The similarity between dividing and multiplying integers lies primarily in the rules for determining the sign of the result.
Sign Rules for Multiplication and Division
Both operations follow the same sign conventions:
| Operation | Rule | Example | Result |
|---|---|---|---|
| Multiplication | Same signs result in a positive answer | 3 x 4 = 12 or (-3) x (-4) = 12 | Positive |
| Multiplication | Different signs result in a negative answer | 3 x (-4) = -12 or (-3) x 4 = -12 | Negative |
| Division | Same signs result in a positive answer | 12 / 3 = 4 or (-12) / (-3) = 4 | Positive |
| Division | Different signs result in a negative answer | 12 / (-3) = -4 or (-12) / 3 = -4 | Negative |
As stated in the reference, "If the two numbers have the same sign, both positive or negative, the answer will be positive. If the two numbers do not have the same sign, a combination of positive and negative, the answer will be negative." This rule applies identically to both multiplication and division.
Examples
Here are a few more examples illustrating the shared rules:
- Positive x Positive = Positive: 5 x 2 = 10
- Negative x Negative = Positive: (-5) x (-2) = 10
- Positive x Negative = Negative: 5 x (-2) = -10
- Negative x Positive = Negative: (-5) x 2 = -10
- Positive / Positive = Positive: 10 / 2 = 5
- Negative / Negative = Positive: (-10) / (-2) = 5
- Positive / Negative = Negative: 10 / (-2) = -5
- Negative / Positive = Negative: (-10) / 2 = -5
Therefore, understanding the sign rules is key to performing both integer multiplication and division accurately. While the operations themselves (multiplying quantities vs. dividing quantities) are different, the process of determining the sign of the result is the same.
