Question

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

Answer 1

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:

`abs(-4)/2timesabs(-1times8)`

`=abs(-4)/2timesabs(-8)`

To solve this, we need to simplify `abs(-4)` and `abs(-8)`. Since it would take 4 steps to walk from `-4` to `0`, we have

`abs(-4)=4`.

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

`abs(-8)=8`.

This allows us to simplify from where we left off:

`abs(-4)/2timesabs(-8)`

`=4/2times8`

`=2times8`

`=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`,

`abs(n)=abs(-n)=n`.

eg: `abs(42)=abs(-42)=42`, because both `42` and `-42` are forty-two steps from 0.