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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).
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.
