Adding and Subtracting Fractions With Like Denominators

Adding and subtracting fractions with like denominators. A fraction is a number that represents some part of something like a pizza that has been divided into equal sized parts. A pizza might be divided into eight equal sized slices. Each pizza slice here is one eighth of the whole pizza. We can write this with fractional notation as one eighth. The denominator is the number on the bottom of a fraction. It tells us how many equal parts we are dividing the whole into. In this case, the pizza is divided into eight parts. The top number, the numerator, tells us how many of those parts we are talking about. In this case, we are talking about one slice of the pizza, so the numerator is one. It's important to remember that in a fraction, each part is the same size. Now that we've got our pizza all sliced up, it's time to divvy it up. Bob, Charles, and Joe are going to share this pizza. Bob gets one slice of the eight slices. Charles gets two slices of the eight slices, and Joe gets three slices of the eight slices. There are two slices left, which go into the fridge for later. Bob's share of the pizza is one piece out of the eight or one eighth. Charles' share is two of the eight pieces or two eighths, and Joe's is three slices of the eight pieces or three eighths. The two pieces of the eight that are left are in the fridge. That's two eighths. All eight slices of the pizza are accounted for. We know that if we added up all these fractions, we'd get eight eighths. And because any number over itself is one, we have one whole pizza. Now, let's look at the numerators of these fractions. One, two, three, and two. Add them all together, and we get eight slices. This works because all the fractions here have the same denominator. And that's the key to adding and subtracting fractions with the same denominator. When adding fractions with the same denominator, we add the numerators and keep the denominator the same. But what about subtraction? Here's some leftover pizza from another pizza party. There are five pieces left or five eighths. Maria eats two slices, which is two eighths. The Jill eats one slice, which is one eighth. So now we have two eighths of the pizza to put back in the fridge to eat another day unless Joe finds it first. Let's try a different problem. One with both addition and subtraction. Two fifths plus three fifths minus one fifth. Note that the denominators are all the same, five. So we can get our answer by adding and subtracting the numerators, and the denominator will stay the same. We can rewrite the problem like this. So two plus three is five. Then subtract one, which leaves us with four. So the answer is four fifths. Here's our rule. When adding or subtracting fractions with the same denominator, add or subtract the numerators and keep the denominator the same.