Associative Property:
The associative property states that the way in which numbers are grouped in an operation does not affect the result. This property holds true for addition and multiplication.
For addition:
(a + b) + c = a + (b + c)
For multiplication:
(a * b) * c = a * (b * c)
Example:
Let's consider the numbers 2, 3, and 4.
Using the associative property for addition:
(2 + 3) + 4 = 5 + 4 = 9
2 + (3 + 4) = 2 + 7 = 9
Using the associative property for multiplication:
(2 * 3) * 4 = 6 * 4 = 24
2 * (3 * 4) = 2 * 12 = 24

Distributive Property:
The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products. This property holds true for both addition and multiplication.
For addition over multiplication:
a * (b + c) = (a * b) + (a * c)
Example:
Let's consider the numbers 2, 3, and 4.
Using the distributive property:
2 * (3 + 4) = 2 * 7 = 14
(2 * 3) + (2 * 4) = 6 + 8 = 14
In conclusion, the associative and distributive properties are important in mathematics as they allow us to manipulate numbers without changing the final result. These properties are fundamental in various mathematical operations and are widely used in algebra and arithmetic.