Algebra 1 Section 3 2 Definitions A ratio

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 should be reduced to lowest terms, just as fractions are. Ratios can be written in various ways: 3 3: 4 3 to 4 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 7 = 312 students 13

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

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

Example 1 A school of 312 children has 168 girls and 20 teachers. d. unit rate, students per teacher 312 students 312 = 20 teachers 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 2. 54 cm 5280 feet 1 inch

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

Definition A proportion is a statement of equality between two ratios. a c = b d 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. a c = b d ab = cd

Example 4 7 x Solve the proportion. = 8 4 7 x = 8 4 8 x = 7(4) 8 x = 28 x = 3. 5

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 250 360 = 9 g

Example 6 250 360 = 9 g 250 g = 9(360) 250 g = 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. 2 u = 5 325

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

Homework: pp. 101 -103