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# Comparing fractions with like numerators and denominators

Video transcript

Let's compare the fraction
4/7 to the fraction 5/7. And what I want you to do right
now is to pause this video and think about which
of these fractions represents a larger quantity. I'm assuming you've
had a go at it, and the one thing that
might jump out at you is that they both have the
same bottom number, which we call the denominator. They both have a
denominator of 7. So one way to think about it is
this is literally 4 sevenths. This is literally 5 sevenths. So we could rewrite 4/7
as literally 4 times 1/7. And we can rewrite 5/7
as literally 5 times 1/7. It's 5/7. So now if I have 4
of something versus 5 of something, which is going
to be a larger quantity? Well, clearly 5 of this
1/7 is going to be more. So 4/7 is smaller,
5/7 is larger. And so what we can do is we
can write a less than symbol. The way that I remember
less than and greater than, is that the point, the
small side of the symbol, always is on the same side
as the smaller number. So this could be read
as 4/7 is less than 5/7, or that 4 times 1/7 is
less than 5 times 1/7. Now, let's do another
scenario, but instead of having the same denominator,
let's have the same numerator. So let's say we
want to compare 3/4 versus-- let's say versus 3/9. Which of these two fractions
is a larger number? And once again, pause
the video and try to think about it on your own. Well, as we mentioned, we don't
have the same denominator here. We have the same
top number instead. Here is the same bottom
number, same denominator. Here we're going to
have the same numerator. We have the 3 right over there. And we could view 3/4 as
literally 3 times 1/4. And we could view 3/9 as
literally 3 times 1/9. So we have 3/4 and we have 3/9. So we really just
have to about what's larger, a fourth or a ninth? Well, think about if you
start with a whole-- think about starting with
a whole like this. And let me make a
whole right over here, so the same sized whole. A fourth is literally
taking the whole and dividing it into 4 pieces. While a ninth is taking the
whole and dividing it into 9. 9 equal sections, I could say. So let's divide this
into 4 equal sections. So my best attempt to
hand draw equal sections. So that's 2 equal
sections and then that looks pretty close
to 4 equal sections. So that right over there is 1/4. And let me draw ninths here. So let me first split this
into 3 equal sections. So those would be third. And then split each of
those into 3 equal sections. So this is my best
attempt at that, at hand drawing
9 equal sections, splitting the whole
into 9 equal sections. So when you see here-- and you
might have already realized this-- if you divide something
into 4 equal sections, each section is
going to be bigger than if you divide it
into 9 equal sections. A ninth is smaller
than a fourth. A ninth is smaller than 1/4. So 3/9 is going to
be smaller than 3/4. So once again, when you want to
do less than or greater than, you want to put the point,
the small side of the symbol, on the same side as
the smaller number. So it would look like this. And this is the
greater than symbol, because what you have on the
left is the larger number. 3/4 is greater than 3/9. And if you actually wanted to
represent not just 1/4 and 1/9, we could actually color it in. 3 times one fourth,
well that's 1, 2, 3. While 3 times 1/9,
or 3/9, is 1, 2, 3. And when you look at it
that way, it's pretty clear. But the important
thing to realize is, is that when the
denominator is larger, you're dividing the
whole into more pieces so each piece will be smaller. So making the denominator larger
makes the fraction smaller. Making the numerator larger
makes the fraction larger.