Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 1

Section 1.1
Chapter 1 – Slide 2

 We read whole numbers in words, but we use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to write them.
 We read the whole number fifty-one, but write it
51, which is called standard form .
 Each of the digits in a whole number in standard form has a place value .
Chapter 1 – Slide 3
1-3

 The place value chart is shown below.
 When we write large numbers we insert commas to separate the digits into groups of three, called periods .
Chapter 1 – Slide 4
1-4

Identify the place value of the 8.
a. 508 b. 8,430,999 c. 6,800,000,002
1-5
Chapter 1 – Slide 5

To Read a Whole Number
Working from left to right,
• read the number in each period and then
• name the period in place of the comma.
Chapter 1 – Slide 6

Example
How do you read the number 521,000,072?
Chapter 1 – Slide 7
1-7

To Read a Whole Number
Working from left to right,
• write the number named in each period and
• replace the period in place of the comma.
Chapter 1 – Slide 8

1.
Write the number six billion, twelve in standard form.
BILLIONS MILLIONS THOUSANDS ONES
O H T O H T O H T O
2.
The treasurer of a company write a check in the amount of three hundred thousand, two hundred eight. Using digits, how would she write this number?
Chapter 1 – Slide 9
1-9

 Expanded form of a number can be written using the number and its place value of its digits. The place value chart is shown below.
5,293 = 5 thousands + 2 hundreds + 9 tens + 3 ones
Expanded form = 5000 + 200 + 90 + 3
BILLIO
NS
MILLIONS THOUSANDS ONES
O H T O H T O H T O
5 2 9 3
Chapter 1 – Slide 10

Write 803 in expanded form.
Write 8,407,800 in expanded form:
1-11
Chapter 1 – Slide 11

1-12
Chapter 1 – Slide 12

1-13
Chapter 1 – Slide 13

Example
Round 89,541 to: a. the nearest thousand b. the nearest hundred.
The Robinson’s are having new windows installed.
The price is $12,870. How much is this to the nearest thousand dollars?
Chapter 1 – Slide 14
1-14

Write in words the amount of money taken in by The Lord of the Rings: The
Two Towers
1-15
Chapter 1 – Slide 15

Round to the nearest ten million dollars the world total for The Lord of the Rings: The
Two Towers .
Chapter 1 – Slide 16

Section 1.2
Chapter 1 – Slide 17

 The Identity Property of Addition
The sum of a number and zero is the original number.
3 + 0 = 3 or 0 + 5 = 5
 The Commutative Property of Addition
Changing the order in which two numbers are added does not affect their sum.
3 + 2 = 2 + 3
5 = 5
Chapter 1 – Slide 18
1-18

 The Associative Property of Addition
When adding three numbers, regrouping addends gives the same sum. Note that the parentheses tell us which numbers to add first.
(4 + 7) + 2 = 4 + (7 + 2)
11 + 2 = 4 + 9
13 = 13
Chapter 1 – Slide 19
1-19

 We add whole numbers by arranging the numbers vertically, keeping the digits with the same place value in the same column. Then we add the digits in each column.
 When the sum of the digits in a column is greater than 9, we must regroup and carry, because only a single digit can occupy a single space.
Chapter 1 – Slide 20
1-20

1.
2.
3.
Add 56 and 39.
Add: 8,935 + 478 + 2,825
What is the perimeter of the region marked off for the construction of a brick patio?
18 feet
27 feet
Chapter 1 – Slide 21
1-21

 We write the whole numbers underneath one another, lined up on the right, so each column contains digits with the same place value.
 Keep the following properties of subtraction in mind.
• When we subtract a number from itself, the result is 0: 6 – 6 = 0
• When we subtract 0 from a number, the result is the original number: 32 – 0 = 32
Chapter 1 – Slide 22
1-22

1-23
Chapter 1 – Slide 23

1.
2.
3.
Subtract: 219 – 58
Find the difference between 400 and 174.
The junior class donated 365 cans of food to the food drive. The senior class donated 286 cans.
How many more cans did the junior class donate?
Chapter 1 – Slide 24
1-24

Attendance
Charles Pickney 24
Congaree Swamp 96
Cowpens National
Kings Mountain
213
257
Fort Sumter
0 50 100 150 200 250
Number of Visitors (thousands) http://www.scprt.com/files/Research/National_and_State_Parks.htm
300
319
350
Which park had the greatest number of visitors?
Chapter 1 – Slide 25
1-25

Attendance
Charles Pickney 24
Congaree Swamp 96
Cowpens National
Kings Mountain
213
257
Fort Sumter
0 50 100 150 200 250
Number of Visitors (thousands) http://www.scprt.com/files/Research/National_and_State_Parks.htm
300
319
350
How many visitors were there at Fort Sumter and
Kings Mountain?
Chapter 1 – Slide 26
1-26

 An estimation can be used to check an answer and see if your answer is “close” to the exact answer.
Chapter 1 – Slide 27
1-27

Example
1.
Compute the sum 8,935 + 478 + 2,825 . Check by estimation.
2.
Subtract 2,387 from 7,329. Check by estimating.
Chapter 1 – Slide 28
1-28

1-29
Section 1.3
Chapter 1 – Slide 29

 Multiplication is repeated addition.
For example, suppose you buy 5 packages of crayons for your child and each package has 6 crayons.
+ + + +
The parts of a product, that is the 6 and 5, are called factors .
Chapter 1 – Slide 30
1-30
6 + 6 + 6 + 6 + 6
30 crayons 6

5 = 30

 The Identity Property of Multiplication
The product of any number and 1 is that number.
3

1 = 3 or 12

1 = 12
 The Multiplication Property of 0
The product of any number and 0 is 0.
3

0 = 0 or 12

0 = 0
Chapter 1 – Slide 31
1-31

 The Commutative Property of Multiplication
Changing the order in which two numbers are multiplied does not affect their product.
3

2 = 2

3
6 = 6
 The Associative Property of Multiplication
When multiplying three numbers, regrouping the factors gives the same product.
(4

7)

2 = 4

(7

2)
28

2 = 4

14
56 = 56
Chapter 1 – Slide 32
1-32

 To multiply whole numbers with reasonable speed, you must commit to memory the products of all single-digit whole numbers.
Chapter 1 – Slide 33
1-33

3.
4.
1.
2.
Multiply: 76 · 6
Multiply: 400

60
5 ft
Calculate the area of the home office.
Multiply: (17)(4)(3)
9 ft
8 ft
14 ft
Chapter 1 – Slide 34
1-34

 An estimation can be used to check an answer and see if your answer is “close” to the exact answer.

1.
2.
Examples
Multiply 412 by 198. Check the answer by estimating.
A class planning their class trip saved $3000 for theatre tickets. Each ticket costs $62, and a total of 28 tickets are needed. By estimating, decide if the class has set aside enough money for the tickets
Chapter 1 – Slide 35
1-35

1-36
Section 1.4
Chapter 1 – Slide 36

 In a division problem, the number that is being used to divide another number is called the divisor . The number being divided is the dividend .
The result is the quotient .
 We can also think of division as the opposite
( inverse ) of multiplication.
Chapter 1 – Slide 37
1-37

Divide and check: 3024 ÷ 6.
49, 021
Compute Then check your answer.
7
Chapter 1 – Slide 38
1-38

When a division problem results in a remainder as well as a quotient, we use this relationship for checking.
(Quotient
×
Divisor) + Remainder = Dividend
We will often write the results of a division problem as <Quotient> R <Remainder> , such as 25 R3.
Chapter 1 – Slide 39
1-39

1.
Find the quotient of 23,399 and 4. Then check.
2.
1,867
Compute and check.
23
3.
4.
Find the quotient and remainder of 12,861 and
63. Then check.
Divide and check: 9,000 ÷ 30.
Chapter 1 – Slide 40
1-40

As for other operations, estimating is an important skill for division. Checking a quotient by estimating is faster than checking it by multiplication, although less exact.
And in some division problems, we only need an approximate answer.
Example An office building has an area of 329,479 square feet. If there are 9 floors in the building, estimate the square footage of each floor.
Chapter 1 – Slide 41
1-41

Section 1.5
Chapter 1 – Slide 42
1-42
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Writing an expression in exponential form provides a shorthand method for representing repeated multiplication of the same factor.
Definition
An exponent (or power ) is a number that indicates how many times another number (called the base ) is used as a factor.
3
•
3
•
3
•
3
•
3 = 3 5
Chapter 1 – Slide 43
1-43
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

1.
4.
Rewrite 4 ∙ 4 ∙ 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 in exponential form.
2.
a.
Compute:
1 7
3.
b.
13 2
Write 8 3 ∙ 4 2 in standard form and evaluate.
Approximately 10,000 seedlings were planted in a state forest. Express this number in terms of a power of 10.
Chapter 1 – Slide 44
1-44
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

1-45
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 45

3.
4.
1.
2.
Evaluate: 34 – 9 ∙ 3.
Find the value of 7 + 3 ∙ (4 ∙ 6 2 ).
Find the value of 7 + 3 ∙ (4 ∙ 6 2 ).
Simplify:
7
 

 2


6 .
1-46
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 46

Definition
The average (or mean ) of a set of numbers is the sum of those numbers divided by however many numbers are in the set.
Example What is the average of 87, 95, and 88?
Chapter 1 – Slide 47
1-47
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

The following shows the high temperatures in
Virginia during one week in November. a. What is the average temperature for the week?
b. Which day(s) has a temperature higher than the average temperature.
1-48
Sun. Mon. Tues. Wed. Thurs. Fri Sat
High
Temp.
42°F 49°F 53°F 39°F 30°F 41°F 54°F
Chapter 1 – Slide 48
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

1.
Evaluate 27 3 using your calculator.
2.
Evaluate 5 + 9 ÷ 3 × 2 by hand and check using your calculator.
1-49
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 49

Section 1.6
1-50
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 50

To Solve Word Problems
• Read the problem carefully
• Choose a strategy (such as drawing a picture, breaking up the question, substituting simpler numbers, or making a table).
• Decide which basic operation(s) are relevant and then translate the words into mathematical symbols.
• Perform the operations.
• Check the solution to see if the answer is reasonable. If it is not, start again by rereading the problem.
Chapter 1 – Slide 51
1-51
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Operation
×
÷
+
−
Meaning
Combining
Taking away
Adding repeatedly
Splitting up
Chapter 1 – Slide 52
1-52
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

1-53
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 53

Sketching even a rough representation of a problem, can provide insight into its solution.
Example: At Greenfield High School, there are 292 freshmen, 213 sophomores, and 524 juniors. If there are
1,036 total students, how many seniors are there in the school?
Greenfield High School
Freshmen Sophomore Junior Senior
292 213 254
Total
1036
Chapter 1 – Slide 54
1-54
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Another effective problem-solving strategy is to break up the given question into a chain of simpler questions.
1-55
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 55

On her way to work, Melinda must travel through
18 traffic lights. If she is stopped by 5, how many more traffic lights did she get a green light than a red light?
 How many traffic lights were green?
 How many did she get stopped by?
 How many more traffic lights were green than red?
Chapter 1 – Slide 56
1-56
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

A word problem involving large numbers often seems difficult just because of these numbers. A good problem-solving strategy is to consider first the identical problem but with simpler numbers.
1-57
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 57

Dinner tickets for a benefit are sold at $12 each. How many dinner tickets must be sold before the benefit profits if the break even amount for the cost of food is
$2,700?
 To determine the operation, substitute a simpler number such as $24 for the break even amount. Because it is a
“fit in” question, we must divide $24 by $12. Going back to the original problem, we see that we must divide $2,700 by 12.
Chapter 1 – Slide 58
1-58
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

When a word problem involves many numbers, organizing the numbers in a table often leads to a solution.
1-59
Example A semi truck driver must travel 1,372 miles to its destination. If the driver travels 65 miles in an hour, how many miles are remaining after 8 hours?
Chapter 1 – Slide 59
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

1-60
After
Hour
1
2
3
4
5
6
7
8
Remaining Miles
1,372 – 65 = 1,307
1,307 – 65 = 1,242
1,242 – 65 = 1,117
1,112 – 65 = 1,047
1,047 – 65 = 982
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 60