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properties of fractions

a

$a$ ,

b

$b$ ,

c

$c$ ,

d

$d$ , and

k

$k$ are real numbers, and if there is nothing being divided by

0

$0$ , then the following properties of fractions apply:

\frac{a}{b} = \frac{c}{d}

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

a d = b c

$a d = b c$

\frac{a}{1} = a

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

\frac{a}{a} = 1

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

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

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

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

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

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

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