WEBVTT

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We have negative 3/4
minus 7/6 minus 3/6.

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And there's many
ways to do this.

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But it immediately
jumps out at me

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that these last two numbers
have a 6 in the denominator.

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So I'm going to worry
about these first.

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I'm going to view this as
negative 7/6 minus 3/6.

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So if we have negative
7/6 minus 3/6,

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that's going to be the same
thing as negative 7 minus 3

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over 6.

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And of course, we
have this negative 3/4

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out front that
we're going to add

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to whatever we get over here.

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So this is these two terms
that I'm adding together.

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Negative 7 minus
3 is negative 10.

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So it's negative 10 over 6.

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And then I'm going to have
to add that to negative 3/4.

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And now I have to worry about
finding a common denominator.

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Let me write that so
they have a similar size.

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So now I have to worry about
finding a common denominator.

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What is the smallest number that
is a multiple of both 4 and 6?

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Well, it might jump out
at you that it's 12.

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You can literally just go
through the multiples of 4.

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Or you could look at
the prime factorization

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of both of these numbers.

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And what's the
smallest number that

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has all of the prime
factors of both of these?

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So you need two 2s, and
you need a 2 and a 3.

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So if you have two 2s and a
3, that's 4 times 3 is 12.

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So let's rewrite this
as something over 12

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plus something over 12.

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Well, to get your
denominator from 4 to 12,

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you have to multiply by 3.

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So let's multiply our
numerator by 3 as well.

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So if we multiply
negative 3 times 3,

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you're going to have negative 9.

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And to get your
denominator from 6 to 12,

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you have to multiply by 2.

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So let's multiply our
numerator by 2 as well so

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that we don't change the
value of the fraction.

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So that's going
to be negative 20.

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And now we're ready to add.

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Our common denominator is 12.

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And so this is going to be
negative 9 plus negative 20,

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or we could even write
that as minus 20,

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over 12, which is equal to--
and we deserve a drum roll now.

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This is negative 29 over 12.

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And 29 is a prime
number, so it's not

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going to share any common
factors other than 1 with 12.

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So we also have this in
the most simplified form.