1. Algebra 1
Section 3.2

2. Definitions
A ratio is a comparison of two numbers by division and is often expressed as a fraction.

3. Definitions A rate is a ratio comparing numbers with different units.
A unit rate is a rate in which the denominator is one.

4. Writing Ratios
Ratios should be reduced to lowest terms, just as fractions are.
Ratios can be written in various ways: 3 4
3 : 4
3 to 4

5. Writing Ratios You will often want to write rates with their units:
4 questions
3 min.

6. Example 1 A school of 312 children has 168 girls and 20 teachers.
a. girls to students
168 girls
312 students 7 13 =

7. Example 1 A school of 312 children has 168 girls and 20 teachers.
b. boys to students
144 boys
312 students 6 13 =

8. Example 1 A school of 312 children has 168 girls and 20 teachers.
c. girls to boys
168 girls
144 boys 7 6 =

9. Example 1 A school of 312 children has 168 girls and 20 teachers.
d. unit rate, students per teacher
312 students
20 teachers
312 20 =
= 15.6 students per teacher

10. Dimensional Analysis
This allows you to convert a rate to an equivalent rate.
A unit multiplier is a rate with different expressions representing the same quantity in the numerator and denominator.

11. Unit Multipliers
Multiplying a rate by a unit multiplier will not change the ratio, since it is equivalent to multiplication by one.
Examples:
1 mile
5280 feet
2.54 cm
1 inch

12. Example 3 Change 17,000 mi/hr to ft/sec. • • • 17,000(5280) ft 602 sec
60 min •
1 min
60 sec
17,000(5280) ft
602 sec = ft
sec
≈ 25,000 ft
sec
≈ 24,933

13. Definition A proportion is a statement of equality between two ratios.c d a b =
a and d are called the extremes.
b and c are called the means.

14. Proportions
The product of the extremes equals the product of the means. c d a b =
ab = cd

15. Example 4 Solve the proportion . x 4 7 8 = x 4 7 8 = 8x = 7(4) 8x = 28

16. Example 6
A car traveled 250 mi on 9 gal of gas. How many gallons are needed to travel 360 mi?
Let g = number of gal needed
360 g
250 9 =

17. Example 6
360 g
250 9 =
250g = 9(360)
250g = 3240
g = 12.96
≈ 13 gallons

18. Example 7 Key: We need the ratio of used cars to total cars sold.
Out of every 5 cars sold, 2 of them are used cars. u
325 2 5 =

19. Example 7 u
325 2 5 =
5u = 2(325)
5u = 650
u = 130
130 used cars

20. Homework: pp