Two Negatives

What is $\left(-3\right) \cdot \left(-1\right)$? Repeated addition cannot answer that, so look at a pattern instead. $\left(-3\right) \cdot 2$ is -6, $\left(-3\right) \cdot 1$ is -3, and $\left(-3\right) \cdot 0$ is 0. Each time the second factor drops by 1, the product grows by 3.

Keep the pattern going, and the next product must grow by 3 again: $\left(-3\right) \cdot \left(-1\right)$ is 3, and $\left(-3\right) \cdot \left(-2\right)$ is 6. A negative times a negative is positive.

Why does that make sense? Multiplying by a negative number flips the sign, just as a minus sign means 'the opposite of'. Flip once and you land on the negative side; flip a second time and you are back on the positive side. So multiply the sizes, and two negatives give a positive answer.