'MU' button in a calculator. How to use.

This article is about calculators.

We will denote entered numbers by capital letters. It is clear that they might be fractional or negative.

For example, to add two numbers $A$ and $B$, we can enter
$$
A \ \fbox{+} \ B \ \fbox{=}.
$$
The result of calculation we will denote by $R$:
$$
R=A+B.
$$

What does the abbreviation 'MU' mean?

$MU$ means mark-up.

How to use 'MU' button? - operations

There are five operations with $\fbox{MU}$ button:

1. $$
   A \fbox{+}\ B\ \fbox{MU}.
   $$
   Result:
   $$
   R_1=\frac{A+B}{B}\cdot 100.
   $$
   A bit of explanation:
   $$
   A+B=B\frac{R_1}{100}.
   $$
   $R_1$ is the sum $A+B$ represented as a percentage of $B$.
2. $$
   A \fbox{-}\ B\ \fbox{MU}.
   $$
   Result:
   $$
   R_2=\frac{A-B}{B}\cdot 100.
   $$
   Explanation:
   $$
   A-B=B\frac{R_2}{100}.
   $$
   $R_2$ is the difference $A-B$ as a percentage of $B$.
3. $$
   A \fbox{×}\ B\ \fbox{MU}.
   $$
   Result:
   $$
   R_3=A\cdot \left(1+\frac{B}{100}\right).
   $$
   It's clear. It's equivalent to
   $$
   A\ \fbox{+} \ B\ \fbox{%}.
   $$
   We add $A$ and $B$ percent of $A$ together:
   $$
   R_3=A+A\cdot\frac{B}{100}.
   $$
4. $$
   A \fbox{÷}\ B\ \fbox{MU}.
   $$
   Result:
   $$
   R_4=\frac{A}{1-\frac{B}{100}}.
   $$
   We can rewrite the higher expression as
   $$
   R_4-A=R_4\cdot\frac{B}{100}.
   $$
   If $R_4$ is price (with markup), and $A$ is cost (without markup) then
   $(R_4-A)$ --- markup, and $B$ --- expression of markup $(R_4-A)$ as a percentage of sell price $R_4$.
5. $$
   A \fbox{÷}\ B\ \fbox{MU}\ \fbox{MU}.
   $$
   Result:
   $$
   R_5=\left| \frac{A}{1-\frac{B}{100}} - A \right|=\left| R_4 - A \right|.
   $$
   It's the module of markup, its absolute value. If the initial data of your task is so that markup might be negative, you should not rely on the function.