Skill: Add integers symbolically

To add integers, first look at their signs.

• Same signs: Add the absolute values, then keep the common sign.
• Different signs: Subtract the smaller absolute value from the larger absolute value. Keep the sign of the integer with the greater absolute value.
• Remember: the absolute value is the distance from zero, so $\vert -8 \vert =8$ and $\vert 13 \vert =13$.

Example: Find

$$-8+13$$

1. The integers have different signs: $-8$ is negative and $13$ is positive.
2. Compare their absolute values: $8$ and $13$. Since $13$ is greater, the answer will be positive.
3. Subtract the smaller absolute value from the larger:

$$13-8=5$$

Therefore,

$$-8+13=5$$

The positive integer has the greater absolute value, so the sum is positive.