Best Answer

No, division is not commutative, because a/b does not necessarily equal b/a.

A simple proof by counter-example:

Assuming a = 10 and b = 5, we test the property of commutativity with:

10/5 = 2

5/10 = 0.5.

This is an example of division failing to be commutative. In general, for a/b to equal b/a, a must equal b. For all other pairs (a,b) the property fails.

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โˆ™ 2011-08-16 04:05:12
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Q: Is division commutative
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Related questions

Is 11 divided by 11 a commutative property?


Does the commutative property work on division?

No, it does not.

Is division of rational numbers commutative?


What is the operations commutative?

division and subtraction

Is division of whole numbers is commutative?


Is mutipucation and division commutative?

Multiplication is commutative. a*b=b*a Division is not commutative Eg: 4/2=2 2/4=1/2 2 is not equal to 1/2

Can division be used in the commutative property?


Which math operations are not commutative?

Subtraction and division.

Are there commutative and associative properties for Subtraction and division?


Which two operations can NOT be used with the commutative property?

Division and subtraction cannot be used with the commutative property.

Are rational number commutative under subtraction and division?


Why is there no commutative property for subtraction or division?

It doesnt exist

What operations dont work for commutative property?

Subtraction, division

Can one formally define a division ring as a field that isn't necessarily commutative?

wedderburn's little theorem says all finite division rings are commutative so they are fields. So if it is a finite division ring, then the answer is NO But for an infinite division ring... I think you can!

Is there a commutative property of division?

There is no commutative property of division. Commutative means to exchange places of numbers. If you exchange the place of numbers in a division problem, you would affect the answer. So, commutative property applies only to addition or multiplication.Not really; for example, 2/1 = 2, and 1/2 = 0.5. However, you can convert any division into a multiplication, and apply the commutative property of multiplication. For example, 6 / 3 = 6 x (1/2), which is the same as (1/2) x 6.

The Commutative Property does not work for which operations?

Addition and multiplication

Is the set of rational numbers a commutative group under the operation of division?

No, it is not.

What is the deffinition of commutative?

Assuming you mean definition, commutative is a property of an operation such that the order of the operands does not affect the result. Thus for addition, A + B = B + A. Multiplication of numbers is also commutative but multiplication of matrices is not. Subtraction and division are not commutative.

Can you give an example that shows that division is not a commutative property?

Commutative property in division Indeed I have the answer. One example would be: 8 divided by 4 = 2 is different from 4 divided by 8 = 0.5 This means that if you alter the order of the dividends, the result of the operation will change. That is why division is not a commutative property. not ha ha ha

Why is there no commutative property for subtraction or division-?

There is no commutative property in subtraction or division because the order of the numbers cannot be change. This means that when multiplying or adding it does not matter the order of the numbers because the answer comes out the same.

Which operatoins are not commutative?

Subtraction, division, cross multiplication of vectors, multiplication of matrices, etc.

Counterexample of division of whole?

1 to the power of one divided equals 2 which is commutative

How are the rules for multiplication and division integers the same?

They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.

Why division is not commutative?

Formally, division is defined as multiplication of the inverse. For example, 4 / 2 is a short form for 4 * (2 ^ (-1)). So in general, a / b = a * (b ^ (-1)) and b / a = b * (a ^ (-1)), which suggests that a / b and b / a are not always equal (so division is not commutative).

Does the commutative property with for division?

No. For example, 2 / 1 is not the same as 1 / 2. However, you can convert any division into a multiplication, and apply the commutative law to the multiplication. For example, 5 divided by 3 is the same as 5 multipled by (1/3). By the commutative property, this, in turn, is the same as (1/3) multiplied by 5.