Chapter 2: Algebraic Properties

This is a review of basic algebraic properties in Pre-Algebra and A1

Commutative Property of Addition

The algebraic property, which states that when we add two or more numbers, the order of the addition does not matter.

a + b = b + a 

Commutative Property of Multiplication

The algebraic property that states that for any two numbers, a and b, their order of multiplication does not matter.

a × b = b × a

Associative Property of Addition

The property which states that for any case of addition with three numbers, a, b, and c, the order of grouping does not matter.

a + (b+c) = b + (a+c)

↓

3 + (2+5) = 2 + (3+5)

Associative Property of Multiplication

The property which states that for any three digits, when multiplied, the group does not matter. 

a * (b*c) = b * (a*c)

The Distributive Property of Multiplication over Addiction

The property which states that when we multiply a group of numbers by a number, that is equivalent to if we were to multiply and then add.

a(b+c)=a*b+a*c

Suppose we had

3(5+2)

According to the Distributive Property, 3(7) is the same as 15 + 6

Distributive Property Over Subtraction 

The property which states that it is equivalent to multiply the outside number to the sum of the parenthesis.

Example: 

3(5-2) = 15-10