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# Adding really simple fractions

### #1

Posted 02 May 2014 - 11:34 AM

Johnny was asked to write the sum of the two fractions * p*/

*and*

**n***/*

**q***where*

**n***,*

**p***and*

**q***are single-digit numbers.*

**n**He remembered that the numerators were to be added, but he thought maybe the denominators should be added as well.

Also, he decided that putting digits next to each other could suggest addition.

So his first try was to say that

* p*/

*+*

**n***/*

**q***=*

**n**

**p***/*

**q***. (where*

**n****n**

**p***and*

**q***are two-digit numbers.)*

**n****n**

Then he remembered the result should not depend on the order of addition,

but he saw that * p*/

*+*

**n***/*

**q***=*

**n**

**q***/*

**p***was just as bad. So he decided to use them both.*

**n****n**His final representation of the sum was

* p*/

*+*

**n***/*

**q***= (*

**n**

**p***+*

**q**

**q***)/*

**p***.*

**n****n**

The puzzle asks: Let * p*,

*and*

**q***be chosen at random from {1, 2, 3, 4, 5, 6, 7, 8, 9}.*

**n**What is the expected error in Johnny's formula?

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #2

Posted 02 May 2014 - 04:44 PM Best Answer

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