Ratio

The ratio of one quantity to another is a way to express their relative sizes, often in the form of a fraction, where the first quantity is the numerator and the second quantity is the denominator. Thus, is s and t are positive quantities, then the ratio of s to t can be written as the fraction . The notation "s to t" or "s:t" is also used to express this ratio.

For e.g. if there are 2 apples and 3 oranges in a basket, we can say that the ratio of the number of apples to the number of oranges is or that it is 2 to 3 or that it is 2:3.

Like fractions, rations can be reduced to the lowest terms. For e.g. if there are 8 apples and 12 oranges in a basket, then the ration of the number if apples to oranges is still 2 to 3. Similarly, the ration 9 to 12 is equivalent to the ration 3 to 4.

If three or more positive quantities are being considered, say and , then their relative sizes can be also be expressed as a ration with the notation " to to ." For e.g. if there are 5 apples, 30 pears, and 20 oranges in a basked, then the ratio of the number of apples to pears to oranges is 5 to 30 to 20. This ratio can be reduced to 1 to 6 to 4 by dividing each number by the greatest common divisor of 5, 30 and 20, which is 5.

A proportion is an equation relating two ratios; for e.g. . To solve a problem involving ratios, you can often write a proportion and solve it by cross multiplication.
Ex. To find a number so that the ratio of to 49 is the same as the ratio of 3 to 21, you can write
Then cross multiply to get and solve for to get