What is Fraction in Mathematics? - Definition and Types

History behind derivation of the word Fraction

Fraction is derived from a Latin word fractus which means broken. Thus, a fraction is generally written to represent a part of any whole.

What is Fraction definition?

A fraction is defined as a part of any whole number.

A fraction is also defined as a ratio of two integers.

Representation of Fraction

A fraction is basically a representation of one integer divided by other integer.

For example - 2:3 is a ratio, where 2 and 3 are integers but to write it as a fraction we need to replace " is to ( : ) " symbol by a slash or solidus ( / ) or a vinculam ( _ ).

So, 2:3 can be written in fraction as 2/3.

Pictorial Representation of Fraction

A circle is cut out in two parts - one past is shaded with orange colour while the other parts is shaded with green colour.

Now to represent orange part of circle as a fraction, it can be written as 1/4.

While to represent green part of circle as a fraction, it can be written as 3/4.

If you add 1/4 and 3/4 it will give you 1 that mean a full circle.

Examples of Fraction

Some examples of fractions are 1/2, 3/2, 1/3, 2/3 etc.

How to pronounce Fraction?

1/2 can be pronounced as 1 by 2. So, to read out any fraction we use " by " for slash.

Various approach to write a Fraction

There are various ways in which we can write the same fraction. Let's understand it with an example.

Let there be a fraction 1/2 then it can be written as

> 0.5 in decimals

> 50% in percentage

> 1:2 in ratio

> 1/2 in division or fraction form

What is numerator in a Fraction?

The integers which are used before slash or solidus ( / ) is called Numerator in a Fraction.

For example- 

1/2 - 1 is numerator

5/2 - 5 is numerator

What is denominator in a Fraction?

The integers which are used after slash or solidus ( / ) is called Denominator in a Fraction.

For example-

1/2 - 2 is denominator

5/2 - 2 is denominator

Note: The denominator in a fraction can never be Zero.

Forms of Fraction or Types of Fraction

Common Fraction: Fraction written in the form of rational number i.e. a/b where a and b are integers and b is not equal to zero is called common fractions.

Simple fraction: Common fraction is also known as simple fraction.

Vulgar fraction: Simple fraction is also known as vulgar fraction.

Examples of common fraction, simple fraction or vulgar fraction are 1/2, 3/4, 2/3 etc.

Complex fraction: A complex fraction is a fraction in which numerator or denominator or both numerator and denominator consists of a fraction.

Examples of complex fractions are 1/2 / 2/3, 4/5 / 1/2 etc.

Compound fraction: A compound fraction is a fraction connected with multiplication of two fractions and connected with the word " of ".

Examples of compound fraction are 1/2 of 3/4, 2/3 of 5/6 etc.

Note:Complex and Compound fractions are now a days outdated and thus not used commonly.

Simple fractions are further classified into two types:

Proper fraction: If the numerator of a fraction is smaller than its denominator then the fraction is termed as proper fraction.

Examples of proper fraction are 1/2, 3/4, 5/6 etc.

Improper fraction: If the numerator of a fraction is greater than its denominator then the fraction is termed as improper fraction.

Examples of improper fraction are 4/3, 5/2, 9/8 etc.

Decimal fraction: If the number is in the form of a decimals i.e. their denominator is not given but it can be easily understood in the power of 10 is called decimal fraction.

Examples of decimal fraction are 0.1, 0.2, 0.03 etc.

0.1 can be written as 1/10.

0.2 can be written as 2/10.

0.03 can be written as 3/100.

Percentage: If the number is in form of percent ( represented by symbol % ) in which the denominator is always 100.

Examples of percentage are 50%, 20% etc.

50% can be written as 50/100.

20% can be written as 20/100.

Ratio: A ratio is a relationship between two or more numbers ( represented by symbol : ).

Examples of ratio are 2:3, 4:5 etc.

2:3 can be written as 2/3.

4:5 can be written as 4/5.

Mixed number: It is a denotation of a whole number and a proper fraction having the same sign.

Mixed numeral: Mixed number is also known as mixed numeral.

Mixed fraction: Mixed number is also known as mixed fraction.

Examples of mixed number, mixed numeral or mixed fraction are 1 1/2, 2 2/5 etc.

1 1/2 can be written as 3/2.

2 2/5 can be written as 12/5.

Unit fraction: A fraction is a simple fraction with numerator 1.

Examples of unit fraction are 1/2, 1/3, 1/5 etc.

Reciprocal of a fraction: The reciprocal of a fraction is another fraction with the numerator and denominator exchanged.

For example: Reciprocal of a fraction 2/3 is 3/2.

Equivalent fraction: Multiplication of the same non-zero number to both numerator and denominator will result to a fraction which is equivalent to original fraction.

For example: Multiplication of 2 to both numerator and denominator of a fraction 3/5 is 6/10 which is equivalent to 3/5.

Invisible denominator: Any fraction is termed as invisible denominator if the denominator of the required fraction is 1. 

For example: Any integers can be written as invisible denominator. 2 can be written as 2/1.

How to convert a simple fraction into a mixed number?

Let's consider a simple fraction 7/3.

Step 1: Now divide 7 by 3. Write Quotient and Remainder.

When dividing 7/3 will gives 2 as Quotient and 1 as Remainder.

Step 2: Write denominator as it is.

Now to write it as a mixed number, Write quotient in place of whole number and the remainder as numerator.

So, 7/3 is written as 2 1/3.

How to convert a mixed fraction into a simple fraction?

Let's consider a mixed fraction 2 3/5.

Step 1: For writing numerator, multiply denominator by the whole number and add numerator to it.

So, numerator = 5*2+3 = 13

Step 2: Write denominator as it is.

So, 2 3/5 can be written as 13/5.

How to reduce a fraction into it's simplest form?

Let's consider a fraction 16/12

Now we need to find a highest common factor of 16 and 12.

Here 16 and 12 has a common factor 4.

Now, divide by 4 to both numerator and denominator.

So, 16/12 can be written in simplest form as 4/3.