The document discusses ratios and proportions. A ratio compares two numbers using division and can compare unlike things using a unit rate. A proportion states that two ratios are equal, which can be used to solve problems such as determining the cost of a certain number of items based on the price of a smaller quantity. Examples are provided of setting up and solving proportions to find unknown values.

1. Understanding Proportion

2. Ratio
 A ratio is the comparison of two numbers
by division.
 A classroom has 16 boys and 12 girls.
 Also written as 16 boys, 16:12 or 16 to 12
12 girls
 Generally, ratios are in lowest terms:
16 = 16/4 = 4
12 12/4 3

3. Ratio, continued
Ratios can compare two unlike things:
Joe earned $40 in five hours
The ratio is 40 dollars or 8 dollars
5 hours 1 hour
When the denominator is one, this is called
a unit rate.

4. Ratio, continued
Let’s look at a classroom:
Ratios can be part-to-part
16 boys
15 girls
Ratios can be part-to-whole
16 boys
31 students

5. Ratio, continued
If a ratio is part-to-whole, you can divide
and find a decimal or a percent.
16 boys
31 students
31/16.00 = .516, or 51.6% are boys

6. Proportion
 Proportion is a statement that says two ratios
are equal.
 In an election, Damon got three votes for each two
votes that Shannon got. Damon got 72 votes. How
many votes did Shannon get?
 Damon 3 = 72 so 3 x 24 = 72
Shannon 2 n 2 x 24 48
n = 48, so Shannon got 48 votes.

7. Proportion, continued
Tires cost two for $75. How much will
four tires cost?
# of tires 2 = 4 so 2 x 2 = 4 tires
cost 75 n 75 x 2 $150
n = 150, so four tires cost $150

8. Proportion, continued
One more way to solve proportions:
2 = 6 2 x n = 6 x 8 2n = 48
8 n 2 2
n = 24

9. Proportion, continued
Now you try!
Three cans of soup costs $5. How much
will 12 cans cost?
# of cans 3 = 12 3 x 4 = 12 cans
cost 5 n 5 x 4 20 dollars
n = 20, so 12 cans cost $20

10. Proportion, continued
Now you try!
Three cans of soup costs $5. How much
will 12 cans cost?
# of cans 3 = 12 3 x 4 = 12 cans
cost 5 n 5 x 4 20 dollars
n = 20, so 12 cans cost $20