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# Intro to absolute value

Learn how to think about absolute value as distance from zero, and practice finding absolute values.
The absolute value of a number is its distance from $0$.
For example, the absolute value of $4$ is $4$:
This seems kind of obvious. Of course the distance from $0$ to $4$ is $4$. Where absolute value gets interesting is with negative numbers.
For example, the absolute value of $-4$ is also $4$:

## Let's practice!

Problem 1A
What is the absolute value of $3$?

## The absolute value symbol

The symbol for absolute value is a bar $|$ on each side of the number.
"the absolute value of $-6$"
we can just write
$|-6|$.

## Let's practice!

Problem 2A
What is $|7|$?

## Want to join the conversation?

• wouldn't the question -(-7+4)it is absolute, be-11?
• Not quite -

Here's the expression: -|-7 + 4|

First, start by working out the expression inside the absolute value bars:
-|-7 + 4|
-|-3|

Then, take the absolute value of the number inside the bars:
-|-3|
-(3)
-3

-|-7 + 4| = -3

Hope this helps!
• What is absolute value in real-life scenarios?
• Absolute values are used when we work with distances. Distances are positive values.

For example: A diver is -15 deep (this places him 15 feet below the surface of the water). How far does he need to travel to get to the surface? He needs to travel |-15| = 15 feet.
Hope this helps.
• how is a<|a| shouldn't a=|a| as they are the same distance from 0?
• a was a negative number while absolute a was a positive number therefore a is less than positive a
• Why cant there be negatives for absolute value?
• There are no negatives for absolute value since absolute value is a measure of distance on a number line. (Distance doesn't have negative values only positive

Hopes this helps!
• How last question is solved is explained below:

In place of "a" let's assume number "3", as "a" is placed towards left of "0" it's considered as "-3" (if "a" was placed towards right of "0" we would consider as "+3").

Therefore ==> a = -3

Note Points:
->Negative numbers are always lesser than 0 and positive numbers.
->Positive numbers are always greater than 0 and negative numbers.
-> Absolute of Negative number or Positive number or "0" always results in Positive number.

Now as per the questions asked, lets implement value of "a" that is "-3" and check True or False

Q1.) a < 0 ===> -3 < 0 ===> True
Q2.) |a| > 0 ===> |-3| > 0 ===> 3 > 0 ===> True
Q3.) a < |a| ===> -3 < |-3| ===> -3 < 3 ===> True
• mucho texto
• this doesn't totally make sense to me.
• So absolute value is the distance a number has from 0. It can never be negative. So lets say that an editor needs to go back -3 pages. The absolute value would be 3. He/she would need to go back 3 pages since there are no negative pages. Hope this helps!
• Can fractions have an absolute value?
• Yes! Think about it is 3/4 of a cm a measurement?
Yes! So, fractions can also have an absolute value.

Hope this helps!