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

3
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our answer.

4
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So let's just multiply these two numbers.

5
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So we have 5/6 times 2/3.

6
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Now when you're multiplying fractions, it's actually a

7
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pretty straightforward process.

8
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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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number is a product of the other two top numbers.

11
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So the numerator in our product is just 5 times 2.

12
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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

14
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it's equal to 10/18.

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

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

17
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And this is the right answer.

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

19
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immediately or you might immediately see that they

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share some common factors.

21
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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.

23
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So divide 10 by 2, divide 18 by 2, and you get 10 divided

24
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by 2 is 5, 18 divided by 2 is 9.

25
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Now, you could have essentially done this step

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earlier on.

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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.

30
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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.

35
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So it's really the same thing we did right here.

36
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We just did it before we actually took the product.

37
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You could actually do it right here.

38
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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.

40
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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.

43
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This is divisible by 2, so that'll become a 3.

44
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And it'll become 5 times 1 is 5 and 3 times 3 is 9.

45
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So either way you do it, it'll work.

46
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If you do it this way, you get to see the things factored out

47
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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.

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