4.4 Add and subtract fractions with common denominators

Model fraction addition

How many quarters are pictured? One quarter plus $2$ quarters equals $3$ quarters.

Remember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that

Let’s use fraction circles to model the same example, $\frac{1}{4}+\frac{2}{4}.$

Start with one $\frac{1}{4}$ piece.
Add two more $\frac{1}{4}$ pieces.
The result is $\frac{3}{4}$ .

So again, we see that

Use a model to find the sum $\frac{3}{8}+\frac{2}{8}.$

Solution

Start with three $\frac{1}{8}$ pieces.
Add two $\frac{1}{8}$ pieces.
How many $\frac{1}{8}$ pieces are there?

There are five $\frac{1}{8}$ pieces, or five-eighths. The model shows that $\frac{3}{8}+\frac{2}{8}=\frac{5}{8}.$

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Add fractions with a common denominator

[link] shows that to add the same-size pieces—meaning that the fractions have the same denominator —we just add the number of pieces.

Model fraction subtraction

Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into $12$ slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or $\frac{7}{12}$ of the pizza) left in the box. If Leonardo eats $2$ of these remaining pieces (or $\frac{2}{12}$ of the pizza), how much is left? There would be $5$ pieces left (or $\frac{5}{12}$ of the pizza).