Properties of Multiplication:
- **Commutative Property**: Changing the order of the numbers being multiplied does not change the product. For example, 3 x 4 = 4 x 3.
- **Associative Property**: Changing the grouping of the numbers being multiplied does not change the product. For example, (2 x 3) x 4 = 2 x (3 x 4).
- **Identity Property**: Multiplying a number by 1 gives the number itself. For example, 5 x 1 = 5.
- **Zero Property**: Multiplying any number by 0 gives 0. For example, 7 x 0 = 0.

Properties of Addition:
- **Commutative Property**: Changing the order of the numbers being added does not change the sum. For example, 2 + 3 = 3 + 2.
- **Associative Property**: Changing the grouping of the numbers being added does not change the sum. For example, (1 + 2) + 3 = 1 + (2 + 3).
- **Identity Property**: Adding zero to any number gives the number itself. For example, 6 + 0 = 6.

Properties of Subtraction:
- **Subtraction is not commutative**: Changing the order of the numbers being subtracted changes the result. For example, 5 - 3 is not equal to 3 - 5.
- **Subtraction is not associative**: Changing the grouping of the numbers being subtracted changes the result. For example, (8 - 4) - 2 is not equal to 8 - (4 - 2).

Properties of Division:
- **Division is not commutative**: Changing the order of the numbers being divided changes the result. For example, 8 ÷ 2 is not equal to 2 ÷ 8.
- **Division is not associative**: Changing the grouping of the numbers being divided changes the result. For example, (10 ÷ 2) ÷ 1 is not equal to 10 ÷ (2 ÷ 1).
- **Division by zero is undefined**: Dividing any number by zero is undefined and not possible in mathematics.