The four rules for multiplying integers determine the sign of the product based on the signs of the numbers being multiplied. Here are the rules, explained clearly:
Integer Multiplication Rules
Understanding the rules for multiplying integers is essential for performing calculations accurately. These rules focus on how the signs (positive or negative) interact.
Here's a breakdown of the four key rules:
| Rule | Description | Example | Result |
|---|---|---|---|
| 1 | Positive × Positive | (+5) × (+3) | Positive (+15) |
| 2 | Positive × Negative | (+5) × (-3) | Negative (-15) |
| 3 | Negative × Positive | (-5) × (+3) | Negative (-15) |
| 4 | Negative × Negative | (-5) × (-3) | Positive (+15) |
Explanation of Each Rule
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Rule 1: Positive × Positive = Positive. When you multiply two positive numbers, the result is always a positive number. For example, 5 multiplied by 3 equals 15.
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Rule 2: Positive × Negative = Negative. When you multiply a positive number by a negative number, the result is always a negative number. For example, 5 multiplied by -3 equals -15.
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Rule 3: Negative × Positive = Negative. This is similar to Rule 2. When you multiply a negative number by a positive number, the result is also a negative number. For example, -5 multiplied by 3 equals -15.
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Rule 4: Negative × Negative = Positive. When you multiply two negative numbers, the result is always a positive number. For example, -5 multiplied by -3 equals 15.
Practical Application
These rules are used in all areas of mathematics involving integer multiplication:
- Algebra: Simplifying expressions.
- Calculus: Performing calculations with derivatives.
- Everyday life: Balancing finances involving credits and debits.
Key Takeaways
- When signs are the same (both positive or both negative), the product is positive.
- When signs are different (one positive and one negative), the product is negative.
