To multiply signed integers, you multiply their absolute values first, then determine the sign of the product based on the signs of the original integers.
Rules for Multiplying Signed Integers
The key rules are summarized below:
- Same Signs: If the two integers have the same sign (both positive or both negative), the product is positive.
- Different Signs: If the two integers have different signs (one positive and one negative), the product is negative.
This can be neatly summarized in a table:
| Integer 1 Sign | Integer 2 Sign | Product Sign |
|---|---|---|
| Positive (+) | Positive (+) | Positive (+) |
| Negative (-) | Negative (-) | Positive (+) |
| Positive (+) | Negative (-) | Negative (-) |
| Negative (-) | Positive (+) | Negative (-) |
Steps for Multiplying Signed Integers:
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Find the Absolute Values: Determine the absolute value of each integer. The absolute value of a number is its distance from zero, and is always non-negative. For example, |-3| = 3 and |5| = 5.
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Multiply the Absolute Values: Multiply the absolute values you found in step 1. This gives you the numerical part of the answer.
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Determine the Sign: Based on the signs of the original integers, determine whether the product is positive or negative, using the rules outlined above.
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Combine Sign and Value: Combine the sign determined in step 3 with the numerical value from step 2.
Examples:
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Example 1: Positive x Positive
- Multiply 3 x 7.
- Both integers are positive.
- 3 x 7 = 21. The product is positive.
- Therefore, 3 x 7 = 21.
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Example 2: Negative x Negative
- Multiply -4 x -2.
- Both integers are negative.
- |-4| x |-2| = 4 x 2 = 8. The product is positive.
- Therefore, -4 x -2 = 8.
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Example 3: Positive x Negative
- Multiply 6 x -5.
- One integer is positive, and the other is negative.
- |6| x |-5| = 6 x 5 = 30. The product is negative.
- Therefore, 6 x -5 = -30.
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Example 4: Negative x Positive
- Multiply -8 x 2.
- One integer is negative, and the other is positive.
- |-8| x |2| = 8 x 2 = 16. The product is negative.
- Therefore, -8 x 2 = -16.
In summary, multiplying signed integers involves multiplying their absolute values and then applying the rules for determining the correct sign of the resulting product.
