# Fractions in lowestÂ terms

## Video transcript

Simplify 48/64 to
lowest terms. Let's see if we can
visualize this. So we have 64. I guess 64 would be a whole,
so let's draw a whole here. So let's say that's a whole. Maybe we're talking
about a candy bar. Let me draw the whole. We're talking about
a whole candy bar. That would be 64 fourths. It would be the whole candy
bar right there. And 48 of the 64, you could
imagine splitting this up into 64 super-small pieces. You wouldn't be able to see what
I drew here, but if we had 48 of them, it would get us
about that much of them, so that would be the 48
out of the 64. So this whole blue area is 64. The 48 is this purple area
right over here. So let me write it over here. 48/64, and we want to write it
in lowest terms, and we'll talk more about what lowest
terms even means. Now, is there a way to group
these 48 or these 64 into groups of numbers that
will maybe simplify them a little bit? And to think about that, you'd
have to think about what is the largest factor that is
common to both 48 and 64? Or you can think of it
as what is their greatest common divisor? Well, the largest number that I
can think of that goes into 48-- you could do it either by
just thinking about it or you could actually write out
all of its factors. But if you were to write all the
factors for 48 and all the factors for 64, the one that
pops out at me as the largest that goes into both is 16. So you could say that 48 is
equal to-- well, what is it? It's 3 times 16, and
64 is 4 times 16. Now this is interesting. So this 48 that we drew in
magenta right here, we could view this as three
groups of 16. So that's one, two--
let me make them a little bit more even. So one, two, three groups of 16,
so that's 16, that's 16, and that is 16. That would be 48. I could draw 16 bars here so
that we have 16 pieces, but that's a group of 16, a group
of 16 and a group of 16. That's what 48 is. Now, 64 is four groups of 16. So we could make, if you look at
the 64, that is a 16, that is a 16, that is a 16, and
then that is another 16. These should all be
the same length. I drew it a little bit off. So what is 48/64 in
lowest terms? We want to write this in as
simple as possible fraction. Well, if we make each of the
pieces equal to 16 of our old pieces, if we make this into one
piece, if we turn 16 into one, then we are talking about
instead of 48/64, we're talking about three. So this is one piece, two
pieces, three pieces of a total of four. So this is going to
be equal to 3/4. And hopefully, you see kind
of a mathematical way of immediately thinking about it. If you can factor this out and
you can actually factor out its greatest common factor, so
48 is 3 times 16, 64 is 4 times 16, and then these
cancel each other out. view This is equivalent
to 3/4 times 16/16. This is the same
thing as that. And 16/16 is 1, and you're
just left with 3/4. Now, if you didn't immediately
recognize that 16 goes into both 48 and 64, you could
do it step by step. So let's say we started
off with 48/64. Now, the key thing to remember
with any fraction, whatever you do to the numerator, you
have to do to the denominator. So let's say we divide the
numerator by 2, we also have to divide the denominator
by 2, so we could get 2. We know that these are
both divisible by 2. They're both even. So that would get us to 24/32. And we'll say, well, look, these
two numbers, those are both divisible by 2. Well, see if we can think
of a larger number. Well, actually, they're both
divisible by 4, so maybe you don't realize that they're
also both divisible by 8. So let's say you
did it with 4. So now we divide the top by 4. So we're going to divide by 4. We get 6. You have to do the same to the
bottom, to the denominator. Divide by 4, you get 8. So 48/64 is the same thing
as 24/32, which is the same thing as 6/8. And these are both divisible
by 2, so if you divide the numerator by 2, you get 3. You divide that the denominator
by 2, you get 4. And so this is the simplest
possible terms, because 3 and 4 share no common factors
greater than 1, so we're in lowest possible terms. So however you want to do it. The easiest way or the fastest
way is to say, hey, 16 is the biggest number that goes
into both of these. Divide both by 16. You get 3/4. And really when you're dividing
the numerator and denominator by 16, you're
turning groups of 16 into one piece or 16 super-small pieces
of the pie into one bigger piece of the pie. So this goes from 64
pieces to 4 pieces. This goes from 48 pieces
to 3 pieces.