In mathematics, the words fraction and rational numbers are the two most often used terms. We have studied them since our childhood, and still, many people get confused in differentiating between them because they resemble one another in appearance. Although these critical mathematical notions are linked in certain ways, there is a significant difference between them. Therefore, before differentiating, let us talk thoroughly about both topics.
Fractions: A fraction is a real number that is always written in a/b form. The portion above the ‘/’ sign is known as the numerator of a fraction, while the part below is known as the denominator. The denominator is the count of the total number of equal parts, while the numerator defines the number of parts we are provided. The numbers in a fraction are always whole numbers, which means that numbers from 0 to infinity. If no denominator is given, we consider it to be 1. If the denominator is 0, then the value of the fraction is undefined, and if the value of the numerator is 0, then the whole fraction is zero.
A fraction, in simple terms, is a small part of the whole. For example, if we cut the bread into four pieces, it is still a whole bread, but a single part of the cut out is ¼ of the bread. The fractional numbers are classified into six types: Proper fractions are those which contain a numerator smaller than the denominator. Improper fractions are fractions that have the denominator smaller than the numerator. The fraction which comprises a whole number and proper fraction is known as a mixed fraction. Fractions that include identical denominators are referred to as fractions. Fractions that include different denominators are known as, unlike fractions. The fractions which have identical values are known as equivalent fractions.
Rational numbers: A real number in the form of c/d where d is not equal to zero is known as a rational number. A rational number is the representation of all integers in the form of a ratio. A rational number can have both positive as well as negative values. The numbers ranging from (– infinity) to positive (infinity) are all rational numbers. Even the positive and negative decimal values fall under rational numbers. The decimal values either terminating or repeating after a special set of values are known as rational numbers. Now that we have learned in-depth about both topics, let us discuss the minute differences that make fractions and rational numbers unique from one another.
|Fractions are only whole or natural numbers. Negative numbers are not considered fractional numbers.||Rational numbers are numbers that include the entire set of numbers, excluding the imaginary numbers. Negative numbers are also rational numbers.|
|All fractions are rational numbers. Numbers without denominators have 1 as their denominator.||All rational numbers are not fractions because fractions require both the numerator and denominator to be positive.|
|Examples – ½, ¾, 88/11, 8, etc.||Examples – 8/3, -27/11, -19, 2, etc.|
|4. The reaction is non-spontaneous||Exothermic reactions are spontaneous reactions|