Why Do We Use the Reciprocal in Fraction Division?

[Taylor_1989]

Could someone show me the proof to why we use the reciprocal in fractions division. I ask this because it seem we are taught the how in math but never the why. Algebra proof would be best thanks.

 

[Number Nine]

It's not a proof, it's a definition. Division is the inverse operation of multiplication, and so dividing by a fraction is the same as multiplying by the inverse of that fraction, which is its reciprocal.

 

[acabus]

My LaTeX always looks so ugly.

$$n = \frac{(\frac{a}{b})}{(\frac{c}{d})}$$
$$n\left(\frac{c}{d}\right) = \frac{a}{b}$$
$$nc = \frac{ad}{b}$$
$$n = \frac{ad}{bc} = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)$$

 

[Taylor_1989]

Thanks for the proof abacus, well appreciated makes things clearer for me.