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# Subtracting mixed numbers 2

Subtracting Mixed Numbers 2. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

They want us to subtract these
two numbers and simplify the answer and write as
a mixed number. We're going to do it two ways. The first way, we're going to
turn both of these into improper fractions and
see what we get. And then the other way, we're
going to subtract the whole number parts and then subtract
the fraction parts and see what we get. So if we turn them both into
improper fractions, let's first turn 8 and 2/3 into
an improper fraction. So it has 3 in the
denominator, and 3 times 8 is 24. 24 plus 2 is 26. So 8 and 2/3 is the same
thing as 26/3. And 5 and 5/6, so we're
going to subtract. We're going to have 6
in the denominator. 6 times 5 is 30. 30 plus 5 is 35. So this simplifies as an
improper fraction to 35/6. Now to subtract, we have to
have a common denominator. 3 and 6 are not the same
denominator, but they are both divisible into 6. 6 is the least common
multiple of 3 and 6. So let's turn them both
into something over 6. So the 26/3, if we put it over
6, to go from 3 to 6 in the denominator, we have to multiply
by 2, so we have to do the same thing in
the numerator. We have to multiply 2 times
26, which is 52. So it's going to be 52/6 minus--
we don't have to change this one here
in orange. It's already over 6-- minus
36/6, which is going to be equal to-- what's 52 minus 35? Let's see, if you add 5
to 35, you get to 40. 15 will get you to 50, and
so we want 2 more, so it's going to be 17. So it's 17/6. This is as an improper
fraction. Now, if we want to write it as
a mixed number, we say how many times does 6 go into 17? Well, 6 times 2 is 12,
so that works. 6 times 3 is too big. It's 18, so it goes
in two times. Now, if you take it into it
two times, you get 12, and then you have 5 left
over, right? To go from 12 to 17, you need
5 so you have 5 left over. You could say 6 goes into 17 two
times, remainder 5, so 17 over 6 is 2 and 5/6. And we're done! Now this is kind of the improper
fraction route, which it'll always work. It'll always work. Sometimes it's easier
or harder, but it will always work. Actually, either route will
always work, but I tend to do it this way. Let's do it separating out
the whole number and the fractional parts. So first we could view
this as 8 minus 5. So let's do this. 8 minus 5-- that's subtracting
the whole number parts-- plus 2/3 minus 5/6. Now, 8 minus 5, that's easy. That's 3. And then over here, though, we
have an interesting-- well, let's try to work it out. Let me do this in a
different color. We want a common denominator
here, and we already saw that 6 is the least common multiple
of 3 and 5, so we could write them both with 6 as
the denominator. 5/6 already has 6 as
the denominator. We don't have to do
anything there. To go from 3 to 6 in the
denominator here, we have to multiply by 2, so let's do the
same thing with this 2. 2 times 2 is 4. So this results in 4/6 minus
5/6, which will give us-- and we haven't covered it yet--
a negative number. If you take 5 from 4, you're
going to go below 0. Now, if we don't want to deal
with that negative number, what we could do, and this is
essentially the same idea as regrouping or borrowing,
although they shouldn't call it borrowing, they should call
it taking, is we can rewrite this 3. That's why this can get a little
bit tricky sometimes. Let me do it over here. Let me draw a line here so we
don't get the two ways of doing the problem confused. We can rewrite the 3 as 2 plus
1, but instead of writing it as 1, we could write
it as 6/6, right? 6 over 6 is 1 plus 2 is 3. And then, if we add it
to these guys, so plus 4/6 minus 5/6. Now, what happened
by doing that? Well, if we throw this 6/6 into
the mix and then we had the 4/6 and then we subtract
the 5 from it, then we're going to have a positive number,
so let's to do it. So we get this 2 right here. So it's 2 plus, and then over
6, we have 6 plus 4-- let me write it. 6 plus 4 minus 5. Now, what's this
going to equal? This is going to be this
2 and what over 6? 6 plus 4 is 10 minus 5 is 5. So you have 2 and 5/6, which
is exactly what we got the other way.