Page 390 - Basic College Mathematics with Early Integers

S E C T I O N 5.2 I PROPORTIONS 367

Concept Check Think about cross products and write the true proportion
5 10
= in two other ways so that each result is also a true proportion.
8 16
(Note: There are no units attached in this proportion.)

Objective Finding Unknown Numbers in Proportions

When one number of a proportion is unknown, we can use cross products to find the
unknown number. For example, to find the unknown number n in the proportion
n 2
= , we first find the cross products.
30 3
# #
n 3 30 2 Find the cross products.
n 2
30 = 3

If the proportion is true, then cross products are equal.
#
#
n 3 = 30 2 Set the cross products equal to each other.
#
n 3 = 60 Write 2 # 30 as 60.
To find the unknown number n, we ask ourselves,“What number times 3 is 60?”
The number is 20 and can be found by dividing 60 by 3.

60
n = Divide 60 by the number multiplied by n.
3
n = 20 Simplify.

Thus, the unknown number is 20.
Check: To check, let’s replace n with this value, 20, and verify that a true propor-
tion results.
20 2
; Replace n with 20.
30 3

20 2
30 3

#
3 20 #
2 30
60 = 60 Cross products are equal.

Finding an Unknown Value n in a Proportion

Step 1: Set the cross products equal to each other.
Step 2: Divide the number not multiplied by n by the number multiplied by n.

Concept Check Answer
8 16 5 8
possible answers: = and =
5 10 10 16