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.

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* = 1.75 and *q* = -2.5.

Since *q* is negative, 1.75 + (-2.5) is 2.5 units from 1.75 in the negative direction.

This can be represented on a number line.

The second arrow ends at -0.75. So, 1.75 + (-2.5) = -0.75.

**SUBTRACTION**

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

First, draw an arrow to represent $1\frac{1}{2}$.

Start at 0 and extend the arrow $1\frac{1}{2}$ units in the positive direction, which is to the right.

Next, draw an arrow to represent subtracting $3\frac{1}{4}$ from $1\frac{1}{2}$.

Start at $1\frac{1}{2}$ and extend the arrow $3\frac{1}{4}$ units in the negative direction, which is to the left.

The second line ends at $-1\frac{3}{4}$. So, $1\frac{1}{2}-3\frac{1}{4}=-1\frac{3}{4}$.