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Commutative Property

Commutative property in mathematics is a property of binary operations. These binary operations are mainly multiplication and addition. A binary operation will be commutative if we change the order of operands then it will not change or affect the end result of the operation. In this we do not change the order of operation which is done for Associative Property of any data Set. In this grouping of Numbers does not matter. We can change the Position of operands used in the Mathematical Expression. For this fundamental property of binary operations only multiplication and addition of numbers are taken. Division and subtraction are not commutative binary operations.
Commutative property definition can be understood as, lets take a set of numbers say ‘S’; now binary operation multiplication ‘*’ is said to be commutative if    a*b = b*a,               for all a, b € S.
Where ‘a’ and ‘b’ are two numbers of set ‘S’. If we change the order of these two numbers or operands then it will not change the final result i.e. it will produce the same result in both the cases.
If any operation does not support this property then that binary operation will be known as Non Commutative.
Similarly for binary operation addition ‘+’ on any given set ‘S’,
a + b = b + a,                for all a, b € S
If any operation supports this property then the operation is said to be commutative.
A binary function is said to be commutative if function on (x, y) will give the same result even if we alter the position of numbers. F: X * X -> Y will be commutative if:
F (a, b) = F (b, a); for all a, b € X.
Commutative properties: Commutative properties of logical connectives are as follows,
Consider ‘X’, ‘Y’ and ‘Z’, three operands of a given set.
Commutative property of conjunction:           (X^ Y) <-> (Y ^X),
Commutative property of disjunction:            (Xν Y) <-> (Y v X),
Commutative property of implication:            (X -> (Y -> Z)) -> (Y -> (X -> Z)),
Commutative property of equivalence:           (X <-> Y) <-> (Y <-> X),
The commutative property of binary operations is not similar to the associative property of operations in mathematics. Change in order or position of operands is allowed in commutative property but it is not allowed in associative property. Similarly associative property allows change in order of operation which is not acceptable in commutative property.

Solve 4 + 5 by using commutative Property of addition?

The meaning of commutative is move around, that’s why Commutative Property is referred to as moving any kind of arithmetic and algebraic function around. In commutative property there are two rules one for addition and other for multiplication. In addition rule we add Numbers as m + n = n + m and in multiplication rule we multiply numbers as mn = nm. Now we solve the given function by using these Properties.
Step1: The given function is  4 + 5. Firstly we write this function according to the commutative property of addition that is m + n = n + m.
4 + 5 = 5 + 4,
Step2: Now we solve both sides one by one. So left hand side is,
4 + 5 = 9.
Step3: Now we solve both sides one by one. So right hand side is,
5 + 4 = 9.
From the above example it is clear that both sides of given function is equal.

Solve 10 + 11 by using commutative Property of addition?

The meaning of commutative is move around that’s why Commutative Property is refers to as moving any kind of arithmetic and algebraic function around. In commutative property there are two rules one for addition and other for multiplication. In addition rule we add Numbers as m + n = n + m and in multiplication rule we multiply numbers as mn = nm. Now we solve the given function by using these Properties.
Step1: The given function is 10 + 11. Firstly we write this function according to the commutative property of addition that is m + n = n + m.
10 + 11 = 11 + 10,
Step2: Now we solve both sides one by one. So left hand side is,
10 + 11 = 21.
Step3: Now we solve both sides one by one. So right hand side is,
11 + 10 = 21.
From the above example it is clear that both sides of given function is equal.

Solve 6 x 12 by using commutative Property of multiplication?

The meaning of commutative is move around that’s why Commutative Property is refers to as moving any kind of arithmetic and algebraic function around. In commutative property there are two rules one for addition and other for multiplication. In addition rule we add Numbers as m + n = n + m and in multiplication rule we multiply numbers as mn = nm. Now we solve the given function by using these Properties.
Step1: The given function is 6 x 12. Firstly we write this function according to the commutative property of multiplication that is mn = nm.
6 x 12 = 12 x 6,
Step2: Now we solve both sides one by one. So left hand side is,
6 x 12 = 72.
Step3: Now we solve both sides one by one. So right hand side is,
12 x 6 = 72.
From the above example it is clear that both sides of given function is equal.

By using commutative Property of multiplication evaluate 7 x 100?

The meaning of commutative is move around that’s why Commutative Property is refers to as moving any kind of arithmetic and algebraic function around. In commutative property there are two rules one for addition and other for multiplication. In addition rule we add Numbers as m + n = n + m and in multiplication rule we multiply numbers as mn = nm. Now we solve the given function by using these Properties.
Step1: The given function is 7 x 100. Firstly we write this function according to the commutative property of multiplication that is mn = nm.
7 x 100 = 7 x 100,
Step2: Now we solve both sides one by one. So left hand side is,
7 x 100= 700.
Step3: Now we solve both sides one by one. So right hand side is,
7 x 100 =700.
From the above example it is clear that both sides of given function is equal.

By using commutative Property of multiplication evaluate 50 x 25?

The meaning of commutative is move around that’s why Commutative Property is refers to as moving any kind of arithmetic and algebraic function around. In commutative property there are two rules one for addition and other for multiplication. In addition rule we add Numbers as m + n = n + m and in multiplication rule we multiply numbers as mn = nm. Now we solve the given function by using these Properties.
Step1: The given function is 50 x 25. Firstly we write this function according to the commutative property of multiplication that is mn = nm.
50 x 25 = 25 x 50,
Step2: Now we solve both sides one by one. So left hand side is,
50 x 25 = 1250.
Step3: Now we solve both sides one by one. So right hand side is,
25 x 50 =1250.
From the above example it is clear that both sides of given function is equal.

Solve 23 + 45 by using commutative Property of addition?

The meaning of commutative is move around that’s why Commutative Property is refers to as moving any kind of arithmetic and algebraic function around. In commutative property there are two rules one for addition and other for multiplication. In addition rule we add Numbers as m + n = n + m and in multiplication rule we multiply numbers as mn = nm. Now we solve the given function by using these Properties.
Step1: The given function is 23 + 45. Firstly we write this function according to the commutative property of addition that is m + n = n + m.
23 + 45 = 45 + 23,
Step2: Now we solve both sides one by one. So left hand side is,
23 + 45 = 68.
Step3: Now we solve both sides one by one. So right hand side is,
45 + 23 = 68.
From the above example it is clear that both sides of given function is equal.