Adding or subtracting a rational number can be represented by moving **left** (in the **negative** direction) or **right** (in the **positive** direction) on a horizontal number line.

The expression *p* + *q* represents the number located |*q*| units from *p* in the

positive or negative direction if *q* is positive or negative, respectively.

**ADDITION**

Adding a positive number indicates moving that many units to the right on a number line.

Adding a negative number indicates moving that many units to the left on a number line.

The expression *p* + *q* represents the number located |*q*| units from *p* in the positive or negative direction if *q* is positive or negative, respectively.

In this case, *p* = -5 and *q* = 7.

Since *q* is positive, -5 + 7 is 7 units from -5 in the positive direction.

This can be represented on a number line.

First, draw an arrow to represent -5.

Start at 0 and extend the arrow 5 units in the negative direction, which is to the left.

Next, draw an arrow to represent adding 7 to -5.

Start at -5 and extend the arrow 7 units in the positive direction, which is to the right.

The second arrow ends at 2. So, -5 + 7 = 2.

**SUBTRACTION**

Subtracting a positive number indicates moving that many units to the left on a number line.

First, draw an arrow to represent 1.

Start at 0 and extend the arrow 1 unit in the positive direction, which is to the right.

Next, draw an arrow to represent subtracting 3 from 1.

Start at 1 and extend the arrow 3 units in the negative direction, which is to the left.

The second line ends at -2. So, 1 − 3 = -2.