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We're asked to add 4/9 and 11/12
and to write our answer

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as a mixed number, and then
simplify and write our answer

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as a mixed number.

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So here we have two fractions
we're adding together, but we

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have different denominators.

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So whenever you add fractions,
the first thing you have to do

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is check the denominators.

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If they're the same, you can
add, but if they're different

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like this, you have to make
them have the same

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denominator.

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So what we have to do is find
a number that both 9 and 12

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will divide into, and that
will be our common

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denominator, and you'll see
why both 9 and 12 have to

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divide into it.

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So let's think about what that
number is, and there's two

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ways of coming up with that
what we could call a least

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common multiple, the smallest
multiple of both 9

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and 12 that is common.

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One way is just to kind of look
at the multiples of 9 and

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see if any of them are
divisible by 12.

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So if you start with 9--
we can do it over here.

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So you have 9, that's
not divisible by 12.

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18 isn't divisible by 12.

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27 isn't divisible by 12.

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36, well, that is
divisible by 12.

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That is 12 times 3.

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So 9 goes into 36 and
12 goes into 36.

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So what we want to do is write
a common denominator.

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So we're going to write 4/9 as
something over 36, and we're

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going to write 11/12 as
something over 36.

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Now, to turn your 9 into
a 36, you have to

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multiply it by 4, right?

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9 times 4 is equal to 36.

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Now, you can't just multiply
the denominator by 4.

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You also have to multiply the
numerator by the same thing.

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So if you multiply the numerator
by 4, you get 4

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times 4 is 16.

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So 4/9 is the exact same
thing as 16/36.

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If you wanted to simplify this
one to 4/9, you divide the

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numerator and the denominator
by 4.

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Now, we do the same
thing over here.

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36, 12 times 3, so we're
multiplying 12 by 3 to get 36.

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Well, if we did that to the
denominator, we also have to

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do that to the numerator,
so 11 times 3 is 33.

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And just like that, we've now
rewritten each of the

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fractions so that they have
the same denominator.

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Both of their denominators
is 36.

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So now we're ready to add.

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If you add these two things,
we'll have 36, because we're

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considering kind of parts of
36 or fractions of 36, and

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then we have 16 plus 33
in the numerator.

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Let me write that down.

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16 plus 33 in the numerator.

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And 16 plus 33 is what?

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6 plus 33 would be 39
and then you have

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another 10, so it's 49.

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So it's equal to 49/36.

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Now, can we simplify this?

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49, it's 7 squared, so it has
1, 7 and 49 as factors.

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This has 1-- it has a bunch
of numbers, but it's not

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divisible by 7, so this is
actually in simplest form, but

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this is an improper fraction.

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The numerator is larger
than the denominator.

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So let's write it as
a proper fraction.

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To do that, we divide
36 into 49.

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36 goes into 49 how
many times?

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Well, it only goes one
time, so it equals 1.

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And how much will
be left over?

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If I divide 36 into 49 one time,
or 1 times 36 is 36,

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then I have 13 left
over to get to 49.

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So it's 1 and 13/36.

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And you can do that manually,
if you like you.

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You'd say 36 into 49.

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36 goes into 49 one time.

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1 times 36 is 36, and
then you subtract.

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9 minus 6 is 3.

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4 minus 3 is 1.

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You have a remainder of 13.

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So that's our answer:
1 and 13/36.

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