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Types of Fractions

There are two types of fractions – proper fractions and improper fractions.

Proper fractions

If, in a fraction, the numerator is lesser than the denominator, then the fraction is called a proper fraction. Some examples are 3/5, 5/7, 1/2, 27/42, 199/2202 and so on.

Since the numerator is less than the denominator, the value of the fraction is less than 1. All proper fractions have a value less than 1.

We can represent a proper fraction pictorially as follows:

proper fraction

 

Improper fractions

On the other hand, if in a fraction, the denominator is greater than the numerator, then the fraction is called an improper function. Some examples are 11/3, 25/17, 5/4, 27/6, 173/72 and so on. 

Since the denominator is greater than the numerator, the value of the fraction is more than 1. All improper fractions have a value more than 1.

The pictorial representation of an improper fraction is:

improper fraction

When the numerator is the same as the denominator, then the fraction has a value of 1. It is also called a whole number, as shown below:

whole number

 

Mixed Numeral

A mixed numeral is a number that is made up of a whole number and a proper fraction. Some examples of mixed numerals are 23/5, 11/4, 145/9, 1962/5, and so on.

mixed numeral

 

While working with fractions, you will be required to convert a mixed numeral to an improper fraction, and vice versa. Let’s now look at how to do these.

 

To convert a mixed numeral to an improper fraction

  1. multiply the denominator of the proper function with the whole number, and then add the numerator
  2. keep the same denominator of the proper function

For example – to convert 13/4 to an improper fraction, we get

(4 x 1) + 3 = 7 is the numerator, and 4 is the denominator.

So 13/4  =  7/4

We can see this in graphical form below:

mixed numeral to an improper fraction

 

To convert an improper fraction to a mixed numeral

  1. divide the numerator with the denominator (to get the whole number)
  2. write the remainder over the same denominator (for the proper fraction)

For example – 11/5  =  2 r 1

Therefore 11/5  =  21/5

improper fraction to mixed numeral