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?
Let us assume that we want to multiply two numbers x and y.
That means we need the value of xy ( x multiplied by y).
We already had operations for finding reciprocal (1/x or 1/y) , Addition x+y and subtraction x-y etc, but not mulitiplication button on the calculator.
Here are the steps I perform for calculation of xy.
First I will evaluate 1/x and keep the value in memory.
Then I will calculate (1/x)+y which is equal to (1+xy)/x.
Then I will divide this value with the value in memory that is 1/x which gives me 1+xy on display.
Now as I had a workable substraction button on my calculator I will substract 1(one) from the value on display(1+xy) which gives me the value of xy.
That is the required answer to this problem as I got xy without using mulitiplication button but using division,addition and substraction.
Solution to this problem.
