HomeGeneralA Detailed Study about Improper Fractions

A Detailed Study about Improper Fractions

A fraction is a part or some portion of a collection or a whole thing. A fraction contains two parts – they are numerator and denominator. The numerator is the top number and the denominator is the bottom number. The numerator tells the part out of the whole thing and the denominator tells how many total parts are there. If in a fraction the numerator is greater than or equal to the denominator, this type of fractions is called improper fractions. 7/5 is an example of an improper fraction. Here 7 is the numerator which is greater than the denominator, 5. But in a proper fraction, the numerator is smaller than the denominator. We will learn about improper fractions in detail in this article.

Types of fractions: Before knowing about Improper fractions in detail, we must know how many types of fractions there are. As we know a fraction denotes the part of the whole thing, suppose you cut bread into 4 equal pieces, and you have eaten two pieces among them then it can be represented as 2/4 bread you have eaten.

There are three types of fractions in arithmetic – 

  • Proper fraction 
  • Improper fraction
  • Mixed fraction

In the proper fraction the numerator is smaller than the denominator, such as 2/4. In an Improper fraction the numerator is greater than or equal to the denominator, such as 8/6. The mixed fraction contains a whole number and a proper fraction, such as 443. An Improper fraction can easily be converted to a mixed fraction.

Improper fraction: 

An improper fraction is a type of fraction in which the numerator is equal to or greater than the denominator. Let’s have some examples- 8/6, 5/4, 9/3. Now you may think how can it happen? Suppose you have a pizza you cut it into 6 pieces and you have 7 friends there to share and eat this pizza. 6 of you have taken the 6 pieces and one friend has left with nothing then you ordered another pizza and cut it and give a piece to that friend. So, here the fraction will be 7/6. An Improper fraction always indicates greater than or equal to1.

An Improper fraction can be simplified by making it a mixed fraction. Now we will discuss it.

Convert Improper fraction to Mixed fraction:

In Improper fraction, the numerator is greater than the denominator. On the other hand, a mixed fraction is a combination of a whole number and a proper fraction. Actually, mixed fraction is the simplified form of an improper fraction. Improper fraction and mixed fraction always present greater than 1. We can easily convert an improper fraction to a mixed fraction or vice versa. There are some basic steps to convert an improper fraction to mixed fraction. There steps are-

  • Firstly, we need to divide the numerator by the denominator. You will get the quotient and the remainder.
  • Now arrange the quotient, remainder and divider in the following way to present the mixed fraction:


Now we will take an easy example to understand it.12/5 is an improper fraction as the numerator (12) is greater than the denominator (5). First of all, we need 12 by 5 and we will get the quotient and the remainder. Here the quotient is 2 and remainder is 2. So, the mixed fraction will be 225.

Convert mixed fraction to improper fraction:

We can convert a mixed fraction into an improper fraction also. Let’s have an example 315is a mixed fraction. Firstly, we have to multiply 5 by 3 and add with the numerator 1, we will get 5×3 + 1= 16. So, the numerator of the improper fraction will be 16 and the denominator will remain the same, that is 5. So the improper fraction of this mixed fraction is  16/5.

We can find out the equivalent fraction of the same fractions which have the equal numerator or denominator value. We can find out the equivalent fractions by multiplying both the numerator and denominator.

So, we have learnt about the improper fractions. You can learn more about fractions and other mathematical topics if you follow the Cuemath app. Download this app and get more information about different mathematical questions.



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