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### Course: Algebra basics>Unit 1

Lesson 2: Absolute value

# Absolute value and number lines

One easy way to think of absolute value is the distance it is from zero. To do that, a number line comes in handy. Watch and learn. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• you know this is so easy. but what im trying to understand is why in the world would anyone ask what the abosulte value of anything is. when will we ever use this in the future. thats like asking me how old I am, and how many years that is. im understanding the concept but why do we need to know how far away a number is from zero
• Well, absolute value is actually used in every day life, as a matter of fact. Here are some real life scenarios.

1 ) You want to find out how far you have travelled in a car or plane etc.
2) You want to know how much points your team has scored from games start, to end
3) You want to know how much time it took you to do ____(whatever)

Not only do we use it in real life situations, but this will be a root concept for other more advanced math work.

And... Why would they teach this concept if no one were to need it? There is always (almost always) a reason behind things.

~Hope this helped
• Can there be absolute values of a decimals and fractions?
• Yes, say for example -0.617 the absolute value of it would be 0.617
• Does |-6| 6= 36?
• Yes, because the spaces (Draw a number line if your confused about "spaces"!) |-6| or -6 from 0 is exactly 6. So to make the equation simpler, you rewrite it. So 6 x 6 = 36. (: Hope this helps!

Absolute Value
<-----(-6)-----(-5)-----(-4)-----(-3)-----(-2)-----(-1)-----(0)----->
The jumps backwards from 0 to -6 is 6. So the absolute value of |-6| is 6.
• Can you explain the actual mathematical significance of absolute value, that is, what does it mean as an expression of quantity. I know what happens when someone asks for the absolute value of a given number. I just don't know why it is the case.
• Usually, the positive or negative sign indicates DIRECTION from a certain point. A negative sign means going in the OPPOSITE DIRECTION of where you chose your positive direction to be. In the case of the number line, positive means going to the right, while negative means going in the opposite direction, or the left.

So adding/subtracting is simply about which direction you go in (right or left). An absolute value ignores that direction and simply tells you how many units or numbers away from zero something is.

If for example you choose north to be the positive, then south(or the opposite of north) is negative. Your friend A is 50 miles north of you. Your friend B is -50 miles away from you, which tells you that he is south of you. However, both of your friends are 50 miles away from you, just in different directions.
• Is zero a positive or negative?
• Zero, is like, well say there are two countries right next to each other. They are positive and negative. They constantly fight. But one day, the presidents of the countries decide to stop the war. They build a giant wall, a boundary that which neither positive or negative can cross. It is zero. Zero is like a black hole. It is neither positive nor is it negative. It is emptiness, the boundary which sets positive and negative apart.
• At , Sal says that 8-12 is equal to -4. I am only in fourth grade, so I haven't learned about this topic yet, but how is it possible to do 8-12? Shouldn't it be 12-8?
• Think about a thermometer (for outdoors). It has positive temperatures (above 0 degrees) and negative temperatures (below zero). 8-12 could represent a day when the temperature started at 8 degrees above zero, then got 12 degrees colder. As the temperature fell, it went down past zero into negative degrees. The temperature ends up at -4 degrees (4 degrees below zero).
• plz explain it like you are taking to a very dumm child that will help me under stand
• What would you do if there was a negative sign in front of the absolute value.
• It stays negative, just take the absolute value symbol off