Holt Algebra 1

2-6 Rates, Ratios, and Proportions2-6 Rates, Ratios, and Proportions

Holt Algebra 1

Lesson Quiz

Lesson Presentation

Warm Up

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

Questions on 2-5

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

Write and use ratios, rates, and unit rates.

Write and solve proportions.

Objectives

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

ratio proportion

rate cross products

scale scale drawing

unit rate scale model

conversion factor

Vocabulary

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

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.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

Reading Math

Read the proportion as

“1 is to 15 as x is to 675”.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

Example 1A: 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 22.2-6 7

Holt Algebra 1

2-6 Rates, Ratios, and Proportions

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?

Check It Out! Example 1a

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 18.2-6 8

Holt Algebra 1

2-6 Rates, Ratios, and Proportions

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.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

Example 2A: 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.

The unit rate is about 3.47 flips/s.

Write a proportion to find an

equivalent ratio with a second

quantity of 1.

Divide on the left side to find x.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

Check It Out! Example 2a

Cory earns $52.50 in 7 hours. Find the unit rate.

The unit rate is $7.50.

Write a proportion to

find an equivalent

ratio with a second

quantity of 1.

Divide on the left side

to find x.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

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.

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2-6 Rates, Ratios, and Proportions

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.

The rate is about 0.17 kilometer per minute.

To convert the second

quantity in a rate,

multiply by a

conversion factor with

that unit in the first

quantity.

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2-6 Rates, Ratios, and Proportions

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.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

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.

The speed is 316,800 feet per hour.

To convert the first quantity

in a rate, multiply by a

conversion factor with

that unit in the second

quantity.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

Check It Out! Example 3a

A cyclist travels 56 miles in 4 hours. What is the cyclist’s speed in feet per second? Round your answer to the nearest tenth, and show that your answer is reasonable.

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Holt Algebra 1

2-6 Rates, Ratios, and Proportions

HOMEWORKSec 2-6: (Pg 118)

2, 4, 8, 10, 13, 22, 23, 24, 26, 27, 29, 31, 35, 36, 39, 40, 44, 45, 66-69, 73-75

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