1. 6.3 Solving Proportions Using Cross Products
LESSON
Solving Proportions Using Cross Products
Every pair of ratios has two cross products. A cross product of two ratios is the product of the numerator of one ratio and the denominator of the other ratio. 3 5 6 10 , 2 3 6 11 ,
Ratios:
Cross products:
3 • 10
5 • 6
2 • 11
3 • 6
Notice that for the ratios and , the ratios are equal and their cross products are also equal. For the ratios and , the ratios are not equal, and neither are their cross products. 3 5 6 10 2 11
You can use cross products to tell whether two ratios form a proportion. If the cross products are equal, then the ratios form a proportion.

2. 6.3 Solving Proportions Using Cross Products 1
LESSON
Solving Proportions Using Cross Products
EXAMPLE 1
Determining if Ratios Form a Proportion
Tell whether the ratios form a proportion. 12 20 32 50 , 12 20 32 50 = ?
Write proportion.
12 • 50
20 • 32 = ?
Form cross products.
600 = 640
Multiply.
ANSWER
The ratios do not form a proportion.

3. 6.3 Solving Proportions Using Cross Products
LESSON
Solving Proportions Using Cross Products
You can use the multiplication property of equality to demonstrate an important property about the cross products of a proportion. a b c d =
Given. 1 bd 1 a b c d = • 1
Multiply each side by bd. Divide out common factors.
ad = cb
Simplify.
This result proves the cross products property.

4. 6.3 Solving Proportions Using Cross Products Cross Products Property
LESSON
Solving Proportions Using Cross Products
Cross Products Property
Words
The cross products of a proportion are equal.
Given that = , you know that 2 • 15 = 5 • 6. 2 5 6 15
Numbers
If = , where b = 0 and d = 0, then ad = bc. a b c d
Algebra
You can use the cross products property to solve proportions.

5. 6.3 Solving Proportions Using Cross Products 2
LESSON
Solving Proportions Using Cross Products
EXAMPLE 2
Writing and Solving a Proportion
Hair Growth Human hair grows about 0.7 centimeter in 2 weeks. How long does hair take to grow 14 centimeters?
SOLUTION 14 x
0.7 2 =
Length of hair grown
Number of weeks
0.7 • x = 2 • 14
Cross products property
0.7x = 28
Multiply.
0.7x 28 = =
0.7
Divide each side by 0.7.
x = 40
Simplify.
ANSWER
Hair takes about 40 weeks to grow 14 centimeters.

6. 6.3 Solving Proportions Using Cross Products
LESSON
Solving Proportions Using Cross Products
Methods for Solving a Proportion
SUMMARY
To solve the proportion = , use one of the following: 5 12 x 36
Equivalent ratios 5 12 x 36 5 12
 3 15 36
 3
Algebra 5 12 x 36 =
36 • •
Multiply each side by 36.
15 = x
Simplify.
Cross products
5 • 36 = 12x
Cross products property
15 = x
Divide each side by 12.