Ratios

Part-to-whole comparisons can be expressed with fractions:

• 2/5 of the fruit are oranges
• 3/5 of the fruit are apples

Part-to-whole comparisons can also be expressed with percents:

• 2/5 = 40/100 = 40% of the fruit are oranges
• 3/5 = 60/100 = 60% of the fruit are apples

These are all two-term ratios as there are only 2 terms. In the ratio 3:2 both 3 and 2 are terms of the ratio.

Example

George has a backpack with 3 DVDs, 4 marbles, 7 comic books, and 1 apple.

a) What is the ratio of comic books to marbles?

b) What is the ratio of DVDs to the total number of items in the bag (including the DVD's)? Express as a fraction and a percent.

Solution:

a) Two ways of writing the ratio are 7 to 4, and 7:4. The 7:4 is the preferred way of writing the ratio. Notice that ratios have no units! Because typically they are measured in the same unit.

Expressed as a fraction, with the numerator (the top part of the fraction) equal to the first quantity (the comic books) and the denominator (the bottom part of the fraction) equal to the second quantity (the number of marbles), the answer would be 7/4.

b) There are 3 DVDs, and 3 + 4 + 7 + 1 = 15 items total.

The answer can be expressed as 3:15. Ratios are usually expressed in simplest form which in this case is 1:5.

As a fraction this would be 3/15 (or the equivalent 1/5) and as a percent it would be 20%.

Three term ratios

A three-term ratio will compare three amounts. In the example previous, George has a backpack with 3 DVDs, 4 marbles, 7 comic books, and 1 apple.

You could compare marbles to comic books to DVDs: four to seven to three or 4:7:3.

What would this three-term ratio be comparing in this example?

7:1:3

(comic books to apples to DVDs)