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closure properties

a+b and ab are unique real numbers

commutative properties

The properties that state the order of the addends or factors does not affect the sum of the products. (switch the order of the numbers)

Associative properties

more than numbers can be added or multiplied in groups of two ; the way the numbers are grouped does not matter, (a+b)+c=a+(b+c) (CHANGING THE PARENTHESIS DOES NOT MATTER)

Identity Properties

adding 0 to a number does not change the number; multiplying a number by 1 does not change the number

property of opposites

a+(-a)=0 #+(-#)=0

property of reciprocals

a*1/a=1

distributive property

a(b+c)=ab+ac

reflexive property

a=a

symetric property

if a=b then b=a

transitive property

If a=b and b=c, then a=c

addition property

if a=b, then a+c=b+c

multiplication property

if a=b, then ac=bc

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