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Mixed Fractions

Last updated date: 29th May 2024
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Fraction, Latin for 'broken' symbolises a part of a whole number, or in a more general way, equal parts of any number. In regular spoken English, the word 'fraction' is spoken as to describe the number of parts there are of a certain size, like one-third, eighty-fifth, etc.

A fraction has two parts, a numerator and a denominator. Numerator comes above the line, and a denominator (that is not a zero) comes below the line separating these two. In Mathematics, there are three types of fractions, proper, improper, and mixed fraction. In this following discussion, students get to learn about mixed fraction, an important topic of Mathematics. This sub-type of fraction helps to simplify the representation of fraction numbers.

Definition of Mixed Fraction

A mixed fraction is a combination of a proper fraction and a whole number. Usually, it represents a number between any two. For instance, 1(1/3) is a mixed fraction, where 1 is a whole number and 1/3 is a fraction, and together they form this subtype of fractions.

This concept is straightforward and easy to grasp. However, students must also know about proper and improper fractions to ensure that they comprehend this topic properly.

1. Proper Fraction

A proper fraction is a vital sub-type that students must know about, and to understand this concept of mixed fraction thoroughly. In this type, the numerator is smaller than its denominator. For example, in a fraction of 3/5, three the numerator is smaller than five.

2. Improper Fraction

In case of an improper fraction, the rules are reversed. Here the numerator is equal or larger than its denominator. For instance, in a fraction of 7/4, 7 the numerator is larger than its denominator, i.e. 4.

A point to note here is that the idea of mixed fractions helps to define improper fraction is a simpler way. In smaller fractions like the one mentioned above, it is not difficult to read them, but in case of a bigger one, it is not easy to read them.

Hence, this idea of a mixed fraction is of great help in this regard.

How to Convert Improper Fractions to Mixed Fractions?

Here are the steps of changing improper fractions to mixed numbers –

Step 1: 

Dividing the numerator with denominator. For instance 15/7


The integer of this division will be the integer of the following mixed fraction, i.e. 2

Step 3: 

The denominator will remain the same with 7

Step 4: 

Therefore, the improper fraction of 15/7 is now a mixed fraction of 2(1/7)

How to Convert Mixed Fraction to Improper Fraction?

Here are the step for convert to improper fraction from a mixed one –

Step 1: 

Taking a cue from the previous one, the first step here is to multiply the denominator with the whole number. Hence, 2X7 = 14

Step 2: 

After that, add the numerator to this result, i.e. 14+1= 15

Step 3: 

Retain the same denominator.

Step 4: 

The conversion of a mixed number to an improper fraction is now complete with 15/7 as the outcome

A mixed fraction is a vital part of Mathematics, and it is essential for students to know about it. It helps them learn how to calculate and represent fractions is a way that does not include decimal placing.

Moreover, using mixed fractions is easier and offer more clarity while reading and representing any complicated fraction numbers. Students can learn more about this concept from the website of India's leading e-learning provider Vedantu. At the website, they will find study materials, exam suggestions, practice sets for various topics that can help students to improve their performance. Furthermore, the live online classes and doubt clearing sessions also aid in exam preparations.

FAQs on Mixed Fractions

1. How to Add Mixed Fractions?

Ans. Adding mixed fractions have two methods, if they have the same denominators, then one can simply add the numerators and obtain a result. If the result is in an improper fraction mode, individuals can simplify it by converting them into mixed fractions. On the other hand, if the denominators are not the same, students can find the LCM of them and multiply them with numerators and denominators in a way that the LCM figure is their new denominator. After that, add the numerators keeping the denominators unchanged. Now, if the answer is in improper form, convert it into a mixed fraction form.

2. What is a Mixed Equivalent Fraction?

Ans. A mixed equivalent fraction is when two mixed fractions equal along with the fact that they are equivalent. Therefore, when equivalent fractions get converted into a mixed one, they have the same quotient, when the numerator is divided by the denominator. For example, 10/4 and 5/2 are two equivalent fractions. Here, the mixed forms are 2(2/4) and 2(1/2), respectively. Hence, the quotient of both of these fractions is the same, i.e. 2.

3. What are the Like and Unlike Fractions?

Ans. The concept of like and unlike fractions are straightforward. Like fraction refers to every fraction that has the same denominator. For example, ½, 3/2, 5/2, 7/2, and so on. Moreover, when these fractions are added, their denominator remains unchanged. On the other hand, unlike fractions, represents fractions that have different denominators such as 1/3, 5/4, 8/9, etc. A point to note here is that simplifying, unlike fractions, is a lengthy process when compared to the like ones.