0:00:00.570,0:00:02.680
We're asked to rewrite[br]the following two

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fractions as fractions with[br]a least common denominator.

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So a least common[br]denominator for two fractions

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is really just going to be the[br]least common multiple of both

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of these denominators over here.

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And the value of[br]doing that is then

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if you can make these[br]a common denominator,

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then you can add[br]the two fractions.

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And we'll see that[br]in other videos.

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But first of all, let's just[br]find the least common multiple.

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Let me write it out[br]because sometimes LCD

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could meet other things.

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So least common denominator[br]of these two things

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is going to be the same thing[br]as the least common multiple

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of the two[br]denominators over here.

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The least common[br]multiple of 8 and 6.

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And a couple of ways to think[br]about least common multiple--

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you literally could just[br]take the multiples of 8 and 6

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and see what they're[br]smallest common multiple is.

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So let's do it that way first.

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So multiples of six[br]are 6, 12, 18, 24 30.

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And I could keep going if we[br]don't find any common multiples

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out of this group here with[br]any of the multiples in eight.

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And the multiples of[br]eight are 8, 16, 24,

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and it looks like we're done.

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And we could keep[br]going obviously-- 32,

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so on and so forth.

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But I found a common[br]multiple and this

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is their smallest[br]common multiple.

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They have other common[br]multiples-- 48 and 72,

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and we could keep adding[br]more and more multiple.

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But this is their[br]smallest common multiple,

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their least common multiple.

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So it is 24.

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Another way that you could have[br]found at least common multiple

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is you could have taken the[br]prime factorization of six

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and you say, hey,[br]that's 2, and 3.

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So the least common multiple has[br]to have at least 1, 2, and 1, 3

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in its prime factorization[br]in order for it

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to be divisible by 6.

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And you could have said, what's[br]the prime factorization of 8?

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It is 2 times 4[br]and 4 is 2 times 2.

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So in order to be[br]divisible by 8,

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you have to have at least three[br]2's in the prime factorization.

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So to be divisible by 6, you[br]have to have a 2 times a 3.

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And then to be divisible by 8,[br]you have to have at least three

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2's.

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You have to have two[br]times itself three times

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I should say.

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Well, we have one 2 and[br]let's throw in a couple more.

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So then you have another[br]2 and then another 2.

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So this part right over here[br]makes it divisible by 8.

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And this part right over[br]here makes it divisible by 6.

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If I take 2 times 2 times 2[br]times 3, that does give me 24.

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So our least common[br]multiple of 8 and 6,

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which is also the least common[br]denominator of these two

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fractions is going to be 24.

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So what we want to do is[br]rewrite each of these fractions

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with 24 as the denominator.

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So I'll start with 2 over 8.

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And I want to write that[br]as something over 24.

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Well, to get the[br]denominator be 24,

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we have to multiply it by 3.

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8 times 3 is 24.

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And so if we don't[br]want to change

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the value of the[br]fraction, we have

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to multiply the numerator and[br]denominator by the same thing.

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So let's multiply the[br]numerator by 3 as well.

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2 times 3 is 6.

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So 2/8 is the exact[br]same thing as 6/24.

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To see that a[br]little bit clearer,

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you say, look, if I have 2/8,[br]and if I multiply this times 3

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over 3, that gives me 6/24.

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And this are the same[br]fraction because 3 over 3

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is really just 1.

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It's one whole.

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So 2/8 is 6/24 let's do[br]the same thing with 5/6.

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So 5 over 6 is equal[br]to something over 24.

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Let me do that in[br]a different color.

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I'll do it in blue.

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Something over 24.

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To get the denominator[br]from 6 to 24,

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we have to multiply it by 4.

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So if we don't want to[br]change the value of 5/6,

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we have to multiply the[br]numerator and denominator

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by the same thing.

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So let's multiply the[br]numerator times 4.

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5 times 4 is 20.

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5/6 is the same thing as 20/24.

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So we're done.

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We've written 2/8 as 6/24 and[br]we've written 5/6 as 20/24.

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If we wanted to add them[br]now, we could literally just

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add 6/24 to 20/24.

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And I'll leave you[br]there because they

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didn't ask us to[br]actually do that.