Page 74 - BUSINESS MATHEMATICS MODULE 1 (WHOLE)_revised 10.20.2020

B. RATIOS AND PROPORTIONS
• Ratio

A ratio is an arithmetic relationship between two amounts, showing the proportion of
one to the other. For example, we can say that in a certain university there are thrice as many

girls as boys taking business mathematics. We can say that the ratio of girls to boys is 3 to 1
and can be expressed, 3:1 (3:1 is read "3 to 1").

In the university we just mentioned, there are 900 students enrolled in its business
mathematics class. Of these, 225 are boys and 675 are girls. A ratio can be found in two ways.

First, we can divide the number of girls (i.e. 675) by the number of boys (i.e. 225) and
expressing the answer, ie. 3, in ratio form, as in 3:1. Secondly, we can find the ratio by

comparing the numerators of fractions that have the same denominator. Thus, we can see that

225 1 675 225 ×3 3 3 1
= while = = . Thus, in our given example, the ratio of girls to boys is,
900 4 900 225 × 4 4 4 4
again, 3:1.

The following examples will further clarify our point.

Example 1:

A department store found that in a given month it sold 78 male umbrellas and 234

umbrellas for women. What was the ratio of sales of male to female umbrellas?

Solution 1.

234 = 3, or a ratio of 3 to 1 (3:1)
78
Solution 2.

Female umbrellas sold: 234
Male umbrellas sold: 78 .

TOTAL 312
234 78 3 3
= ∙ = female umbrellas
312 78 4 4
or a ratio of 3:1
1
78 = 78 ∙ = male umbrellas
1
312 78 4 4

Page | 5.4 BUSINESS MATHEMATICS: MODULE 1