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

- multiply the denominator of the proper function with the whole number, and then add the numerator
- 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

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

For example – = 2 r 1

Therefore = 2