Transcript Slide 1

7-3 Proportions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
7-3 Proportions
Warm Up
Use the table to write each ratio.
Brown bears
Giraffes
Monkeys
Polar Bears
1.
2.
3.
4.
3
2
17
4
giraffes to monkeys
polar bears to all bears
monkeys to all animals
all animals to all bears
2:17
4:7
17:26
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
Learn to write and solve proportions.
7-3 Proportions
Vocabulary
proportion
7-3 Proportions
A proportion is an equation that shows
two equivalent ratios.
2
4
__
__
=
1
2
4
8
__
__
=
2
4
2
6
__
__
=
1
3
Reading Math
2
4
__
__
Read the proportion
=
as “two is to
1
2
one as four is to two.”
7-3 Proportions
Additional Example 1: Modeling Proportions
Write a proportion for the model.
First write the ratio of hearts to stars.
4
number of hearts
__
number of stars = 8
Next separate the hearts and stars into two
equal groups.
7-3 Proportions
Additional Example 1 Continued
Now write the ratio of hearts to stars in each
group.
2
number of hearts = __
number of stars
4
4
2
__
__
A proportion shown by the model is 8 = 4 .
7-3 Proportions
Check It Out: Example 1
Write a proportion for the model.
First write the ratio of faces to moons.
2
number of faces
__
number of moons = 6
Next separate the faces and moons into two
equal groups.
7-3 Proportions
Check It Out: Example 1 Continued
Now write the ratio of faces to moons in each
group.
1
number of faces = __
number of moons
3
2
1
__
__
A proportion shown by the model is 6 =
.
3
7-3 Proportions
CROSS PRODUCTS
Cross products in proportions are equal
4 =
__
8
8•2=
2
__
4
4•4
16 = 16
3 = ___
9
__
5
15
5 • 9 = 3 • 15 6
45 = 45
9 =
__
6
• 3 =
3
14
2
__
__ = __
2
7
1
9 • 2 7 • 2 = 14 • 1
18 = 18
14 = 14
7-3 Proportions
Additional Example 2: Using Cross Products to
Complete Proportions
Find the missing value in the proportion.
5
n
__
__
=
6
18
6 • n = 5 • 18
6n = 90
90
6n
___
= ___
6
6
n = 15
Find the cross products.
The cross products are equal.
n is multiplied by 6.
Divide both sides by 6 to undo
the multiplication.
7-3 Proportions
Check It Out: Example 2
Find the missing value in the proportion.
3
n
__
__
=
5
15
5 • n = 3 • 15
5n = 45
45
5n
___
= ___
5
5
n=9
Find the cross products.
The cross products are equal.
n is multiplied by 5.
Divide both sides by 5 to undo
the multiplication.
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?
1 tbsp ____
f
_____
=
6 gal
4 gal
1 tbsp ____
f
_____
=
6 gal
4 gal
6•f =1•4
Let f be the amount of fertilizer
for 4 gallons of water.
Write a proportion.
The cross products are equal.
7-3 Proportions
Caution!
In a proportion, the units must be in
the same order in both ratios.
tbsp ___
tbsp
___
=
gal
gal
gal
gal
___
___
or
=
tbsp tbsp
7-3 Proportions
Additional Example 3 Continued
6f = 4
4
6f
___
= __
6
6
2
f = __ tbsp
3
f is multiplied by 6.
Divide both sides by 6 to undo
the multiplication.
Write your answer in simplest
form.
2 tbsp of fertilizer for 4 gallons
You would use __
3
of water.
7-3 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?
3 tbsp ____
f
_____
=
9 gal
2 gal
Let f be the amount of fertilizer
for 2 gallons of water.
3 tbsp ____
f
_____
=
9 gal
2 gal
Write a proportion.
9•f =3•2
The cross products are equal.
7-3 Proportions
Check It Out: Example 3 Continued
9f = 6
6
9f
___
= __
9
9
2
f = __ tbsp
3
f is multiplied by 9.
Divide both side by 9 to undo the
multiplication.
Write your answer in simplest
form.
2 tbsp of fertilizer for 2 gallons
You would use __
3
of water.
7-3 Proportions
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
7-3 Proportions
Lesson Quiz
1. Write a proportion for the model.
2
1
__
__
=
6
3
Find the missing value in each proportion.
9 = __
45
p = __
5
2. __
3. __
5
x
36
6
x = 25
p = 30
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? 9 g
7-3 Proportions
Lesson Quiz for Student Response Systems
1. Identify a proportion for the model.
A.
B.
C.
D.
7-3 Proportions
Lesson Quiz for Student Response Systems
2. Identify the missing value in the
proportion.
A. x = 168
B. x = 56
C. x = 72
D. x = 49
7-3 Proportions
Lesson Quiz for Student Response Systems
3. Identify the missing value in the
proportion.
A. n = 6
B. n = 51
C. n = 34
D. n = 102
7-3 Proportions
Lesson Quiz for Student Response Systems
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