Question

Is a fraction a real number, rational number, irrational number?

Answer 1

Hint: The fractions are defined as the parts of a whole. Rational and Irrational numbers both are real numbers but different with respect to their properties. Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also.

Complete step-by-step answer:
In other words, fraction is also termed as a portion or section of any quantity.
Real numbers can be defined as the union of both the rational and irrational numbers. They can be either positive or negative and are denoted by the symbol “R”. A rational number is the one which can be represented in the form of \[\dfrac{p}{q}\] where p and q are integers and \[q \ne 0\]. But an irrational number cannot be written in the form of simple fractions. Thus, irrational numbers are any real numbers that are not rational.
Rational numbers are numbers which can be expressed as a fraction and also as positive numbers, negative numbers and zero. And, irrational numbers could be written in decimals but not in the form of fractions, which means it cannot be written as the ratio of two integers. Irrational numbers have endless non-repeating digits after the decimal point.
Thus, a fraction of two integers is a rational number. It is also a real number.
Integers are the numbers: \[0,1, - 1,2, - 2,3, - 3,...\]
Rational numbers are: \[ - \dfrac{{17}}{4},12.23,5,\dfrac{1}{2},...\]
Irrational numbers are: \[\sqrt 2 ,\sqrt {3,} \pi ,...\]

Hence, a fraction is a rational number and also a real number.
So, the correct answer is “ rational number and also a real number”.

Note: The word rational is derived from the word ‘ratio’, which actually means a comparison of two or more values or integer numbers and is known as a fraction. In simple words, it is the ratio of two integers. As per the definition, the rational numbers include all integers, fractions and repeating decimals. Rational numbers are finite and repeating decimals whereas irrational numbers are infinite and non-repeating. There are infinitely many rational numbers, but they do not form a continuous line. The continuous line of numbers is called the real number line.