Simplifying ratios
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: \(5:10:15 = 1:2:3\)