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## Algebra basics

# 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(210 votes)
- 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(162 votes)

- Can there be absolute values of a decimals and fractions?(49 votes)
- Yes, say for example -0.617 the absolute value of it would be 0.617(8 votes)

- Does |-6| 6= 36?(38 votes)
- 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.(12 votes)

- 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.(27 votes)
- 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.(7 votes)

- Is zero a positive or negative?(10 votes)
- 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.(8 votes)

- What would you do if there was a negative sign in front of the absolute value.(3 votes)
- It stays negative, just take the absolute value symbol off(4 votes)

- Do you always have to draw a number line? Also do you need those 2 lines at the sides of the number?(3 votes)
- No you don't always have to use a number line. It just makes it easier to understand in the video. Yes, you do need the 2 lines on the sides of the number because it is the absolute value sign.(5 votes)

- At3:25, 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?(0 votes)
- 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).(15 votes)

- I am confused about this absolute value stuff. I don't understand it.(5 votes)
- it's easy as one two three all you have to do if it has two lines then it the number on the inside negative or not it a whole but if negative or positive with put the lines then it is what is is.(0 votes)

- What if you get a decimal?(4 votes)

## Video transcript

We're told to plot these values
on a number line. And you see every one of
these values have an absolute value sign. So let's take a little bit of
a review of what absolute value even is. The way I think about
it, there's two ways to think about it. The first way to think about
it is, how far is something from 0? So let me plot this
negative 3 here. So let me do a number line. This isn't the number line for
our actual answer, or to this command-- plot these values
on a number line. I'm just first going to plot
the numbers inside the absolute value sign, and then
we're going to take the absolute value and plot those,
just like they're asking us to do. So on this number line, if this
is 0, if we go to the negative, we're going to
go to the left of 0. So this is negative 1, negative
2, negative 3. Negative 3 sits right over
there, so this is negative 3 right there. The absolute value of negative
3 is essentially saying, how far are you away from 0? How far is negative 3 from 0? And you say, well, it's
1, 2, 3 away from 0. So you'd say that the absolute
value of negative 3 is equal to positive 3. Now that's really the conceptual
way to imagine absolute value. How far are you away from 0? But the easy way to calculate
absolute value signs, if you don't care too much about the
concept, is whether it's negative or positive, the
absolute value of it's always going to be positive. Absolute value of negative
3 is positive 3. Absolute value of positive
3 is still positive 3. So you're always going to get
the positive version of the number, so to speak. But conceptualy, you're just
saying how far away are you from 0. So let's do what they asked. So that first value, on this
number line, so all of these are absolute values. So they're all going to
be positive values. So they're all going to
be greater than 0. So let me draw my number
line, like this. I can do a straighter number
line than that. Let's see. Well, that's a little
bit straighter. And let's say, if this is 0,
this would be negative 1, then you'd have 1, 2,
3, 4, 5, 6, 7. I think that'll do the trick. So this first quantity here--
I'll do it in orange --the absolute value of negative 3,
we just figured out, that is positive 3. So I'll plot it right over
there, positive 3. Then this next value, right
here, the absolute value of 7. If we look over here,
1, 2, 3, 4, 5, 6, 7. 7 is how far away from 0? It is 7 away from 0. So the absolute value
of 7 is equal to 7. So you already see the
pattern there. If it's negative, it just
becomes positive. If it's already positive,
it just equals itself. So plotting this value,
I'll just place it right over there. So the absolute value
of 7 is 7. Absolute value of negative
3 is positive 3. Let me mark out the 0 a little
bit better, so you see relative to 0. Now we have the absolute
value of 8 minus 12. Well, first of all, let's figure
out what 8 minus 12 is. So if you take 12 away from
8, you're at negative 4. 12 less than 8 is negative 4. And you can do that on a number
line if you don't quite remember how to do this. But if you, you know, if you
take 8 away from 8, you're at 0, and then you take another
one, you're at negative 1, negative 2, negative 3, all
the way to negative 4. So this is equal to the absolute
value of negative 4. If we just plot negative 4, we
go 1, 2, 3, negative 4 is right over there. But if we're taking its absolute
value, we're saying how far is negative 4 from 0? Well it's 4 away from 0. 1, 2, 3, 4. So this is equal
to positive 4. So we'll plot it right here. This number line is the answer
to this command up here. So the absolute value of 8 minus
12, which is negative 4, is positive 4. Then we have the absolute
value of 0. So how far is 0 from 0? Well, it's 0 away from 0. The absolute value of 0 is 0, so
you can just plot it right over there. And we have one left. Let me pick a suitable
color here. The absolute value
of 7 minus 2. Well, 7 minus 2 is 5, so this
is the same thing as the absolute value of 5. How far is 5 away from 0? Well, it's just 5 away. It's almost, you
know, too easy. That's what makes
it confusing. If I were to plot 5,
it's 1, 2, 3, 4, 5. It is 1, 2, 3, 4,
5 spaces from 0. So the absolute value
of 5 is 5. So you plot it just like that. So conceptually, it's how
far you are away from 0. But if you think about it in
kind of just very simple terms, if it's a negative
number, it becomes a positive version of it. If it's a positive number
already, it just equals itself when you take the
absolute value.