Adding and Subtracting Like Fractions
Lets first discuss how to add and subtract like fractions. Suppose that we want to add and . A diagram can help us understand what is involved. First we shade one-fifth of the diagram, then another three-fifths.
We see in the diagram that the total shaded area is four-fifths, so . Note that we added the original numerators to get the numerator of the answer but that the denominator stayed the same.
The diagram shows how to subtract like fractions by computing . If we shade four-fifths of the diagram and then remove the shading in one-fifth, three-fifths remain shaded. Therefore . Note that we could have gotten this answer simply by subtracting numerators without changing the denominator.
The following rule summarizes how to add or subtract fractions, provided that they have the same denominator.
To Add (or Subtract) Like Fractions
Applying the rule, we get
Be careful not to add the denominators when adding like fractions.
So the sum of .
Find the difference between .
In the following diagram, how far is it from the college to the library via city hall?
Examining the diagram, we see that
To find the distance from the college to the library via city hall, we add.
The distance is 1 mile.
According to one study, of the people who exercise regularly live at least to age 70, in contrast to only of the people who do not exercise regularly. What is the difference between these two fractions?
Subtracting, we get . Therefore the difference between these fractions is . We can check our answer by adding to to get .