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Hi Students, welcome to **Amans Maths Blogs (AMB)**. In this article, we will study about **fractions**, which is in the syllabus of** Class 7 Maths**. It is the notes of **fractions **chapter which help for the students who study in class 7 in any school.

In this notes, we discuss about **definition of fractions**, **types of fractions**, **fractions calculator**, **fractions to decimals,** **fractions to percentage **etc.

So let discuss one by one.

Contents

# Fractions

As we have already learnt about the integers and the rational numbers.

The integers are the set of natural numbers, zero and negative of natural number.

For example: 12, -9, 1, 0 etc

Read : Concepts of Integers

And, a number that can be represented in the form of p/q, where **p and q are INTEGERS** and q ≠ 0 is called as rational numbers. For example: 5/3, -2/5, 16, 2/9 etc.

Read : Concepts of Rational Numbers

Now, a fraction can be defined as below.

A number that can be represented in the form of p/q, where **p and q are WHOLE numbers** and q ≠ 0 is called as fraction. For example: 5/3, 2/5, 1/2, 2/9 etc.

Thus, by the definitions of rational numbers and fractions, we can say that:

In a fraction p/q (q ≠ 0), the number (p) written over the line known as **NUMERATOR** and the number (q) written below the line is known as **DENOMINATOR** is called as fraction.

For example: in the fraction 15/22, 15 is the numerator and 22 is the denominator.

# Types of Fractions

There are following types of fractions.

## Proper Fractions

A fraction in which the numerator is less than the denominator, then the fraction is known as **Proper Fractions**.

For example: 3/7, 1/8, 9/11; all are proper fractions.

## Improper Fractions

A fraction in which the numerator is greater than the denominator, then the fraction is known as **Improper Fractions**.

For example: 12/5, 13/8, 5/2; all are improper fractions.

## Mixed Fractions

A fraction which is addition of a whole number and a proper fraction is known as **Mixed Fractions**.

For example: ; all are mixed fractions.

## Complex Fractions

A fraction which is the fractions of fractions, means the numerator and the denominator, both are fractions is known as **Complex Fractions**.

For example: is a complex fractions.

A complex fraction (a/b) / (p/q) can be simplified as

Thus, can be simplified as = (1/2) x (5/3) = 5/6

## Equivalent Fractions

A fraction p/q in which the numerator (p) and the denominator (q) is multiplied by a natural number (k) is known as **Equivalent Fractions** of p/q.

For example: ; the fractions 5/7 and 15/21 are equivalent fractions to each other.

## Vulgar Fractions

A fraction p/q in which the denominator (q) is cannot be in the form of 10^{n}, n ∈ N (natural numbers) is known as **Vulgar Fractions**.

For example: 15/7 is the vulgar fraction as 7 cannot be written in the form of 10^{n} for any natural number n.

## Like Fractions

The fractions with same denominator are known as **Like Fractions**.

For example: 5/7 and 2/7 are like fractions.

## Unlike Fractions

The fractions with different denominators are known as **Unlike Fractions**.

For example: 5/7 and 2/3 are unlike fractions.

# Fractions Additions

In this section, we learn how to add two fractions, that may be with same denominator and different denominator.

## Addition of Fractions With Same Denominator

To add two fractions with same denominator, simply we add the numerators and leaves the same denominators.

To understand better the concept of addition of fractions with same denominator, let start with an example:

Suppose we need to add and . In these two fractions, the denominators are same and that is 7.

Thus, to add these two fractions, we simply add the numerators 5 and 13 and we keep the same denominator 7 in the sum.

Therefore, we get .

## Addition of Fractions With Different Denominator

To add two fractions with different denominators, first we need to find equivalent factions of both the given fractions which have the common denominators.

To get the equivalent fractions with common denominators, we need to find the LCM of the denominators of the given fractions.

And, finally, we add them as the addition of two fractions with same denominators.

To understand better the concept of addition of fractions with different denominators, let start with an example:

Suppose we need to add the fractions and .

In these two fractions, the denominators are different; 5 and 3.

First we need to find the equivalent fractions of and which have common denominators.

For this, we find the LCM of denominators (5 and 3). LCM (5 and 3) = 15.

Thus, we need to find the equivalent fractions of and which have common denominator as 15.

Now, the equivalent fraction of with denominator 15 is and the equivalent fraction of with denominator 15 is .

Thus, we get .

To add these fractions, we simply add the numerators 39 and 40.

Thus, we get . Thus, the addition of and is .

# Fractions Subtractions

In this section, we learn how to subtract two fractions, that may be with same denominator and different denominator.

## Subtraction of Fractions With Same Denominator

To subtract two fractions with same denominator, simply we subtract the numerators and leaves the same denominators.

To understand better the concept of subtraction of fractions with same denominator, let start with an example:

Suppose we need to subtract and . In these two fractions, the denominators are same and that is 7.

Thus, to subtract these two fractions, we simply subtract the numerators 5 and 13 and we keep the same denominator 7 in the difference.

Therefore, we get .

## Subtraction of Fractions With Different Denominator

To subtract two fractions with different denominators, first we need to find equivalent factions of both the given fractions which have the common denominators.

To understand better the concept of subtraction of fractions with different denominators, let start with an example:

Suppose we need to subtract the fractions and .

In these two fractions, the denominators are different; 5 and 3.

First we need to find the equivalent fractions of and which have common denominators.

For this, we find the LCM of denominators (5 and 3). LCM (5 and 3) = 15.

Thus, we need to find the equivalent fractions of and which have common denominator as 15.

Now, the equivalent fraction of with denominator 15 is and the equivalent fraction of with denominator 15 is .

Thus, we get .

# Fractions Multiplication

To multiply the fractions, we simply multiply the numerators of the fractions and the denominators of the fractions whether the fractions have same denominator or different denominator.

And finally, we find the simplest fraction of the multiplication.

To understand better the concept of multiplication of fractions, let start with an example:

Suppose we need to multiply the fractions and .

Thus,

# Fractions Division

To divide the fractions, we multiply one of the fractions to the reciprocal of other fraction.

It means, if a/b and p/q are two fractions, then its division is

To understand better the concept of multiplication of fractions, let start with an example:

Suppose we need to divide the fraction by . Then,

# Fractions Simplifications

When more than one mathematical operator are in the expression of fractions, then we need to use PEMDAS rule to simplify the fractions.

Read : Difference between PEMDAS PEDMAS BODMAS BEDMAS

Let we understand with an example.

We need to simplify 12/7 x 21 + 15/4 ÷ 3/7 – 4/3.

Thus, by using PEMDAS rule, we get

12/7 x 21 + 15/4 ÷ 3/7 – 4/3

= (12/7 x 21) + 15/4 ÷ 3/7 – 4/3 [Multiplication]

= (12 x 3) + 15/4 ÷ 3/7 – 4/3

= 36 + (15/4 ÷ 3/7) – 4/3 [Division]

= 36 + (15/4 x 7/3) – 4/3

= 36 + (5/4 x 7) – 4/3

= 36 + 35/4 – 4/3

= (36 + 35/4) – 4/3 [Addition]

= (179/4 – 4/3) [Subtraction]

= (537 – 16) / 12

= 521 / 12

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