Today let’s take a look at adding
fractions with common denominators. But first, let’s look at this
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
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
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.