Commutative Properties of Whole Numbers.

Raju and Suresh are best friends.

One day they got apples from a Garden.

Raju got and Suresh got apples respectively

Raju keeps his apples in the basket first, then Suresh keeps his apple in the basket too.

Now, the total numbers of apples in the basket are .

Then they drew out their apples from the basket.

Now, again they kept the apples in the basket, but in reverse order, first Suresh put his apples in the basket than Raju.

Again, the total number of apples in the basket are .

From this situation, we observe that, whatever the order of putting the numbers, but the result of their addition is always the same.

So, we can say that, whole numbers are commutative under addition.

Let’s understand Commutative property of whole numbers.

Commutative property states that order does not matter.

In general, we show commutative property of whole numbers under addition. As

Now, suppose we have two whole numbers & , and if we subtract them in different order, as

We see that on subtracting two whole numbers in different order, we get two different answers. So

So, we get that order of subtraction changes the value of result, which implies whole numbers are not commutative under subtraction.

Now, if we have two whole numbers and , and we multiply them in different order, still we get same value .

So, in general, we can say that whole numbers are commutative under multiplication.

Now, let’s check commutative property of whole numbers under division, consider two numbers & and divide them. As

We get two numbers in fractional form, which are not equal to each other.

So, we can say that whole numbers are not commutative under division.

Revision

The commutative property of whole numbers under different operations(addition, subtraction, multiplication and division) is as

The commutative property of whole numbers under addition operation.

The commutative property of whole numbers under multiplication operation.

However, subtraction of whole numbers is not commutative in nature.

Also, whole numbers are not commutative under division.

The End