Dividing fractions. Finding a number by its fraction

Dividing fractions:

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

— multiply by the reciprocal of the second fraction (where

c\neq 0

). Whole from a fractional part: if

\frac{m}{n}

x

equals

k

, then

\frac{m}{n}\cdot x = k

, so

x = k:\frac{m}{n}=k\cdot\frac{n}{m}

Division → multiply by the reciprocal

Cancel when possible before and after multiplying

“Find the whole from a part” is the same equation in

x

Dividing fractions: explained

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