# Adding and Subtracting with Negatives

Adding any number to its opposite —also called the additive inverse—always gives zero as the result. For example:

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

Once you know this, there are several ways to think about addition.

### Algebra Tile Method

Let yellow tiles represent positive numbers, and red tiles represent negative numbers.

**
Example 1:
**

The addition problem $5+\left(-2\right)$ can be represented as

Group the two negative tiles with two positive tiles.

Since $2+\left(-2\right)=0$ , these tiles disappear. We are left with $3$ positive tiles.

So
**
$5+\left(-2\right)=3$
**
.

**
When both numbers are negative
**
, we have only negative tiles, so the answer is also negative.

**
Example 2:
**

The addition problem $-3+\left(-4\right)$ can be represented as

The result is simply $7$ negatives tiles.

So
**
$-3+\left(-4\right)=-7$
**
.

### Number Line Method

When you
**
add a positive
**
number, you move to the
**
right
**
on the number line.

When you
**
add a negative
**
number, you move to the
**
left
**
on the number line.

**
Example 3:
**

Add $6+\left(-8\right)$ using a number line.

Start at $6$ , and move $8$ units to the left.

$6+\left(-8\right)=-2$

Subtracting a number is the same as adding its opposite.

So,
**
subtracting a positive
**
number is like adding a negative; you move to the
**
left
**
on the number line.

**
Subtracting a negative
**
number is like adding a positive; you move to the
**
right
**
on the number line.

**
Example 4:
**

Subtract $-4-\left(-7\right)$ .

Start at $-4$ , and move $7$ units to the right.

$-4-\left(-7\right)=3$ .