Comparing fractions with different denominators

- [Voiceover] What I
want to do in this video

is get some practice comparing fractions

with different denominators.

So, let's say I wanted to
compare two over four, or 2/4,

and I want to compare that
to five over 12, or 5/12.

And I encourage you to
pause the video if you

could figure out which one
is greater, 2/4 or 5/12,

or maybe they are equal.

So, let's think about this a little bit.

When I just look at it, it's
not obvious which one is larger

and there's several ways
that we can look at this.

One way is we can try to
have the same denominator.

We can rewrite these so that we

can have the same denominator.

So one way to think about it, can I write

two over four as something over 12?

Well, let's think about it.

If instead of having fourths,
if you have twelfths,

you now have three times as many sections

that you've divided something into.

So, two pieces would then turn

into three times as many pieces.

So, you multiply the
numerator by three, as well.

If you multiply the denominator by three,

you multiply the numerator
by three, as well.

So, 2/4 is the same thing as 6/12.

Another way to think about it is

two is half of four, six is half of 12.

Now, can we compare 6/12 to 5/12?

Well, I have more twelfths here.

I have six of them versus 5/12.

Now, I can make the comparison.

And I can say, look if
I have six of something,

in this case, this thing
I have six of is twelfths,

that's going to be more than
having five of the twelfths.

So, 6/12 is greater than 5/12,

and I always think of
the greater than sign,

you're always going to be opening

to whichever one is larger.

So, this is the greater than sign.

So if 6/12 is greater than 5/12,

then 2/4 is greater than 5/12,

because 2/4 and 6/12 are
the exact same thing.

Now, let's tackle another one.

This one might be a little
bit more interesting.

Let's say we want to compare

three over five and we want to compare

that to 2/3, two over three.

And like always, pause the video

and see if you can figure this out.

And I'll give you a
hint, try to rewrite both

of these so that they
have the same denominator.

So, let's try to do that.

So, five isn't a multiple of three,

three isn't a multiple of five,

so we need to find a common denominator.

Well, a common denominator
would be something

that is divisible by both five and three.

So the easiest thing I can think of is 15,

which is five times three.

So, let's write 3/5 as something over 15,

and let's write 2/3 as something over 15.

So, 2/3 I'm going to write
as something over 15.

Well, to go from five to
15, I multiply it by three.

So, I multiplied by three.

So, if I multiply the
denominator by three,

I need to multiply the numerator by three.

So, multiply by three.

So, 3/5 is going to be
the same thing as 9/15.

I multiplied the numerator
and the denominator

both by the same number, which
doesn't change its value.

I'm just rewriting it, so 3/5
is the same thing as 9/15.

And now, let's look at 2/3.

To go from three to 15,
you multiply by five.

So, you do the same
thing with the numerator.

We need to multiply the numerator by five.

Two times five is 10, so 2/3
is the same thing as 10/15.

And now, we can make a comparsion

because we have a certain
number of fifteenths

compared to another number of fifteenths.

So what's larger, 9/15 or 10/15?

Well 10, if you have 10 of
something, it's going to be more.

So, 10/15 is larger than 9/15.

So, I've put the symbol that
opens to the larger one.

And so this one is the less than symbol.

9/15 is less than 10/15,

but since 9/15 is the same thing as 3/5

and 10/15 is just another
way of rewriting 2/3,

we can also put the
less than symbol there.

3/5 is less than 2/3.