7-4 proportions warm up warm up lesson presentation lesson presentation problem of the day problem...
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7-4 Proportions
Warm Up
Lesson Presentation
Problem of the Day
Lesson Quizzes
7-4 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
7-4 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
7-4 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
__
7-4 Proportions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
7-4 Proportions
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
9 g
2 6
__ 1 3
__=
9 5
__ 45 x
__ p 36
__ 5 6
__
7-4 Proportions
1. Identify a proportion for the model.
A. B.
C. D.
Lesson Quiz for Student Response Systems
7-4 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
7-4 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
7-4 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