What is the difference between asosiated and distributive properties.
What is the difference between asosiated and distributive properties.
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 subtractiona × (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.
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 subtractiona × (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.
