Are fraction rational number

Answer 1

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.

Note: Mathematicians do not generally use the term "fractions." They usually only talk about rational numbers. Fractions are more or less a term that is used for pedagogical reasons.

It's kind of funny. Someone uses a term not used in math to teach math, then makes up tons of tests about "fractions, improper and proper fractions," etc. and tests you on them, even though they are not mathematical terms. Go figyah!

Answer 2

Yes