In this video segment we’ll be answering the question, how do you add and

subtract or combine fractions with like denominators.

Well it’s a very simple process because you have like denominators. You have the

same piece sizes that you’ve cut that whole into. So all you're doing when

you're adding or subtracting is you’re counting up how many of those same piece

sizes that you have.

So the steps are, combine your numerators over your common denominator.

So if we look at it theoretically, we have A over B plus C over D, we have the

situation of having like denominators here. So we have our piece sizes being B,

and A and C is how many of those we have.

So we simply combine them, A plus C and put it over what the piece size was to

begin with, which is B.

So let's look at that with numbers so it’s a little bit clearer.

All right, so we have two situations set up here. We have 2/5 plus 1/5 and 2/5

minus 1/5.

Now please notice that all of these holes are the same size and I have all of

the holes cut into the same piece size, which is fifths.

So let's look at that first one where we are adding. So we start out with 2/5 or

2 of these pieces that are of the size of being a 1/5 of the whole, and then

We’re going to gather up 1 more of those pieces that are fifths to give us a

total of 3/5.

So if we use our rule and look at the symbolic representation below, we have 2/5

plus 1/5.

Since we have a common piece size, we simply gather up how many of those we have

in the numerator by combining them and put them over the common denominator.

So we have 3/5 in that first example.

Now if we look down where were subtracting these, we start out with 2/5. So we

start out with 2 of these pieces that are in fifths, or that are of the size of

being a fifth, and then we end up taking one of those pieces away.

So we started out with 2 of those pieces that are fifths, but then we end up

taking 1 of those pieces away. So we end up with 1/5.

And if we look at it symbolically, we combine our numerators 2 and negative 1 or

2 minus 1 over that common piece size of fifths. So 2 minus 1 leaves us with

1/5.

So a lot of times, it's much easier to look at fractions in the form of

pictures.

So hopefully this helped you understand that all you're doing is collecting up

how many of the same piece sizes that you have whenever you're adding or

subtracting fractions. So you're either gathering up more if you're adding them

or you’re taking some away from what you have if you're subtracting. Now this is

only in the case where you have a common denominator or you have a common piece

size between the fractions. If you don't have that, that's for another video.

So I hope that this has been helpful for you. If you have any other questions

about adding or subtracting fractions with common denominators, please contact

your Highlands instructor.

Thank you.