# Question #bf504

Oct 12, 2016

$4 \frac{7}{11} \div \frac{1}{11} = 51$

#### Explanation:

$4 \frac{7}{11} \div \frac{1}{11} = \left(4 + \frac{7}{11}\right) \div \frac{1}{11}$

$= \left(\frac{44}{11} + \frac{7}{11}\right) \div \frac{1}{11}$

$= \left(\frac{51}{11}\right) \div \frac{1}{11}$

$= \frac{\frac{51}{11}}{\frac{1}{11}}$

$= \frac{\frac{51}{11}}{\frac{1}{11}} \cdot \frac{11}{11}$

$= \frac{\frac{51}{11} \cdot 11}{\frac{1}{11} \cdot 11}$

$= \frac{51}{1}$

$= 51$

A common trick when dividing by a fraction is to take its reciprocal and then multiply, i.e.

$x \div \frac{a}{b} = x \cdot \frac{b}{a}$

The process used above shows why this works:

$x \div \frac{a}{b} = \frac{x}{\frac{a}{b}} = \frac{x \cdot \frac{b}{a}}{\frac{a}{b} \cdot \frac{b}{a}} = \frac{x \cdot \frac{b}{a}}{1} = x \cdot \frac{b}{a}$