Ratios

A ratio express the proportion of two commodities in relation to each other (as opposed to in relation to the whole, as a fraction or percentage does).

Rules

Add both numbers in a ratio to get the total amount with respect to each.

A ratio expresses quantity in relation to the other. This is not to be mixed up with parts of the whole. If the ratio of Democrats to Republicans at a conference is 6 to 4, then Republicans make up 40% of the conference (4 divided by 6 + 4). If guitar players make up 70% of the rock band seminar and drummers make up 30%, then the ratio of guitarists to drummers is 7 to 3.

Practice

1. Of the 50 lawyers at the meeting, 22 are bankruptcy lawyers; the remainder are divorce lawyers. What is the ratio of bankruptcy lawyers to divorce lawyers?

2. The ratio of stocks to bonds in the portfolio is 4 to 9. If there are 169 items in the portfolio, how many of them are bonds?

3. The ratio of ratio questions to non-ratio questions on the math quiz is 4 to 5. If there are a total of 36 questions, how many are ratio questions?

Comments

As alluded, the most common mistake area in ratios is forgetting that the ratio is an expression of one quantity in relation to each other and not the total amount. Whenever presented with a ratio, a test taker must add the two numbers to get the whole amount.

Answers to Practice Questions

1. 11 to 14

The ratio is 22 to (number of divorce lawyers) = 22 to (50 - 22) = 22 to 28 = 11 to 14

2. 117

The ratio of stocks to bonds is 4 to 9. Thus, the fraction of the portfolio which is bonds is =

Always remember to add both numbers in a ratio to get the total amount.

multiplied by 169 is 117.

3. 16

The ratio of ratio questions to non-ratio questions is 4 to 5. Thus, the fraction of the quiz which is math questions is = multiplied by 36 is 16.