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Regina rode her bike 2 and 1/4
miles from her house to school

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and then 1 and 5/8 miles
to her friend's house.

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How many miles did Regina
ride in total?

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So she first rode 2 and 1/4
miles, and then she

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rode 1 and 5/8 miles.

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then she rode 1 and 5/8 miles

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So the sum is the total number
of miles she rode.

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So to take this sum, we've seen
that we can add the whole

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number parts, because this is
really the same thing as 2

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plus 1/4 plus 1 plus 5/8, so we
can just switch the order,

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if you want to view
it that way.

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So we can add the 2 plus the 1
first, and then we get-- let

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me do that here.

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So 2 plus the 1, you get 3, and
then we need to add the

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1/4 plus 5/8.

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And to add these two fractions,
we have to find the

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least common multiple
of 4 and 8.

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That'll be our new
denominator.

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8 is divisible by both 8 and 4,
so that is the least common

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multiple of 4 and 8, so our
common denominator will be 8.

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Obviously, 5/8 will
still be 5/8.

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Now to go from a denominator
of 4 to 8, you have to

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multiply the denominator by 2,
so we also need to multiply

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the numerator by 2,
so 1 times 2 is 2.

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And, of course, we still
have this 3 out there.

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So 2 and 1/4 plus 1 and 5/8 is
the same thing as this right

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here, and this is equal to-- we
have our 3 plus, and then

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over 8 we add the 2 plus 5.

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We have 7/8.

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So this is going to be equal
to 3 and 7/8 miles.

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She rode a total of
3 and 7/8 miles.

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Now, I want to make one
thing very clear.

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So far when we've been adding
these mixed numbers, the

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fraction part always ended
up as a proper fraction.

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The numerator was smaller
than the denominator.

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But I want to do a quick example
to show you what you

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do when the numerator is not
smaller than the denominator.

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So let's say we had 1 and
5/8 plus 2 and 4/8.

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So if you add just the
whole number parts, 1

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plus 2, you get 3.

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Plus 5/8 plus 4/8, 5/8
plus 4/8 is 9/8, so

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you get 3 plus 9/8.

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Now it would be really strange
to just say, OK, that's the

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same thing as 3 and 9/8, because
you have a mixed

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number with a whole number
and an improper fraction.

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If you're going through the
trouble of making it a mixed

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number, the fraction better
be a proper fraction.

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So what you need to do is
rewrite 9/8, and you know that

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9/8 is the same thing
as 1 and 1/8, right?

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8 goes into 9 one time with 1
left over, so it's 1 and 1/8.

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So this is the same thing
as 3 plus 1 and 1/8.

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So now we can add the
whole number parts.

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3 plus 1 is equal to 4, and then
you have your 1/8 over

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there: 4 and 1/8.

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I just wanted to give you that
special circumstance when your

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fraction part ends
up improper.