Arithmetic properties

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Here are a list of arithmetic properties.


In mathematics, there are five properties that involve addition.

  • Commutative Property of Addition

When two numbers are added, the result will be the same regardless of the order. For example: $1+2=2+1$

  • Associative Property of Addition

When a quantity of numbers greater than three are added together, the result will be the same no matter which order the numbers were added in. For example: $5+(9+2)=(5+9)+2$

  • Identity Property of Addition

The sum of any number(positive or negative, fraction, decimal, etc) and zero will equal that number. Of course, $0+0=0$. Other examples include: $5+0=5$ and $1214214+0=1214214$.

  • Additive Inverse Property

Very simple, $x+y=0$, $x=-y$ or vice versa. A number plus another number equals zero.

  • Distributive Property

Note that this is the only property in which both addition and multiplication are used. When the sum of two numbers is multiplied by a third number, the product is equal to each addend multiplied by the same third number. For example: $7(8+9)=7*8+7*9$.


There are four properties that involve multiplication, plus the distributive property which also involves addition.

  • Commutative Property of Multiplication

When two numbers are multiplication, the product will be the same regardless of the order they were multiplied in. For example: $4*6=6*4$

  • Associative Property of Multiplication"'

Basically the same as the associative property of addition, except you are using multiplication instead. For example: $(8*2)*31=8*(2*31)$

  • Multiplicative Identity

The product of any number and one is the number. For example: $514*1=514$

  • Multiplicative Inverse

A number multiplied by another number equals one. For example: $1/5*5=1$

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