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

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our answer.

3
00:00:05,570 --> 00:00:07,450
So let's just multiply
these two numbers.

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00:00:07,450 --> 00:00:13,090
So we have 5/6 times 2/3.

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00:00:13,090 --> 00:00:15,030
Now when you're multiplying
fractions, it's actually a

6
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pretty straightforward
process.

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00:00:17,470 --> 00:00:20,190
The new numerator, or the
numerator of the product, is

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

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00:00:22,880 --> 00:00:25,340
number is a product of the
other two top numbers.

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

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00:00:29,240 --> 00:00:37,250
So it's equal to 5 times 2 over
6 times 3, which is equal

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

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it's equal to 10/18.

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00:00:44,710 --> 00:00:50,820
And you could view this as
either 2/3 of 5/6 or 5/6 of

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00:00:50,820 --> 00:00:53,640
2/3, depending on how you
want to think about it.

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And this is the right answer.

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

18
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immediately or you might
immediately see that they

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share some common factors.

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

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terms, we want to divide
them both by 2.

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

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

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Now, you could have essentially
done this step

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earlier on.

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00:01:20,630 --> 00:01:22,530
You could've done it actually
before we did the

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multiplication.

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You could've done
it over here.

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

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

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

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

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

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

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We just did it before we
actually took the product.

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You could actually
do it right here.

37
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So if you did it right over
here, you'd say, well, look, 6

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times 3 is eventually going
to be the denominator.

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5 times 2 is eventually going
to be the numerator.

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

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Let's divide the denominator
by 2.

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

43
00:02:07,550 --> 00:02:13,630
And it'll become 5 times 1
is 5 and 3 times 3 is 9.

44
00:02:13,630 --> 00:02:15,210
So either way you do
it, it'll work.

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

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

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

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put things in lowest terms.