1. Additional Whole Number Operations
Math 081
Additional
Whole Number
Operations
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2. Multiplying Integers
We are learning to…multiply and divide integers by looking for patterns.

3. Multiplication of Integers-8
Evaluate: = ________
Repeated addition is the same thing as:__________________
...so can be written:________
Evaluate: = ______________
. ..so can be written:________
Multiplication
4(-2)
-12
Multiplication
3(-4)

4. Multiplication of Integers
-35
Evaluate: = ______________
...Rewrite as a multiplication problem:_________
Evaluate: = ______________
Evaluate: = ______________
5(-7)
-24
2(-12) -5
5(-1)

5. Multiplication of Integers
I know that: (positive number) × (negative number) =
_______________________________________.
The ______________________________ property of multiplication allows me to multiply in any order.
So I also know that (negative number) × (positive number) =
Negative Number
Commutative
Negative Number
Evaluate the expressions below.

6. Multiplication of Integers
Negative
Negative
Negative × Positive = _______________ and Positive × Negative = _______________
If the signs in a multiplication problem are different the solution is:_______________
I know that a: positive × positive = ______________
Now follow the pattern: (+)(–) = ______________
(–)(+) = ______________
(+)(+) = ______________
So… (–)(–) = ______________
I know that a: negative × negative = _________________________
If the signs in a multiplication problem are the same the solution is:_______________
Negative
Positive
Negative
Negative
Positive
Positive
Positive
Positive

7. Which of the following statements is NOT true?
A negative multiplied by a negative is a positive product.
A positive multiplied by a negative is a negative product.
A negative multiplied by a negative is a negative product.
A negative multiplied by a positive is a negative product.

8. 2.1 and 2.2 Dividing Whole Numbers
Objectives
1. Write division problems in three ways.
2. Identify the parts of a division problem.
3. Divide 0 by a number.
4. Recognize that a number cannot be divided by 0.
5. Divide a number by itself.
6. Divide a number by 1.
7. Use short division.
8. Use multiplication to check the answer to a division
problem.
9. Use tests for divisibility.
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9. Copyright © 2010 Pearson Education, Inc. All rights reserved.
Just as 4  5, 4 × 5, and (4)(5) are different ways of indicating multiplication, there are several ways to write 20 divided by ÷ 4 = 5
Being divided
Being divided
Divided by
Being divided
Divided by
Divided by
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10. Copyright © 2010 Pearson Education, Inc. All rights reserved.
Parallel
Example 1
Using Division Symbols
Write the division problem 21 ÷ 7 = 3 using two other symbols. This division can also be written as shown below.
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11. In division, the number being divided is the dividend, the number divided by is the divisor, and the answer is the quotient.
dividend ÷ divisor = quotient
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12. Identifying the Parts of a Division Problem
Parallel
Example 2
Identifying the Parts of a Division Problem
Identify the dividend, divisor, and quotient.
36 ÷ 9 = 4 b.
quotient
dividend
divisor
dividend
quotient
divisor
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Parallel
Example 3
Dividing 0 by a Number
Divide.
0 ÷ 21 =
b. 0 ÷ 1290 = c. d.
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Parallel
Example 4
Changing Division Problems to Multiplication
Change each division problem to a multiplication problem. a. b. c. 90 ÷ 9 = 10
becomes 3  9 = 27 or 9  3 = 27
becomes 8  7 = 56 or 7  8 = 56
becomes 9  10 = 90 or 10  9 = 90
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Parallel
Example 5
Dividing 0 by a Number
All the following are undefined. a. b. c. 25 ÷ 0
is undefined
is undefined
is undefined
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Parallel
Example 6
Dividing a Nonzero Number by Itself
Divide. a. 25 ÷ 25 = b. c. 1 1 1
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Parallel
Example 7
Dividing Numbers by 1
Divide. a. 15 ÷ 1 = b. c. 15 72 34
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Parallel
Example 11
Checking Division by Using Multiplication
Check each answer. a. (divisor  quotient) + remainder = dividend (4  135) = 542 R2
Matches
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Parallel
Example 11
Checking Division by Using Multiplication
Check each answer. b. (divisor  quotient) + remainder = dividend (8  154) = 1235 R3
Does not match original dividend.
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Parallel
Example 12
Testing for Divisibility by 2
Are the following numbers divisible by 2?
128
4329
Because the number ends in 8, which is an even number, the number is divisible by 2.
Ends in 8
The number is NOT divisible by 2.
Ends in 9
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Parallel
Example 13
Testing for Divisibility by 3
Are the following numbers divisible by 3?
2128
b. 27,306
Add the digits.
= 13
Because 13 is not divisible by 3, the number is not divisible by 3.
Add the digits.
= 18
Because 18 is divisible by 3, the number is divisible by 3.
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Parallel
Example 14
Testing for Divisibility by 5
Are the following numbers divisible by 5?
17,900 b c
The number ends in 0 and is divisible by 5.
The number ends in 5 and is divisible by 5.
The number ends in 7 and is not divisible by 5.
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Parallel
Example 15
Testing for Divisibility by 10
Are the following numbers divisible by 10?
18,240 b c
The number ends in 0 and is divisible by 10.
The number ends in 5 and is not divisible by 10.
The number ends in 8 and is not divisible by 10.
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2.4 Order of Operations
Objectives
1. Use the order of operations.
2. Use the order of operations with exponents.
3. Use the order of operations with fractions bars.
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Parallel
Example 1
Using the Order of Operations a.
÷ 4 b.
3 − 24 ÷ 4 + 9
3 − 23
3 + (−6) − 6
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36. Evaluate:
-14
-30 20 -8

37. Evaluate:
315
-105 3
-76

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Parallel
Example 2
Parentheses and the Order of Operations a.
−5(8 – 4) – 3 b.
3 + 4(4 – 9)(20 ÷ 4)
−5(4) – 3
(–5)(20 ÷ 4)
−20 – 3
(–5) (5)
3 + (–20) (5)
−20 + (– 3)
3 + (–100)
−23
–97
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Parallel
Example 3
Exponents and the Order of Operations a.
52 − (−2)2 b.
(−7)2 − (5 − 8)2 (−4)
(−7)2 − (− 3)2 (−4)
25 − 4
49 − 9(−4) 21
49 − (−36)
(+36) 85
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Parallel
Example 4
Fraction Bars and the Order of Operations
Simplify.
First do the work
in the numerator.
Then do the work
in the denominator.
−14 + 3(5 – 7)
6 – 42 ÷ 8
−14 + 3(– 2)
6 – 16 ÷ 8
−14 + (– 6)
6 – 2 4
−20
Denominator
Numerator
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41. 2.5 Using Equations to Solve Application Problems
Objectives
1. Translate word phrases into expressions
with variables.
2. Translate sentences into equations.
3. Solve application problems.
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As you read an application problem, look for indicator words that help you.
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Translating Word Phrases into Expressions
Write each word phrase as an expression
Words
Expression
A 4 plus nine
7 more than 3
−12 added to 4
3 less than 8
7 decreased by 1
14 minus -8
4 + 9 or 9 + 4
3 + 7 or 7 + 3
− or 4 + (−12)
8 – 3
7 – 1
14 – (-8)
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Translating Word Phrases into Expressions
Write each word phrase as an expression.
Words
Algebraic Expression
3 times 4
Twice the number 5
The quotient of 8 and -2
30 divided by 15
The result is
3(4)
2(5) =
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