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# Adding fractions with different signs

Video transcript

Find the sum 3 and 1/8 plus
3/4 plus negative 2 and 1/6. Let's just do the
first part first. It's pretty straightforward. We have two positive numbers. Let me draw a number line. So let me draw a number line. And I'll try to focus in. So we're going to
start at 3 and 1/8. So let's make this 0. So you have 1, 2, 3,
and then you have 4. 3 and 1/8 is going to
be right about there. So let me just draw
its absolute value. So this 3 and 1/8 is going to
be 3 and 1/8 to the right of 0. So it's going to be exactly that
distance from 0 to the right. So this right here, the
length of this arrow, you could view it as 3 and 1/8. Now whenever I like to deal with
fractions, especially when they have different denominators
and all of that, I like to deal with them
as improper fractions. It makes the addition
and the subtraction, and, actually, the
multiplication and the division a lot easier. So 3 and 1/8 is the same
thing as 8 times 3 is 24, plus 1 is 25 over 8. So this is 25 over 8, which is
the same thing as 3 and 1/8. Another way to think
about it, 3 is 24 over 8. And then you add 1/8 to
that, so you get 25 over 8. So this is our starting point. Now to that, we are
going to add 3/4. We are going to add 3/4. So we're going to
move another 3/4. We are going to
move another 3/4. It's hard drawing these arrows. We're going to move
another 3/4 to the right. So this right here,
the length of this that we're moving
to the right is 3/4. So plus 3/4. Now where does this put us? Well, both of these
are positive integers. So we can just add them. We just have to find
a like denominator. So we have 25 over 8. We have 25 over 8 plus 3/4. That's the same thing as we need
to find a common denominator here. The common denominator, or
the least common multiple of 4 and 8 is 8. So it's going to be
something over 8. To get from 4 to 8,
we multiply by 2. So we have to multiply
3 by 2 as well. So you get 6. So 3/4 is the same thing as 6/8. If we have 25/8 and
we're adding 6/8 to that, that gives
us 25 plus 6 is 31/8. So this number right over here,
this number right over here, is 31/8. And it makes sense
because 32/8 would be 4. So it should be a little
bit less than four. So this number right
over here is 31/8. Or the length of this arrow, the
absolute value of that number, is 31/8, a little
bit less than 4. If you wanted to write that as a
mixed number, it would be what? It would be 3 and 7/8. So that's that right over here. This is 31/8. That's that part
right over there. Now to that, we want to
add a negative 2 and 1/6. So we're going to add
a negative number. So think about what negative
2 and 1/6 is going to be like. So let me do this in a
new color, do it in pink. Negative 2 and 1/6. So we're going to
subtract, or I guess we're going to say we're
going to add a negative 1. We're going to add a negative
2 and then a negative 1/6. So let me draw. So negative 2 and 1/6, we
could literally draw like this. Negative 2 and 1/6 we
could draw with an arrow that looks something like that. So this is negative 2 and 1/6. Now, there's a couple
ways to think about it. You could just say,
hey, look, when you add this arrow,
this thing that's moving to the left-- we
could put it over here, and you would get straight
to negative 2 and 1/6. But we're adding this
negative 2 and 1/6. It's the same thing
as subtracting a positive 2 and 1/6. We're moving 2 and
1/6 to the left. And we're going to end up with
a number whose absolute value is going to look
something like that. And it's actually going
to be to the right. So it's not going to only
be its absolute value. Well, its absolute
value is going to be the number since it's
going to be a positive number. So let's just think
about what it is. This value right
here, which is going to be the answer to
our problem, is just going to be the difference
of 31/8 and 2 and 1/6. And it's the positive
difference because we're dealing with a positive number. So we just take 31/8. And from that, we will
subtract 2 and 1/6. So let's do this. So this orange value is going
to be 31/8 minus 2 and 1/6. So 2 and 1/6 is the
same thing as 6 times 2 is 12 plus 1 is 13. Minus 13/6. And this is equal
to, once again, we need to get a common
denominator over here. And it looks like 24 will be
the common denominator, 24. And let me make it very clear. This is the 31/8. And this is the 2 and 1/6. This right here
is the 2 and 1/6. So 31/8 over 24. You have to multiply by 3
to get to the 24 over here. So we multiply by 3 on the 31. That gives us 93. And then to go from 6 to 24,
you have to multiply by 4. We do that in another color. You have to multiply
it by 4, so we have to multiply by
4 up here as well. So 4 times 13, let's see. 4 times 10 is 40. 4 times 3 is 12. So that's 52. So this is going to be equal
to 93 minus 52 over 24. And that is-- so 93 minus 52. 3 minus 2 is 1. 9 minus 5 is 4. So it is 41/24 and positive. And you can see that here just
by looking at the number line. This right here is 41 over 24. And it should be a
little bit less than 2 because 2 would be 48 over 24. So this would be 48 over 24. And it makes sense that we're
a little bit less than that.