Transcript Chapter 1

Chapter 1
Whole Numbers
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 1 – Slide 1
Section 1.1
Introduction to Whole Numbers
Chapter 1 – Slide 2
Reading and Writing Whole
Numbers



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
Reading and Writing Whole
Numbers

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
Example
Identify the place value of the 8.
a. 508
b. 8,430,999
c. 6,800,000,002
Chapter 1 – Slide 5
1-5
Reading and Writing Whole
Numbers
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?
1-7
Chapter 1 – Slide 7
Reading and Writing Whole
Numbers
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
Example
1.
Write the number six billion, twelve in standard
form.
BILLIONS
O
2.
MILLIONS
H
T
THOUSANDS
O
H
T
ONES
O
H
T
O
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
Writing Whole Numbers in
Expanded Form

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
O
MILLIONS
H
T
THOUSANDS
O
H
T
ONES
O
5
H
2
T
9
O
3
Chapter 1 – Slide 10
Example
Write 803 in expanded form.
Write 8,407,800 in expanded form:
Chapter 1 – Slide 11
1-11
Rounding Whole Numbers
Chapter 1 – Slide 12
1-12
Rounding Whole Numbers
Chapter 1 – Slide 13
1-13
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
Example
Write in words
the amount of
money taken in
by The Lord of
the Rings: The
Two Towers
Chapter 1 – Slide 15
1-15
Example
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
Adding and Subtracting
Whole Numbers
Chapter 1 – Slide 17
Identities and Properties

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
1-18
Chapter 1 – Slide 18
Identities and Properties

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
1-19
Chapter 1 – Slide 19
Adding Whole Numbers


1-20
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
Example
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
1-21
Chapter 1 – Slide 21
Subtracting Whole Numbers


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.
•
•
1-22
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
Subtracting Whole Numbers
1-23
Chapter 1 – Slide 23
Example
1.
2.
3.
1-24
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
Example
Attendance
Charles Pickney
24
Park
Congaree Swamp
96
Cowpens National
213
Kings Mountain
257
Fort Sumter
319
0
50
100
150
200
250
Number of Visitors (thousands)
300
350
http://www.scprt.com/files/Research/National_and_State_Parks.htm
Which park had the greatest number of visitors?
1-25
Chapter 1 – Slide 25
Example
Attendance
Charles Pickney
24
Park
Congaree Swamp
96
Cowpens National
213
Kings Mountain
257
Fort Sumter
319
0
50
100
150
200
250
Number of Visitors (thousands)
300
350
http://www.scprt.com/files/Research/National_and_State_Parks.htm
How many visitors were there at Fort Sumter and
Kings Mountain?
1-26
Chapter 1 – Slide 26
Estimating Sums and Differences

1-27
An estimation can be used to check an answer and
see if your answer is “close” to the exact answer.
Chapter 1 – Slide 27
Example
1.
Compute the sum 8,935 + 478 + 2,825 . Check
by estimation.
2.
Subtract 2,387 from 7,329. Check by estimating.
1-28
Chapter 1 – Slide 28
Section 1.3
Multiplying Whole Numbers
1-29
Chapter 1 – Slide 29
The Meaning and Properties of
Multiplication

Multiplication is repeated addition.
For example, suppose you buy 5 packages of
crayons for your child and each package has 6
crayons.
+
6
+
+
6 +
+
6 + 6 +
+
6
30 crayons 6  5 = 30
1-30
The parts of a
product, that is
the 6 and 5, are
called factors.
Chapter 1 – Slide 30
Identities and Properties

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
1-31
Chapter 1 – Slide 31
Identities and Properties

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
1-32
Chapter 1 – Slide 32
Multiplying Whole Numbers

1-33
To multiply whole numbers with reasonable
speed, you must commit to memory the products
of all single-digit whole numbers.
Chapter 1 – Slide 33
Example
1.
2.
3.
4.
Multiply: 76 · 6
Multiply: 400  60
5 ft
Calculate the area of the home office.
Multiply: (17)(4)(3)
8 ft
9 ft
14 ft
1-34
Chapter 1 – Slide 34
Estimating Sums and Differences
An estimation can be used to check an answer
and see if your answer is “close” to the exact
answer.
Examples


1.
2.
1-35
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
Section 1.4
Dividing Whole Numbers
1-36
Chapter 1 – Slide 36
The Meaning and Properties of
Division


1-37
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
Example
Divide and check: 3024 ÷ 6.
Compute
49, 021
. Then
check your answer.
7
1-38
Chapter 1 – Slide 38
Remainders
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.
1-39
Chapter 1 – Slide 39
Example
1.
2.
Find the quotient of 23,399 and 4. Then check.
Compute
1, 867
and check.
23
3.
4.
1-40
Find the quotient and remainder of 12,861 and
63. Then check.
Divide and check: 9,000 ÷ 30.
Chapter 1 – Slide 40
Checking by Estimating
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.
1-41
Chapter 1 – Slide 41
Section 1.5
Exponents, Order of Operations,
and Averages
Chapter 1 – Slide 42
1-42
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Exponents
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 = 35
1-43
Chapter 1 – Slide 43
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Example
Rewrite 4 ∙ 4 ∙ 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 in exponential form.
Compute:
1.
2.
a.
b.
3.
4.
1-44
17
132
Write 83 ∙ 42 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
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
1-45
Chapter 1 – Slide 45
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Example
1.
2.
3.
4.
Evaluate: 34 – 9 ∙ 3.
Find the value of 7 + 3 ∙ (4 ∙ 62).
Find the value of 7 + 3 ∙ (4 ∙ 62).
Simplify:
2

7  4 8  2   6  .


1-46
Chapter 1 – Slide 46
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Averages
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?
1-47
Chapter 1 – Slide 47
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Example
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.
Sun. Mon. Tues. Wed. Thurs. Fri
High 42°F 49°F
Temp.
1-48
53°F
39°F
30°F
Sat
41°F 54°F
Chapter 1 – Slide 48
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Calculator Examples
1.
2.
1-49
Evaluate 273 using your calculator.
Evaluate 5 + 9 ÷ 3 × 2 by hand and check using
your calculator.
Chapter 1 – Slide 49
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Section 1.6
More on Solving Word Problems
Chapter 1 – Slide 50
1-50
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Solving Word Problems
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.
1-51
Chapter 1 – Slide 51
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Four Basic Operations
1-52
Operation
Meaning
+
Combining
−
Taking away
×
Adding repeatedly
÷
Splitting up
Chapter 1 – Slide 52
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Clue Words
1-53
Chapter 1 – Slide 53
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Drawing a Picture
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
292
213
254
1-54
Senior
Total
1036
Chapter 1 – Slide 54
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Breaking Up the Question
Another effective problem-solving strategy is to
break up the given question into a chain of
simpler questions.
1-55
Chapter 1 – Slide 55
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Example
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?



1-56
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
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Substituting Simpler Numbers
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
Chapter 1 – Slide 57
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Example
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.
1-58
Chapter 1 – Slide 58
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Making a Table
When a word problem involves many numbers,
organizing the numbers in a table often leads to a
solution.
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?
1-59
Chapter 1 – Slide 59
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Making A Table - Continued
After
Hour
Remaining Miles
1
1,372 – 65 = 1,307
2
1,307 – 65 = 1,242
3
1,242 – 65 = 1,117
4
5
1,112 – 65 = 1,047
6
1,047 – 65 = 982
7
8
1-60
Chapter 1 – Slide 60
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