# 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:
**

$\begin{array}{l}-56\xf7\left(-7\right)=8\\ 56\xf7\left(-7\right)=-8\end{array}$

See also: Adding and Subtracting with Negatives and Multiplying and Dividing with Negatives