WEBVTT

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Add.

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Simplify the answer and write
as a mixed number.

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And we have three mixed numbers
here: 3 and 1/2 plus

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11 and 2/5 plus 4 and 3/15.

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So we've already seen that we
could view this as 3 plus 1/12

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plus 11 plus 2/5-- let
me write that down.

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This is the same thing as 3
plus 1/12 plus 11 plus 2/5

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plus 4 plus 3/15.

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The mixed number 3 and 1/12
just literally means 3 and

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1/12 or 3 plus 1/12.

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And since we're just adding
a bunch of numbers, order

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doesn't matter, so we
could add all the

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whole numbers at once.

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So we have 3 plus 11 plus 4,
and then we can add the

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fractions: the 1/12 plus
2/5 plus 3/15.

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Now, the blue part's pretty
straightforward.

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We're just adding numbers.

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3 plus 11 is 14 plus 4 is
18, so that part right

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there is just 18.

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This will be a little bit
trickier, because we know that

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when we add fractions, we have
to have the same denominator.

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And now we have to make all
three of these characters have

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the same denominator and that
denominator has to be the

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least common multiple
of 12 and 5 and 15.

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Now, we could just do it kind
of the brute force way.

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We could just look
at the multiples.

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We could pick one of these guys
and keep taking their

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multiples, and then figuring
out whether those multiples

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are both divisible
by 5 and 15.

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Or the other way we can do
it is take the prime

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factorization of each of these
numbers, and just say that the

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least common multiple has
to contain the prime

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factorization each of these
guys, which means it contains

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each of those numbers.

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So let me show you what
I'm talking about.

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If we take the prime
factorization of 12, 12 is 2

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times 6, 6 is 2 times 3, so 12
is equal to 2 times 2 times 3.

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That's the prime factorization
of 12.

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Now, if we do 5, prime
factorization of 5, well, 5 is

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just 1 and 5, so 5 is
a prime number.

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It is the prime factorization
of 5.

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There's just a 5 there.

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This 1 is kind of useless.

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So 5 is just 5.

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And then 15, let's do 15.

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Actually, when I did the prime
factorization of 5, I should

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have said, look, 5 is prime.

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There's no number larger than
1 that divides into it, so

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it's actually silly to even
make a tree there.

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And now let's do 15, 15's
prime factorization.

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15 is 3 times 5, and now both
of these are prime.

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So we need something that has
two 2's and a 3, so let's look

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at the 12 right there.

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So our denominator has to have
at least two 2's and a 3, so

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let's write that down.

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So it has to be 2
times 2 times 3.

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It has to have at least that.

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Now, it also has to have
a 5 there, right?

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Because it has to be a
common multiple of 5.

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5's another one of those prime
factors, so it's got to have a

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5 in there.

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It didn't already have a 5.

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And then it also has to
have a 3 and a 5.

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Well, we already have a 5.

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We already have a 3 from the
12, and we already have a 5

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from the 5, so this number will
be divisible by all of

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them, and you can see that
because you can see it has a

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12 in it, it has a 5 in it,
and it has a 15 in it.

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So what is this number?

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2 times 2 is 4.

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4 times 3 is 12.

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12 times 5 is 60.

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So the least common multiple
of 12, 5 and 15 is 60.

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So this is going to be plus.

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We're going to be over 60.

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So all of these are going
to be over 60.

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All of these three fractions
are over 60.

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Now, to go from 12 to 60,
we have to multiply the

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denominator by 5, so we also
have to multiply the numerator

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by 5, so 1 times 5 is 5.

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5/60 is the same
thing as 1/12.

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To go from 5 to 60 in the
denominator, we have to

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multiply by 12, so we
have to do the same

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thing for the numerator.

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12 times 2 is 24.

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The last one, 15 to 60, you have
to multiply by 4, so you

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have to do the same thing
in the numerator.

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4 times 3 is 12.

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And now we have the
same denominator.

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We are ready to add.

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So let's do that.

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So this is going to be 18 plus,
and then over 60, we

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have 5 plus 24, which is 29.

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29 plus 12, let's see, 29
plus 10 would be 39

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plus 2 would be 41.

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It would be 41.

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And as far as I can tell,
41 and 60 do not

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have any common factors.

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41 actually looks prime to me.

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So the final answer
is 18 and 41/60.

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