Multiplying integers involves understanding how the signs (positive or negative) of the numbers affect the result. Here's a breakdown of the rules, as indicated by your provided references, with examples:
Basic Rules of Integer Multiplication
The core principle of multiplying integers revolves around these rules:
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Positive x Positive = Positive: When you multiply two positive integers, the result is always a positive integer.
- Example: 3 x 4 = 12
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Negative x Negative = Positive: Multiplying two negative integers results in a positive integer. This is a crucial rule to remember. Note: This is different than what is mentioned in reference 2.
- Example: (-3) x (-4) = 12
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Positive x Negative = Negative or Negative x Positive = Negative: When multiplying a positive integer and a negative integer (in either order), the outcome will always be a negative integer. This aligns with the provided reference 3.
- Example: 3 x (-4) = -12
- Example: (-3) x 4 = -12
Table Summary
| Integer 1 | Integer 2 | Result | Example |
|---|---|---|---|
| Positive | Positive | Positive | 2 x 5 = 10 |
| Negative | Negative | Positive | -2 x -5 = 10 |
| Positive | Negative | Negative | 2 x -5 = -10 |
| Negative | Positive | Negative | -2 x 5 = -10 |
Step-by-Step Guide to Multiplying Integers
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Multiply the absolute values: Ignore the signs of the integers and multiply the numerical values.
- Example: To multiply -6 x 7, multiply 6 x 7, which equals 42.
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Determine the sign of the result: Apply the rules from above. If the signs of the original integers are the same (both positive or both negative), the result is positive. If the signs are different (one positive, one negative), the result is negative.
- Example: Since -6 and 7 have different signs, -6 x 7 = -42.
Practical Application
- Temperature changes: If the temperature drops 2 degrees every hour for 3 hours, the total change is (-2) x 3 = -6 degrees (a drop of 6 degrees).
- Financial calculations: If you owe \$5 each to 4 different people, this can be represented as (-5) x 4 = -20 (you owe \$20 in total).
Conclusion
Multiplying integers is all about understanding the impact of the signs. By following the simple rules outlined above, you can confidently multiply any set of integers. Always remember to handle the numerical values first and then apply the rules for positive and negative signs to determine the final sign of the product.
