Ratio

A ratio is an expression of the relationship between two measures of the same attribute. Usually written as a:b it expresses how much of a and b are consistently combined in a whole, e.g. the ratio of weedkiller to water is 1:100, or the relationship of a to b, e.g. the scale on a map is 1 cm:100m. Common use distinguishes rates, which have two measurements of different units, e.g. kilometres per hour, and ratios, which have two or more measures of the same attribute. Both imply a division, although a ratio is not usually expressed in the form of a decimal fraction. As an example, suppose 15 lollies are shared between Molly and Dolly in the ratio 2:3. That means that for every 2 lollies that Molly receives, Dolly receives 3. So Molly gets 2 lollies out of every 5 (or 2/5 of the 15 lollies) and Dolly gets 3 lollies out of every 5 (or 3/5 of the 15 lollies).
In situations in which the ratio describes composition of a whole four fractional relationships exist. For example, in the ratio a:b, a/(a+b) gives the fraction of the whole made up by a. Similarly, b/(a+b) gives the fraction of the whole made up by b. So for a bag containing jelly beans in the ratio 3 black:5 red, 3/8 of the jellybeans are black and 5/8 are red.
In the ratio a:b, a/b describes the multiplicative relationship between the amount of a and the amount of b. Similarly this is b/a for the multiplicative relationship b to a. So for the jellybean example above, there are 3/5 as many black jellybeans as red, and there are 5/3 as many red jellybeans as black.