Applying Ratios and Rates MODULE 8 - Little Elm ISD

Applying Ratios and Rates

? ESSENTIAL QUESTION How can you use ratios and rates to solve real-world problems?

8 MODULE

LESSON 8.1

Comparing Additive and Multiplicative Relationships

6.4.A

LESSON 8.2

Ratios, Rates, Tables, and Graphs

6.5.A

LESSON 8.3

Solving Problems with Proportions

6.5.A

LESSON 8.4

Converting Measurements

6.4.H

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Real-World Video

Chefs use lots of measurements when preparing meals. If a chef needs more or less of a dish, he can use ratios to scale the recipe up or down. Using proportional reasoning, the chef keeps the ratios of all ingredients constant.

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201

Are YOU Ready?

Complete these exercises to review skills you will need for this chapter.

Graph Ordered Pairs (First Quadrant)

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EXAMPLE

y

10

8

A

6

4

2 x

O 2 4 6 8 10

To graph A(2, 7), start at the origin. Move 2 units right. Then move 7 units up. Graph point A(2, 7).

Graph each point on the coordinate grid above.

1. B(9, 6)

2. C(0, 2)

3. D(6, 10)

4. E(3, 4)

Write Equivalent Fractions

EXAMPLE

_1_4 21

=

1_4__?__2 21 ? 2

=

_2_8 42

_1_4 21

=

1_4__?__7 21 ? 7

=

_ 2 3

Multiply the numerator and denominator by the same number to find an equivalent fraction. Divide the numerator and denominator by the same number to find an equivalent fraction.

Write the equivalent fraction.

5.

_6_ 8

=

_____

32

9.

_5_ 9

=

__2_5__

6.

_4_ 6

=

_____

12

10.

_5_ 6

=

__2_0__

7.

_1_ 8

=

_____

56

11.

_3_6_ 45

=

__1_2__

8.

_9__ 12

=

_____

4

12.

_2_0_ 36

=

__1_0__

Multiples

EXAMPLE

List the first five multiples of 4. 4 ? 1 = 4 4 ? 2 = 8 4 ? 3 = 12 4 ? 4 = 16 4 ? 5 = 20

List the first five multiples of each number.

13. 3

14. 7

Multiply 4 by the numbers 1, 2, 3, 4, and 5.

15. 8

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202 Unit 3

Reading Start-Up

Visualize Vocabulary

Use the words to complete the graphic. Comparing Unit Rates

Single item

Ratio of two quantities that have different units

Rate in which the second quantity is

one unit

Numbers that follow a rule

Understand Vocabulary

Complete the sentences using the preview words.

1. A equivalent measurements.

is a rate that compares two

Vocabulary

Review Words

equivalent ratios (razones equivalentes) factor (factor) graph (gr?fica) pattern (patr?n) point (punto) rate (tasa) ratio (raz?n) unit (unidad) unit rate (tasa unitaria)

Preview Words

conversion factor (factor de conversi?n) hypotenuse (hipotenusa) legs (catetos) proportion (proporci?n) scale drawing (dibujo a escala) scale factor (factor de escala)

2. The two sides that form the right angle of a right triangle are

called

. The side opposite the right angle in a

right triangle is called the

.

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Active Reading

Tri-Fold Before beginning the module, create a tri-fold to help you learn the concepts and vocabulary in this module. Fold the paper into three sections. Label one column "Rates and Ratios," the second column "Proportions," and the third column "Converting Measurements." Complete the tri-fold with important vocabulary, examples, and notes as you read the module.

Module 8 203

MODULE 8

Unpacking the TEKS

Understanding the TEKS and the vocabulary terms in the TEKS will help you know exactly what you are expected to learn in this module.

6.4.H

Convert units within a measurement system, including the use of proportions and unit rates.

Key Vocabulary

unit rate (tasa unitaria) A rate in which the second quantity in the comparison is one unit.

What It Means to You

You will convert measurements using unit rates.

UNPACKING EXAMPLE 6.4.H

The Washington Monument is about 185 yards tall. This height is almost equal to the length of two football fields. About how many feet is this?

185

yd

?

_3__ft_ 1 yd

=

_18_5__yd_ 1

?

_3__ft_ 1 yd

= 555 ft

The Washington Monument is about 555 feet tall.

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6.5.A

Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs and proportions.

Key Vocabulary

ratio (raz?n) A comparison of two quantities by division.

rate (tasa) A ratio that compares two quantities measured in different units.

What It Means to You

You will use ratios and rates to solve real-world problems such as those involving proportions.

UNPACKING EXAMPLE 6.5.A

The distance from Austin to Dallas is about 200 miles. How far

apart

will

these

cities

appear

on

a

map

with

the

scale

of

_1_i_n_.

50 mi

?

__? _ 200

=

_1_ 50

? = 4 inches

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204 Unit 3

8.1 LESSON Comparing Additive and Multiplicative Relationships

Proportionality-- 6.4.A Compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships.

? ESSENTIAL QUESTION How do you represent, describe, and compare additive

and multiplicative relationships?

EXPLORE ACTIVITY

6.4.A

Discovering Additive and Multiplicative Relationships

A Every state has two U.S. senators. The number of electoral votes a state has is equal to the total number of U.S. senators and U.S. representatives.

The number of electoral votes is the number of representatives.

Complete the table.

Representatives

1

2

5

25

41

Electoral votes

3

4

Describe the rule: The number of electoral votes is equal to

the number of representatives plus / times

.

B Frannie orders three DVDs per month from her DVD club.

Complete the table.

Months

1

2

4

13

22

DVDs ordered

3

6

Describe the rule: The number of DVDs ordered is equal to

the number of months plus / times

.

Reflect

1. Look for a Pattern What operation did you use to complete the tables in A and B ?

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Lesson 8.1 205

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