Skill: Compare absolute values

Absolute value tells how far an integer is from $0$ on a number line. It is always nonnegative.

To compare absolute values:

1. Find the absolute value of each integer.
2. Compare the resulting nonnegative numbers.

Example: Compare $\vert -8 \vert$ and $\vert 5 \vert$.

• $-8$ is $8$ units from $0$, so $\vert -8 \vert =8$.
• $5$ is $5$ units from $0$, so $\vert 5 \vert =5$.
• Since $8>5$, we have

$$\vert -8 \vert > \vert 5 \vert .$$

Even though $-8$ is less than $5$, its absolute value is greater because $-8$ is farther from $0$.