## 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.

### EXAMPLE 4.53

#### Solution

 $\frac{3}{5}+\frac{1}{5}$ Add the numerators and place the sum over the common denominator. $\frac{3+1}{5}$ Simplify. $\frac{4}{5}$

### EXAMPLE 4.54

#### Solution

 $\frac{x}{3}+\frac{2}{3}$ Add the numerators and place the sum over the common denominator. $\frac{x+2}{3}$

Note that we cannot simplify this fraction any more. Since $x$ and $2$ are not like terms, we cannot combine them.

### EXAMPLE 4.55

#### Solution

We will begin by rewriting the first fraction with the negative sign in the numerator.

$-\frac{a}{b}=\frac{-a}{b}$

 $-\frac{9}{d}+\frac{3}{d}$ Rewrite the first fraction with the negative in the numerator. $\frac{-9}{d}+\frac{3}{d}$ Add the numerators and place the sum over the common denominator. $\frac{-9+3}{d}$ Simplify the numerator. $\frac{-6}{d}$ Rewrite with negative sign in front of the fraction. $-\frac{6}{d}$

#### Solution

 $\frac{2 n}{11}+\frac{5 n}{11}$ Add the numerators and place the sum over the common denominator. $\frac{2 n+5 n}{11}$ Combine like terms. $\frac{7 n}{11}$

#### Solution

 $-\frac{3}{12}+\left(-\frac{5}{12}\right)$ Add the numerators and place the sum over the common denominator. $\frac{-3+(-5)}{12}$ Add. $\frac{-8}{12}$ Simplify the fraction. $-\frac{2}{3}$

#### EXAMPLE 4.59

Solution

 $\frac{23}{24}-\frac{14}{24}$ Subtract the numerators and place the difference over the common denominator. $\frac{23-14}{24}$ Simplify the numerator. $\frac{9}{24}$ Simplify the fraction by removing common factors. $\frac{3}{8}$

#### Example 4.60Solution

 $\frac{y}{6}-\frac{1}{6}$ Subtract the numerators and place the difference over the common denominator. $\frac{y-1}{6}$

The fraction is simplified because we cannot combine the terms in the numerator.

#### Solution

Remember, the fraction $-\frac{10}{x}$ can be written as $\frac{-10}{x}$.

 $-\frac{10}{x}-\frac{4}{x}$ Subtract the numerators. $\frac{-10-4}{x}$ Simplify. $\frac{-14}{x}$ Rewrite with the negative sign in front of the fraction. $-\frac{14}{x}$

#### Solution

 $\frac{3}{8}+\left(-\frac{5}{8}\right)-\frac{1}{8}$ Combine the numerators over the common denominator. $\frac{3+(-5)-1}{8}$ Simplify the numerator, working left to right. $\frac{-2-1}{8}$ Subtract the terms in the numerator. $\frac{-3}{8}$ Rewrite with the negative sign in front of the fraction. $-\frac{3}{8}$