Chapter 1 The Whole Numbers

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Chapter 1The Whole Numbers
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Chapter Outline

• Tips for Success in Mathematics
• Place Value and Names for Numbers
• Adding Whole Numbers and Perimeter
• Subtracting Whole Numbers
• Rounding and Estimating
• Multiplying Whole Numbers
• Dividing Whole Numbers
• An Introduction to Problem Solving
• Exponents, Square Roots, and Order of Operations

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1.1
Tips for Success in Mathematics
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Section Objectives

• Getting Ready for This Course
• General Tips for Success
• Using This Text
• Getting Help
• Preparing for and Taking an Exam
• Managing Your Time

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Getting Ready for This Course
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 5
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General Tips for Success
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 6
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General Tips for Success
CONTINUED
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 7
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Using This Text
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 8
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Using This Text
CONTINUED
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 9
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Getting Help
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 10
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Preparing for and Taking an Exam
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 11
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Preparing for and Taking an Exam
CONTINUED
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 12
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Managing Your Time
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 13
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1.2
Place Value and Names for Numbers
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Section Objectives

• Place Value of a Digit in a Whole Number
• Whole Numbers in Words and in Standard Form
• Writing a Whole Number in Expanded Form
• Reading Tables

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Place Value of a Digit in a Whole Number
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 16
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Whole Numbers in Words and in Standard Form
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 17
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Writing a Whole Number in Expanded Form
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 18
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Reading Tables
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 19
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1.3
Adding Whole Numbers and Perimeter
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Section Objectives

• Adding Whole Numbers
• Finding the Perimeter of a Polygon
• Solving Problems by Adding

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Adding Whole Numbers
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 22
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Adding Whole Numbers
CONTINUED
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 23
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Adding Whole Numbers
CONTINUED
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 24
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Finding the Perimeter of a Polygon
Line Segments
Rectangle
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 25
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Solving Problems by Adding
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 26
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Solving Problems by Adding
EXAMPLE
The state of Hawaii has 1851 miles of urban
highways and 2291 miles of rural highways. Find
the total highway mileage in Hawaii. (Source
U.S. Federal Highway Administration)
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 27
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1.4
Subtracting Whole Numbers
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Section Objectives

• Subtracting Whole Numbers
• Subtracting With Borrowing
• Solving Problems by Subtracting

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Subtracting Whole Numbers
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 30
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Subtracting With Borrowing
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 31
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Solving Problems by Subtracting
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 32
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Solving Problems by Subtracting
EXAMPLE
Dyllis King is reading a 503-page book. If she
has just finished reading page 239, how many more
pages must she read to finish the book?
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 33
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1.5
Rounding and Estimating
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Section Objectives

• Rounding Whole Numbers
• Estimating Sums and Differences
• Solving Problems by Estimating

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Rounding Whole Numbers
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 36
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Estimating Sums and Differences
EXAMPLE
Estimate the sum by rounding each number to the
nearest hundred.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 37
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Solving Problems by Estimating
EXAMPLE
Jared Nuss scored 89, 92, 100, 67, 75 and 89 on
his biology tests. Round each score to the
nearest ten to estimate his total score.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 38
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1.6
Multiplying Whole Numbers and Area
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Section Objectives

• Using the Properties of Multiplication
• Multiplying Whole Numbers
• Multiplying by Whole Numbers Ending in Zero(s)
• Finding the Area of a Rectangle
• Solving Problems by Multiplying

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Using the Properties of Multiplication
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 41
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Using the Properties of Multiplication
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 42
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Using the Properties of Multiplication
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 43
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Multiplying Whole Numbers
EXAMPLE
Use the distributive property to multiply 3 and
79.
SOLUTION
Write 79 in expanded form.
Apply the Distributive Property.
Multiply.
Add.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 44
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Multiplying Whole Numbers
EXAMPLE
Multiply 624 by 3.
SOLUTION
Carry the one.
Carry the one.
3(2) 6 and 6 1 7
3(0) 0 and 0 1 1
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 45
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Multiplying Whole Numbers
EXAMPLE
Multiply 91 by 72.
SOLUTION
2(91) 182
7(91) 637
Add.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 46
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Multiplying Whole Numbers Ending in Zero(s)
EXAMPLE
Multiply 3 by 9000.
SOLUTION
3 zeros attached to 27.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 47
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Finding the Area of a Rectangle
EXAMPLE
Find the area of the following rectangle.
SOLUTION
inches
inches
square inches
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 48
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Solving Problems by Multiplying
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 49
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1.7
Dividing Whole Numbers
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Section Objectives

• Dividing Whole Numbers
• Performing Long Division
• Solving Problems by Dividing
• Finding Averages

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Dividing Whole Numbers
dividend
quotient
divisor
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 52
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Performing Long Division
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 53
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Solving Problems by Dividing
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 54
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Solving Problems by Dividing
EXAMPLE
Find the quotient of 78 and 5.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 55
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Finding Averages
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 56
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1.8
An Introduction to Problem Solving
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Section Objectives

• Solving Problems Involving Addition, Subtraction,
  Multiplication, or Division
• Solving Problems Using More Than One Operation

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Solving Problems Including Addition, Subtraction,
Multiplication, or Division
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 59
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Solving Problems Including Addition, Subtraction,
Multiplication, or Division
EXAMPLE
1. UNDERSTAND the problem. There are 24 hours in
a day. How many hours are in a week?
SOLUTION
2. TRANSLATE the problem.
3. SOLVE the problem.
CHECK
Lets see if our answer is reasonable by also
estimating.

• INTERPRET the results.
• The answer is reasonable since 168 is close to
  our estimated answer of 200.
• There are 168 hours in a week.

Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 60
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Solving Problems Using More Than One Operation
EXAMPLE
1. UNDERSTAND the problem. Find the total cost
of 10 computers at 2100 each and 7 boxes of
diskettes at 12 each.
SOLUTION
2. TRANSLATE the problem.
3. SOLVE the problem.
4. INTERPRET the problem. The total cost is
21,084.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 61
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1.9
Exponents, Square Roots, and Order of Operations
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Section Objectives

• Using Exponential Notation
• Evaluating Exponential Expressions
• Evaluating Square Roots
• Using the Order of Operations
• Finding the Area of a Square

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Using Exponential Notation
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 64
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Using Exponential Notation
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 65
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Evaluating Exponential Expressions
EXAMPLE
Evaluate 26.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 66
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Evaluating Square Roots
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 67
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Using the Order of Operations
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 68
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Using the Order of Operations
EXAMPLE
Evaluate .
SOLUTION
Write 32 as 9
Divide 9 by 3
Add 3 to 6
Divide 9 by 9
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 69
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Finding the Area of a Square
EXAMPLE
Find the area of the following square.
4 meters
SOLUTION
Since all sides of a square are equal, we can
assume that the area is 42 meters.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 70