Fractions are amongst the most common terms that are used in maths for determining the parts of a whole object. There are generally six types of fraction:

1. Proper fraction

2. Improper fraction

3. Mixed fraction

4. Like fraction

5. Unlike Fraction

6. Equivalent fraction

The kinds of fraction are classified depending on the numerator and the denominator of the given fraction. We will discuss here in this article about the different types of fractions and have a look at the types of fraction with example.

In the earlier classes, you came across the concept of the whole numbers to measure different quantities. However, in the real-life scenarios, all the measured quantities cannot be in the form of the perfect whole numbers. You might have to deal with the parts and portions of the whole things, and this is when the concept of the fraction comes into the picture.

 

Fraction and its Types

A fraction refers to the ratio of two numbers. The upper number of the fraction is known as the numerator and the lower number of the fraction is called the denominator. When the whole of something is divided into several numbers of parts, each part is called a fraction. Consider the example given below:

 

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Let us learn about these different types of fraction in maths in detail.

 

Proper and Improper Fraction

Let us learn about what is proper and improper fraction.

 

Proper Fraction

A fraction in which the numerator is less than the denominator is known as a proper fraction. 

1. The value of the proper fraction after the further simplification of the fraction is always less than 1. 

Consider the example below:

 

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Improper Fraction

A fraction where the numerator is greater than the denominator, then it is known as an improper fraction.

1. All the natural numbers can be easily represented in the form of fractions when the denominator is equal to 1 always. 

2. The simplification of the improper fraction would result in the value that is greater than or equal to 1 but is not less than 1. 

Consider the following example:

 

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Mixed Fraction

A mixed fraction refers to the combination of the natural number and the fraction. It is basically a kind of an improper fraction.

1. Mixed fractions are always possible to be converted into a proper fraction.

2. An improper fraction can also be converted into the mixed fraction.

3. The value of the mixed fraction is greater than 1 always.

Consider the given example:

 

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Like and Unlike Fractions

Like Fractions

The fractions that have the same denominators are called as the like like fractions. Consider the following example:

 

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The simplification of the like fractions is easier since the denominators are the same. For example, you have to simplify the following equations:

 

\[\frac{2}{5} + \frac{5}{5} + \frac{6}{5} + \frac{8}{5} + \frac{9}{5}\]

 

= \[\frac{2 + 5 + 6 + 8 + 9}{5} = \frac{30}{5} = 6\]

 

Unlike Fractions

The fractions that have unequal denominators or different kinds of denominators are referred to as the unlike fractions. Consider the example given:

 

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The simplification of the unlike fractions is a bit tricky and lengthy since you first need to factorize the denominators and then simplify them in the case of the addition and subtraction. 

 

For example, you need to add \[\frac{1}{2}\]and \[\frac{1}{3}\].

 

You first need to find the LCM of the two numbers 2 and 3 which is 6.

 

Then, multiply \[\frac{1}{2}\] by 3 and \[\frac{1}{3}\] by 2. 

 

The fractions that you would get are \[\frac{3}{6}\] and \[\frac{2}{6}\].

 

When you add them together, you get

 

\[\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\]

 

Equivalent Fractions

When two or more than two fractions have the same result after the simplification and they represent the same portion of the whole object, then such types of fractions are equal to one another and are known as the equivalent fractions. Consider the following example:

 

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Solved Examples

Let us now look at some of the solved examples based on the types of fractions worksheets.

 

Example 1:

\[\frac{4}{7}\]of a number results to 84. Find out the number.

 

Solution:

According to the given problem,

 

\[\frac{4}{7}\]of the number = 84

 

Hence, the number = \[84 \times \frac{7}{4}\]

 

Solving \[84 \times \frac{7}{4}\], you get,

 

\[21 \times 7 = 147\]

 

Hence, the given number is 147.

 

Example 2:

One – half of the students in a school are girls, and \[\frac{3}{5}\] of these girls are studying in the lower classes. What fraction of these girls are studying in the lower classes?

 

Solution:

The fraction of the girls studying in a school = \[\frac{1}{2}\]

 

The fraction of the girls studying in the lower classes = \[\frac{3}{5} {\text{of}} \frac{1}{2}\]

 

= \[\frac{3}{5} \times \frac{1}{2}\]

 

Solving this, you would get,

 

= \[\frac{3}{5} \times \frac{1}{2} = \frac{3}{10}\]

 

Therefore, the fraction of the girls studying in the lower classes is \[\frac{3}{10}\].FAQs (Frequently Asked Questions)