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properties of fractions

If $a$ , $b$ , $c$ , $d$ , and $k$ are real numbers, and if there is nothing being divided by $0$ , then the following properties of fractions apply:

$\frac{a}{b} = \frac{c}{d}$ if and only if $a d = b c$

$\frac{a}{1} = a$ and $\frac{a}{a} = 1$

$\frac{a k}{b k} = \frac{a}{b} \cdot \frac{k}{k} = \frac{a}{b}$

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

$\frac{a}{b} = \frac{a \cdot k}{b \cdot k}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$