Question

Question #6ccf9

Answer 1

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

Explanation:

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

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

`2-:1/2=2*2/1 = 4`

If both are fractions, we do the same thing:

`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` equal to the quotient that we want to calculate:

`x=a/b-:c/d = (a/b)/(c/d)`

now mulitply both sides by `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`