Chapter 2.7

Solve Proportions Using Cross Products

Cross Product Property

• In a proportion, a cross product is the product of the numerator of one ratio and the denominator of the other ratio. The following property involving cross products can be used to solve proportions.

Use the cross products property EXAMPLE

Write original proportion.

8 15 = x 6

Solve the proportion = . 8

x

6

15

Cross products property

Simplify. 120 = 6x

Divide each side by 6. 20 = x

The solution is 20. Check by substituting 20 for x in the original proportion.

ANSWER

= 8

x

6

15

Use the cross products property EXAMPLE

Substitute 20 for x.

CHECK

Cross products property

Simplify. Solution checks.

8

20

6

15 = ?

8 15 = 20 6 ?

120 = 120

EXAMPLE Standardized Test Practice

What is the value of x in the proportion = ? 4

x

8

3 x –

A – 6 B – 3 C 3 D 6

SOLUTION

4

x =

8

x – 3 Write original proportion.

Cross products property 4(x – 3) = x 8

4x – 12 = 8x Simplify.

Subtract 4x from each side. –12 = 4x

Divide each side by 4. –3 = x

EXAMPLE Standardized Test Practice

The value of x is –3. The correct answer is B.

ANSWER

A B C D

Write and solve a proportion

EXAMPLE

x

280 =

8 amount of food

100 weight of seal

SOLUTION

STEP 1

Write a proportion involving two ratios that compare the amount of

food with the weight of the seal.

Each day, the seals at an aquarium are each fed 8 pounds of food for

every 100 pounds of their body weight. A seal at the aquarium weighs

280 pounds.

How much food should the seal be fed per day?

Seals

Write and solve a proportion

EXAMPLE

STEP 2

Solve the proportion.

8

100

x

280 = Write proportion.

8 280 = 100 x Cross products property

2240 = 100x Simplify.

22.4 = x Divide each side by 100.

ANSWER

A 280 pound seal should be fed 22.4 pounds of food per

day.

EXAMPLE 1

Solve the proportion. Check your solution.

On Your Own

= 4

a

24

30 1.

5 ANSWER

EXAMPLE 2 On Your Own

3

x =

2

x – 6 2.

18 ANSWER

Solve the proportion. Check your solution.

EXAMPLE 2 On Your Own

4

m

5 =

m – 6 3.

18 ANSWER

Solve the proportion. Check your solution.

EXAMPLE 4

Use the scale on a map On Your Own

6. The ship model kits sold at a hobby store have a scale of 1 ft : 600

ft. A completed model of the Queen Elizabeth II is 1.6 feet long.

Estimate the actual length of the Queen Elizabeth II.

Model ships

ANSWER about 960 ft