1. Learn to write and solve proportions.

2. Vocabulary
proportion

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

4. 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.

5. 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 = .

6. Check It Out: 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.

7. Check It Out: Example 1 Continued
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 = .

8. Cross products in proportions are equal4 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

9. 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

10. Check It Out: 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

11. 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.

12. In a proportion, the units must be in the same order in both ratios.
Caution!
In a proportion, the units must be in the same order in both ratios.
tbsp
gal
___
tbsp
gal
___ =
gal
tbsp
___
gal
tbsp
___ or =

13. 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.

14. 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
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.

15. Check It Out: 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.