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.