1. 8-2 Proportions Warm Up Problem of the Day Lesson Presentation
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. 8-2 Proportions Warm Up Use the table to write each ratio.
Course 1
8-2
Proportions
Warm Up
Use the table to write each ratio.
1. giraffes to monkeys
2. polar bears to all bears
3. monkeys to all animals
4. all animals to all bears
Brown bears 3
Giraffes 2
Monkeys 17
Polar Bears 4
2:17
4:7
17:26
26:7

3. 8-2 Proportions Problem of the Day
Course 1
8-2
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

4. Course 1
8-2
Proportions
Learn to write and solve proportions.

5. Insert Lesson Title Here
Course 1
8-2
Proportions
Insert Lesson Title Here
Vocabulary
proportion

6. Course 1
8-2
Proportions
A proportion is an equation that shows two equivalent ratios. 2 1 __ 4 = 4 2 __ 8 = 2 1 __ 6 3 = 2 1 __ 4 2 __
Read the proportion = as “two is to
one as four is to two.”

7. Additional Example 1: Modeling Proportions
Course 1
8-2
Proportions
Additional Example 1: Modeling Proportions
Write a proportion for the model.
First write the ratio of hearts to stars.
number of hearts
number of stars 4 8 __ =
Next separate the hearts and stars into two equal groups.

8. Additional Example 1 Continued
Course 1
8-2
Proportions
Additional Example 1 Continued
Now write the ratio of hearts to stars in each group.
number of hearts
number of stars 2 4 __ = 4 8 __ 2 4 __
A proportion shown by the model is = .

9. 8-2 Proportions Try This: Example 1 Write a proportion for the model.
Course 1
8-2
Proportions
Try This: Example 1
Write a proportion for the model.
First write the ratio of faces to moons.
number of faces
number of moons 2 6 __ =
Next separate the faces and moons into two equal groups.

10. 8-2 Proportions Try This: Example 1
Course 1
8-2
Proportions
Try This: Example 1
Now write the ratio of faces to moons in each group.
number of faces
number of moons 1 3 __ = 2 6 __ 1 3 __
A proportion shown by the model is = .

11. Cross products in proportions are equal
Course 1
8-2
Proportions
CROSS PRODUCTS
Cross products in proportions are equal 4 8 __ 2 = 3 5 __ 9 15
___ = 9 6 __ 3 2 = 14 7 __ 2 1 =
8 • 2 =
4 • 4
5 • 9 =
3 • 15
6 • 3 =
9 • 2
7 • 2 =
14 • 1
16 = 16
45 = 45
18 = 18
14 = 14

12. Additional Example 2: Using Cross Products to Complete Proportions
Course 1
8-2
Proportions
Additional Example 2: Using Cross Products to Complete Proportions
Find the missing value in the proportion. 5 6 __ n 18 =
Find the cross products.
6 • n =
5 • 18
The cross products are equal.
6n = 90
n is multiplied by 6. 6n 6
___ 90 6
___ =
Divide both sides by 6 to undo the multiplication.
n = 15

13. 8-2 Proportions Try This: Example 2
Course 1
8-2
Proportions
Try This: Example 2
Find the missing value in the proportion. 3 5 __ n 15 =
Find the cross products.
5 • n =
3 • 15
The cross products are equal.
5n = 45
n is multiplied by 5. 5n 5
___ 45 5
___ =
Divide both sides by 5 to undo the multiplication.
n = 9

14. 8-2 Proportions Helpful Hint
Course 1
8-2
Proportions
Helpful Hint
In a proportion, the units must be in the same order in both ratios.
tsp lb
___
tsp lb
___ = lb
tsp
___ lb
tsp
___ or =

15. Additional Example 3: Measurement Application
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?
1 tbsp
6 gal
_____ f
4 gal
____
Let f be the amount of fertilizer for 4 gallons of water. =
1 tbsp
6 gal
_____ f
4 gal
____ =
Write a proportion.
6 • f = 1 • 4
The cross products are equal.

16. Additional Example 3 Continued
Course 1
8-2
Proportions
Additional Example 3 Continued
6f = 4
f is multiplied by 6. 6f 6
___ 4 6 __
Divide both sides by 6 to undo the multiplication. = 2 3 __
Write your answer in simplest form.
f = tbsp 2 3 __
You would use tbsp of fertilizer for 4 gallons of water.

17. 8-2 Proportions Try This: Example 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?
3 tbsp
9 gal
_____ f
2 gal
____
Let f be the amount of fertilizer for 2 gallons of water. =
3 tbsp
9 gal
_____ f
2 gal
____ =
Write a proportion.
9 • f = 3 • 2
The cross products are equal.

18. Try This: Example 3 Continued
Course 1
8-2
Proportions
Try This: Example 3 Continued
9f = 6
f is multiplied by 9. 9f 9
___ 6 9 __
Divide both side by 9 to undo the multiplication. = 2 3 __
Write your answer in simplest form.
f = tbsp 2 3 __
You would use tbsp of fertilizer for 2 gallons of water.

19. Insert Lesson Title Here
Course 1
8-2
Proportions
Insert Lesson Title Here
Lesson Quiz
1. Write a proportion for the model.
Find the missing value in each proportion.
= =
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? 2 6 __ 1 3 __ = 9 5 __ 45 x __ p 36 __ 5 6 __
x = 25
p = 30
9 g