Holt McDougal Algebra 2

2-2 Proportional Reasoning 2-2 Proportional Reasoning

Holt Algebra 2

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt McDougal Algebra 2

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Warm UpWrite as a decimal and a percent.

1.

2.

0.4; 40%

1.875; 187.5%

3. The distance from Max’s house to the park is 3.5 mi. What is the distance in feet? (1 mi = 5280 ft)

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Apply proportional relationships to rates, similarity, and scale.

Objective

Holt McDougal Algebra 2

2-2 Proportional Reasoning

ratioproportionratesimilarindirect measurement

Vocabulary

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Recall that a ratio is a comparison of two numbers by division and a proportion is an equation stating that two ratios are equal. In a proportion, the cross products are equal.

Holt McDougal Algebra 2

2-2 Proportional Reasoning

If a proportion contains a variable, you can cross multiply to solve for the variable. When you set the cross products equal, you create a linear equation that you can solve by using the skills that you learned in Lesson 2-1.

Holt McDougal Algebra 2

2-2 Proportional Reasoning

In a ÷ b = c ÷ d, b and c are the means, and a and d are the extremes. In a proportion, the product of the means is equal to the product of the extremes.

Reading Math

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Solve each proportion.

Example 1: Solving Proportions

A.

=16 24 p 12.9

14 c 88 132

=B.

C.

= y 77 12 84

15 2.5 x 7

=D.

Holt McDougal Algebra 2

2-2 Proportional Reasoning

4 = r + 3 9 + m = 15

9 45 5 4

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Percent is a ratio that means per hundred.

For example:

30% = 0.30 =

Remember!

30100

Because percents can be expressed as ratios, you can use the proportion

to solve percent problems.

Holt McDougal Algebra 2

2-2 Proportional Reasoning

A poll taken one day before an election showed that 22.5% of voters planned to vote for a certain candidate. If 1800 voters participated in the poll, how many indicated that they planned to vote for that candidate?

Example 2: Solving Percent Problems

Holt McDougal Algebra 2

2-2 Proportional Reasoning

At Clay High School, 434 students, or 35% of the students, play a sport. How many students does Clay High School have?

Check It Out! Example 2

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Opener-SAME SHEET-4/20Solve each proportion.

1. 2.

3. The results of a recent survey showed that 61.5% of those surveyed had a pet. If 738 people had pets, how many were surveyed?

4. Gina earned $68.75 for 5 hours of tutoring. Approximately how much did she earn per minute?

k = 8 g = 42

$0.23

1200

Holt McDougal Algebra 2

2-2 Proportional Reasoning

A rate is a ratio that involves two different units. You are familiar with many rates, such as miles per hour (mi/h), words per minute (wpm), or dollars per gallon of gasoline. Rates can be helpful in solving many problems.

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Ryan ran 600 meters and counted 482 strides. How long is Ryan’s stride in inches? (Hint: 1 m ≈ 39.37 in.)

Example 3: Fitness Application

. metersstrides

Ryan’s stride length is approximately 49 inches.

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Check It Out! Example 3

Luis ran 400 meters in 297 strides. Find his stride length in inches.

Luis’s stride length is approximately 53 inches.

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Similar figures have the same shape but not necessarily the same size. Two figures are similar if their corresponding angles are congruent and corresponding sides are proportional.

The ratio of the corresponding side lengths of similar figures is often called the scale factor.

Reading Math

Holt McDougal Algebra 2

2-2 Proportional Reasoning

Example 5: Nature Application

The tree in front of Luka’s house casts a 6-foot shadow at the same time as the house casts a 22-fot shadow. If the tree is 9 feet tall, how tall is the house?Sketch the situation. The triangles formed by using the shadows are similar, so Luka can use a proportion to find h the height of the house.

=6

9 h22

=Shadow of tree Height of tree

Shadow of house Height of house

6h = 198

h = 33

The house is 33 feet high.

9 ft

6 ft

h ft

22 ft

Holt McDougal Algebra 2

2-2 Proportional Reasoning

A 6-foot-tall climber casts a 20-foot long shadow at the same time that a tree casts a 90-foot long shadow. How tall is the tree?

Sketch the situation. The triangles formed by using the shadows are similar, so the climber can use a proportion to find h the height of the tree.

= 20 6 h

90=

Shadow of climber Height of climber

Shadow of treeHeight of tree

20h = 540

h = 27

The tree is 27 feet high.

6 ft

20 ft

h ft

90 ft

Check It Out! Example 5

Holt McDougal Algebra 2

2-2 Proportional Reasoning

6. A 12-foot flagpole casts a 10 foot-shadow. At the same time, a nearby building casts a 48-foot shadow. How tall is the building? 57.6 ft

Lesson Quiz: Part III