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# Fractions on a number line

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.