WEBVTT
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What I want to do in this video is order these fractions from least to greatest
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And, the easiest way--and the way that people are sure to get the right answer--
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is to find a common denominator, because if we can't find a common denominator,
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these fractions are difficult to compare: 4/9 v. 3/4 v. 4/5, 11/12, 13/15.
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You can try to estimate them, but you'll be able to directly compare them if
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they all have the same denominator. So, the trick here is to first find the common denominator.
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And there is many ways to do it, you could just pick one of these numbers,
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and take all of its multiples until you find a multiple that is divisible by all of the rest.
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Another way to do it is to look at the prime factorization of each of these numbers.
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and then the 'least common multiple' of them would have each of those prime numbers in it.
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Let's do it that second way, and then verify it.
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So, 9 is 3*3, so our LCM is going to have at least one 3*3 in it.
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And then 4 is the same thing as 2*2.
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So, we will also have 2*2 in our prime factorization (LCM).
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5 is a prime number, so we'll put 5 right there.
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And then, 12 is the same thing as 2*6, and 6 = 2*3.
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So, in our LCM, we have to have two 2's, but we already have two 2's, and we already have one 3.
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Another way to think about it, is that something that is divisible by both 9 and 4
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is going to be divisible by 12.
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And then finally, we need it to be divisible by 15's prime factors.
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15 is the same thing as 3*5.
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So once again, we already have 3 and 5.
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So, this is our least common multiple (LCM).
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So, LCM is going to be equal to 3*3*2*2*5 =180
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So, our LCM is 180. So, we want to rewrite all of these fractions with 180 in the denominator.
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So, our first fraction, 4/9, is what over 180?
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To go from 9 to 180, we have to multiple 9 by 20.
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So, to get the denominator to equal 180, we multiple by 20.
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Since we don't want to change the value of the fraction, we should also multiple by the 4 by 20.
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4*20 = 80. So, 4/9 is the same thing as 80/180.
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Now, let's do 3/4. What do we have to multiple the denominator by to equal 180?
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You can divide 4 into 180 (180/4 = x) to figure that out.
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4*45 = 180. Now, you also have to multiple the numerator by 45.
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3*45 = 135. So, 3/4 equals 135/180.
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Now let's do 4/5. To get 180 from 5, multiple 5 by 36.
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Have to multiple numerator by same number, 36.
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So, 144/180.
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And then we have only two more to do.
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180/12 = 15. Same for numerator, 15. So, 11/12 = 165/180.
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And then finally, we have 13/15.
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To get 180 from 15, multiply 15 by 12--15*10 = 150, 30 remaining for 180. 15*2 = 30. So, 15*12 = 180.
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Multiple numerator by same number, 13.
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We know 12*12 = 144, so just add one more 12 = 156.
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So, we've rewritten each of these fractions with the new common denominator.
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Now, it is very easy to compare them. We only have to look at their numerators.
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Foe example, the smallest numerator is 80, so 4/9 is the least of these numbers.
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The next smallest number looks like 135, which was 3/4.
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And then the next one is going to be the 144/180, which was 4/5.
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Next is 156/180, which was 13/15.
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Finally, we have 165/180, which was 11/12.
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And, we're done! We have finished our ordering.