A fraction represents a part of a whole thing or, in other words, a certain number of equal parts in which an object is broken into. Generally speaking, a fraction refers to how many parts of a certain size are being referred to. Some of the real-life examples of fractions are equal portions of pizza, cake, a bar of chocolate, etc. It is expressed in words like one-fourth, three-fifth, etc. The word fraction is derived from the Latin word “fractus” which means ‘to break’. The Egyptians were among the first to learn to use fractions to resolve their practical problems regarding the division of food, supplies, etc.

In Mathematics, the fraction is denoted by a numerical value, representing the portion or section of any whole quantity. When a whole is divided into equal parts, each part or a combination of parts is a fraction of the whole. If the parts of the whole are unevenly divided, they don’t form fractions.

Parts of a Fraction

All fractions consist of two parts: numerator and denominator

  • The numerator denotes how many portions of the whole are represented. It is placed in the upper part of the fraction.
  • The denominator denotes how many equal parts the whole has been divided into. It is placed in the lower part of the fraction. 

For example, if an object is divided into 8 equal parts, then to indicate 5 parts out of it, the fraction 5/8 is used. Here 5 is the numerator and 8 is the denominator.

Types of Fractions

Based on the value of numerator and denominator, fractions can be of different types that are listed below:

Proper Fraction

The fractions in which the numerator is less than the denominator is called proper fraction. Example: 5/8, 3/7, 2/15, etc.

Improper Fraction

The fraction in which the numerator is more than or equal to the denominator is called an improper fraction. Example: 7/3, 5/2, 12/5, etc.

Mixed Fraction

An improper fraction can be denoted as a combination of a whole and a proper fraction. This is called a mixed fraction.

Unit Fraction

Fractions with numerators as 1 are known as unit fractions. Example: 1/2, 1/4, 1/5, etc.

Equivalent Fraction

These are fractions that represent the same value that means it is the same portion of a whole but denoted differently. Equivalent fractions are obtained by multiplying or dividing both numerator and denominator of a fraction by the same number.

For example, the equivalent function of 3/5 = 3/5 * 2/2 =6/10

Like and Unlike Fractions

Fractions having the same denominators are called Like fractions. Example: 3/12, 5/12, 8/12

Fractions that have different denominators are Unlike fractions. Example: 2/5, 7/11, 9/16


A number expressed in decimal has two parts namely a whole-number part and a decimal part, separated by a dot (.) called a decimal point. Example, 3.75 is a decimal number with whole-number part = 3 and decimal part = .75

A decimal number can be expressed as a fraction form also. Converting decimal to fraction is done by following steps:

  1. Write the decimal number without the decimal point. Consider it as the numerator of a fraction.
  2. In the denominator of that numerator, write 1 followed by as many zeros as the number of digits contained in the decimal part of the given decimal number.
  3. The fraction thus obtained can be reduced to the simplest form to get the fraction that is equivalent to the decimal number. For example, 2.625 can be written as 2625/1000 which is equal to 21/8 in simplest form. So, the decimal number 2.625 can be converted into the fraction 21/8. This is a basic topic and you can learn more about it in detail from