Operations with Common Fractions

\begin{align} \frac{a}{c}+\frac{b}{c} &= \frac{a+b}{c} \\ \\ \frac{a}{c}+\frac{b}{d} &= \frac{ad+cb}{cd} \\ \\ \frac{a}{c}-\frac{b}{c} &= \frac{a-b}{c} \\ \\ \frac{a}{c}-\frac{b}{d} &= \frac{ad-cb}{cd} \\ \\ \frac{a}{c}\times b &= \frac{ab}{c} \\ \\ a\times \frac{b}{c} &= \frac{ab}{c} \\ \\ \frac{a}{c}\times \frac{b}{d} &= \frac{ab}{cd} \\ \\ \frac{a}{c}\div \frac{b}{d} &= \frac{ad}{bc} \\ \\ \frac{a}{c}\div b &= \frac{a}{bc} \\ \\ a\div \frac{b}{c} &= \frac{ac}{b} \\ \end{align}

\begin{align} \textrm{If}\; k &\neq 0, \textrm{then} \\ \\ \frac{a}{b} &= \frac{ka}{kb} \\ \end{align}

\begin{align} \textrm{If}\; k &\neq 0, \textrm{then} \\ \\ \frac{ka}{kb} &= \frac{ka\div k}{kb\div k}= \frac{a}{b} \\ \end{align}