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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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Does 30 go into 21?
Every rational number "goes into" every other rational number. In this case, the quotient is 0.7 .
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).
Is every rational number a fraction?
Every fraction is a rational number, but not every rational number is a fraction.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.Both 22/7 and 1/3 are fractions, therefore they are both rational numbers. They also are repeating decimals, as 22/7 = 3.142857142857142857... (notice that the 142857 repeats) and as 1/3 = .333...An irrational number, on the other hand, neither terminates nor repeats.(The confusion about 22/7 may come because that fraction is often used to represent the number pi. It is not the number pi, just an approximation. The number pi is a decimal that begins 3.1415... and continues on without terminating or repeating. )But even though every fraction is a rational number, not every rational number is a fraction. Basically because rational numbers do not have to express a part of a whole. It can express a whole, as in an integer. And an integer is not a fraction.
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.
Does 30 go into 21?
Every rational number "goes into" every other rational number. In this case, the quotient is 0.7 .
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.
Is every rational number a fraction?
Every fraction is a rational number, but not every rational number is a fraction.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.Both 22/7 and 1/3 are fractions, therefore they are both rational numbers. They also are repeating decimals, as 22/7 = 3.142857142857142857... (notice that the 142857 repeats) and as 1/3 = .333...An irrational number, on the other hand, neither terminates nor repeats.(The confusion about 22/7 may come because that fraction is often used to represent the number pi. It is not the number pi, just an approximation. The number pi is a decimal that begins 3.1415... and continues on without terminating or repeating. )But even though every fraction is a rational number, not every rational number is a fraction. Basically because rational numbers do not have to express a part of a whole. It can express a whole, as in an integer. And an integer is not a fraction.
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.
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.
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.
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 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 every integer a rational number or is every rational number an integer?
Every integer is a rational number.
