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Is the quotient of two nonzero numbers always a rational number?
Wiki User
∙ 12y ago
Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.
Wiki User
∙ 12y ago
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What is always the result of dividing an integer when the divisor is nonzero?
A rational number is always the result of dividing an integer when the divisor is nonzero.
Is a rational number a real number?
Yes, a rational number is a real number. A rational number is a number that can be written as the quotient of two integers, a/b, where b does not equal 0. Integers are real numbers. The quotient of two real numbers is always a real number. The terms "rational" and "irrational" apply to the real numbers. There is no corresponding concept for any other types of numbers.
Is the quotient of two rational numbers always a real number?
A real number is any number so yes it is always a real number * * * * * Except if the second number is 0, in which case the quotient is not defined.
Can you multiply an irrational number by a rational number and the answer is rational?
The product of an irrational number and a rational number, both nonzero, is always irrational
Are integers always sometimes or never rational numbers?
All integers are rational numbers, but not all rational numbers are integers.2/1 = 2 is an integer1/2 is not an integerRational numbers are sometimesintegers.
Should the quotient of an integer and a nonzero integer always be rational?
No.
Is the quotient of an integer divided by a nonzero integer always be a rational number Why?
Yes, always. That is the definition of a rational number.
Can the quotient of an integer be divided by a nonzero integer a rational number always?
Yes, it is.
Is the quotient of an integer divided by a nonzero integer always a rational number?
Yes.
Is a quotient of an integer divided by a nonzero integer always a rational number?
Because that is how a rational number is defined!
Why is the quotient of an integer divided by a nonzero integer always a rational number?
Because that is how a rational number is defined!
Should the quotient of an integer divided by nonzero integer always be a rational number?
Yes, by definition.
Should the quotient of an integer divided by a nonzero integer always be a rational number?
I had this name question for homework :| no
Is the quotient of two rational number always rational numbers?
yes
What if two rational numbers are divided is the quotient always going to be a rational number?
Not if the second rational number is 0: in that case the quotient is not defined. Otherwise the answer is yes.
Why the product of nonzero rational number and a rational number is an irrational?
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
Is a rational number divided by an irrational number always irrational?
No. If we let x be irrational, then 0/x = 0 is a counterexample. However, if we consider nonzero rational numbers, then our conjecture is true. We shall prove this by contradiction. Suppose we have nonzero rational numbers x and y, and an irrational number z, such that x/z = y. Since z is not equal to 0, x = yz. Since y is not equal to 0, x/y = z. Since x/y is a quotient of rational numbers, x/y is rational. Therefore, z is rational, contradicting our assumption that z was irrational. QED.
