# What Is A Commutative Property

According to the commutative property, the numbers that we operate on can be moved or swapped from their place without causing any change to the result that we get. However, the property is not valid for the operations of subtraction and division; it is only valid for addition and multiplication. Let’s see.

## What is meant by the term “commutative property”?

According to the commutative property, often known as the commutative law, when two numbers are added together or multiplied together, then a change in their places does not change the result. This is something that we have already covered in the introduction.

## Historys

Even if the beginning of the commutative property’s official use didn’t occur until the late 18th century, the concept has been around since ancient times.

The word “commutative” comes from the French word “commute,” which means to switch or move around. The suffix “-ative,” which means “tend to,” was added to the end of the word to give it its current meaning. Therefore, the literal meaning of the phrase is to change places or position oneself in a different manner. It states that the outcome will not change even if we switch the places of the integers in the equation.

## Formula for the Commutative Property

In the event that we are given two numbers, A and B, then the formula for the commutative property of numbers is as follows:

- A + B = B + A
- A × B = B × A
- A – B ≠ B – A
- A ÷ B ≠ B ÷ A

According to the formulation for the commutative property, the result of adding or multiplying two numbers does not depend on the sequence in which the numbers were added or multiplied. However, when carrying out operations like as subtraction and division on any two real numbers, the order of the numbers is essential, and as a result, it cannot be altered.

## Addition possesses a property known as commutativity.

According to the commutative property of addition, the value of the sum cannot be affected by shifting the order in which the addends are included in the calculation. If “A” and “B” are two integers, then the commutative property of addition can be represented using those numbers.

## What is Addition Commutative?

Addition is commutative if the order of two numbers is immaterial to the sum. In other words, a + b = b + a.

For example, 3 + 4 = 4 + 3 and 5 – 6 = 6 – 5.

## What Is Multiplication Commutative?

Multiplication is commutative if the order of two numbers does not matter when multiplied together.

For example: 2 *4 = 4 *2, 3 *3 = 3 *3, 7 *8 = 8 *7 and so on…

## What Is Division Commutative?

Division is commutative if it doesn’t matter which number you divide by first or second number divider. For example: Division by two or five (2 or 5) will always give the same result.

## What is Multiplication Commutative?

Commutative property of multiplication states that when two numbers are multiplied together, their order does not matter. The result is always the same no matter where the numbers are placed in the multiplication equation. For example, if you multiply 2 × 5 = 10 and then change the order of multiplication to 5 × 2 = 10, they both give you the same result – 10.

When two numbers are multiplied together as many times as possible using all possible combinations, they will always get back to their original state (i.e., they will return to 1). We call this operation “multiplication inverses”. For example:

1 × 2 = 2

2 × 1 = 2

2 × 3 = 6

3 × 2 = 6

## Examples of Commutative Property

Examples of Commutative Property

Transitive Property: If a is equal to b, and b is equal to c, then a is equal to c.

Example 1: 3+3=6, 6+6=12. Therefore, 3+6=12.

Example 2: If a+b=c and b+a=d, then a+d=b+c.

Example 3: If 5×1 = 5×2, then 5×2 = 5×1.

Inverse Property: If a*b = c then a/c = b/c (If you multiply by the inverse of something it will be canceled out).

Commutative Property: A*B = B*A. When you flip the order of two numbers the answer does not change! A number of times another number can be reversed without affecting the result.

## Commutative Property Of Addition Example

In math, the commutative property of addition is a property of addition that says that rearranging the order of addition doesn’t change the result.

The commutative property of addition says that “a + b = b + a” and that “a + (b + c) = (a + b) + c”.

So if you add 5 and 6 together, you get 11. You can also rearrange those numbers so that 6 comes before 5: 6 + 5 = 11. The answer is the same regardless of which number goes first or second when adding them together.

Commutative Property Of Multiplication Example

In math, we also have the commutative property of multiplication, which says that “a x b = b x a”. For example: 2 x 3 = 3 x 2

## Commutative Property Of Multiplication Example

The Commutative Property Of Multiplication is the property of multiplication where the order of the operations does not matter.

The Commutative Property Of Multiplication states that:

For all real numbers a, b and c, we have: