7-4 Proportions

Learn to write and solve proportions.

7-4 Proportions

Vocabulary

proportion

7-4 Proportions

A proportion is an equation that shows two equivalent ratios.

Read the proportion = as “two is to

one as four is to two.”

21__ 4

2__=

42__ 8

4__=

21__ 6

3__=

21__ 4

2__

Reading Math

7-4 Proportions

Additional Example 1: Modeling Proportions

Write a proportion for the model.

number of heartsnumber of stars

48__=

First write the ratio of hearts to stars.

Next separate the hearts and stars into two equal groups.

7-4 Proportions

Additional Example 1 Continued

Now write the ratio of hearts to stars in each group.

number of heartsnumber of stars

24__=

A proportion shown by the model is = .48__ 2

4__

7-4 Proportions

Check It Out: Example 1

Write a proportion for the model.

number of facesnumber of moons

26__=

First write the ratio of faces to moons.

Next separate the faces and moons into two equal groups.

7-4 Proportions

Check It Out: Example 1 Continued

Now write the ratio of faces to moons in each group.

number of facesnumber of moons

13__=

A proportion shown by the model is = .26__ 1

3__

7-4 Proportions

Cross products in proportions are equal

CROSS PRODUCTS

35__ 9

15___=4

8__ 2

4__= 9

6__ 3

2__= 14

7 __ 2

1__=

8 • 2 = 4 • 4 5 • 9 = 3 • 15

16 = 16 45 = 45

6 • 3 = 9 • 2

18 = 18

7 • 2 = 14 • 1

14 = 14

7-4 Proportions

Additional Example 2: Using Cross Products to Complete Proportions

Find the missing value in the proportion.

6n 6

___

56__ n

18 __= Find the cross products.

6 • n = 5 • 18 The cross products are equal.

6n = 90 n is multiplied by 6.

90 6

___= Divide both sides by 6 to undo the multiplication.

n = 15

7-4 Proportions

Check It Out: Example 2

Find the missing value in the proportion.

5n 5

___

35__ n

15 __= Find the cross products.

5 • n = 3 • 15 The cross products are equal.

5n = 45 n is multiplied by 5.

45 5

___= Divide both sides by 5 to undo the multiplication.

n = 9

7-4 Proportions

Additional Example 3: Measurement Application

According to the label, 1 tablespoon of plant fertilizer should be used per 6 gallons of water. How many tablespoons of fertilizer would you use for 4 gallons of water?

f4 gal

____1 tbsp 6 gal

_____ = Let f be the amount of fertilizer for 4 gallons of water.

f4 gal

____1 tbsp 6 gal

_____ = Write a proportion.

6 • f = 1 • 4 The cross products are equal.

7-4 Proportions

In a proportion, the units must be in the same order in both ratios.

Caution!

tbspgal

___tbspgal

___=

galtbsp

___galtbsp

___=or

7-4 Proportions

Additional Example 3 Continued

f is multiplied by 6.

Divide both sides by 6 to undo the multiplication.

Write your answer in simplest form.

6f = 4

6f 6

___ 4 6

__=

f = tbsp 2 3

__

You would use tbsp of fertilizer for 4 gallons of water.

2 3

__

7-4 Proportions

Check It Out: Example 3

According to the label, 3 tablespoons of plant fertilizer should be used per 9 gallons of water. How many tablespoons of fertilizer would you use for 2 gallons of water?

f2 gal

____3 tbsp 9 gal

_____ = Let f be the amount of fertilizer for 2 gallons of water.

f2 gal

____3 tbsp 9 gal

_____ = Write a proportion.

9 • f = 3 • 2 The cross products are equal.

7-4 Proportions

Check It Out: Example 3 Continued

f is multiplied by 9.

Divide both side by 9 to undo the multiplication.

Write your answer in simplest form.

9f = 6

9f 9

___ 6 9

__=

f = tbsp 2 3

__

You would use tbsp of fertilizer for 2 gallons of water.

2 3

__