Adding and subtracting fractions

So we're asked to add 3/15 plus
7/15, and then simplify

the answer.

So just the process when you
add fractions is if they

already-- well, first of all, if
they're not mixed numbers,

and neither of these are, and
if they have the same

denominator.

In this example, the
denominators

are already the same.

The denominator is 15.

So if you add these two
fractions, your sum is going

to have the same denominator,
15, and your numerator is just

going to be the sum of the
numerator, so it's going to be

3 plus 7, or it's going
to be equal to 10/15.

Now, if we wanted to simplify
this, we'd look for the

greatest common factor in both
the 10 and the 15, and as far

as I can tell, 5 is the largest
number that goes into

both of them.

So divide the 10 by 5 and you
divide the 15 by 5, and you

get-- 10 divided by 5 is 2
and 15 divided by 5 is 3.

You get 2/3.

Now, to understand why this
works, let's draw it out.

Let's split something
up into 15 sections.

So let me split it up
into 15 sections.

Let me see how well
I can do this.

Well, actually, even a better
way, an easier way might be to

draw circles.

So let me do the 15 sections.

So let me draw.

So that is one section
right over there.

That is one section and then if
I copy and paste it, that

is a second section, and then
a third section, fourth

section, and then we have
a fifth section.

Let me copy and paste
this whole thing.

So that's five sections
right there.

Let me copy and then
paste that.

So that is 10 sections,
and then let me

do it one more time.

So that is 15 sections.

So you can imagine this whole
thing is like a candy bar or

something, and we have now split
it up into 15 sections.

Now, what is 3/15?

Well, it's going to be
3 of the 15 sections.

So 3/15 is going to be one,
two, three: 3/15.

Now, to that, were adding
7 of the 1/15

sections, or 7 of the sections.

So we're adding 7
of those to it.

So that's one, two, three,
four, five, six, seven.

And you see now, if you take the
orange and the blue, you

get one, two, three, four, five,
six, seven, eight, nine,

ten of the sections, or
10 of the 15 sections.

And then to see why this is the
same thing as 2/3, you can

just split this candy bar into
thirds, so each third would

have five sections in it.

So let's do that.

One, two, three, four, five,
so that is 1/3 right there.

One, two, three, four,
five, that is

another third right there.

And notice, when you do it like
this, we have filled out

exactly two-- one, two--
of the thirds.

This is the third third, but
that's not filled in.

So 10/15 is the same
thing as 2/3.