Download Multiplying Integers

Chapter 2
Integers and
Introduction to
Variables
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2.5
Multiplying and
Dividing Integers
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying Integers
Consider the following pattern of products.
First factor
decreases by 1
each time.
3  5 = 15 Product
2  5 = 10 decreases by 5
each time.
15= 5
05= 0
This pattern continues as follows.
–1  5 = -5
–2  5 = -10
–3  5 = -15
This suggests that the product of a negative number and a positive
number is a negative number.
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Multiplying Integers
Observe the following pattern.
2  (–5) = -10
1  (–5) = -5
0  (–5) = 0
Product
increases by 5
each time.
This pattern continues as follows.
– 1  (– 5) = 5
– 2  (–5) = 10
–3  (– 5) = 15
This suggests that the product of two negative numbers is a
positive number.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
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Multiplying Integers
The product of two numbers having the same
sign is a positive number.
24=8
– 2  (–4) = 8
The product of two numbers having different
signs is a negative number.
2  (–4) = – 8
–2  4 = – 8
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
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Multiplying Integers
Product of Like Signs
( + )( + ) = +
(–)(–) = +
Product of Different Signs
(–)( + ) = –
( + )(–) = –
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Helpful Hint
If we let ( – ) represent a negative number and ( + )
represent a positive number, then
The product
of an even
number of
negative
numbers is
a positive
result.
(–)(–)=(+)
(–)(–)(–)=(–)
(–)(–)(–)(–)=(+)
(–)(–)(–)(–)(–)=(–)
The product
of an odd
number of
negative
numbers is
a negative
result.
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Dividing Integers
Division of integers is related to multiplication of
integers.
6
= 3 because
3· 2 =6
2
–6 =
–3 because
2
–3 · 2 = –6
6 = –3 because
–2
– 3· (–2) = 6
– 6=
3 because
–2
3 · (–2) = –6
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
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Dividing Integers
The quotient of two numbers having the same
sign is a positive number.
12 ÷ 4 = 3
–12 ÷ (– 4 ) = 3
The quotient of two numbers having different
signs is a negative number.
–12 ÷ 4 = – 3
12 ÷ (–4) = –3
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Dividing Numbers
Quotient of Like Signs
( )

( )
( )

( )
Quotient of Different Signs
( )

( )
( )

( )
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Evaluating Expressions
Evaluate 7xy for x = –5 and y = 8.
Replace x with –6 and y with 8 in 7xy.
7xy = 7 (–6)(8)
= – 42 · 8
= –336
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Solving Problems by Multiplying and
Dividing Integers
Joe Norstrom lost $400 on each of seven consecutive
days in the stock market. Represent his total loss as a
product of signed numbers and find his total loss.
7  (400)  2800
Joe Norstrom’s total loss is $2800.
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