>> Hi, this is Julie Harland,
and I'm your Math Gal.
Please visit my website
at yourmathgal.com
where you can search for any
of my videos organized
by topic.
On this video, we're going
to add and subtract some mixed
numbers that have unlike
denominators
and we're also dealing
with negative numbers.
So you have to be pretty good
at your fractions by now
and working with positive
and negative numbers.
Here's our first problem.
So, we have negative 3 1/4
plus 2 5/6.
So I have mixed numbers
and I also have
unlike denominators.
So there are two different
ways to deal with this.
You can get a common
denominator first
or what you could do is change
these to improper fractions
and get a common
denominator second.
I think it's easier
to get a common
denominator first.
So let's do that.
What's the least common
denominator between 4 and 6?
Well, lots of ways
to figure it out
and hopefully you've got 12.
This is one way I figure
out to be 12.
So I need to rewrite 1/4
in terms of 12 and I have
to write the 5/6
in terms of 12.
So what I'm going
to do is move this
over a little bit.
Let's see, plus 2 5/6,
I guess I'll do it like this,
plus 2 5/6.
I may just leave myself some
space right here to deal
with this fraction,
each of these fractions.
So, I need to have 12s
in the denominator, right?
So, for this first fraction
1/4, how do I change the 1/4
to 12s?
I need to multiply the
denominator by 3
so the numerator also is going
to be 3 and for 5/6 I need
to multiply the denominator
by 2 so numerator by 2
so I'm going to instead
of thinking
of just 3 1/4 it's negative 3
3/12 and this is going
to be 2 10/12.
Now notice I'm just
multiplying the fraction
by that not the 2.
It's a little strange the way
it looks, but hopefully you
understand what I was doing.
Now, I'm adding a negative
number and a positive number.
So that means I have
to take their difference
and take the sign
of the larger absolute value
which is right here negative,
is more negatives.
So, my answer I know is going
to be negative.
What do we do?
We have to then subtract
these numbers.
So I've got
to take 3 3/12 minus 2 10/12.
That's supposed to be a 12.
A little problem here
because I've got 3 minus 10
if I subtracted the numerator.
So I would have to borrow
if I wanted to keep this
with mixed numbers.
Let's go ahead and do that.
If I borrow,
that means that becomes 1 3/12
so basically the numerator I
get to add 12 to it.
So, you might show this
differently
but that's 15/12 minus 10/12.
So that's going to be 10/12.
Keep in mind 3 is the same
as 2 plus 1
and 1 can be written as 12/12
so that's why this new
numerator 3 plus 12 is going
to be 15.
So my answer should be
negative 5/12.
Now a lot of people have
trouble doing it
with the mixed numbers.
So the other way to do it is
to write everything
as improper fractions.
So, instead,
let's take what we have here
and write each of these
as improper fractions.
So, remember this minus sign
just goes in front
and you're really just
changing 3 3/12
to an improper fraction.
So it's [inaudible]
and I have 12 times 3 is 36
plus 3 is 39 plus all right
second fraction 12 times 2 is
24 plus 10 is 34.
Now I'm adding
with the same denominator.
So when I add the 2
numerators,
notice you're going
to get negative 39 plus 34
that's negative 5/12.
So you would still get
negative 5/12.
So our answer is negative 5/12
and I think most people kind
of like doing it this way
unless they are really huge
numbers like if it was 109
and, you know, 3/17,
sometimes that's kind
of tricky putting them
into improper fractions.
Here's our second problem.
Again, we need
to get a common denominator.
We also might note we're doing
subtraction here.
I have a negative number
so I could begin if I want
by writing
that as negative 8 1/2 plus
negative 4 2/9.
That's up to you.
I need to get a
common denominator.
Between 2 and 9 is going
to be 18.
So that will be negative 8
and we're going to have
to multiply this numerator
by 9/9 so that'll be 9/18.
I have to do the same thing
with 2/9.
If it helps you
to see what I'm doing here I'm
doing 1/2 by 9/9 that's how I
got the 9/18
and then the 2/9 I'm going
to multiply by 2/2
to get a denominator of 18
so that's where this 4/18
comes from.
So now I'm adding two
negative numbers.
This one is going
to be a little bit easier
to just keep
with my mixed numbers
because I'm adding two
negatives so I just add the
whole number parts
and add the fractional parts.
So, if you want to do
that writing it
down like this, think of this
as adding down negative 8
and negative 4 add
up to negative 12
and then I've got actually I'm
not going to write the
negative signs;
that makes it more confusing.
You know the answer is going
to be negative
so we're adding the two whole
number parts, the 8 9/19
and the 4 4/18 that's going
to be 13/18
so the answer is negative 12
and 13/18.
I'm sure many
of you could just add
right here.
You don't have to go
to the side.
So, in this case,
I think it was easier leaving
it in terms of mixed numbers
but you could have taken
and written 8 9/18
as an improper fraction,
taken the 4 4/18 write time
as an improper fraction
and done the entire problem
and then when you change it
back to a mixed number you
should also get negative
12 13/18.
All right here's our
last problem.
We have negative 5 5/12 minus
negative 1 4/9.
So, first thing I'm going
to do is say, oh,
minus a negative that's going
to be plus a positive.
So, let's do that first.
Now, we need
to get a common denominator
for 12 and 9.
I'm going to go over here.
Three goes into both of those
so the common denominator is
going to be 36.
So I know I'm going
to write this first one
with a denominator of 36
and this is now a plus
and write the second one
with a denominator of 36.
So, we want to write 5/12
with a denominator of 36
and I want to write the 4/9
with a denominator of 36.
So, the first one is multiply
by 3 over 3,
15 will be your new numerator,
but the second one, 4/4,
16 will be your new numerator.
So, 5/12 I said was 15/36
so that goes up here
and 4/9 I've got 16/36.
So now I'm doing negative 5
16/36 plus 1 16/36
and adding the negative
and a positive number.
So, that means I have
to take the difference
and take the sign
of the larger.
So I know my answer is going
to be negative
because this is the bigger
one, the negative 5 is bigger
than the 1.
So, my answer I know will be
negative and I now have
to subtract.
So the next step is to go back
and remember how to do this.
How do you do 5 15/36 minus
the 1 16/36?
Well, you can't do 15 minus 16
so, again, you're going
to have to borrow
so if you want to keep it
as mixed numbers.
If you borrow from that,
you're going
to get this will be a 4
and then you have 1 15/36
which means you add 36
to that numerator,
which is a 51/36 minus
1 16/36.
So, then we can subtract
and what's 15 minus 16,
35 I hope, 35/36.
So now I go back over here
to my problem and you know
that the answer is going
to be negative
so it's negative 3 and 35/36.
Now, you also could have
changed each of these
into improper fractions.
So, the other way to do this
to subtract the 5 15/36 minus
the 1 16/36 is you would have
to multiply 36 times 5
and I have a video showing you
an easy way to multiply by 5,
that's 180 plus 15,
it's 195/36
and also multiply 36 times 1,
36 plus 16 is 52.
You want to subtract,
I think that is 143 I hope,
143/36.
Okay, that's actually
subtracting but, again,
the answer is going to have
to have a negative sign
in front of it, right?
So this is just
like your side work just
like over here we did our
side work.
So our question is is
that the same thing?
Well, let's check it
out if it's the same thing.
What's 36 times 3?
It's 108 and you add 35
which is 143.
So, the new numerator would be
that's the same thing
as 143/36.
So, two ways
of getting the answer.
Ah, boy, lots
of arithmetic here
but our final answer could
either be written like this
or negative 143/36.
[ Silence ]
Please visit my website
at yourmathgal.com
where you can view all
of my videos
which are organized by topic.