# i am getting little bit confuse in Associative propertyand Distributive property. please explain it

Associative Property of Numbers

The associative property of addition tells us that we can group numbers in a sum in any way we want and still get the same answer.
If 'a', 'b' & 'c' are three numbers, then (a + b) + c = a + (b + c)

For example, let us consider three numbers 5, 10 and 15.

Now, (a + b) + c = (5 + 10) + 15 = 15 + 15 = 30

and a + (b + c) = 5 + (10 + 15) = 5 + 25 = 30

Hence,  (a + b) + c = a + (b + c)

The associative property of multiplication tells us that we can group numbers in a product in any way we want and still get the same answer.

If 'a', 'b' & 'c' are three rational numbers, then (a × b) × c = a × (b × c)

You can also verify this property by considering any numerical value of a, b and c.

Distributive Property:

Distributive property for multiplication over addition

a × (b + c) = a × b + a × c

a × (b + c) means that first of all we need to add b and c, then this result is multiplied with a.

Multiply a with b and a with c. The sum of the products, a × b + a × c is same as the a × (b + c).

Consider a, b, c equals to 2, 4 and 6 respectively.

Now, a × (b + c) =  2 × (4 + 6) = 2 × 10 = 20

and a × b + a × c = 2 × 4 + 2 × 6 = 8 + 12 = 20

Hence, a × (b + c) = a × b + a × c
Distributive property for multiplication over subtraction
a × (b  c) = a × b  a × c

a × (b  c) means that first of all we need to subtract c from b, then this result is multiplied with a.

Multiply a with b and a with c. The difference of the products, a × b  a × c is same as the a × (b  c).

You can also verify this property by considering any numerical value of a, b and c.

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