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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.
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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.
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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.
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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. | |
