# 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.*

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

- $\begin{array}{rlll}{\displaystyle \frac{5}{9}}\hspace{0.17em}+\hspace{0.17em}{\displaystyle \frac{2}{9}}\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{4}{9}}& \hspace{0.17em}=\hspace{0.17em}& {\displaystyle \frac{5\hspace{0.17em}+\hspace{0.17em}2\hspace{0.17em}-\hspace{0.17em}4}{9}}& \begin{array}{l}{\leftarrow \hspace{0.17em}}{\text{sumofnumerators}}\\ {\leftarrow \hspace{0.17em}}{\text{samedenominators}}\end{array}\\ \hspace{0.17em}=\hspace{0.17em}& {\displaystyle \frac{3}{9}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{1}{3}}& {\leftarrow \hspace{0.17em}}{\text{finalresultinlowestterms}}\end{array}$

# CAUTION

When ...

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