Algebra 1 Properties (OST Lesson 1)

Addition Property of Equality

If you add something to one side of an equation, you must add the same thing to the other side.

Division Property of Equality

If you divide one side of an equation by something, you must divide the other side by the same thing.

Multiplication Property of Equality

If you multiply one side of an equation by something, you must multiply the other side by the same thing.

Subtraction Property of Equality

If you subtract something from one side of an equation, you must subtract the same thing from the other side.

Commutative Property of Addition

The order in which you add two numbers does not change the sum. Ex: a+b=b+a

Commutative Property of Multiplication

The order in which you multiply two numbers does not change the product. Ex: ab=ba

Identity Property of Multiplication

The product of a number and 1 is the number. Ex: a×1=a

Inverse Property of Multiplication

The product of a number and its reciprocal is 1. Ex: n×(¹/ₙ)= 1

Multiplication Property of Zero

The product of any number and zero is zero

Identity Property of Addition

The sum of a number and 0 is the number. Ex: a+0=a

Inverse Property of Addition

The sum of a number and its opposite is 0. ex: a+(-a)= 0

Associative Property of Multiplication

The way you group three numbers in a product does not change the product. Ex: (ab)c=a(bc)

Associative Property of Addition

The way you group three numbers in a sum does not change the sum. Ex: (a+b)+c=a+(b+c)

Distributive Property

a(b+c)=ab+ac and a(b−c)=ab−ac

Property of -1

the product of a number and -1 is the opposite of the number