Today let’s take a look at adding fractions with common denominators. But first, let’s look at this circle.
This circle is made up of eight equal parts. And if we shade just one of them, then we call it what as a fraction. That’s right! we call it one-eighth.
So here it is, our one-eighth. What would happen if we added another one-eighth piece? It would look like this. And another, and still another, and here again. Now that we’ve added that final piece, we have eight pieces to make one whole.
We represent this whole piece by saying it’s eight over eight. But what if we only wanted to look at this part of the circle? We would say that this part of the circle is three-eighths. In other words, if we add one-eighth plus one-eighth plus one-eighth, we get three-eighths.
Here’s another example. This pizza is cut into eight slices. The whole pizza can be represented by a fraction of eight over eight. But what if you ate one of those slices? We no longer have a whole pizza, but we have seven slices, seven-eighths of pizza. Another way to represent that is by saying eight-eighths minus one- eighth equals seven-eighths.
I want you to look carefully at the denominator in this problem. Notice that the denominator doesn’t change. Well at no point in our pizza problem did we change the number of slices the pizza was cut into. Because we are working with the same whole number, that does not change. When adding or subtracting fractions with the same denominator, the denominator doesn’t change.
Let’s break down the fraction two-thirds into its equal parts. two-thirds equals one-third plus one-third, very simply. Let’s do the same thing for five-eighths. five-eighths is made up of five one-eighth pieces, so one-eighth plus one-eighth plus one-eighth plus one-eighth plus one-eighth equals five-eighths.
What do you think would happen if you saw something like this, five- eighths minus one-eighth? Well, we should remember that when adding and subtracting fractions with the same denominator, the denominator doesn’t change. This means that whatever the answer is, it’s going to have a denominator of eight. But remember that five-eighths is made up of five one-eighth pieces, and now we just need to take one of those one-eighth pieces away.
After we take that one-eighth away, how many one eighth pieces would we be left with? Four-eighths. So here we’re taking two one-eighth pieces away from five one-eighth pieces. The denominator doesn’t change, and we subtract two from five. So there’s three-eighths remaining.
Here’s another example, we wanna add one-fifth and two-fifths. Our denominator doesn’t change, and we add the one and the two together for three-fifths. Let’s look at one of the ways we might use these type of problems in the real world.
You are baking some cookies. The recipe calls for three-eighths cup of flour you can only find a one-eighth cup- measuring cup. What could you do? Write an equation to show what you did. You would start out by adding one-eighth cup plus another one-eighth cup plus one more one-eighth cup for a total of three-eighths of a cup.
But don’t forget, the question asked us to write an equation. Here’s what your equation might look like: one-eighth plus one-eighth plus one-eighth equals three-eighths. Now you’re on your way to making great cookies and adding and subtracting fractions.