Properties of Addition and Multiplication

Closure Addition

A + B is a real number. - Real + Real = Real

Closure Multiplication

AB is a real number. Real x Real = Real

Commutative Addition

A + B = B + A (they switch spots)

Commutative Multiplication

AB = BA (they switch spots)

Associative Addition

(A + B) + C = A + (B + C) (when you multiply terms, the group changes - just like how friends change)

Associative Multiplication

(AB)C = A(BC) (when you multiply terms, the group changes - just like how friends change)

Identity Addition

A + 0 = A, 0 = A = A (what you do to a number to help keep/get the identical number in return)

Identity Multiplication

A x 1 = A, 1 x A = A (what you do to a number to help keep/get the identical number in return)

Inverse Addition

A + (-A) = 0 (what you do to get rid of with is what you started with)

Inverse Multiplication

A x 1/A = 1, A does not = 0 (what you do to get rid of with is what you started with)

Distributive Addition/Multiplication

A(B + C) = AB + AC

Rational numbers

Numbers that do have an ending to them, can be fractions or decimals (ratio) when the numbers aren’t whole numbers. (EX. square root of 4 or 3/4)

Irrational numbers

Numbers that never have an ending or repeat in decimal form when it’s not written in a fraction. (EX. PI or 1/3)

Integers

Can ONLY be WHOLE numbers; no fractions or decimals (EX. 1 or -4)

Natural numbers

Numbers that you naturally learn when counting on you fingers (digits 0-10).