You have a calculator whose multiplication button is broken. The only operations that work are addition (x+y), subtraction (x-y), and reciprocation (1/x).

Can you use this calculator to multiply two numbers?

Start with (1/x)+(1/y)

(1/x)+(1/y)

=(y/xy)+(x/xy) //find lowest common denominator

=(y+x)/(xy)     //simplification

=(x+y)/(xy)     //commutative property of addition

Multiply by 1/(x+y)

[(x+y)/(xy)] * [1/(x+y)]

Cross-cancel the instances of (x+y), yielding:

1/(xy)

do another reciporication (sp?) and you're done.

Posted by microRFFR on 2005-01-20 23:27:26