What exactly is a distributive property? And associative and commutative.

Question

Please explain too.

Answer 1

Distributive property under addition: a(b+c) =a b +ac

example:  2(3+4)= (2)(3)+(2)(4)

 (2)(7) = 6+8

14=14

14=14

Associative property under addition:(a+b)+c =a+(b+c)

example:(2+3)+4 =2+(3+4)

5+4=2+7

9=9

Commutative property under addition:a+b =b+a

example: 2+3 =3+2

5=5

 

Answer 2

Associative Property of Addition:
Associative property of addition states that it doesn't change the sum how you group numbers
i.e., (a + b) + c = a + (b + c)

Commutative Property:
Commutative property is one of the basic properties of numbers.
The word "commute" means "exchange" or "swap over"
.
Commutative property states that numbers can be added or multiplied in any order.
 

Commutative Property of Addition:
Commutative Property of Addition states that changing the order of addition does not change the sum. i.e., a + b = b + a.

Example:
4 + 6 = 6 + 4. Whether you add 4 to 6 or 6 to 4, sum is same and you get 10 both ways.

Commutative Property of Multiplication:
Commutative Property of Multiplication states that changing the order of factors does not change the product. i.e., a * b = b * a.

Examples:
2 * 5 = 5 * 2. Whether you multiply 2 by 5 or 5 by 2, the product is the same, i.e. 10.