7-3 Proportions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

7-3 Proportions

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

4Polar Bears

17Monkeys

2Giraffes

3Brown bears

26:7

7-3 Proportions

Problem of the Day

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

7-3 Proportions

MA.6.A.2.2 …Compare ratios and rates.

Also MA.6.A.3.2

Sunshine State Standards

7-3 Proportions

Vocabulary

proportion

7-3 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

7-3 Proportions

Additional Example 1A: Modeling Proportions

Julio spent $10 to buy 4 books at a garage sale. How much would Julio pay for 8 books at the garage sale?

x = $10 2 = $20

The cost for 8 books at the garage sale is $20.

$10 4

___ x 8

___= Write a proportion that compares total cost to number of books.

$10 4

___ x 8

___=

2

2

Think: 4 2 = 8 and $10 2 = x.

7-3 Proportions

Check It Out : Example 1A

Paul spent $15 on 3 CDs at a store where all CDs are the same price. How much would it cost for Paul to buy 9 CDs?

$15 3

= x9

x = 15 X 3

= $45

7-3 Proportions

Check It Out : Example 1B

Beth drove 120 miles in 2 hours. She continues driving at the same rate and does not stop. How far will she have driven in 6 hours?

120 2

= x6

x = 120 X 3

= 360 miles

7-3 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

7-3 Proportions

Additional Example 2A: 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

7-3 Proportions

Additional Example 2B: Using Cross Products to Complete Proportions

Find the missing value in the proportion.

36 3

___

39__ 4

n __= Find the cross products.

9 • 4 = 3 • n The cross products are equal.

36 = 3n n is multiplied by 3.

3n 3

___= Divide both sides by 3 to undo the multiplication.

n = 12

7-3 Proportions

Check It Out: Example 2A

Find the missing value in each proportion.

35__ n

15 __=

5 • n = 3 • 15

5n = 45

n = 9

7-3 Proportions

Check It Out: Example 2B

Find the missing value in each proportion.

49

__ n27 __=

9 • n = 4 • 27

9n = 108

n = 12

7-3 Proportions

Check It Out: Example 2C

Find the missing value in each proportion.

213__ 6

n __=

2 • n = 6 • 13

2n = 78

n = 39

7-3 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.

7-3 Proportions

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

Caution!

tbspgal

___tbspgal

___=

galtbsp

___galtbsp

___=or

7-3 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

__

7-3 Proportions

Check It Out: Example 3

To make a certain shade of pink paint, mix 8 gallons of white paint with 3 gallons of red paint. How many gallons of white paint would you mix with 15 gallons of red paint to make this shade of pink?

n 15 __8

3 __ =

3 • n = 8 • 15

3 • n = 120

n = 40 gallons

7-3 Proportions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

7-3 Proportions

Lesson Quiz

1. Angelo bought 4 songs online for $2. How much would Angelo pay for 12 songs?

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 = 30

x = 25

9 g

9 5

__ 45 x

__ p 36

__ 5 6

__

$6

7-3 Proportions

1. Rudy spent $15 on 3 CDs at a store where

all CDs are the same price. How much would

it cost for Rudy to buy 12 CDs?

A. $50 B. $45

C. $60 D. $75

Lesson Quiz for Student Response Systems

7-3 Proportions

2. Identify the missing value in the

proportion.

A. x = 168 B. x = 56

C. x = 72 D. x = 49

Lesson Quiz for Student Response Systems

7-3 Proportions

3. Identify the missing value in the

proportion.

A. n = 6 B. n = 51

C. n = 34 D. n = 102

Lesson Quiz for Student Response Systems

7-3 Proportions

4. According to the label, 1 tablespoon of mixed fruit concentrate should be used to prepare 200 ml of juice. How many tablespoons of concentrate would you use to prepare 800 ml of juice?

A. 2 tbsp B. 3 tbsp

C. 4 tbsp D. 5 tbsp

Lesson Quiz for Student Response Systems