Basic Mathematics for College Students

428 Chapter 5 Ratio, Proportion, and Measurement

SECTION 5.2

Proportions

Objectives

1 Write proportions.

2 Determine whether

proportions are true or false.

3 Solve a proportion to find an

unknown term.

4 Write proportions to solve

application problems.

One of the most useful concepts in mathematics is the equation.An equationis a

statement indicating that two expressions are equal. All equations contain an =

symbol. Some examples of equations are:

4  4 8, 15.6 4.3 11.3, , and

Each of the equations shown above is true. Equations can also be false. For example,

3  2 6 and

are false equations.

In this section, we will work with equations that state that two ratios (or rates) are

equal.

Write proportions.

Like any tool, a ladder can be dangerous if used improperly. When setting up an

extension ladder, users should follow the 4-to-1 rule:For every 4 feet of ladder

height, position the legs of the ladder 1 foot away from the base of the wall. The

4-to-1 rule for ladders can be expressed using a ratio.

Remove the common units of feet.

The figure on the right shows how the 4-to-1 rule

was used to properly position the legs of a ladder 3 feet

from the base of a 12-foot-high wall. We can write a

ratio comparing the ladder’s height to its distance from

the wall.

Since this ratio satisfies the 4-to-1 rule, the two ratios and must be equal.

Therefore, we have

Equations like this, which show that two ratios are equal, are called proportions.

Proportion

A proportionis a statement that two ratios (or rates) are equal.

Some examples of proportions are

• Read as “1 is to 2 as 3 is to 6.”

•

Read as “3 waiters are to 7 tables

as 9 waiters are to 21 tables.”

3 waiters

7 tables



9 waiters

21 tables

1

2



3

6

4

1



12

3

12

3

4

1

Remove the common

units of feet.

12 feet

3 feet



12 feet

3 feet



12

3

4 feet

1 foot



4 feet

1 foot



4

1

1

 40 (5) 8

 16  8  2

1

2

 10  5

3 ft

12 ft