## Add and Subtract Fractions with Common Denominators

Read this text. Pay special attention to the sections on fraction addition and subtraction. They provide an overview of how to add and subtract fractions with the same denominator. Complete the practice questions and check your answers.

### Add and Subtract Fractions with Common Denominators

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

$\begin{array}{ccc} \dfrac{1}{4} & \dfrac{2}{4} & \dfrac{3}{4} \\ \text { one quarter +} & \text { two quarters =} & \text { three quarters } \end{array}$

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

 Start with one $\dfrac{1}{4}$ piece. $\dfrac{1}{4}$ Add two more $\dfrac{1}{4}$ pieces. \begin{align}+\dfrac{2}{4} \\\text{___}\end{align} The result is $\dfrac{3}{4}$. $\dfrac{3}{4}$

So again, we see that

$\dfrac{1}{4}+\dfrac{2}{4}=\dfrac{3}{4}$

#### Add Fractions with a Common Denominator

Example 4.52 shows that to add the same-size pieces - meaning that the fractions have the same denominator - we just add the number of pieces.

If $a$, $b$, and $c$ are numbers where $c≠0$, then

$\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

To add fractions with a common denominators, add the numerators and place the sum over the common denominator.

#### 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 $\dfrac{7}{12}$ of the pizza) left in the box. If Leonardo eats 2 of these remaining pieces (or $\dfrac{2}{12}$ of the pizza), how much is left? There would be 5 pieces left (or $\dfrac{5}{12}$ of the pizza).

$\dfrac{7}{12}-\dfrac{2}{12}=\dfrac{5}{12}$

Let's use fraction circles to model the same example, $\dfrac{7}{12}-\dfrac{2}{12}$.

Start with seven $\dfrac{1}{12}$ pieces. Take away two $\dfrac{1}{12}$ pieces. How many twelfths are left?

Again, we have five twelfths, $\dfrac{5}{12}$.

#### Subtract Fractions with a Common Denominator

We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.

#### FRACTION SUBTRACTION

If $a, b$, and $c$ are numbers where $c \neq 0$, then

$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$

To subtract fractions with common denominators, we subtract the numerators and place the difference over the common denominator.