Algebra 1 Section 3.2

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

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

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

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

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

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

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

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

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.

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

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

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.

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

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

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 =

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

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 =

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

Homework: pp. 101-103