1. Proportions
An equation that states that two ratio are equal is called a proportion.
These are proportions:

2. Example Solve:
Cross Multiply y 3y = 60 3 3
y = 20

3. Example Solve:
Cross Multiply 9x = 90 9 9
x = 10

4. Example Solve:
Cross Multiply
65x =
130 65 65
x = 2

5. Example Solve:
Cross Multiply 5 = 2w 2 2 5
= w 2

6. 3.9 Word Problems W/Proportions For example:
Mr. Sexton can eat 8 hamburgers in 2 hours. How many hamburgers can he eat in 7 hours?
Think of it as a Proportion!
8 hamburgers
? hamburgers =
2 hours
7 hours
What if? 8 x 2 7 = = 2 7 8 x 2x = 56 2x = 56 2 2 2 2 x = 28
hamburgers x = 28

7. 3.9 Word Problems W/Proportions Example 2:
If it takes 14 gallons of water to wash one car, how many cars can be washed with 98 gallons.
Think of it as a Proportion!
14 gallons
98 gallons =
1 car
? cars 14 98 = 1 x
14x = 98 14 14 x = 7
cars

8. 3.9 Word Problems W/Proportions Example 3:
On a map, 2 inches represents 25 miles. How many miles does an 6 inch line segment represent?
Think of it as a Proportion!
2 inches
6 inches =
25 miles
? miles 2 6 = 25 x 2x =
150 2 2 x = 75
miles

9. 3.9 Word Problems W/Proportions You Try:
If 5 pounds of hamburgers will serve 6 people. How much hamburger is needed to serve 36 people?
Think of it as a Proportion!
5 pounds
? pounds =
6 people
36 people 5 x = 6 36 6x =
180 6 6 x = 30
pounds