# Fractions $\frac{Numerator}{Denominator} = Numerator ÷ Denominator$ ## Addition/Subtraction $\frac{a}{b} \pm \frac{c}{d} \Leftrightarrow \frac{ad}{bd} \pm \frac{cb}{bd} \Leftrightarrow \frac{ad \pm cb}{bd}$ ## Multiplication $\frac{a}{b} * \frac{c}{d} \Leftrightarrow \frac{ac}{bd}$ ## Division to Multiplication $\frac{\frac{a}{b}}{\frac{c}{d}} \Leftrightarrow \frac{a}{b} ÷ \frac{c}{d} \Leftrightarrow \frac{a}{b} * \frac{d}{c} \Leftrightarrow \frac{ad}{bc}$ $\frac{a}{\frac{1}{b}} \Leftrightarrow a ÷ \frac{1}{b} \Leftrightarrow ab$ $\frac{\frac{1}{a}}{b} \Leftrightarrow \frac{1}{a} ÷ b \Leftrightarrow \frac{1}{ab} \Leftrightarrow ab^{-1}$ $\frac{1}{\frac{a}{b}} \Leftrightarrow 1 * \frac{b}{a} \Leftrightarrow \frac{b}{a} \Leftrightarrow \frac{1}{a} * b \Leftrightarrow a^{-1}b$ $\frac{1}{\frac{1}{a}} \Leftrightarrow a$ $\frac{a}{b} = c \Leftrightarrow bc = a \Leftrightarrow \frac{a}{c} = b$ ## Exponential $(\frac{1}{a})^x \Leftrightarrow (a^{-1})^x \Leftrightarrow a^{-x} \Leftrightarrow \frac{1}{a^{x}}$