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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. 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):

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.

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