# How do you evaluate abs(-4)/2timesabs(-1times8)?

Dec 4, 2016

The answer is $16$.

#### Explanation:

Taking the absolute value of a number means finding its distance from 0.

First, we simplify within the absolute value bars as much as we can:

$\frac{\left\mid - 4 \right\mid}{2} \times \left\mid - 1 \times 8 \right\mid$

$= \frac{\left\mid - 4 \right\mid}{2} \times \left\mid - 8 \right\mid$

To solve this, we need to simplify $\left\mid - 4 \right\mid$ and $\left\mid - 8 \right\mid$. Since it would take 4 steps to walk from $- 4$ to $0$, we have

$\left\mid - 4 \right\mid = 4$.

Similarly, since the distance between $- 8$ and $0$ is 8, we have

$\left\mid - 8 \right\mid = 8$.

This allows us to simplify from where we left off:

$\frac{\left\mid - 4 \right\mid}{2} \times \left\mid - 8 \right\mid$

$= \frac{4}{2} \times 8$

$= 2 \times 8$

$= 16$

## Bonus:

The clever shortcut for simplifying absolute values is to simply take the positive value of the number inside. In other words, for all positive numbers $n$,

$\left\mid n \right\mid = \left\mid - n \right\mid = n$.

eg: $\left\mid 42 \right\mid = \left\mid - 42 \right\mid = 42$, because both $42$ and $- 42$ are forty-two steps from 0.