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In algebra, a ratio is the relationship between two quantities. It is expressed as the quotient of one magnitude divided by another, or as a relation between several variables.


Note the use of words such as "times", "parts", "number", etc. This occurs because ratios are unitless; the units cancel out of the ratio. e.g. 3kg/5kg = 3000g/5000g = 3/5.

Ratios are not exactly the same thing as fractions. For example, if I have three pennies and five nickels, then the ratio of pennies to nickels is 3:5 or 3/5 (this indicates that there are three fifths as many pennies as nickels, but the fraction of coins which are pennies is 3/(3+5) = 3/8 (this indicates that the chances of a randomly selected coin being a penny are three in eight).

The most common thing to do with ratios is multiply them. For example, if there are two snorts for every giggle, and three giggles for every guffaw, then (since 2sn/1gig × 3gig/guf = 6sn/guf) there are six snorts for every guffaw. Note that the intermediate unit "giggle" canceled out of the expression. Note also that each fraction in the expression was equal to one, which is how we know that their product (6sn/guf) is also equal to one. Similarly, if I know there are two guffaws, then I can multiply by 6 snorts per guffaw (6sn/guf = one, the multiplicative identity) to learn that there are 12 snorts.

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