1. 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)

2. 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

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)

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)

5. 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, = - 11,
y + 0 = y

6. 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

7. 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

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