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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 , , , , 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: ## 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 , , , , 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: 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: ## 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 2 , 1 , 14 , 196 , and so on. 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 1 to an improper fraction, we get

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

So 1 = We can see this in graphical form below: ## 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 – =  2 r 1

Therefore =  2  