6 Types of Fractions (With Definition, Examples & Uses)

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As societies began to form and grow the need for different types of numbers was felt by humans. Fractions in different forms like proper fractions, improper fractions, mixed fractions, like fractions, unlike fractions, or equivalent fractions are used for a long.

In this article, we’ll understand different types of fractions with examples.

Different Types of Fractions

The fractions are broadly classified based on 

• individual fraction
• group of fractions

Classification Based on Individual Fraction

In this classification, a single fraction is considered and classified based on its numerator and denominator.

The numerator and denominator are the main parts of any fraction. The numerator is the number that is written on the top of the horizontal bar, while the number that is written on the bottom is called the denominator. The numerator indicates the number of parts that are being considered, whereas, the denominator indicates the total number of parts in the whole.

On the basis of numerator and denominator fractions are classified into three broad categories:

• Proper fractions
• Improper fractions
• Mixed fractions

Proper Fraction Definition

A proper fraction is a fraction in which the numerator is less than the denominator. It is called a proper fraction owing to its proper adherence to the definition of a fraction and the need for a fraction.

Proper Fraction Examples

For example $\frac {5}{7}$ is a proper fraction as $5$ (numerator) < $7$ (denominator).

$\frac {11}{67}$ is a proper fraction as $11$ (numerator) < $67$ (denominator).

Note: 

• Fraction is a part of a whole, where the part is represented by the numerator and the whole is represented by the denominator. And further part is always less than the whole. That’s the reason where the numerator is less than the denominator, the fraction is called ‘proper’.
• Proper fractions are always less than $1$.

Examples of proper fractions are

• $3$ out of $8$ equal slices of a cake represented as $\frac {3}{8}$ 
• $93$ out of $100$ marks in an exam represented as $\frac {93}{100}$
• $7$ girls out of $10$ children in a group represented as $\frac {3}{10}$
• $39$ pages read out of a total of $250$ pages in a book represented as $\frac {39}{250}$
• ₹$57$ spent from ₹100 given by your father represented as $\frac {57}{100}$
• $17$ blue marbles in my collection of $50$ marbles represented as $\frac {17}{50}$

Types of Fractions – Improper Fraction

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

The meaning of improper fraction is defined from the meanings of the words “Improper” and “Fraction”.

• “Improper” means unacceptable, inappropriate, and so on.
• The “Fraction” means a part of the whole quantity.

As per their meanings, it is not acceptable to consider either a whole quantity or the sum of a whole quantity and a part of another whole quantity as a fraction. So, the unacceptable fraction is called an improper fraction.

Improper Fraction Examples

Let’s consider the following example to understand the term ‘improper fraction’.

Imagine you order a pizza that has $8$ slices. Your friends eat all the $8$ slices. And you realize you didn’t get any. You order another pizza. After eating $3$ slice of it you realize you are done eating.

So, how much pizza did your friends, and you have in all?

Your friends first had all eight slices of $1$ pizza, and then you had $3$ slices out of the size of the second pizza.

So, the total pizza eaten is $\frac{8 + 3}{8} = \frac {11}{8}$ { slices of pizza. And that’s an improper fraction with a numerator greater than the denominator.

Examples of some other mixed fractions are $\frac{17}{8}$, $\frac{63}{4}$, $\frac{109}{10}$, $\frac{83}{51}$. In all these fractions numerator is greater than the denominator.

Note: 

• Improper fractions can be represented as mixed fractions.
• Improper fractions are always greater than $1$.

Mixed Fractions

A mixed fraction is a mix of a whole number and a proper fraction.

Improper Fraction Examples

For example, $ 7 \frac {3}{4}$ is a mixed fraction as it is a combination of 

• whole number i.e., $7$
• proper fraction i.e., $\frac {3}{4}$

$-2 \frac{4}{9}$ is a mixed fraction with $-2$ a whole part and $\frac{4}{9}$ a fractional part.

Note:  

• Mixed fractions can always be converted into improper fractions.
• Improper fractions can be converted into mixed fractions.
• A mixed fraction is always greater than 1.

Types of Fractions in a Group

In this classification, a group of fractions (two or more) is considered and classified. According to this classification, the fractions are classified into three categories:

• Like fractions
• Unlike fractions
• Equivalent fractions

Like Fractions

Two or more fractions are called like fractions if their denominators are the same. 

For example $\frac {2}{7}$, $\frac {5}{7}$, $\frac {4}{7}$, $\frac {3}{7}$, $\frac {6}{7}$ are like fractions.

We can perform addition and subtraction only on like fractions. If we want to add or subtract unlike fractions, first of all, they are converted into like fractions.

Note: $\frac {2}{3}$, $\frac {2}{4}$, $\frac {2}{5}$, $\frac {2}{6}$, $\frac {2}{7}$ are not like fractions.

Unlike Fractions

Two or more fractions are called unlike fractions if their denominators are different. 

For example $\frac {2}{7}$, $\frac {5}{9}$, $\frac {2}{19}$, $\frac {3}{11}$, $\frac {12}{49}$ are unlike fractions.

To perform addition or subtraction on unlike fractions, first of all, they need to be converted into like fractions. Multiplication and division can be performed on unlike fractions without converting them into like fractions.

Equivalent Fractions

Equivalent fractions are fractions that have different numerators and different denominators but are equal to the same value when simplified or reduced. 

For example, $\frac {2}{4}$, $\frac {3}{6}$, and $\frac {4}{8}$ are all equivalent fractions because they all get reduced to $\frac {1}{2}$.

Special Fractions – Unit Fractions

Unit fractions are those fractions in which the numerator is $1$ and the denominator is a positive integer.

For example, $\frac {1}{5}$, $\frac {1}{4}$, $\frac {1}{35}$, $\frac {1}{78}$, and so on are unit fractions.

Note: $\frac {2}{1}$, $\frac {7}{1}$, $\frac {32}{1}$, $\frac {56}{1}$ are not unit fractions.

Practice Problems

1. Which of the following are the type of a fraction based on numerator and denominator?
   • Proper fraction, Improper fraction, Mixed fraction, Like Fractions, Unlike fractions, Equivalent fractions
2. Which of the following is the type of fractions when they are in a group?
   • Proper fraction, Improper fraction, Mixed fraction, Like Fractions, Unlike fractions, Equivalent fractions
3. In proper fractions, the numerator is greater than the denominator.
   • True
   • False
4. In improper fractions, the numerator is greater than the denominator.
   • True
   • False
5. Like fractions have the same numerator.
   • True
   • False
6. Unlike fractions have the same numerator.
   • True
   • False
7. Fractions having the same value but different numerators and denominators are called _______.
   • Equal fractions
   • Equivalent fractions

FAQs

Conclusion

Broadly the fractions are of two types – proper fractions and improper fractions. Improper fractions can also be expressed as mixed fractions. When fractions are in a group, they are classified as like fractions, unlike fractions, or equivalent fractions.

Recommended Reading

• What is Fraction?  – Definition, Examples & Types
• Mixed Fractions – Definition & Operations (With Examples)
• Multiplication and Division of Fractions
• Addition and Subtraction of Fractions (With Pictures)