2-6 Rates, Ratios, and Proportions

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1 2-6 Rates, Ratios, and Proportions Warm Up Lesson Presentation Lesson Quiz

2 Bell Quiz 2-6(a) Solve each equation. Check your answer. 1. 6x = m = Multiply pts possible

3 Questions on 2-5

4 Bell Quiz 2-6(b) Solve each equation = m r + 20 = n + 6 3n = (2t 3) = 6(t + 2) Solve for x. 5. 2x + 3y = pts possible

5 Questions on 2-6(a)

6 Objectives Write and use ratios, rates, and unit rates. Write and solve proportions.

7 Vocabulary ratio proportion rate cross products scale scale drawing unit rate scale model conversion factor

8 A ratio is a comparison of two quantities by division. The ratio of a to b can be written a:b or, where b 0. Ratios that name the same comparison are said to be equivalent. A statement that two ratios are equivalent, such as, is called a proportion.

9 Reading Math Read the proportion as 1 is to 15 as x is to 675.

10 Example 1: Using Ratios The ratio of the number of bones in a human s ears to the number of bones in the skull is 3:11. There are 22 bones in the skull. How many bones are in the ears? Write a ratio comparing bones in ears to bones in skull. Write a proportion. Let x be the number of bones in ears. Since x is divided by 22, multiply both sides of the equation by 22.

11 Check It Out! Example 1 The ratio of games lost to games won for a baseball team is 2:3. The team has won 18 games. How many games did the team lose? Write a ratio comparing games lost to games won. Write a proportion. Let x be the number of games lost. Since x is divided by 18, multiply both sides of the equation by 18.

12 A rate is a ratio of two quantities with different units, such as Rates are usually written as unit rates. A unit rate is a rate with a second quantity of 1 unit, such as or 17 mi/gal. You can convert any rate to a unit rate.

13 Example 2: Finding Unit Rates Raulf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is about 3.47 flips/s.

14 Check It Out! Example 2 Cory earns $52.50 in 7 hours. Find the unit rate. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is $7.50.

15 A rate such as in which the two quantities are equal but use different units, is called a conversion factor. To convert a rate from one set of units to another, multiply by a conversion factor.

16 Example 3A: Converting Rates Serena ran a race at a rate of 10 kilometers per hour. What was her speed in kilometers per minute? Round your answer to the nearest hundredth. To convert the second quantity in a rate, multiply by a conversion factor with that unit in the first quantity. The rate is about 0.17 kilometer per minute.

17 Helpful Hint In example 3A, 1 hr appears to divide out, leaving kilometers per minute, which are the units asked for. Use this strategy of dividing out units when converting rates.

18 Example 3B: Converting Rates A cheetah can run at a rate of 60 miles per hour in short bursts. What is this speed in feet per minute? Step 1 Convert the speed to feet per hour. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the second quantity. The speed is 316,800 feet per hour.

19 HOMEWORK Sec 2-6: (Pg 118) 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 22, 23, 24, 26, 27, 29, 31, 35, 36, 39, 40, 44, 45

2-6 Rates, Ratios, and Proportions. Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

2-6 Rates, Ratios, and Proportions Warm Up Lesson Presentation Lesson Quiz 2-6 1 Questions on 2-5 2-6 2 Objectives Write and use ratios, rates, and unit rates. Write and solve proportions. 2-6 3 Vocabulary