Equivalent & Simplified Ratios

Equivalent ratios are two ratios that represent the same proportion of quantities within a whole

• E.g. The ratio 5 : 10 is equivalent to 20 : 40

Equivalent ratios are frequently used when the values involved take on a real-life meaning

• E.g. A cake recipe involves flour and butter being mixed in the ratio 3 : 2

  • 3 g of flour and 2 g of butter would not lead to a very big cake

  • An equivalent ratio of 300 : 200 gives a more realistic 300 g of flour and 200 g of butter

You can find an equivalent ratio by multiplying (or dividing) each part of the ratio by the same value

• E.g. Multiply each part of the ratio 2 : 3 : 7 by 4 to find an equivalent ratio of 8 : 12 : 28

• Ratios can be scaled up or down to suit the context of a question

The size of each part in the ratio, relative to the others, is still the same

• The actual values in the equivalent ratio may be more meaningful in the context of the situation

Finding an equivalent ratio is similar to finding equivalent fractions

• However it is crucial to remember that 1 : 4 is not equivalent to $\frac{1}{4}$

In questions you will be given information that will allow you to find the multiplier

• The information may be about the one part of the ratio, or it may be about the whole 

• You can then use this to find the other parts of the equivalent ratio and answer the question

Simplifying a ratio involves finding an equivalent ratio where the numbers involved are smaller

• E.g. The ratio 45 : 30 is equivalent to 9 : 6

The need to simplify a ratio often arises when the initial ratio has been given using large values from a real-life context

A ratio is in its simplest form when

• All of the values in the ratio are integers

• There are no common factors between each of the values in the ratio

• E.g. The simplest form of the ratio 45 : 30 is 3 : 2

Divide each part of the ratio by the same value

• This value should be a common factor of all parts of the ratio

  • Ideally, the highest common factor (HCF) should be used to get the ratio into its simplest form in one go

  • If the HCF is not used, we can repeat the process of simplifying

• E.g. Divide all parts of the ratio 30 : 66 : 12 by 6 to find the ratio in its simplest form 5 : 11 : 2