8-2 Proportions

Course 1

Warm Up

Lesson Presentation

Problem of the Day

Warm UpUse the table to write each ratio.

1. giraffes to monkeys2. polar bears to all bears3. monkeys to all animals4. all animals to all bears

2:174:7

17:26

Course 1

8-2 Proportions

Brown bears 3

Giraffes 2

Monkeys 17

Polar Bears 4

26:7

Problem of the Day

A carpenter can build one doghouse in one day. How many doghouses can 12 carpenters build in 20 days?240

Course 1

8-2 Proportions

Learn to write and solve proportions.

Course 1

8-2 Proportions

Vocabulary

proportion

Insert Lesson Title Here

Course 1

8-2 Proportions

Course 1

8-2 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__

Course 1

8-2 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.

Course 1

8-2 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__

Course 1

8-2 Proportions

Try This: 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.

Course 1

8-2 Proportions

Try This: Example 1

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__

Course 1

8-2 Proportions

CROSS PRODUCTS

Cross products in proportions are equal

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

Course 1

8-2 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

Course 1

8-2 Proportions

Try This: 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

Course 1

8-2 Proportions

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

Helpful Hint

tsp lb

___tsp lb

___=

lbtsp

___ lbtsp

___=or

Course 1

8-2 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.

Course 1

8-2 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

__

Course 1

8-2 Proportions

Try This: 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.

Course 1

8-2 Proportions

Try This: 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

__

Lesson Quiz

1. Write a proportion for the model.

Find the missing value in each proportion.

2. = 3. =

4. The label on a bottle of salad dressing states

that there are 3 grams of fat per tablespoon. If

you use 3 tablespoons, how many grams of fat

would you be getting?

p = 30x = 25

Insert Lesson Title Here

9 g

Course 1

8-2 Proportions

2 6

__ 1 3

__=

9 5

__ 45 x

__ p 36

__ 5 6

__