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Every number can be written as a quotient.

Every rational number can be written as a quotient of whole numbers.

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โˆ™ 2011-11-16 18:42:05
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Q: Can every rational number be written as a quotient?
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Does 30 go into 21?

Every rational number "goes into" every other rational number. In this case, the quotient is 0.7 .


Is every rational number a fraction?

Every rational number can be written as a vulgar or an improper fraction - even whole numbers can be written as x/1 - for example, 7 is equal to 7/1. The definition of rational is "can be rewritten as a ratio" - or, in most cases, a fraction.New answer:A fraction is a number that expresses part of a whole as a quotient of integers (where the denominator is not zero).A rational number is a number that can be expressed as a quotient of integers (where the denominator is not zero), or as a repeating or terminating decimal. Every fraction fits the first part of that definition. Therefore, every fraction is a rational number.But even though every fraction is a rational number, not every rational number is a fraction.Why? Consider this:Every integer (all the whole numbers, including zero, and their negatives....-3,-2,-1,0,1,2,3...) is a rational number, because it can be expressed as a quotient of integers, as in the case of 4 = 8/2 or 1 = 3/3 or -3 = 3/-1 and so on. So integers such as 4 or 1 can be expressed as the quotient of integers.But an integer is not a fraction. 4 is an integer, but it is not a fraction. 4 is not expressed as the quotient of integers. The difference here is in the wording.A fraction is a number that expresses part of a whole. An integer does not express a part. It only expresses a whole number.A rational number is a number that can be expressed as a quotient of integers, or as part of a whole, but fraction is a number that is (must be) expressed as a quotient of integers, or as part of a whole - there is a difference. The difference is subtle, but it is real.In a nutshell, the fractions are a subset of the rational numbers. The rational numbers contain the integers, and fractions don't.


Why are fractions rational numbers but not every rational number is a fraction?

'Rational' in a mathematic sense means 'can be written as a finite fraction'. Since you can obviously write a fraction as a fraction - by a triviality - it is rational. Rational numbers also include the integers; however these can also be written as fractions in the form a/1, so technically every rational number is a fraction.Note to the author of the above quote: - I don't believe that is correct. Here's why:A fraction is a number that expresses part of a whole as a quotient of integers (where the denominator is not zero).A rational number is a number that can be expressed as a quotient of integers (where the denominator is not zero), or as a repeating or terminating decimal. Every fraction fits the first part of that definition. Therefore, every fraction is a rational number.But even though every fraction is a rational number, not every rational number is a fraction.Why? Consider this:Every integer (all the whole numbers, including zero, and their negatives....-3,-2,-1,0,1,2,3...) is a rational number, because it can be expressed as a quotient of integers, as in the case of 4 = 8/2 or 1 = 3/3 or -3 = 3/-1 and so on. So integers such as 4 or 1 can be expressed as the quotient of integers.But an integer is not a fraction. 4 is an integer, but it is not a fraction. 4 is not expressed as the quotient of integers. The difference here is in the wording.A fraction is a number that expresses part of a whole. An integer does not express a part. It only expresses a whole number.A rational number is a number that can be expressed as a quotient of integers, or as part of a whole, but fraction is a number that is (must be) expressed as a quotient of integers, or as part of a whole - there is a difference. The difference is subtle, but it is real.In a nutshell, the fractions are a subset of the rational numbers. The rational numbers contain the integers, and fractions don't.


What is meaning of rational?

Mathematics a rational number is any number that can be expressed as the quotient a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted Q (for quotient).


What is the relationship of rational numbers and real number?

The set of rational numbers is a subset of the set of real numbers. That means that every rational number is a real number, but not every real number is rational. The square root of 2 is an example of a real number that isn't rational; that is, it can't be expressed as the quotient of two integers.


What number divides out into 2 and five sevenths?

Each and every rational number except 0. Once you leave the domain of integers, all rational numbers (excluding 0) divide into every other rational number with a quotient that is rational. The above can be extended to real numbers.


Can a number that is represented by a fraction be a rational number?

Definitely. A rational number is a number that can be written as a ratio. Every fraction is a ratio. Therefore every fraction represents a rational number.


Every irrational number can be expressed as a quotient of integers?

The statement is false; in fact, no irrational number can be exactly expressed as a quotient of integers because this property is the definition of rational numbers.


Is 100 a rational number?

Yes, 100 is a rational number.A rational number is any number that can be expressed as the quotient a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number.


Can every rational number be written as a fraction?

Yes


Is 37 squared a rational or irrational number?

372 = 1,369 is an integer; therefore, it is a rational number. In fact, the square of any integer is always an integer; this is because the sum or product of any two integers is an integer. And every integer is a rational number; this is because a rational number is defined as the quotient obtained by dividing one integer into another; and because every integer is the quotient obtained by dividing that integer by the integer 1.


Is every integer a rational number or is every rational number an integer?

Every integer is a rational number.

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