Understanding Ratios and Proportions

A ratio is a comparison of two similar quantities obtained by dividing one quantity by the other. Ratios are written with the : symbol.

Example 1: The ratio of 6 to 3 is

6 ÷ 3  or  6 / 3  =  6 : 3 = 2

Example 2: The ratio of 3 to 6 is

3 ÷  6 or  3 / 6 = 3 : 6 = 1 / 2

Example 3

Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and 1 orange.

1) What is the ratio of books to marbles?
Expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second, the answer would be 7/4.
Two other ways of writing the ratio are 7 to 4, and 7:4.

2) What is the ratio of videocassettes to the total number of items in the bag?
There are 3 videocassettes, and 3 + 4 + 7 + 1 = 15 items total.
The answer can be expressed as 3/15, 3 to 15, or 3:15.

Proportions

A proportion is a statement of the equality of two ratios.

Example: 6 : 3  =  2 : 1 or 6 / 3  =  2 / 1 are ways to write the proportion expressed as: 6 is to 3 as 2 is to 1

Example: 2 : 8  =  1 : 4 or 2 / 8  =  1 / 4 are ways to write the proportion expressed as: 2 is to 8 as 1 is to 4

When two ratios are equal, then the cross products of the ratios are equal.

That is, for the proportion, a:b = c:d , a x d = b x c