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