When dividing two fractions why do you multiply the dividend by the reciprical of the division?

Question

Form your answer in a paragraph please.

Answer 1

I quote my own answer to a previous poster:

"We wish to discover what happens when you divide some number n by a fraction p/q. Set the result equal to x. Then:

x=n/(p/q)

Multiply both sides by p/q:

x*p/q = n

Multiply both sides by q:

x*p = n*q

Divide both sides by p:

x = n*q/p

But x=n/(p/q). Therefore n/(p/q) = n*(q/p) and we see that dividing by a fraction is the same as multiplying by the reciprocal of that fraction. Q.E.D. "

Answer 2

I've had to learn the hard way that somethings in math just don't....add up to say the least. Like, they make no sense whatsoever. U just have to do it n not think about it (as crazi as that sounds)

but i can tell u that the reason y u multiply the dividend by the reciprocal of the division is bcuz dividing fractions can be as easy as multiplying fractions, if we invert and multiply. If we multiply a fraction by its reciprocal, the result equals one. Because some fractions end up equalling one, when we multiply by 1, we don't change the values in the problem.

Answer 3

division is nothing but multiplication by the reciprocal
suppose you are dividing (a/b) by (c/d)
then by the above rule you must multiply (a/b) by the reciprocal of (c/d)
reciprocal of (c/d) is (d/c)
so (a/b) divided by (c/d)=(a/b)*(d/c)

Answer 4

Should I form my answer in a paragraph?

Answer 5

Because, it works. And the rest is meaningless.