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Answer 1 · 2016-03-11T20:34:22

Dividing fractions is done by multiplying the reciprocal of the divisor.

First let's make sure we know which is the divisor:

![http://math.tutorvista.com/number-system/http://dividend.html](https://useruploads.socratic.org/DxH8fPm7RUCcdBK8iXi4_ddq.jpg)

When using fractions, we simply convert the division into a multiplication by taking the reciprocal of the divisor, for example:

$2 \div \frac{1}{2} = 2 \cdot \frac{2}{1} = 4$ $2-:1/2=2*2/1 = 4$

If both are fractions, we do the same thing:

$\frac{1}{2} \div \frac{1}{2} = \frac{1}{2} \cdot \frac{2}{1} = 1$ $1/2-:1/2=1/2*2/1=1$

which makes sense, since anything divided by itself is one!

PROOF:

to prove this, lets set $x$ $x$ equal to the quotient that we want to calculate:

$x = \frac{a}{b} \div \frac{c}{d} = \frac{\frac{a}{b}}{\frac{c}{d}}$ $x=a/b-:c/d = (a/b)/(c/d)$

now mulitply both sides by $\frac{c}{d}$ $c/d$

$c/d*x = (a/b)/color(red)cancel(color(black)(c/d))*color(red)cancel(color(black)(c/d))=a/b$

multiply both sides by $d/c$

$x=a/b*d/c$

therefore

$a/b-:c/d=a/b*d/c$