifies to 4/5 by dividing the numerator and denominator by the common factor of 2. 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 The highest common factor (HCF) of two numbers is the largest number which will divide exactly into both of them, for example, the highest common factor of 24 and 36 is 12. 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:
\(6:12 = 1:2\)
Image caption, A ratio of 6:12 with 6 red coloured counters and 12 yellow coloured counters spread out horizontally
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Question
Simplify these ratios fully:
- \(4:6\)
- \(9:12\)
- \(5:10:15\)
- Divide both numbers by 2: \(4:6 = 2:3\)
- Divide both numbers by 3: \(9:12 = 3:4\)
- Divide all numbers by 5: \(5:10:15 = 1:2:3\)
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 - Edexcel
- Direct and inverse proportion - Edexcel
