ccbc math 081 textbook 3 edition - ccbc faculty...

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CCBC Math 081 Textbook 3rd Edition

Chapter Sections Page

Chapter 1 Integers

1.1 Introduction to Integers 1.2 Absolute Value 1.3 Addition of Integers 1.4 Subtraction of Integers Mid-Chapter 1 Review 1.5 Multiplication and Division of Integers 1.6 Exponents and Roots 1.7 Order of Operations Chapter 1 Summary Chapter 1 Review

1 11 17 23 41 43 52 61 68 70

Chapter 2 Applications of Integers

2.1 Translation of Words into Expressions 2.2 Geometry Mid-Chapter 2 Review 2.3 Statistics: Mean, Median, and Mode 2.4 Bar Graphs, Line Graphs, and Tables 2.5 Applications Chapter 2 Summary Chapter 2 Review

72 81 100 102 109 121 129 131

Chapter 3 Fractions

3.1 Introduction to Fractions 3.2 Multiplication of Fractions and of Mixed Numbers 3.3 Division of Fractions and of Mixed Numbers Mid-Chapter 3 review 3.4 Addition of Fractions and of Mixed Numbers 3.5 Subtraction of Fractions and of Mixed Numbers 3.6 Order of Operations 3.7 U.S. Measurement Conversions 3.8 Application Problems Chapter 3 Summary Chapter 3 Review

137 160 177 186 188 211 229 235 244 257 260

Chapter 4 Decimals

4.1 Introduction to Decimals 4.2 Converting Between Decimals and Fractions 4.3 Addition and Subtraction of Decimals Mid-Chapter 4 Review 4.4 Multiplication and Division of Decimals 4.5 Metric Measurement 4.6 Applications Chapter 4 Summary Chapter 4 Review

263 276 283 296 298 314 322 336 338

http://faculty.ccbcmd.edu/~lwalte19/Math081C1S1Text.pdf




http://faculty.ccbcmd.edu/~lwalte19/Math081C1MCR.pdf




http://faculty.ccbcmd.edu/~lwalte19/Math081C1Summary.pdf

http://faculty.ccbcmd.edu/~lwalte19/Math081C1Review.pdf





























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Chapter 5 Algebra

5.1 Introduction to Algebra 5.2 Algebraic Properties 5.3 Distributive Property Mid-Chapter 5 Review 5.4 Solving Equations Using the Addition Property of Equality 5.5 Solving Equations Using the Multiplication Property of Equality 5.6 Solving Equations Using the Addition and Multiplication Properties of

Equality 5.7 Translating English Sentences into Mathematical Equations and Solving Chapter 5 Summary Chapter 5 Review

344 357 380 386 387 396 403 413 420 422

Chapter 6 Ratios, Rates, and Proportions

6.1 Ratios 6.2 Rates 6.3 Unit Rates Mid-Chapter 6 Review 6.4 Proportions 6.5 Applications Chapter 6 Summary Chapter 6 Review

425 431 435 442 443 450 459 460

Chapter 7 Percents and Applications

7.1 Introduction to Percents and Conversions Among Fractions, Decimals, and Percents

7.2 Translating and Solving Percent Problems Mid-Chapter 7 Review 7.3 Circle Graphs 7.4 Financial Applications of Percents 7.5 Application Problems Chapter 7 Summary Chapter 7 Review

467 478 488 490 502 516 526 528





























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Dedication

This book is dedicated to all of the hard working CCBC Students taking Math 081. We hope that you will

be very successful in your mathematical journey, having had a solid foundation after completing this

course.

Nearly all Community College of Baltimore County Mathematics Department faculty members

contributed in some way to the production of the textbook.

Thank you to the following CCBC faculty members who edited portions of the Math 081 textbook for the

3rd edition:

Kathy Baranoski

Tim Howell

Lisa Sallee

Molly Stube

Tejan Tingling

Cathy Permut

A special thank you to the following CCBC faculty members for leading in the editing and rewriting of the

Math 081 textbook for the 3rdedition:

Jean Ashby

Lisa Brown

Alberta Latorre

Thank you to the following CCBC faculty members who produced the videos for the 3rd edition of the

Math 081 textbook:

Chapter 1 – Lisa Brown

Chapter 2 – Sarah Miller

Chapter 3 – Lisa Brown


Chapter 5 – Bob Brown


Chapter 7 – Lisa Brown and Greg Stiffler

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This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.

To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/.

http://creativecommons.org/licenses/by-nc/4.0/

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To the student,

For each written example in this textbook, you will find a similar practice problem with a video link to a

YouTube video. You can access an online version of the textbook at:

http://www.ccbcmd.edu/math_science/math/math081text.html

You can watch each problem individually by clicking on the online version’s link, or you can type in the

printed link into any browser. At the end of each section you also have the option to watch all of the

problems in that section in one video by clicking on the link or entering in the printed link that follows

“Watch All:”.

At the end of each section, you will find a set of exercises with problems for you to practice. In the

middle and at the end of each chapter, you will find a set of review problems. After chapter 2, 4 and 6,

you will find cumulative review problems.

Thanks to Alberta Latorre, every chapter has a Chapter Summary at the end that will summarize the

major topics of each section.

http://www.ccbcmd.edu/math_science/math/math081text.html

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CHAPTER 1: INTEGERS

CHAPTER 1 CONTENTS

1.1 Introduction to Integers

1.2 Absolute Value

1.3 Addition of Integers

1.4 Subtraction of Integers

1.5 Multiplication and Division of Integers

1.6 Exponents and Roots

1.7 Order of Operations

Image from www.misterteacher.com

http://www.misterteacher.com/

CCBC Math 081 Introduction to Integers Section 1.1 Third Edition 10 pages

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1.1 Introduction to Integers

There once was a line full of numbers

That never did sleep nor did slumber

There are many good reasons

To compute in all seasons

In Fall, Winter, Spring, and the Summer

This little known limerick by an even lesser known

mathematician-poet is convincing proof that everyone

should learn mathematics. Even if your dreams of being

an artist – a writer, a singer, a painter, an actor – are

slow to materialize in the waking world, mathematical

skills are valuable in the present and in the future, at

home and for so many different jobs and careers. In

fact, the author of the limerick pays the bills with his

mathematical skills, while still having the time to

explore many different avenues of artistic creativity.

A good “number sense,” as it is called, is the very

foundation for understanding mathematics. However,

some students feel that they are allergic to math and that

working with integers (also called signed numbers) will

send them into mathematical sneezing fits.

So, in this chapter, when we perform arithmetic with

integers, we will look at a few different strategies. I am

confident that at least one of the strategies will make

“sense” to you!

Image from Microsoft Office Clip Art

Images from Microsoft Office Clip Art

Image from Microsoft Office Clip Art

3 -2

4

-1


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Soon you will learn to perform operations on integers. This means that you will learn to add,

subtract, multiply, and divide integers. But first, you should understand what integers are.

So, let’s begin by defining the integers as well as other kinds of numbers used in math.

Numbers can be classified into different groups (number systems). Three number systems are

described in the following chart.

NUMBER SYSTEMS

Natural

Numbers

The natural numbers are also called the counting numbers.

The natural numbers are {1, 2, 3, 4, 5, . . . }.

Look at the natural numbers on the number line below.

Note: There is no greatest or “last” natural number. The arrow on the number

line indicates that the numbers continue on endlessly.

Whole

Numbers

The whole numbers include the set of natural numbers and the number 0.

The whole numbers are {0, 1, 2, 3, 4, 5, . . . }.

Look at the whole numbers on the number line below and notice that the number 0

is included.

Note: There is no greatest or “last” whole number. The arrow on the number

line indicates that the numbers continue on endlessly.

Integers

The integers are the positive and negative counting numbers and the number 0.

The integers are { … , -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5, … }.

Look at the integers on the number line below.

Note: There is no least or “first” integer and there is no greatest or “last” integer.

The arrows on the number line indicate that the numbers continue on endlessly.


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Practice 1: Circle each number system that the given number belongs to, and cross out each

number system that the given number does not belong to.

a. 7 Natural numbers Whole numbers Integers

b. – 5 Natural numbers Whole numbers Integers

c. – 2 Natural numbers Whole numbers Integers

d. 0 Natural numbers Whole numbers Integers

Answer:

a. 7 Natural numbers Whole numbers Integers

b. – 5 Natural numbers Whole numbers Integers

c. – 2 Natural numbers Whole numbers Integers

d. 0 Natural numbers Whole numbers Integers

Watch it: http://youtu.be/-t-vLNULus8

(To view video links in another window, press the control key as you click the link.)

http://youtu.be/-t-vLNULus8


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POSITIVE AND NEGATIVE INTEGERS

The set of integers can be categorized into three distinct groups (subsets):

Positive Integers {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , … }

Zero { 0 }

Negative Integers {… , -11 , -10 , -9 , -8 , -7 , -6 , -5 , -4 , -3 , -2 , -1}

Look at these subsets on the number line below.

Imagine yourself standing at the number 0, holding a gift card that you received for your

birthday. The gift card allows you to take 5 free steps, but it’s up to you to decide whether to

take those steps to the right or to the left.

If you start at 0 and take 5 steps to the right, you will arrive at positive 5, written simply as 5.

If you start at 0 and take 5 steps to the left, then you will arrive at negative 5, written as –5.

negative integers positive integers zero


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Practice 2: Place each of the following numbers on the number line. (For a frame of

reference, the numbers 0 and 1 are given.)

Write these numbers on the number line: 2 5 3 1 6 6

Answer:

Watch it: http://youtu.be/_T8xuW0joNY

Practice 3: What is the value of each of the capital letters? (For a frame of reference, the

numbers 0 and –6 are given.)

A = B = C = D = E = F =

Answer: A = -4 B =5 C = -2 D = 2 E = 6 F = -5

Watch it: http://youtu.be/Abo1iiqwsm4

0 1

0

A B C D E F

– 6

http://youtu.be/_T8xuW0joNY

http://youtu.be/Abo1iiqwsm4


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Real Numbers Before we continue our study of integers, we should point out that the number line is a densely

populated line. The integers are few and far between, mathematically speaking. There are many

more numbers on the number line than just the integers. For instance, there are fractions and

decimals. Look at the location of some fractions and decimals on the number line below.

The fractions and decimals belong to a number system called the Rational Numbers. You will

study these numbers in Chapter 3 and Chapter 4 of this book. You will study other non-integers

in future math courses. So, to help you become familiar with the various kinds of numbers used

in mathematics, an overview of the number systems is presented below in diagram form. The

diagram describes each number system and allows you to see the relationships among them.

Strangely Beautiful Fact: If you pick any real number (integer, fraction, decimal) on the number

line, there is no real number “right next to it” on either side. That is, there is no closest real

number either to the right or the left. There are also no gaps or holes in the number line. Strange.

Beautiful. Fact. This is why mathematicians say that the real number line is a continuum.

Watch All: http://youtu.be/c_SqQTq78sg

REAL NUMBERS

All #'s on number line

RATIONAL NUMBERS

#'s that can be expressed as below

INTEGERS

{ ..., -3, -2, -1, 0, 1, 2, 3, ...}

OPPOSITES OF NATURAL NUMBERS

{ ..., -3, -2, -1}

WHOLE NUMBERS

{ 0, 1, 2, 3, ...}

ZERO

0

NATURAL NUMBERS

{ 1, 2, 3, ...}

FRACTIONS

1/2 -5/8

DECIMALS

decimals that end or repeat a pattern

-8.65 2.575757...

IRRATIONAL NUMBERS

decimals that do not end or repeat a pattern

7.45182453... π

-1.75 ¾ -3½

2.5

http://youtu.be/c_SqQTq78sg


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1.1 Introduction to Integers Exercises

1. Name each set of numbers shown below.

{0, 1, 2, 3, 4, 5, . . . }

{1, 2, 3, 4, 5, . . . }

{ … , -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5, … }

2. Circle each number system that the given number belongs to, and cross out each number

system that the given number does not belong to. (The first number is done for you.)

3. Place each of the following numbers on the number line. The number 0 is already shown.

1 –5 3 –2 7 –4

4. What is the value of each of the points named by the capital letters on the number line?

(For a frame of reference, the number 0 is given.)

A = B = C = D = E = F =

- 3 belongs to the natural numbers whole numbers integers

1 belongs to the natural numbers whole numbers integers




0 6

0

A B C D E F

– 6


9

5. Circle all the integers in the list of numbers below.

1 5 3

7, 6, 0.4, , 9, 0, 1.8, 4, 3 ,2 8 4

6. Circle all the positive integers in the list of numbers below.

5 17, 6.2, 0.4, , , 0, 8, 4.3, 3,

2 7

7. Circle all the negative integers in the list of numbers below.

5 2 1 35.9, , , , , 0, .6, 4 , ,

9 5 2 4


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1.1 Introduction to Integers Exercises Answers

1. Whole Numbers

Natural Numbers (or Counting Numbers)

Integers

2.

3.

4. A 3 B 4 C 1 D 2 E 5 F 4

5.

6.

7.





-1 belongs to the natural numbers whole numbers integers

0 -4 3 -2 1 7 -5

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