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Chapter 2—Integers
27 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 wholenumber values. The only significant difference is dealing with the + and – signs that are assigned to the integer values.
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:  Multiply the two factors, disregarding the signs.
 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  
 Multiply the absolute value of the terms.
  + 5  x  +2  = 10 
 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  
 Multiply the absolute value of the terms.
  –8  x  –3  = 24 
 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:  Multiply the factors, disregarding the signs.
 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  
 Multiply the absolute value of the terms.
  – 7  x  +2  = 14 
 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):
 Multiply the two factors, disregarding the signs.
 Show the product as a positive integer.
To multiply integers that have opposite signs:
 Multiply the factors., disregarding the signs.
 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.  