Basic Mathematics for College Students

This factor decreases Look for a

by 1 each time. pattern here.

4( 3 )?

4( 2 )?

4( 1 )?

4( 0 ) 0

4( 1 )  4

4( 2 )  8

4( 3 )  12

–12 –8 –4 0

A graph of the products

???

From the pattern, we see that the product increases by 4 each time. Thus,

, , and

These results illustrate that the product of two negative integers is positive.As a check,

think of it as losing four debts of $3. This is equivalent to gaining $12. Therefore,

We have seen that the product of two positive integers is positive, and the

product of two negative integers is also positive. Those results illustrate the following

rule.

4($3)$12.

4(1)  4 4(2)  8 4(3)  12

Multiplying Two Integers That Have the Same (Like) Signs

To multiply two integers that have the same sign, multiply their absolute

values. The final answer is positive.

166 Chapter 2 The Integers

2 Multiply two integers that have the same sign.

To develop a rule for multiplying two integers that have the same sign, we will first

consider , which is the product of two positive integers. We say that the signs of the

factors are like.By the definition of multiplication, means that we are to add 3

four times.

Write 3 as an addend four times.

The result is 12, which is a positive number.

As expected, the result is positive.

To develop a rule for multiplying two negative integers, consider the following

list, where we multiply by factors that decrease by 1. We know how to find the first

four products. Graphing those results on a number line is helpful in determining the

last three products.

 4

 12

4(3) 3  3  3  3

4(3)

4(3)

 

Caution! When writing multiplication involving signed numbers, do not write

a negative sign next to a raised dot (the multiplication symbol). Instead,

use parentheses to show the multiplication.

6(2) 6  2 and 6(2)  6  2