Solving Proportions Using Cross Products

6.3
Solving Proportions Using
Cross Products
Goal: Solve proportions using cross products.
Vocabulary
Cross
product:
A cross product of two ratios is the product of the
numerator of one ratio and the denominator of the
other ratio.
Example 1
Determining if Ratios Form a Proportion
Tell whether the ratios form a proportion.
4 8
a. , b. 1 2
2 6 4 2
21 , 2 0
35
Solution
4
a. 8 4
Write proportion.
2 6 2
4 p 42 26 p 8 Form cross products.
168
208
Multiply.
Answer: The ratios
do not form
a proportion.
b. 1 2
21 20
Write proportion.
35 12 p 35 21 p 20 Form cross products.
420
420
Multiply.
Answer: The ratios
form
a proportion.
Cross Products Property
Words The cross products of a proportion are equal.
Numbers Given that 2 5 6
, you know that 2 p 15 5 p 6 .
15
Algebra If a b c , where b 0 and d 0, then ad bc .
d
Lesson 6.3 Solving Proportions Using Cross Products 107

Example 2
Writing and Solving a Proportion
Earnings You earn $68 mowing 4 lawns. How much would you
earn if you mowed 7 lawns?
Solution
6 8
4
x 7
Money earned
Lawns mowed
68
p 7 4 p x Cross products property
476
4x
Multiply.
476
4
4 x
Divide each side by 4 .
4
119
x
Simplify.
Answer: If you mowed 7 lawns, you would earn $119 .
Checkpoint
Tell whether the ratios form a proportion.
9
1. 1 5
2. 1 2 6
3 9 65
45
2 8
yes
no
Use the cross products property to solve the proportion.
3. 1 4 x 4
4.
42
6 9 1 6
x
2 36
108 Chapter 6 Notetaking Guide