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