Math

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

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

Thus, the set of 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.

## Explanation

A number can be written as 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, the 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: proper, improper, mixed, and unit.

A fraction is always positive, whereas a rational number can be positive or negative. Thus, the rational numbers contain 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.

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