Aproportionis a statement of equality of two rations. For example,^35 ¼ 159
is a proportion. A proportion consists of four terms, and it is usually
necessary to find one of the terms of the given proportion given the other
three terms. This can be done by cross-multiplying and then dividing both
sides of the equation by the numerical coefficient of the variable.
EXAMPLE:Find the value of x:
5
6
¼
x
42
:
SOLUTION:
5
6
¼
x
42
6 x¼ 5 42 Cross-multiply
6 x¼ 210
61 x
61
¼
210
6
Divide by 6
x¼ 35
EXAMPLE:Find the value ofx:
10
x
¼
30
6
:
SOLUTION:
10
x
¼
30
6
30 x¼ 10 6 Cross-multiply
30 x¼ 60
301 x
301
¼
60
30
Divide by 30
x¼ 2
The strategy used to solve problems involving proportions is to identify
and write the ratio statement and then write the proportion.
EXAMPLE:If an airplane can travel 360 miles in 3 hours, how far can it
travel in 5 hours?
52 LESSON 6 Using Proportions