# Definition of Fraction

A fraction is a part of the whole. Such as a piece of cake from a whole cake.

(1/2) is a fraction where 1 = numerator & 2 = denominator

## 1. Examples of fractions

*Number of girls in a school from all students.**A piece of pizza from whole pizza.**2/4 part of the whole circle.**A piece of an Apple from the whole apple.*

## 2. Types of fractions

There are different types of fractions which we use in mathematics as well as in our daily life-

### 1.) Proper fraction

The fraction in which numerator is less than its denominator.

*Example:- (1/4), (5/8), (2/5), etc.*

In the above examples, all the numerator is less than from denominator.

### 2.) Improper fraction

The fraction in which numerator is more than its denominator.

*Example:- (12/5), (13/2), (47/3), etc.*

In the above examples, all the numerator is more than from denominator.

### 3.) Mixed fraction

The fraction in which we show

**quotient,****remainder**&**divisor**as**2³/₄**.*Example:- (2³/₄), (5²/₈).*

In the above examples, colours show the position of quotient, remainder & divisor.

## 3. Equivalent fraction

The fraction which is equal to the other fractions then they are known as equivalent fractions.

*Examples:- (1/2) & (2/4) are equivalent to each other. But why they are equivalent. Let's discuss-*

*If we reduce (2/4) in the lowest form*

*(2/4)÷(2/2) = (1/2)*

*Here we get (1/2) & it is equal to (1/2). So both fractions*

*(1/2) & (2/4)*

*are equivalent to each other.*

## 4. Addition of fractions

We add different whole numbers & integers. Here we are discussing how to add the fractions.

### Add the fractions (1/2) & (2/4).

We can add fractions in different ways-

#### 1.) By Equivalent fraction-

Solve-

= (1/2) + (2/4)

*{In equivalent fraction we will make both fractions equal by multiply (1/2) from 4 & multiply (2/4) from 2 as below}*

= (1/2)×(4/4) + (2/4)×(2/2)

= (1×4)/(2×4) + (2×2)/(4×2)

=(4/8) + (4/8)

*{ Here both fractions making equal, now we will add both the fractions }*

*=*(4 + 4)/8

= 8/8

=1

*{ Here we get our answer 1}*

#### 2.) By L.C.M.

Solve-

= (1/2) + (2/4)

*{ In L.C.M. we will take L.C.M. of both denominator}*

*=*L.C.M. of both denominator 2 & 4 will be 4.

= {(1×2) + (2×1)}÷4

= {2 + 2} ÷ 4

= 4 ÷ 4

= 1

*{ Here we get our answer 1}*

## 5. Multiplication of fractions

### Multiply the fractions (3/5) & (4/7)

We can multiply both fractions as below-

Solve-

= (3/5) × (4/7)

*{ Multiply both numerator 3 & 4 to each other & multiply both denominator 5 & 7 to each other}*

= (3×4) / (5×7)

= 12/35

*{ Here we get our answer (12/35) }*

## 6. Division of fractions

### Divide the fractions (4/5) & (7/2)

We can divide both fractions as below-

Solve-

= (4/5) ÷ (7/2)

*{ Now we will do reciprocal of (7/2) as (2/7) & change the sign of ÷ to × }*

= (4/5) × (2/7)

*{ Multiply both numerator 4 & 2 to each other & multiply both denominator 5 & 7 to each other}*

= (4×2) / (5×7)

= 8/35

*{ Here we get our answer (8/35).*

## 7. Subtraction of fractions

### Subtract the fraction (4/5) & (3/5)

We may subtract the fraction (4/5) & (3/5) with the help of L.C.M. & equivalent method.

But we are solving it directly because here both denominators are the same.

Solve-

= (4/5) - (3/5)

= (4 - 3) / 5

= 1/5

*{ Here we get our answer (1/5) }.*