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# Adding mixed numbers word problem

Adding Mixed Numbers Word Problem. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Regina rode her bike 2 and 1/4
miles from her house to school and then 1 and 5/8 miles
to her friend's house. How many miles did Regina
ride in total? So she first rode 2 and 1/4
miles, and then she rode 1 and 5/8 miles. So the sum is the total number
of miles she rode. So to take this sum, we've seen
that we can add the whole number parts, because this is
really the same thing as 2 plus 1/4 plus 1 plus 5/8, so we
can just switch the order, if you want to view
it that way. So we can add the 2 plus the 1
first, and then we get-- let me do that here. So 2 plus the 1, you get 3, and
then we need to add the 1/4 plus 5/8. And to add these two fractions,
we have to find the least common multiple
of 4 and 8. That'll be our new
denominator. 8 is divisible by both 8 and 4,
so that is the least common multiple of 4 and 8, so our
common denominator will be 8. Obviously, 5/8 will
still be 5/8. Now to go from a denominator
of 4 to 8, you have to multiply the denominator by 2,
so we also need to multiply the numerator by 2,
so 1 times 2 is 2. And, of course, we still
have this 3 out there. So 2 and 1/4 plus 1 and 5/8 is
the same thing as this right here, and this is equal to-- we
have our 3 plus, and then over 8 we add the 2 plus 5. We have 7/8. So this is going to be equal
to 3 and 7/8 miles. She rode a total of
3 and 7/8 miles. Now, I want to make one
thing very clear. So far when we've been adding
these mixed numbers, the fraction part always ended
up as a proper fraction. The numerator was smaller
than the denominator. But I want to do a quick example
to show you what you do when the numerator is not
smaller than the denominator. So let's say we had 1 and
5/8 plus 2 and 4/8. So if you add just the
whole number parts, 1 plus 2, you get 3. Plus 5/8 plus 4/8, 5/8
plus 4/8 is 9/8, so you get 3 plus 9/8. Now it would be really strange
to just say, OK, that's the same thing as 3 and 9/8, because
you have a mixed number with a whole number
and an improper fraction. If you're going through the
trouble of making it a mixed number, the fraction better
be a proper fraction. So what you need to do is
rewrite 9/8, and you know that 9/8 is the same thing
as 1 and 1/8, right? 8 goes into 9 one time with 1
left over, so it's 1 and 1/8. So this is the same thing
as 3 plus 1 and 1/8. So now we can add the
whole number parts. 3 plus 1 is equal to 4, and then
you have your 1/8 over there: 4 and 1/8. I just wanted to give you that
special circumstance when your fraction part ends
up improper.