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## Arithmetic

### Course: Arithmetic>Unit 18

Lesson 4: Absolute value

# 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 start color #11accd, 4, end color #11accd:
This seems kind of obvious. Of course the distance from 0 to 4 is start color #11accd, 4, end color #11accd. Where absolute value gets interesting is with negative numbers.
For example, the absolute value of minus, 4 is also start color #11accd, 4, end color #11accd:

## Let's practice!

Problem 1A
• Current
What is the absolute value of 3?

## The absolute value symbol

The symbol for absolute value is a bar vertical bar on each side of the number.
"the absolute value of minus, 6"
we can just write
vertical bar, minus, 6, vertical bar.

## Let's practice!

Problem 2A
• Current
What is vertical bar, 7, vertical bar?

## 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
• I can smell colors and see smells
• Ooo Interesting?
• So this i basicly a washing machine whatever you put in it it becomes celan like lets say 3 is clean and u put it in to the
washing machine (Absloute) and i becomes 3 clean.But if u put -3 whic is dirty it becomes clean when you put it in the machine (Absloute)
• 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.