Page 449 - Basic College Mathematics with Early Integers

426 C HAPTE R 5 I RATIO, PROPORTION, AND MEASUREMENT

Definitions and Concepts Examples

Section 5.2 Proportions

A proportion is a statement that two ratios or rates are 1 4
= is a proportion.
equal. 2 8
6 9
USING CROSS PRODUCTS TO DETERMINE WHETHER PROPORTIONS Is = a true proportion?
10 15
ARE TRUE OR FALSE
Cross products
Cross products
#
#
# # 6 15 10 9
a d b c
a c 6 = 9
b = d 10 15
#
#
If cross products are equal, the proportion is true. 6 15 10 9 Are cross products equal?
If ad = bc, then the proportion is true. 90 = 90
If cross products are not equal, the proportion is false. Since cross products are equal, the proportion is a true
If ad Z bc, then the proportion is false. proportion.

FINDING AN UNKNOWN VALUE n IN A PROPORTION n 5
Find n: =
Step 1: Set the cross products equal to each other. 7 8
Step 1:

n = 5
7 8
#
#
n 8 = 7 5 Set the cross products equal to each other.
#
n 8 = 35 Multiply.
Step 2: Divide the number not multiplied by n by the Step 2:
number multiplied by n.
35
n = Divide 35 by 8, the number multiplied by n.
8
3
n = 4
8

Section 5.3 Proportions and Problem Solving

Given a specified ratio (or rate) of two quantities, a pro- On a map, 50 miles corresponds to 3 inches. How many
portion can be used to determine an unknown quantity. miles correspond to 10 inches?
1. UNDERSTAND. Read and reread the problem.
2. TRANSLATE. We let n represent the unknown
number. We are given that 50 miles is to 3 inches as
n miles is to 10 inches.

miles : 50 n ; miles
=
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inches : 3 10 ; inches