Adding and Subtracting with Negatives

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

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

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

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

Example 1:

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

Group the two negative tiles with two positive tiles.

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

So $5 + (- 2) = 3$ .

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

Example 2:

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

The result is simply $7$ negatives tiles.

So $- 3 + (- 4) = - 7$ .

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 $6 + (- 8)$ using a number line.

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

$6 + (- 8) = - 2$

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 $- 4 - (- 7)$ .

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

$- 4 - (- 7) = 3$ .