Introduction :
Algebra holds many laws. The followings are the basic algebraic laws. They are Associative law, distributive law and commutative law. In math associative property states that changes in group do not change the answer means the moving of brackets does not affect the answer. In math associative law consists of two types of operations. They are addition and multiplications.
Associative Property:
Associativeproperty:
In math associative property states that changes in group do not change the answer means the moving of brackets does not affect the answer. Associative law consists of two types of operations.
Two types of associative property as follows
Addition
Multiplication
Addition:
The addition of numbers is same. In math the associative property for addition says that grouping of numbers does not change the result or answer.
x + (y + z) = (x + y) +z
Example:
4 + (6 +3) = (4 + 6) +3
Multiplication:
The product of more numbers is same. Associative property for multiplication says that grouping of numbers does not change the result or answer.
x * (y * z) = (x * y) * z
Example:
7 * (2 * 8) = (7 *2) *8
Associative property is true for addition and multiplication but fails for both subtraction and division.
Algebra is widely used in day to day activities watch out for my forthcoming posts on how to solve word problems in algebra 2 and how to solve an algebraic expression. I am sure they will be helpful.
Example Sums for Associative Property:
Example sums for associative property:
Example 1:
5 + (8 + 2) = (5 + 8) +2
5 * (8 * 2) = (5 * 8) * 2
Through the above problem prove both the associative property of addition and the associative property of multiplication
Associative property of addition:
Proof:
5 + (8 + 2) = (5 + 8) +2
LHS:
5 + (8 + 2)
= 5 + (10)
= 15
RHS:
(5 + 8) +2
=13 +2
=15
Left hand side equal to right hand side so the associative property of addition is proved
Associative property of multiplication:
Proof:
5 * (8 * 2) = (5 * 8) * 2
LHS:
5 * (8 * 2)
= 5 * (16)
= 80
RHS:
(5 * 8) * 2
= (40) * 2
= 80
Left hand side equal to right hand side so the associative property multiplication is proved
Example 2:
7 + (3 + 5) = (7 + 3) +5
Through the above problem prove the associative addition property.
Associative property of addition:
Proof:
7 + (3 + 5) = (7 + 3) +5
LHS:
7 + (3 + 5)
=7 + (8)
=15
RHS:
(7 + 3) +5
= (10) +5
=15
Left hand side equal to right hand side so the associative property of addition is proved
Algebra holds many laws. The followings are the basic algebraic laws. They are Associative law, distributive law and commutative law. In math associative property states that changes in group do not change the answer means the moving of brackets does not affect the answer. In math associative law consists of two types of operations. They are addition and multiplications.
Associative Property:
Associativeproperty:
In math associative property states that changes in group do not change the answer means the moving of brackets does not affect the answer. Associative law consists of two types of operations.
Two types of associative property as follows
Addition
Multiplication
Addition:
The addition of numbers is same. In math the associative property for addition says that grouping of numbers does not change the result or answer.
x + (y + z) = (x + y) +z
Example:
4 + (6 +3) = (4 + 6) +3
Multiplication:
The product of more numbers is same. Associative property for multiplication says that grouping of numbers does not change the result or answer.
x * (y * z) = (x * y) * z
Example:
7 * (2 * 8) = (7 *2) *8
Associative property is true for addition and multiplication but fails for both subtraction and division.
Algebra is widely used in day to day activities watch out for my forthcoming posts on how to solve word problems in algebra 2 and how to solve an algebraic expression. I am sure they will be helpful.
Example Sums for Associative Property:
Example sums for associative property:
Example 1:
5 + (8 + 2) = (5 + 8) +2
5 * (8 * 2) = (5 * 8) * 2
Through the above problem prove both the associative property of addition and the associative property of multiplication
Associative property of addition:
Proof:
5 + (8 + 2) = (5 + 8) +2
LHS:
5 + (8 + 2)
= 5 + (10)
= 15
RHS:
(5 + 8) +2
=13 +2
=15
Left hand side equal to right hand side so the associative property of addition is proved
Associative property of multiplication:
Proof:
5 * (8 * 2) = (5 * 8) * 2
LHS:
5 * (8 * 2)
= 5 * (16)
= 80
RHS:
(5 * 8) * 2
= (40) * 2
= 80
Left hand side equal to right hand side so the associative property multiplication is proved
Example 2:
7 + (3 + 5) = (7 + 3) +5
Through the above problem prove the associative addition property.
Associative property of addition:
Proof:
7 + (3 + 5) = (7 + 3) +5
LHS:
7 + (3 + 5)
=7 + (8)
=15
RHS:
(7 + 3) +5
= (10) +5
=15
Left hand side equal to right hand side so the associative property of addition is proved
