Question #6ccf9

1 Answer
Mar 11, 2016

Answer:

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

Explanation:

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

http://math.tutorvista.com/number-system/dividend.html

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#