Basic Technical Mathematics, 11th Edition

6.6 Addition and Subtraction of Fractions

• Lowest Common Denominator • Addition and Subtraction of Fractions • Complex Fractions

From arithmetic, recall that the sum (or difference) of a set of fractions that all have the same denominator is the sum (or difference) of the numerators divided by the common denominator.

Addition and Subtraction of Fractions

$$\begin{array}{l}{\displaystyle \frac{a}{c}}\hspace{0.17em}+\hspace{0.17em}{\displaystyle \frac{b}{c}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{a\hspace{0.17em}+\hspace{0.17em}b}{c}}\\ {\displaystyle \frac{a}{c}}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{b}{c}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{a\hspace{0.17em}-\hspace{0.17em}b}{c}}\end{array}$$

Because algebraic expressions represent numbers, this fact is also true in algebra. Addition and subtraction of such fractions are illustrated in the following example.

EXAMPLE 1 Combining basic fractions

1. $\begin{array}{rlll}{\displaystyle \frac{5}{9}}\hspace{0.17em}+\hspace{0.17em}{\displaystyle \frac{2}{9}}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{4}{9}}& \hspace{0.17em}=\hspace{0.17em}& {\displaystyle \frac{5\hspace{0.17em}+\hspace{0.17em}2\hspace{0.17em}-\hspace{0.17em}4}{9}}& \begin{array}{l}\leftarrow \hspace{0.17em}\text{sum of numerators}\\ \leftarrow \hspace{0.17em}\text{same denominators}\end{array}\\ \hspace{0.17em}=\hspace{0.17em}& {\displaystyle \frac{3}{9}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{3}}& \leftarrow \hspace{0.17em}\text{final result in lowest terms}\end{array}$

2. .6-4 Full Alternative Text

CAUTION

When ...