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Is the set of rational numbers a commutative group under the operation of division?
Wiki User
∙ 9y ago
No, it is not.
Wiki User
∙ 7y ago
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Why are the rules for multiplying and dividing rational numbers the same?
The question has no sensible answer because its proposition is not true. Multiplication is commutative, division is not, so the rules are NOT the same.
Is the set of rational numbers closed under division and Why?
No. Zero is a rational number, but division by zero is not defined.
Is the sum of rational numbers always rational?
Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.
What is a counterexample for the rational numbers are closed under the operation of taking a square root?
2 = 2/1 is rational. Sqrt(2) is not rational.
Is 0 a rational number?
Zero is a rational number. Rational numbers are numbers that can be represented by the division of two integers. Zero is zero divided by anything besides zero, so zero is rational.
Is division of rational numbers commutative?
No
How are rational numbers not commutative?
Numbers, by themselves are neither commutative nor are they non-commutative. Commutativity is a property that belongs to a mathematical operation on a set of numbers. However, since the question does not specify what operation you have in mind, it is not possible to give a more helpful answer. The basic operations of arithmetic are addition, subtraction, multiplication and division, but there are many more mathematical operations.
Does commutative property work for fractions?
Yes. Both the commutative property of addition, and the commutative property of multiplication, works:* For integers * For rational numbers (i.e., fractions) * For any real numbers * For complex numbers
Why in a rational number denominatior is not zero?
Division by 0 is not a valid mathematical operation - not just for rational numbers.
Why is division not closed for rational numbers give an example?
If a set is closed under an operation. then the answer will be a part of that set. If you add, subtract or multiply any two rational numbers you get another national number. But when it comes to division, it is closed except for one number and that is ZERO. eg 3.56 (rational number) ÷ 0 = no answer. Since no answer is not a rational number, that rational numbers are not closed under the operation of division.
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.
Is there commutative property of subtraction for rational numbers?
No, there is not.
Is division of whole numbers is commutative?
No!
List the commutative rings of rational numbers?
Yes
Are rational numbers are commutative with respect to multiplication?
Yes, they are.
Are rational numbers commutative for multiplication?
Yes, they are.
Why are the rules for multiplying and dividing rational numbers the same?
The question has no sensible answer because its proposition is not true. Multiplication is commutative, division is not, so the rules are NOT the same.
