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Chapter 2—Integers

2-7 Multiplying Signed Integers

When you complete the work for this section, you should be able to:
  • Demonstrate a mastery of the procedures for multiplying signed integers.

The basic procedure for multiplying integers is identical to multiplying whole-number values. The only significant difference is dealing with the + and – signs that are assigned to the integer values.

fig0207_01.jpg (7546 bytes)

Terminology for the multiplication of signed integers.

 

Procedure Preview

Multiplying Signed Integers

The procedure for multiplying signed integers is:

Step 1: Multiply the absolute value of the factors.
Step 2: Give the appropriate sign to the product:
  • Positive if the both factors have the same sign.
  • Negative if the factors have opposite signs.

Note: Zero has no sign.

Multiplying Integers Having the Same Sign

Procedure

When the factors have the same sign—both positive or both negative—the product is always positive.

So:

  1. Multiply the two factors, disregarding the signs.
  2. Show the product as a positive integer.

Multiplying integers having the same sign.

Notice that:

When the signs of the two factors are the same, the product is positive.

Example 1

Problem

(+ 5) x (+ 2) = __

Procedure
  1. Multiply the absolute value of the terms.
| + 5 | x | +2 | = 10
  1. Assign the appropriate sign to the product.
Signs are the same, so the sign of the product is +:

+10

Solution

(+ 5) x (+ 2) = ( +10)

Or you might this example expressed more simply as 5 x 2 = 10, which looks exactly like multiplication for whole numbers.

Example 2

Problem

( – 8) x ( – 3) = ___

Procedure
  1. Multiply the absolute value of the terms.
| –8 | x | –3 | = 24
  1. Assign the appropriate sign to the product.
Signs are identical, so the signof the product is +:

+24

Solution

( – 8) x ( – 3) = ( +24)

Or you might see it expressed more simply as 
– 8 x – 3 = 24.

Examples and Exercises #1

Multiplying Integers Having the Same Sign

Use these interactive examples and exercises to strengthen your understanding and build your skills:

Multiplying Integers Having Opposite Signs

Procedure

When the factors have the opposite sign—one is positive an the other is negative—the product is always negative.

So:

  1. Multiply the factors, disregarding the signs.
  2. Show the product as a negative integer.
 


Multiplying integers having opposite signs.

Notice that:

When the signs of the two factors are different, the product is negative.

 

Example 3

Problem

( – 7) x ( + 2) = ___

Procedure
  1. Multiply the absolute value of the terms.
|  – 7 | x | +2 | = 14
  1. Assign the appropriate sign to the product.
Signs are opposite, so the sign of the product is –:

– 14

Solution

( – 7) x ( + 2) = ( – 14)

Or you might express this answer more simply as
– 7 x 2 = –14

Examples and Exercises #2

Multiplying Integers That Have Opposite Signs

Use these interactive examples and exercises to strengthen your understanding and build your skills:

Lesson Summary

To multiply integers that have the same sign (both positive or both negative):

  1. Multiply the two factors, disregarding the signs.
  2. Show the product as a positive integer.

To multiply integers that have opposite signs:

  1. Multiply the factors., disregarding the signs.
  2. Show the product as a negative integer.

Examples and Exercises

Multiplying Signed Integers

These examples and exercises will show you that you've mastered the whole idea of multiplying signed integers.

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015