Commutative Property in mathematics refers to changing the order of the integers or variables in an expression.

The property only applies to term addition and multiplication. This law states that if the positions of two terms are switched while adding or multiplying them, the result remains unchanged (total or product of terms).

## What exactly is the commutative property?

The Property is derived from the word commute, which means to move or change position. Commutative in mathematics refers to changing the order of the integers or variables in an expression.

we need to find the sum of 10 + 20. It will suddenly occur to you that the answer is 30. Let us now swap the positions of the numbers, 20 + 10. We discover that the total remains at 30.

What about multiplying? Take the same example (10 x 20 = 200). Changing the order of the numbers 20 x 10 = 200 yields the same result.

As a result, the commutative property holds for both addition and multiplication. You’re probably wondering if subtraction and division also adhere to the commutative property. We’ll find out soon along with the property, in this article.

### Formulas Concerning the Commutative Property

If you have two positive integer values let’s say K and L. The commutative property of these integers on different operations will then be expressed as follows:

Addition has the commutative property: K + L = L + K.

Multiplication has the commutative property: K x L = L x K.

Subtraction has the commutative property: K – L L – K

The division has the commutative property: K L L K

the left-hand side is not equal to the right-hand side in the commutative property of subtraction and division. when performing subtraction and division the order of the numbers is critical.

#### What is the Addition Commutative Property?

We’ve only touched on the property of addition so far. Let us now go over this section and the commutative property of more examples.

The result does not change if we change the order or orientation of two numbers that have been added. This is known as the addition commutative property. For example, if we have two positive integers ‘X’ and ‘Y,’ the commutative property of addition is written as

X + Y = Y + X

Example 1: Assume ‘X’ is 4 and ‘Y’ is 9. Using the property of addition, compute the sum of the numbers.

We’ve been given X = 4 and Y = 9. Therefore,

X + Y = 4 + 9 = 13

Example 2: Assume ‘X’ is 10 and ‘Y’ is 7. Find the sum of the numbers if their positions change.

We’ve been given X = 10 and Y = 7. We also know that the property holds.

X + Y = 10 + 7 = 17

#### What is Multiplication’s Commutative Property?

The property of addition must now be understood. Let us now delve into this section, where we will learn the concept, as well as examples of the commutative property of multiplication

results,

result does not change if we swap the positions of two numbers multiplied in an expression. This is known as multiplication’s property. For example, given two positive integers ‘W’ and ‘Z,’ the property of multiplication is given as

Z x W = W x Z

Example 1: Assume ‘W’ is 5 and ‘Z’ is 12. Using the property of multiplication, calculate the product of the numbers.

Solution: Assume W = 5 and Y = 12. Therefore,

W x Z = 5 x 12 = 60

demonstrates that the property of multiplication holds in all cases.

Example 2: Assume ‘W’ is 21 and ‘Z’ is 6. Find the product of the expression of the numbers’ position changes.

W = 21 and Z = 6 are the solutions. In the previous question, we demonstrated that the property holds for multiplication.

W x Z = 21 x 6 = 126

As a result, even if the numbers change positions, the product remains at 126.

### subtraction property examples

Subtraction’s property can be represented as K – L = L – K, where K and L are positive integers.

For the exam, suppose K is 5 and L is 9.

When we enter the values into the left-hand side formula, we get

K – L => 5 – 9 = -4

Putting the values on the right side of the formula yields

L – K => 9 – 5 = 4

We can see that changing the order of the numbers in subtraction changes the value of the result because -4 is not equal.

The property for subtraction holds only in one case when the values of K and L are equal.

Let K and L be equal to 9. The property of subtraction is then used.

K – L = 9 – 9 = 0 and

L – K = 9 – 9 = 0

The left-hand side equals the right-hand side, demonstrating the commutative property of subtraction in only one case.

### Division property examples

the property of division can be expressed as M N = N M.

Assume M is equal to 8 and N is equal to 4.

We get this by substituting the value on the left side of the expression.

M ÷ N => 8 ÷ 4 = 2

by substituting the value on the expression’s left side, we get

N ÷ M => 4 ÷ 8

we see that changing the orientation of the numbers produces different results. As a result, the division’s commutative property is also invalid.

The property for division is only valid in one case: when the values of M and N are equal.

Let M and N be equal to 8. The property of division is then used.

M ÷ N = 8 ÷ 8 = 1 and

N ÷ M = 8 ÷ 8 = 1

the left-hand side = right-hand side = 1 demonstrating that the property of division is valid in only one case.

#### Associative vs. Commutative Property

the article discusses a variety of commutative property concepts. many students are still confused about the associative properties. Both of these properties, without a doubt, deal with the movement of terms within an expression, and both are only valid in cases of addition and multiplication. there are significant differences between the two. See the table below to see how the property differs from the associative property.

Commutative Property |
Associative Property |

Commutative property in mathematics means to commute or switch, swap, or change the order of the numbers in any expression. | Associative property in mathematics means to associate, come together, or group the numbers in any expression. |

Commutative property deals with two numbers. | Associative property deals with more than two numbers. |

The commutative property is expressed as: K x L = L x The |
The associative property is expressed as: (K x L) x M = K x (L x M) |

Example 13 x 4 = 4 x 13 = 52 |
Example (13 x 4) x 8 = 13 x (4 x 8) = 416 |