PROPER AND IMPROPER FRACTIONS

Proper Fraction :

In a proper fraction, the numerator is always smaller than the denominator. 

Examples : 

2/5,  3/11

Improper Fraction :

In an improper fraction, the numerator is equal to or larger than the denominator. 

7/5,  3/2, 1/1

Difference between Proper Fraction and Improper Fraction

Proper Fraction

The value of a proper fraction is always greater than 0 but less than 1.

Improper Fraction

The value of an improper fraction is always equal to 1 or larger than 1. 

The picture shown below clearly illustrates this. 

Mixed Numerals

Mixed numeral is a quantity which is expressed as a whole number and a proper fraction.

Always its value will be greater than or equal to 1. 

The picture given below clearly illustrates this. 

Conversions

1.  An improper fraction can be converted into a mixed numeral and vice versa. 

2. A proper fraction can never be converted into a mixed numeral. 

3. When we convert a mixed numeral into a fraction, always, we will get an improper fraction. 

Converting an Improper Fraction to Mixed Numeral 

The picture given below illustrates, how to convert an improper fraction into mixed number. 

Converting a Mixed Numeral into an Improper Fraction

The picture given below illustrates how to write a mixed number as an improper fraction.

Conversions between Different Types of Fractions

Example 1 :

Write the following improper fraction as mixed number.

275/3

Solution :

When we divide 275 by 3 as explained in the above picture, 3 goes into 275 by 91 times and we will have 2 left in 275.

By using the method explained in the picture above, the mixed fraction or mixed number which is equal to 275/3 is  

91

Example 2 :

Write the following improper fraction as mixed number.

75/8

Solution :

When we divide 75 by 8 as explained in the above picture, 8 goes into 75 by 9 times and we will have 3 left in 75.

By using the method explained in the picture above, the mixed fraction or mixed number which is equal to 75/8 is 

9

Example 3 :

Convert the following mixed number into an improper fraction.

2⁴⁄₇


Solution :

Improper fraction  =  18/7

Example 4 :

Convert the following mixed number into an improper fraction.

12⁸⁄₉

Solution :

Improper fraction  =  116/9

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