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Math Properties are formulas that describe something true. It contains a math symbol (operation) and type of property. For example, the commutative property of multiplication is ${\displaystyle 1=a\times b=b\times a}$. They are very useful for understanding how operations work. They are used in problems so that way you don't have to solve the problem, but you just have to think of math properties. For example, you want to find if ${\displaystyle (a+b)+c=a+(b+c)}$. You don't need to plug in many values to find if they are equal, but you just need to remember these properties. Some operations' properties are equal and some are not.

All Properties

Properties	Addition	Subtraction	Multiplication	Division	Exponentiation
Associative	${\displaystyle (a+b)+c=a+(b+c)}$	${\displaystyle (a-b)-c\neq a-(b-c)}$	${\displaystyle (a\times b)c=a(b\times c)}$	${\displaystyle (a/b)\div c\neq a\div (b/c)}$	${\displaystyle (a^{b})^{c}\neq a}$^${\displaystyle (b^{c})}$
Commutative	${\displaystyle a+b=b+a}$	${\displaystyle a-b\neq b-a}$ but ${\displaystyle a-b=-b-a}$	${\displaystyle ab=ba}$	${\displaystyle a\div b\neq b\div a}$ but ${\displaystyle a/b=1\div (b/a)}$	${\displaystyle a^{b}\neq b^{a))$
Distributive	${\displaystyle x(a+b)=xa+xb}$	${\displaystyle x(a-b)=xa-xb}$	${\displaystyle x(ab)=(xa)(xb)}$	${\displaystyle x(a/b)\neq (xa)/(xb)}$	${\displaystyle x(a^{b})\neq (xa)}$^${\displaystyle (xb)}$
Identity	${\displaystyle a+0=a}$	${\displaystyle a-0=a}$	${\displaystyle a\times 1=a}$	${\displaystyle a\div 1=a}$	${\displaystyle a^{1}=a}$
Zero	${\displaystyle a+0=a}$	${\displaystyle a-0=a}$	${\displaystyle a\times 0=0}$	${\displaystyle a\div 0=undefined}$	${\displaystyle a^{0}=1}$

Here are some extra properties that I discovered.

1. ${\displaystyle a}$^${\displaystyle (b+c)=a^{b}\times a^{c))$

And some extra properties that you learn in elementary school.

1. ${\displaystyle a/a=1}$ if ${\displaystyle a\neq 0}$
2. ${\displaystyle a/0=undefined}$

--GelatinPlayz (talk) 04:52, 7 September 2024 (UTC)