without changing the sum; a + b = b + a commutative property of addition The property of addition that allows two or more addends to be added in any order without changing the sum; a + b = b + a Examples: c + 4 = 4 + c (2 + 5) + 4r = 4r + (2 + 5)

Commutative Property of Multiplication The Product of two numbers is the same regardless of the order in which they are multiplied. Examples A · B = B · A -3 · 2 = 2 · -3

The property which states that for all real numbers Associative Property of Addition The property which states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping: (a + b) + c = a + (b + c) Example: (2 + 3) + 4 = 2 + (3 + 4)

Associative Property of Multiplication The Product of three or more numbers is the same regardless of the way in which they are grouped. Examples (A · B) · C = A · (B · C) (4 · 2) · -3 = 4 · (2 · -3)

Identity property of addition The property which states that the sum of zero and any number or variable is the number or variable itself. For example, 4 + 0 = 4, - 11 + 0 = - 11, y + 0 = y

The product of any number and 1 is the number. Identity Property of Multiplication The product of any number and 1 is the number. Examples A · 1 = A -382 · 1= -382

The product of any fraction and it’s reciprocal is 1. Inverse (Reciprocal) The product of any fraction and it’s reciprocal is 1. Examples 𝟕 𝟖 · 𝟖 𝟕 = 1 𝟔 𝟏 · 𝟏 𝟔 = 1

distributive Property Examples 𝟐 𝟑+𝟓 =(𝟐·𝟑)+(𝟐·𝟓) 𝟐 𝟑 ( 𝟏 𝟐 + 𝟑 𝟕 ) = ( 𝟐 𝟑 · 𝟏 𝟐 ) + ( 𝟐 𝟑 · 𝟑 𝟕 )