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Let's add four elevenths to nine over thirteen
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In order to add these two fractions we need to find a common denominator
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And that common denominator used to be the least common multiple of eleven and thirteen
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And these two numbers don't share any common factors
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So their least common multiple is really just going to be the product of eleven and thirteen
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So we could say thirteen times eleven
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Thirteen times one is thirteen
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Thirteen times another one is thirteen
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Or you could say thirteen times ten is a hundred and thirty
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And we get: three, four, one - one hundred and forty-three
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So that's going to be our common denominator
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So I'll write it over here:
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Something over one hundred and forty-three plus
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Something else over one hundred and forty-three
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And to go from four elevenths to something over one forty-three
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We multiply the eleven times thirteen
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--Or we multiply the denominator times thirteen--
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So we're going to have to multiply the numerator times thirteen as well
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And four times thirteen--let's see: four times ten is forty
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Four times three is twelve, so it gives us fifty-two
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And you can work that out by hand if you like
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Four times thirteen is fifty-two
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And then to go from thirteen to one forty-three we multiply by eleven
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So if we multiply the denominator by eleven
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(if we don't want to change the value of the fraction)
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We have to multiply the numerator by eleven
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Nine times eleven is ninety-nine
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And now we're ready to add: this is equal to--our common denominator is one hundred and forty-three
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And fifty-two plus ninety-nine
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--Fifty-two plus a hundred would be one hundred and fifty two
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And this is going to be one less than that
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So it's going to be one hundred and fifty-one
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And I think that's about as simplified as we can get
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As far as I know, it doesn't look like there are any common factors between one fifty-one and one forty-three
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So we just get one fifty-one over one forty-three
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--We can write this as a mixed number
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Because one forty-three goes into one fifty-one one time
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One times one forty-three is one forty-three
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When you subtract--let's see, this can become an eleven
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This is a four
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Eleven minus three is eight
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You have a remainder of eight
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So one fifty-one over one forty-three is the same thing as one and eight one forty-thirds
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And now it becomes even more clear that these can't be simplified anymore
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And we are done--this is the same thing as one and eight one forty-thirds