Multiplying and Dividing Integers

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Multiplying and Dividing Integers
Section 2.4
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Consider the following pattern of products.
3 ? 5 15
First factor decreases by 1 each time.
Product decreases by 5 each time.
2 ? 5 10
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.
Martin-Gay, Prealgebra, 5ed
3
What is the sign of the product of two negative
numbers?
Observe the following pattern.
2 ? (- 5) - 10
Product increases 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 two negative
numbers is a positive number.
Martin-Gay, Prealgebra, 5ed
4
Multiplying Numbers

• 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
Martin-Gay, Prealgebra, 5ed
5
Multiplying Numbers

• Product of Like Signs

( )( )
( - )( - )
Product of Different Signs
-
-
( - )( )
( )( - )
Martin-Gay, Prealgebra, 5ed
6
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
( - ) ( - ) ( - ) ( - )
( - ) ( - ) ( - ) ( - ) ( )
( - ) ( - ) ( - ) ( - ) ( - ) ( - )
Martin-Gay, Prealgebra, 5ed
7
Division of integers is related to multiplication
of integers.
Martin-Gay, Prealgebra, 5ed
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Dividing Numbers

• 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
Martin-Gay, Prealgebra, 5ed
9
Dividing Numbers

• Quotient of Like Signs

Quotient of Different Signs
Martin-Gay, Prealgebra, 5ed