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associative and distributivity property with example
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associative and distributivity property with example Related: Propert...
Associative Property:
Take any three rational numbers a, b and c. Firstly add a and b and then add c to the sum. (a + b) + c. Now again add b and c and then a to the sum, a + (b + c). Is (a + b) + c and a + (b + c) same? Yes and this is how associative property works. It states that you can add or multiply numbers regardless of how they are grouped.

For example, given numbers are 5, -6 and 23
( 5 – 6 ) + 23
= -1 + 23
= – 13
Now, 5 + ( -6 + 23 )
=  – 13
In both the groups the sum is the same.
Addition and multiplication are associative for rational numbers.
Subtraction and division are not associative for rational numbers.

Distributive Property:
Distributive property states that for any three numbers x, y and z we have

  x x ( y + z ) = (x x y) +( x x z)
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associative and distributivity property with example Related: Propert...
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.
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associative and distributivity property with example Related: Properties of Rational Numbers - 1, Maths, Class 8,?
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