Math

# Are all Integers and Fractions Rational Numbers? [Explained]

Rational numbers are numbers that can be written in the form p/q, where p and q are integers

and q ≠ 0.

## Are All Integers Rational Numbers?

Integers are numbers that can be positive, negative, or zero, but cannot be a fraction. This implies that all the natural numbers, 0 (zero), and the negative of all the natural numbers are set of integers. Integers can be denoted by Z and can be expressed as  Z = {-5,-4,-3, -2, -1, 0,1,2,3,4,5…}.

Rational numbers can be written as p/q, where p and q are integers and q ≠ 0. If the signs of numerator and denominator are either both positive or both negative, the rational number is known as Positive Rational Number (For example -2/-1, -4/-2, 6/3). If the signs of the numerator and denominator are opposite to each other, the rational number is known as a Negative Rational Number (For example -2/1, 9/-3, etc.)

Thus, the set of the rational numbers contains all integers i.e. all integers are rational numbers. For example, -2 and 4 can be written in the form p/q, 2/1 =2 and 4/1 = 4, so they are rational numbers.

## Are Fractions Rational Numbers?

A number that can be written in the form of p/q, q ≠ 0 where p and q are whole numbers known as fractions. A fraction is part of a whole number. Kindly note that all counting numbers including 0 (zero) form the set of whole numbers. Its set is represented by R. Therefore, R = {0, 1, 2, 3, 4,5, 6,7,8,9,10…} is the set of the whole numbers.

A fraction has two parts namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. For example 2/3, 7/8, 9/4, etc. There are types of fractions namely proper, improper, mixed, and unit fractions.

A fraction is always positive whereas a rational number can be positive or negative. Thus, the set of the rational numbers contains all fractions i.e. all fractions are integers.

In conclusion, integers and fractions are a subset of rational numbers i.e. fractions and integers are rational numbers.

### Bolarinwa Olajire

A tutor with demonstrated history of working in the education industry. Skilled in analytical skills. Strong education professional with a M. SC focused in condensed matter.