Types of Fractions

The three types of fractions are :

Proper fraction

Improper fraction

Mixed fraction

Proper fraction:

Fractions whose numerators are less than the denominators are called proper fractions.

For examples:

Types of Fractions

Two parts are shaded in the above diagram. Total number of equal parts is 3. Therefore, the shaded part can be represented as 2/3 in fraction. The numerator (top number) is less compared to the denominator (bottom number). This type of fraction is called proper fraction.


Proper Fraction

Improper fraction:

Fractions with the numerator either equal to or greater than the denominator are called improper fraction.

Fractions like 5/4, 17/5, 5/2 etc. are not proper fractions. These are improper fractions. The fraction 7/7 is an improper fraction.

The fractions 6/5, 10/3, 13/10, 15/4 are the examples of improper fractions. The top number (numerator) is greater than the bottom number (denominator). Such type of fraction is called improper fraction.

Note: Every natural number can be written as a fraction in which 1 is it's denominator. For example, 2 = 2/1, 25 = 25/1, 53 = 53/1, etc. So every natural number is an improper fraction.

Mixed fraction:

A combination of a proper fraction and a whole number is called a mixed fraction.

21/3, 45/2, 111/10 and 75/11 are examples of mixed fraction.

In other words:

A fraction which contains of two parts: (i) a natural number and (ii) a proper fraction, is called a mixed fraction, e.g., 32/5, 73/4, etc.

In 3 2/5, 3 is the natural number part and 2/5 is the proper fraction part.

In Fact, 32/5 means 3 + 2/5.

Property 1:

A mixed fraction may always e converted in to an improper fraction.

Multiply the natural number by the denominator and add to the numerator. This new numerator over the denominator is the required fraction.

31/2 = (3 × 2 + 1)/2 = (6 + 1)/2= 7/2.

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Property 2:

An important fraction can be always be converted in to a mixed fraction.

Divide the numerator by the denominator to get the quotient and remainder. Then the quotient is the natural number part and the remainder over the denominator is the proper fraction part of the required mixed fraction.

Example: 43/6 can be converted into a mixed fraction as follows:

6 |43
  - 42

Dividing 43 by 6, we get quotient = 7 and remainder = 1.

Therefore, 43/6

= 71/6.

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Note: Proper fraction is between 0 to 1. Improper fraction is 1 or greater than 1. Mixed fraction is grater than 1.


Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Interesting Fact about Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions

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