# Operations with Negatives

## Adding and Subtracting with Negatives

The first thing to know is that $x$ and its additive inverse, $-x$ , add up to zero. So:

$\begin{array}{l}-999+999=0\\ 2.5+\left(-2.5\right)=0\\ 1+\left(-1\right)=0\end{array}$

### Number Line Method

Start at $0$ . When you add a positive number, or subtract a negative number, move to the right .

When you add a negative number, or subtract a positive number, move to the left .

## Multiplying and Dividing with Negatives

### Multiplying with Negatives

The product of two numbers with the same sign is positive. The product of two numbers with different signs is negative.

Example:

$\begin{array}{l}\left(-3\right)\left(-7\right)=21\\ \left(3\right)\left(-7\right)=-21\end{array}$

### Dividing with Negatives

The quotient of two numbers with the same sign is positive. The quotient of two numbers with different signs is negative.

Example:

$\begin{array}{l}-56÷\left(-7\right)=8\\ 56÷\left(-7\right)=-8\end{array}$