Adding and subtracting fractions

How to add and subtract 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 to 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 third, 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.

This is the third third, but that's not filled in.
So 10/15 is the same thing as 2/3.