Multiplication is essentially a shortcut for adding the same number multiple times.
Positive Integers: $2 + 2 + 2 = 6$, which is the same as $2 \times 3$.
Negative Integers: $-2 – 2 – 2 = -6$, which is the same as $-2 \times 3$.
When multiplying two integers, the sign of the result depends entirely on the signs of the numbers you are multiplying:
| Signs of Integers | Resulting Sign | Example |
| Positive $\times$ Positive | Positive (+) | $12 \times 7 = 84$ |
| Negative $\times$ Negative | Positive (+) | $-12 \times -7 = 84$ |
| Positive $\times$ Negative | Negative (-) | $12 \times -7 = -84$ |
| Negative $\times$ Positive | Negative (-) | $-12 \times 7 = -84$ |
Note: Multiplying any integer by zero always results in zero (e.g., $-2 \times 0 = 0$ or $2 \times 0 = 0$).
Subtraction can often be thought of as “adding the opposite.” This is especially helpful when dealing with negative numbers.
When you subtract a negative number, the two negative signs next to each other become a positive.
Example: Subtract $-7$ from $12$
Solution: $12 – (-7) = 12 + 7 = 19$
The same “double negative” rule applies here.
Example: Subtract $-7$ from $-12$
Solution: $-12 – (-7) = -12 + 7 = -5$
In this case, you are moving further left on the number line.
Example: Subtract $7$ from $-12$
Solution: $-12 – 7 = -19$