# Algebraic Properties

Commutative Property of Multiplication

Changing the order of the factors will not change the product.

Identity Property of Multiplication

1 multiplied to any given number will equal the given number.

Commutative Property of Multiplication

Changing the order of the factors will not change the product.

Associative Property of Multiplication

Changing the grouping of the factors will not change the product.

Subtraction undoes the operation called addition.

Inverse Property of Multiplication

Multiplying by the reciprocal undoes the operation called multiplication.

Multiplicative Property of Zero

The product of any number and 0 is 0.

Changing the order of the numbers will not change the sum.

Changing the grouping of the terms will not change the sum.

Zero added to any given number will equal the given number.

Distributive Property

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

Subtraction undoes the operation called addition.

Inverse Property of Multiplication

Division undoes the operation called multiplication.

Distributive Property

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

Combining Like Terms

Add like terms together to make one term.

Subtraction undoes the operation called addition.

Inverse Property of Multiplication

Division undoes the operation called multiplication.

Reflexive Property of Equality

0

Subtraction Property of Equality

States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.

Symmetric Property of Equality

If a = b, then b = a. This allows for rewriting an equation with the variable on the left, if desired.

If a = b, then a + c = b + c. This allows for adding the same number to both sides of an equation.

Multiplication Property of Equality

If a = b, then a × c = b × c. This allows for multiplying both sides of an equation by the same number

Division Property of Equality

If a = b and c ≠ 0, then a ÷ c = b ÷ c. This allows for dividing both sides of an equation by the same non-zero number.

Substitution Property of Equality

This property allows you to substitute quantities for each other into an expression as long as those quantities are equal.