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### Course: Arithmetic > Unit 4

Lesson 3: Fractions on the number line# Fractions on a number line

Together, we'll explore how to represent fractions on a number line. We'll review dividing a whole, like a circle, into equal parts and selecting a fraction. Then, we'll apply this concept to a number line, dividing the interval between 0 and 1 into equal sections and labeling fractions. We'll emphasize that fractions are numbers that can be plotted on a number line, not just parts of shapes. Created by Sal Khan.

## Want to join the conversation?

- What happens if the numerator is at 0? like, 0/6? How do you put it in the number line?(28 votes)
- If the numerator of a fraction is 0, like

0/6, the fraction equals 0. So, on a number line, you'd place it right at the start, where the number 0 is.

If you were to draw out a shape to represent the fraction, none of the pieces would be shaded.(15 votes)

- how do you mark oversized fractions on a number line like 15/5(6 votes)
- Since we're working with fifths - 1/5 or one fifth part of one whole- (5/5 would be a whole or 1) we can write out a number line, say, up to 3 with each number being a whole. Like this < 0 - - - - 1 - - - - 2 - - - - 3 >. Then we can cut up each space between each whole into five equal parts. Each part is 1/5 of each one whole. If we count up the fifths, up to fifteen fifths or 15/5, we get up to 3 on the line. This makes sense if you think about fifteen fifths, or 15/5 being 15 divided by 5, which is of course 3. Or as having 15 slices of pie. If 5 slices make one pie, then 15 slices is enough to put together 3 whole pies.(32 votes)

- Hi, I really don't understand why we have number lines. Can anyone answer my question?

Please and thank you.(9 votes)- A number line is a useful way of visualizing numbers and operations on numbers.

You will encounter number lines in higher levels of math.

In algebra, a number line is used to graph solutions of equations and inequalities in one variable. A coordinate plane (with a number line used for each axis) is used for graphing solutions of equations and inequalities in two variables.

In statistics, number lines are often used to graph data visually (for example bar graphs, histograms, line graphs, line plots, box plots, and scatterplots).

Have a blessed, wonderful day!(2 votes)

- how are yall so dang smart in the comments.(4 votes)
- How will I put 1/2 on a number line?

Is it the same as 1/5?(4 votes)- You put a fraction on the number line the same way you would put a whole number or decimal. 1/2 is the same as 0.5 which means it's gonna go halfway between 0 and 1.

1/5 is 0.2 so it goes between 0.1 and 0.3 and therefore not the same as 1/2(1 vote)

- my teacher says never count the zero it's in the number line though why shouldn't we count it?(4 votes)
- You write it, but don't count it because it's supposed to be the starting point.(1 vote)

- How can i be good at solving fractions questions?(3 votes)
- I don’t understand it?(3 votes)
- Uh oh my gosh this is so hard(3 votes)
- what class is dis(2 votes)

## Video transcript

We've already seen that
if we take a whole, and in this example, the whole
is this entire green circle. And if we were to split it into
5 equal sections-- 1, 2, 3, 4, 5. So we've split it into
5 equal sections-- and if we were to select 1
of those 5 equal sections. So let's say we select this
section right over here, that we have selected
1/5 of the whole, 1 out of the 5 equal sections. We could do the exact same
thing on a number line. Everything we've been doing so
far has to deal with shapes, but we could do the exact
same idea on a number line. So let me draw a
number line here. So let me draw it pretty big
so we get a sense of things. So it will go all
the way to there. And let's say that this is
0, this is 1, and this is 2. And of course, we
could keep going if we had more space to 3,
4, and on and on and on. And what I want to do,
instead of taking a circle and dividing it into
5 equal sections, I want to take the section of
our number line between 0 and 1 and divide it into
5 equal sections. So let me see if I can do this. So 1, 2, 3, 4, 5. That looks pretty good. I'm drawing it as exact
as I can with my hand. But let's just assume
these are 5 equal sections. So what would you think would
be a good label for this number right over here? Well, it's the exact same idea. Between 0 and 1,
I've traveled 1 out of the 5 equal
sections towards 1. And actually, let me make it
a little bit neater than that. We could make the equal sections
look a little bit better. 1, 2, 3, 4, 5. And what we're
thinking about is this. What should we call
this number here? This number is clearly
between 0 and 1. It's clearly closer to 0. And we've gone 1 out of the
5 equal sections towards 1. Well, it makes complete
sense that, look, we had 5 equal sections here. And we've traveled
1 of them towards 1. So we should call this
number right over here 1/5. So when we're talking
about a fraction, 1/5, it's not just talking about,
hey, what part of a pizza pie have I eaten or
something like that. This is actually a number. This is a number. And we can actually plot
it on the number line. Now you might say, OK,
well, that's fair about 1/5. But what about all
these other slashes? What numbers would we call that? Well, we can make
the exact same idea. If up here, instead of
shading in 1 out of the 5 equal sections, if I shaded in
2 of the 5 equal sections, then I wouldn't say this
is 1/5 any more. I would say that this 2/5. And so if I go 2 of the
equal sections towards 1, then I should call this
number right over here 2/5. And I could keep going. This right over here
should be 3, 3/5. This right over here,
I've gone 1, 2, 3, 4 out of the 5 sections towards 1. So I could call this 4/5. And I could keep going. I could call this
right over here-- I've traveled 5 out of the
5 equal sections towards 5, so I could call this
right over here 5. Let me do it in that red color. I could call this
right over here 5/5. You might say, wait, but
5/5, we've gotten to 1. And that's exactly right. If I were to shade in
5 things over here-- let me do that
little bit cleaner. That's not the
color I want to use. If I were to shade in
5 things over here, we've already seen that
shading in 5 things-- let me make this a
little bit neater-- if this is now 5
over 5 or 5/5, we've already seen that
this is a whole. And over here, if we've traveled
5/5 of the way towards 1, we've gotten to the whole 1. 5/5 is the exact
same thing as 1. It is equal to a whole.