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Studying for a test? Prepare with these 6 lessons on Module 5: Fractions as numbers on the number line.

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# Comparing fractions visually

Video transcript

We have four fractions
written over here. And what I want
you to do is think about which of these fractions
is the smallest value, which of these is the largest
value, and which of these might be equal. And there's two ways
that you could do it. You could try to plot
them on a number line, or you could try to
depict them visually. So pause the video now
and try it on your own. So let's plot these
on a number line. So let me give ourselves
another little number line right over here. Let me see, I can draw one. So let's say this is my number
line-- draw it as straight as I can. So that's my number line. That is 0. Let's say that this is
1, and then that is 2. So let's first try to plot
where 1/2 is on the number line. So we can split the
section between 0 and 1 into 2 equal sections. And 1/2, would mean
that I would have gone one of those
2 equal sections. So if I just go that
far, I should be at 1/2. So this right over here is 1/2. Now let's think about 2/4. Well, to do 2/4,
we want to split the section between 0 and
1 into 4 equal sections. So let's do that. So 0-- so that's 1 equal
section, 2 equal sections, 3 equal sections,
and 4 equal sections. So where we do end up if we go
2 out of those 4 equal sections? Well we would end up--
1, 2 equal sections, so we end up right over here. 2/4, we end up at
the exact same place. So at least based on how
we've drawn the number line, it looks like 1/2
is equal to 2/4. Let me write that down. 1/2 is equal to 2/4. Now what about 4/8? Well let's split the part
of our number line between 0 and 1 to 8 equal sections. So if we take each of
those 4 equal sections and split them into 2-- So now
we have 1, 2, 3, 4, 5, 6, 7, 8. I can't draw it
perfectly, but I'm trying to make them
equal sections. Now it's 8 equal sections. And now we're going
to go 4 of them. Starting at 0, we're
going to go 1, 2, 3, 4. So we end up at the
same place again. This is also equal to 4/8. So 1/2 is equal to 2/4,
which is equal to 4/8. Now, what about 3/8? Well, we've already
split our number line into 8 equal sections--
let's go 3 of them. 1, 2, 3. So 3/8 is right over here. 3/8 is less than 1/2, it's less
than 2/4, it's less than 4/8. It is a smaller number. Let's see if that
also makes sense when we try to
visually depict or try to visually draw
these fractions. So I've done that
right over here. And this is one 1/2. So all of these rectangles
are the exact same size. And this purple
one over here I've split into 2 equal sections,
and we shaded in one of them. So we see that this is 1/2. Now here I shaded in 2 out
of the 4 equal sections, and you see that this
looks the exact same size as the 1/2 right over here. We started with rectangles
of the same size. If you shade in 1/2 or 2/4,
it looks exactly the same. And that makes sense, because
if you took this one right over here, if you took
this first one and you divided each of your 2 equal
sections into 2 equal sections, so you split it again, then you
see that this is equal to 2/4. Now what about 4/8? Here I've split it up where
I have this one, this one, this one, and this
one shaded in. But if you rearrange
them, you could see that you could get
exactly the same amount of the rectangle shaded in. And if you want to
see that, divide each of these 4 into 2-- so
divide those into 2 and those into 2. Notice I now have 1, 2, 3, 4 out
of the 8 equal squares shaded in. These two things are equal. So let me make it clear. This is an equal fraction, which
is an equal fraction of that which is equal fraction of that And here, this is 3 out of 8. You see that it's less than
this region right over here. This one we've
literally filled in half of the entire rectangle--
4 out of the 8. If we did 4 out of the 8 here,
we would have also had to fill in this one right over
here, which we didn't. We only filled in
3 out of the 8. So it makes sense
that 3/8 is a smaller part of our whole than
4/8, or 2/4, or 1/2. And likewise, it's
a smaller number.