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

Question

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

Ankush Jain · Accepted Answer

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
Ã— b) Ã— c = a Ã— (b
Ã— 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
aÃ— (b+ c) =
aÃ— b+ aÃ—
c

aÃ— (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, aÃ—
b+ aÃ— c is same as the
aÃ— (b+ c)
Consider a, b, c equals to 2, 4 and 6 respectively
Now, aÃ— (b+ c) =
2Ã— (4+ 6) = 2 Ã—
10 = 20
and aÃ— b+
aÃ— c = 2Ã— 4+
2Ã— 6 = 8 + 12 = 20

Hence, aÃ— (b+ c) =
aÃ— b+ aÃ—
c

Distributive property for multiplication over
subtraction

aÃ— (bâ€“
c) = aÃ—
bâ€“ aÃ—
c

aÃ— (bâ€“
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,
aÃ— bâ€“
aÃ— c is same as the
aÃ— (bâ€“
c)
You can also verify this property by considering any numerical
value of a, b and c