Question #bf504

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Question #bf504

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Answer 1 · 2016-10-12T22:09:04

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

Explanation:

$4 \frac{7}{11} \div \frac{1}{11} = (4 + \frac{7}{11}) \div \frac{1}{11}$ $4 7/11 -: 1/11 = (4+7/11)-:1/11$

$= (\frac{44}{11} + \frac{7}{11}) \div \frac{1}{11}$ $=(44/11+7/11)-:1/11$

$= (\frac{51}{11}) \div \frac{1}{11}$ $=(51/11)-:1/11$

$= \frac{\frac{51}{11}}{\frac{1}{11}}$ $=(51/11)/(1/11)$

$= \frac{\frac{51}{11}}{\frac{1}{11}} \cdot \frac{11}{11}$ $=(51/11)/(1/11)*11/11$

$= \frac{\frac{51}{11} \cdot 11}{\frac{1}{11} \cdot 11}$ $=(51/11*11)/(1/11*11)$

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

$= 51$ $=51$

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

$x \div \frac{a}{b} = x \cdot \frac{b}{a}$ $x-:a/b = x*b/a$

The process used above shows why this works:

$x \div \frac{a}{b} = \frac{x}{\frac{a}{b}} = \frac{x \cdot \frac{b}{a}}{\frac{a}{b} \cdot \frac{b}{a}} = \frac{x \cdot \frac{b}{a}}{1} = x \cdot \frac{b}{a}$ $x-:a/b = x/(a/b) = (x*b/a)/(a/b*b/a) = (x*b/a)/1=x*b/a$

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Question #bf504

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