Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Bellringer: Solve each equation.

1. |x| = -19

2. Marc makes $80.50 for working 8 hours. What is his

hourly rate?

3. 2|x + 1| = 20

4.

No Solutions

5 y 2 10

Marc makes $10.06 per hour

y = 25=

x = -11, 9

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions2-7 Rates, Ratios, and Proportions

Holt Algebra 1

•BellringerBellringer

•Review Day: Quiz TOMORROWReview Day: Quiz TOMORROW

•Proportions, rates, ratiosProportions, rates, ratios

•Evaluating Absolute Value Evaluating Absolute Value

•Evaluating multi-step EquationsEvaluating multi-step Equations

Holt McDougal Algebra 1

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Students will be ready to ace the quiz tomorrow morning!

Objectives

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

What is this called? 4: 9

What is another way to write 4:9?

Ratio

4 9

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

In the proportion , the products a • d and

b • c are called cross products. You can solve

a proportion for a missing value by using the

Cross Products property.

Cross Products Property

WORDS NUMBERS ALGEBRA

In a proportion, cross products are equal.

2 • 6 = 3 • 4

If and b ≠ 0

and d ≠ 0then ad = bc.

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Example 4: Solving Proportions

Solve each proportion.

3(m) = 5(9)

3m = 45

m = 15

Use cross products.

Divide both sides by 3.

Use cross products.

6(7) = 2(y – 3)

42 = 2y – 6+6 +648 = 2y

24 = y

A. B.

Add 6 to both sides.Divide both sides by 2.

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Check It Out! Example 4

Solve each proportion.

y = −20

–12 –124g = 23

g = 5.75

A. B.

Use cross products.

Divide both sides by 2.

Use cross products.

Subtract 12 from both sides.

Divide both sides by 4.

2y = –40

2(y) = –5(8) 4(g +3) = 5(7)

4g +12 = 35

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

More examples…

• 3 gallons of paint cover 200 square feet. How many gallons will cover 300 square feet?

3 x200 300

=

900 = 200x 4.5 = x

4.5 gallons of paint will cover 300 square feet.

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

More examples…

• Making 5 apple pies requires 2 pounds of apples. How many pounds of apples are needed to make 18 pies?

5 18 2 x

=

36 = 5x7.2 = x

7.2 pounds of apples are need to make 8 pies

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

More examples…

• Tony can run 10 blocks in 4 minutes. How long does it take him to run 15 blocks, at the same speed.

10 20 4 x

=

80 = 10x8 = x

It will take Tony 8 minutes to run 15 blocks

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Check It Out! Example 2

Cory earns $89.50 in 8 hours. Find the unit rate.

The unit rate is $11.19 per hour.

-Cory earns $11.19 per hour.

89.5 = 8x

89.5 x 8 1

=

11.19 = x

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

The ratio of games won to games lost for the Miami Heat basketball team is 3:2. The team has won 18 games. How many games did the team lose?

Check It Out! Example 1

The team lost 12 games.

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

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.

The unit rate is about 3.47 flips/s.

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Check It Out! Example 2

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.7.5 = x

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Example 5A: Scale Drawings and Scale Models

A contractor has a blueprint for a house drawn to the scale 1 in: 3 ft.

A wall on the blueprint is 6.5 inches long. How long is the actual wall?

blueprint 1 in. actual 3 ft.

x • 1 = 3(6.5)

x = 19.5The actual length of the wall is 19.5 feet.

Write the scale as a fraction.

Let x be the actual length.

Use the cross products to solve.

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Past Review

Solve for x.

5x – 8 = 32+ 8 + 8

5x = 40

x = 8 (Divide by 5)

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

Past Review…

• Solve for x.

4x – 6x + 8 = -4-2x + 8 = -4

- 8 - 8

-2x = -12

x = 6 (Divide by -2)

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

More Word Problems…

1. In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there?162

2. Nuts cost $10.75 for 3 pounds. Find the unit rate in dollars per pound. $3.58/lb

3.

4. A scale model of a car is 9 inches long. The scale is 1:18. How many inches long is the car it represents?

16

162 in.

Holt McDougal Algebra 1

2-7 Rates, Ratios, and Proportions

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