Page 165 - Basic College Mathematics with Early Integers

2.5
Objectives MULTIPLYING AND DIVIDING INTEGERS

Multiply Integers.
Multiplying and dividing integers is similar to multiplying and dividing whole numbers.
Divide Integers.
One difference is that we need to determine whether the result is a positive number or
Evaluate an Algebraic Expression a negative number.
by Multiplying or Dividing.
Objective Multiplying Integers
Solve Problems by Multiplying
or Dividing Integers.
Consider the following pattern of products.
#
First factor 3 2 = 6
decreases by
#
2 2 = 4 Product decreases by 2 each time.
1 each time.
#
1 2 = 2
#
0 2 = 0 Î
This pattern can be continued, as follows.
#
-1 2 =-2
#
-2 2 =-4
#
-3 2 =-6
This suggests that the product of a negative number and a positive number is a neg-
ative number.
What is the sign of the product of two negative numbers? To find out, we form
another pattern of products. Again, we decrease the first factor by 1 each time, but
this time the second factor is negative.
#
2 1-32 =-6
#
1 1-32 =-3 Product increases by 3 each time.
#
0 1-32 = 0
Î
This pattern continues as:
#
-1 1-32 = 3
#
-2 1-32 = 6
#
-3 1-32 = 9
This suggests that the product of two negative numbers is a positive number. Thus
we can determine the sign of a product when we know the signs of the factors.

Multiplying Numbers

The product of two numbers The product of two numbers hav-
having the same sign is a positive ing different signs is a negative
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number. number.

Product of Like Signs Product of Different Signs

1+21+2 =+ 1-21+2 =-
1-21-2 =+ 1+21-2 =-

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