1. 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 girls
Generally, ratios are in lowest terms:
16 = 16/4 = /

2. Understanding Proportion

3. Ratio, continued Ratios can compare two unlike things:
Joe earned $40 in five hours
The ratio is 40 dollars or 8 dollars hours 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. 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 = 72 so 3 x 24 = 72
Shannon n x
n = 48, so Shannon got 48 votes.

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

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

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

9. = x
5x = 600
Answer: x= 120

10. 12:36 = 3: m
12m = 108
Answer: m= 9

11. Solving Word Problems
Grace and James are on a swimming team. Their swim training is 200 meters and usually takes them 3 minutes. How long, at this rate, would it take them to complete an 800-meter swim?

12. 1. Set up the proportion:
meters = 800
minutes n
2. Use cross-products
200 n= 2400.
3. Divide both sides by 200
n=12
Answer: 800-meter swim will take them 12 minutes.

13. A car travels 125 miles in 3 hours. How far would it travel in 5 hours?

14. A car travels 125 miles in 3 hours. How far would it travel in 5 hours?
Step 1 Set up the proportion.
miles = h
hours
Step 2 Solve for the missing value (h).
125(5) = 625 then, 625=3h
Step 3 Divide both 625 and 3h by 3
Answer: or 208 1/3 miles