# Multiply, add, divide, subtract … the answer’s always 1! Why?

A STAFF REPORT FROM THE STRAIGHT DOPE SCIENCE ADVISORY BOARD

Dear Straight Dope:

Why can you take a number, multiply it by itself, add your original number to the answer, divide the original number into that answer and then subtract your original number into that answer and your answer will always be 1?

CKDextHavn and Ian reply:

Not if your number is 0, but otherwise piece o’ cake.. Take the steps out of order to see what’s going on. First, take your number and square it, per step one. Then, divide it by itself, per step 3, leaving you with your number. OK, step 2 adds the number back, but step 3 applies to this number separately from the first (per the distributive property), which means you’re actually only adding the number over itself, or 1. So, what you’ve got to this point is your number, plus 1. Then, of course, subtract your number out (per step 4), and all you’re left with is 1.

The algebraically inclined may prefer to do it this way. Suppose your number is A:

Then the first step is A x A

Second step is to add the number: A x A + A

Divide by your number: [( A x A) + A)] / A = A + 1

Subtract your number: A + 1 – A = 1, surprise … unless, as Ian notes, you start with zero … then the division step gives you a headache.

SDSTAFF Ian replies:

Oh, sure, CK, bring algebra into it. Mathist.

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