Ratios

A ratio is a way to compare two or more quantities or numbers. It is often written as ‘first value: second value’.
Ratios can convey the same information as fractions. For example, a ratio of 2:3 is equivalent to 2/3.
To represent the ratio of three values, for instance, you write it as ‘first value: second value: third value’. For example, the ratio of 2, 3, and 4 would be written as 2:3:4.
When comparing quantities using ratios, those quantities should be in the same units. Always convert all quantities to the same unit before working out any ratios.
Scaling up or down with ratios involves multiplying or dividing each part of the ratio by the same amount to maintain its value.
To share a quantity in a given ratio, find the total number of parts in the ratio, divide the quantity by the total number of parts, and then multiply each part of the ratio by this value.
Equivalent ratios are those which can be simplified to the same ratio. For example, the ratios 2:3 and 4:6 are equivalent because they can both be simplified to 2:3.
When asked to solve problems involving ratios, it can be helpful to draw a diagram or use a table to organize the information.
Knowledge of cross multiplication can be used to solve problems that involve ratios.
Keep in mind, the order of values in ratios is important. The ratio 3:4 is not the same as the ratio 4:3; these represent different comparisons.
It is helpful to remember that the ratio of quantities does not change if both quantities increase or decrease by the same factor. For example, the ratios of 2:3, 4:6, 6:9 and so on, all carry the same relative comparison.
The proportion is another way of comparing quantities or numbers, and it can be expressed as a:b = c:d. This implies ‘a is to b as c is to d’.
To solve proportion problems, carry out cross multiplication. This involves multiplying the first term of the first ratio by the second term of the second ratio and equating this product with that obtained by multiplying the second term of the first ratio by the first term of the second ratio.