Scottsdale Community College
Basic Arithmetic
Student Workbook
Development Team
Donna Gaudet
Amy Volpe
Jenifer Bohart
Second Edition
April, 2013
This work is licensed under a
Creative Commons Attribution-ShareAlike 3.0 Unported License.
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The basic arithmetic operations are addition, subtraction, multiplication and division, although arithmetic also includes more advanced operations, such as manipulations of percentages, square roots, exponentiation, logarithmic functions, and even trigonometric functions, in the same vein as logarithms
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Scottsdale Community College
Basic Arithmetic
Student Workbook
Development Team
Donna Gaudet
Amy Volpe
Jenifer Bohart
Second Edition
April, 2013
This work is licensed under a
Creative Commons Attribution-ShareAlike 3.0 Unported License.
ii
iv
WORKOOK & SUPPORTING COMPONENTS
This workbook is designed to lead students through a basic understanding of numbers
and arithmetic. The included curriculum is broken into twelve lessons (see Table of
Contents page for lesson titles). Each lesson includes the following components:
MINILESSON
- The MiniLesson is the main instructional component for each lesson.
- Ideas are introduced with practical situations.
- Example problems (marked with a star) are to be completed by watching video
links and taking notes/writing down the problem as written by the instructor.
Video links can be found at http://sccmath.wordpress.com or may be located
within the Online Homework Assessment System.
- You Try problems help reinforce lesson concepts and should be worked in the
order they appear showing as much work as possible. Answers can be checked in
Appendix A.
PRACTICE PROBLEMS
- These problems can be found at the end of each lesson. If you are working
through this material on your own, the recommendation is to work all those
problems. If you are using this material as part of a formal class, your instructor
will provide guidance on which problems to complete. Your instructor will also
provide information on accessing answers/solutions for these problems.
ASSESS YOUR LEARNING
- The last part of each lesson is a short assessment. If you are working through this
material on your own, use these assessments to test your understanding of the
lesson concepts. Take the assessments without the use of the book or your notes
and then check your answers. If you are using this material as part of a formal
class, your instructor will provide guidance on which problems to complete. Your
instructor will also provide information on accessing answers/solutions for these
problems.
ONLINE HOMEWORK ASSESSMENT SYSTEM
- If you are using these materials as part of a formal class and your class utilizes an
online homework/assessment system, your instructor will provide information as
to how to access and use that system in conjunction with this workbook.
v
- LESSON 1 – WHOLE NUMBERS TABLE OF CONTENTS
- MINILESSON.....................................................................................................................................................................................................
- LESSON 1 -‐ PRACTICE PROBLEMS
- LESSON 1 – ASSESS YOUR LEARNING
- LESSON 2 – INTRODUCTION TO FRACTIONS
- MINILESSON..................................................................................................................................................................................................
- LESSON 2 -‐ PRACTICE PROBLEMS
- LESSON 2 – ASSESS YOUR LEARNING
- LESSON 3 – FRACTION ADDITION & SUBTRACTION
- MINILESSON..................................................................................................................................................................................................
- LESSON 3 -‐ PRACTICE PROBLEMS
- LESSON 3 – ASSESS YOUR LEARNING
- LESSON 4 – FRACTION MULTIPLICATION & DIVISION
- MINILESSON..................................................................................................................................................................................................
- LESSON 4 – PRACTICE PROBLEMS
- LESSON 4 – ASSESS YOUR LEARNING
- LESSON 5 -‐ DECIMALS.....................................................................................................................................................................................
- MINILESSON..................................................................................................................................................................................................
- LESSON 5 -‐ PRACTICE PROBLEMS
- LESSON 5 – ASSESS YOUR LEARNING
- LESSON 6 -‐ PERCENTS
- MINILESSON..................................................................................................................................................................................................
- LESSON 6 – PRACTICE PROBLEMS
- LESSON 6 – ASSESS YOUR LEARNING
- LESSON 7 – RATIOS, RATES, & PROPORTIONS
- MINILESSON...............................................................................................................................................................................................
- LESSON 7 -‐ PRACTICE PROBLEMS
- LESSON 7 – ASSESS YOUR LEARNING
- LESSON 8 -‐ STATISTICS
- MINILESSON...............................................................................................................................................................................................
- LESSON 8 -‐ PRACTICE PROBLEMS
- LESSON 8 – ASSESS YOUR LEARNING
- LESSON 9 – UNITS & CONVERSIONS
- MINILESSON...............................................................................................................................................................................................
- LESSON 9 -‐ PRACTICE PROBLEMS
- LESSON 9 – ASSESS YOUR LEARNING
- LESSON 10 – GEOMETRY I: PERIMETER & AREA
- MINILESSON...............................................................................................................................................................................................
- LESSON 10 – PRACTICE PROBLEMS
- LESSON 10 – ASSESS YOUR LEARNING
- LESSON 11 – GEOMETRY II: VOLUME & TRIANGLES.....................................................................................................................
- MINILESSON...............................................................................................................................................................................................
- LESSON 11– PRACTICE PROBLEMS.................................................................................................................................................
- LESSON 11 – ASSESS YOUR LEARNING
- LESSON 12 – SIGNED NUMBERS
- MINILESSON...............................................................................................................................................................................................
- LESSON 12 – PRACTICE PROBLEMS
- LESSON 12 – ASSESS YOUR LEARNING
- ANSWERS TO YOU-‐TRY PROBLEMS
- BASIC ARITHMETIC -‐ CUMULATIVE REVIEW
- BASIC ARITHMETIC -‐ CUMULATIVE REVIEW -‐ Answers
LESSON 1 – WHOLE NUMBERS
INTRODUCTION
We will begin our study of Basic Arithmetic by learning about whole numbers. Whole
numbers are the numbers used most often for counting and computation in everyday life.
The table below shows the specific whole-number related objectives that are the
achievement goal for this lesson. Read through them carefully now to gain initial
exposure to the terms and concept names for the lesson. Refer back to the list at the end
of the lesson to see if you can perform each objective.
Lesson Objective Related Examples
Identify the place value of a digit or digits in a given number. 1, YT
Read and write whole numbers. 2, YT
Round whole numbers to a given place. 3, YT5, YT
Rewrite an exponential expression in factored form. 8
Compute numerical expressions using exponents. 12, 13, YT
Use correct order of operations to evaluate numerical expressions. 9, 10, 11, YT
Solve whole number applications with a problem-solving process 16, YT
KEY TERMS
The key terms listed below will help you keep track of important mathematical words and
phrases that are part of this lesson. Look for these words and circle or highlight them
along with their definition or explanation as you work through the MiniLesson.
- Whole Numbers
- Number Line
- Place Value
- Round Whole Numbers
- Exponent
- Power
- Factor
- Factored Form
- Mathematical Operations
- Order of Operations (PEMDAS)
- Solution Work Flow
- Complete Solution
- Disjointed Solution
- Problem Solving Process
LESSON CHECKLIST
Use this page to track required components for your class and your progress on each one.
Component
Required?
Y or N
Comments Due Score
Mini-Lesson
Online
Homework
Online
Quiz
Online
Test
Practice
Problems
Lesson
Assessment
To round a number means to approximate that number by replacing it with another
number that is “close” in value. Rounding is often used when estimating. For example, if
I wanted to add 41 and 3 7 , I could round each number to the nearest ten (40 and 40) then
add to estimate the sum at 80.
When rounding, the analogy of a road may help you decide which number you are closer
to. See the image below. The numbers 43, 45, and 46 are all rounded to the nearest tens
place. Note that a number in the middle of the “road” is rounded up.
Example 3:
a. Round 40,963 to the nearest tens place.
b. Round 40,963 to the nearest hundreds place.
c. Round 40,963 to the nearest thousand
d. Round 40,963 to the nearest ten thousand
YOU TRY
- Write the number 12,304,652 using words.
____________________________________________________________________
- Round 12,304,652 to the nearest million. ______________________________
- Round 12,304,652 to the nearest hundred. _______________________________
- What place does the digit 3 occupy in the number 12,304,652? _________________
EXPONENTS
Exponents are also called powers and indicate repeated multiplication.
Worked Example 8 : 3
4
Note: There are 4 factors of 3 in the exponential expression 3
4
. When we write
4
= 3 ⋅ 3 ⋅ 3 ⋅ 3 , we have written 3
4
in factored form.
On your calculator , you can compute exponents a couple of ways as follows:
a) If you are raising a number to the second power (for example 4
2
), look for
an x
2
key on your calculator. Then, enter 4x
2
= or ENTER and you should
get 16.
b) If you are raising a number to a power other than 2, look for a carrot key (^).
For example 4
5
= 4^5= and you should get 1024. Note that you can also use
the (^) key even when raising to the 2
nd
power (also called “squaring”).
ORDER of OPERATIONS
Addition, subtraction, multiplication, and division are called mathematical operations.
When presented with more than one of these in an expression, we need to know which
one to address first. The chart below will help us.
P Simplify items inside Parenthesis ( ), brackets [ ] or other grouping symbols first.
E Simplify items that are raised to powers (Exponents)
M Perform Multiplication and Division next
D (as they appear from Left to Right )
A Perform Addition and Subtraction on what is left.
S (as they appear from Left to Right)
Example 9: Evaluate 8 + 5 ∙ 2
Example 10: Evaluate 24 ÷ (4 + 2)
Example 11: Evaluate 20 – (8 – 2) ÷ 3 ∙ 4
Example 12: Evaluate
2
Example 13: Evaluate
2
YOU TRY
- Evaluate by hand, showing all possible steps. Try to use good solution flow as
discussed on the previous page.
2
Insert check mark to verify same result via calculator: __________
- Evaluate by hand, showing all possible steps. Try to use good solution flow as
discussed on the previous page.
Insert check mark to verify same result via calculator: __________
APPLICATIONS WITH WHOLE NUMBERS
“Applications” ask you to use math to solve real-world problems. To solve these
problems effectively, begin by identifying the information provided in the problem
(GIVEN) and determine what end result you are looking for (GOAL). The GIVEN
should help you write mathematics that will lead you to your GOAL. Once you have a
result, CHECK that result for accuracy then present your final answer in a COMPLETE
SENTENCE
Even if the math seems easy to you in this application, practice writing all the steps, as
the process will help you with more difficult problems.
Example 16: Amy drives to Costco to buy supplies for an upcoming event. She is
responsible for providing breakfast to a large group of Boy Scouts the next weekend.
Hashed browns are on her list of supplies to purchase and she needs to buy enough to
serve 100 people. The hashed browns are sold in packs of 8 boxes and each box in the
pack will serve 4 people. A) How many packs should she buy minimum and B) How
many people will she be able to serve with this purchase?
GIVEN: [Write down the information that is provided in the problem. Diagrams can be
helpful as well.]
GOAL: [Write down what it is you are asked to find. This helps focus your efforts.]
MATH WORK: [Show your math work to set up and solve the problem.]
CHECK: [Is your answer reasonable? Does it seem to fit the problem? A check may not
always be appropriate mathematically but you should always look to see if your result
makes sense in terms of the goal.]
FINAL RESULT AS A COMPLETE SENTENCE: [Address the GOAL using a
complete sentence.]
LESSON 1 - PRACTICE PROBLEMS
- Identify the place value of the digit “6” in each of the following numbers.
a. 356,
b. 6,456,
c. 300,
d. 461,345,
e. 6,540,345,
f. 405,978,
- Write each of the following whole numbers in words.
a. 356,
b. 6,456,
c. 300,
d. 461,345,
e. 6,540,345,
f. 405,978,
- Write each of the following in “factored” form and then compute the final result.
a. 2
3
b. 3
5
c. 4
2
d. 5
4
e. 6
3
f. 7
2
b. Jenelle financed a 2012 Chevy Camaro on 60-month terms for $673 per
month. If the MSRP on the car was $35,000 and she put no money down,
how much over the MSRP did she end up paying?
c. In the winter, the farmer’s market sees an average of 1516 visitors each
Sunday. In the summer, they see an average of 4278 visitors each Sunday.
How many more visits are there in the summer than in the winter (on
average)?
d. There are 12 reams of paper in a given box. How many reams are there in
25 boxes?