Below Zero

A negative number is a number less than zero. On a number line, positive numbers sit to the right of zero and negative numbers sit to the left. The number $-3$ is three units to the left of zero, and 3 is three units to the right. Negative numbers describe temperatures below zero, floors below ground level, and money owed.

Adding a negative number moves to the left on the number line: $5-8 = -3$. Subtracting a number is the same as adding its opposite. So subtracting a negative number moves to the right: $2+6 = 2+6 = 8$. Two minus signs in a row make a plus.

When you multiply or divide, look at the two signs. Two numbers with the same sign give a positive result. Two numbers with different signs give a negative result. For example, $-3\cdot 4 = -12$, $-3\cdot \left(-4\right) = 12$, $\frac{-12}{4} = -3$ and $\frac{-12}{-4} = 3$.

Solving an equation works the same way when a negative number appears. You still undo the operation on both sides. The only difference is that the arithmetic carries a sign. From now on, the answer $x$ can turn out to be negative, and a negative answer is a correct solution.