# Using All 4 Aritmetic Operations on the Same Number

## X + X - X × X ÷ X = X; X ≠ 0

## If you use all 4 aritmetic operations on the same number, you get back to the same number!

This is true for all numbers except **zero(0)** since division by zero is undefined.

According to the "**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally" Rule, the multiplication is done first, but even if you do the addition first,...

- 5 + 5 = 10
- 10 - 5 = 5
- 5 × 5 = 25
- 25 ÷ 5 = 5

[You're back to the number you started with!]

**Exponentiation** is not an aritmetic operation; numbers in exponentiation problems have a "triangular" relationship. To get back to the number you started with in exponentiation, you have 2 options to choose from: **radicals & logarithms.** Plus, exponentiation is NOT commutative!

__In other words,__

## X^{Y} is not always equal to Y^{X}.

Back to Index Page Back to Math Trick Menu

© Derek Cumberbatch