Multiplying Fractions

We're asked to multiply 5/6
times 2/3 and then simplify

our answer.

So let's just multiply
these two numbers.

So we have 5/6 times 2/3.

Now when you're multiplying
fractions, it's actually a

pretty straightforward
process.

The new numerator, or the
numerator of the product, is

just the product of the two
numerators, or your new top

number is a product of the
other two top numbers.

So the numerator in our product
is just 5 times 2.

So it's equal to 5 times 2 over
6 times 3, which is equal

to-- 5 times 2 is 10 and
6 times 3 is 18, so

it's equal to 10/18.

And you could view this as
either 2/3 of 5/6 or 5/6 of

2/3, depending on how you
want to think about it.

And this is the right answer.

It is 10/18, but when you look
at these two numbers, you

immediately or you might
immediately see that they

share some common factors.

They're both divisible by 2,
so if we want it in lowest

terms, we want to divide
them both by 2.

So divide 10 by 2, divide 18 by
2, and you get 10 divided

by 2 is 5, 18 divided
by 2 is 9.

Now, you could have essentially
done this step

earlier on.

You could've done it actually
before we did the

multiplication.

You could've done
it over here.

You could've said, well, I have
a 2 in the numerator and

I have something divisible by 2
into the denominator, so let

me divide the numerator by
2, and this becomes a 1.

Let me divide the denominator
by 2, and this becomes a 3.

And then you have 5 times 1
is 5, and 3 times 3 is 9.

So it's really the same thing
we did right here.

We just did it before we
actually took the product.

You could actually
do it right here.

So if you did it right over
here, you'd say, well, look, 6

times 3 is eventually going
to be the denominator.

5 times 2 is eventually going
to be the numerator.

So let's divide the numerator by
2, so this will become a 1.

Let's divide the denominator
by 2.

This is divisible by 2,
so that'll become a 3.

And it'll become 5 times 1
is 5 and 3 times 3 is 9.

So either way you do
it, it'll work.

If you do it this way, you get
to see the things factored out

a little bit more, so it's
usually easier to recognize

what's divisible by what, or you
could do it at the end and

put things in lowest terms.