Fraction For Class 4, deals with various concepts which are as under:-

- Proper Fraction | Improper Fraction | Mixed Fraction
- Like Fractions | Unlike Fractions
- Fraction in Simplest Form
- Equivalent Fraction
- Conversion of Mixed Fraction into an Improper Fraction
- Conversion of Improper Fraction into Mixed Fraction
- Comparing Fractions
- Addition of Like Fractions and Unlike Fractions
- Subtraction of Like Fractions or Unlike Fractions

#### Fraction For Class 4 – Proper Fraction | Improper Fraction | Mixed Fraction

**Proper Fraction**

Proper Fraction is a Fraction whose numerator is less than its denominator.

i.e Numerator < Denominator

For Example – , , are Proper Fractions.

**Improper Fraction**

Improper Fraction is a Fraction whose numerator is greater than or equal to its denominator.

i.e Numerator ≥ Denominator

For Example – , , are Improper Fractions.

**Mixed Fraction**

Mixed Fraction is a Fraction having a combination of a Whole number or a Proper Fraction.

For Example – , , are Improper Fractions.

__Question 1__

Is an Improper Fraction?

__Explanation :__

In the given Fraction, Numerator = 12

The Denominator = 7

Here, 12 > 7

i.e, Numerator > Denominator

Hence, is an Improper Fraction

__Question 2__

Is an Improper Fraction?

__Explanation :__

In the given Fraction, Numerator = 3

The Denominator = 4

Here, 3 < 4

i.e, Numerator < Denominator

Hence, is not an Improper Fraction

__Question 3__

Is a Proper Fraction?

__Explanation :__

In the given Fraction, Numerator = 3

The Denominator = 8

Here 3 < 8

i.e, Numerator < Denominator

Hence, is a Proper Fraction.

__Question 4__

Is a Proper Fraction?

__Explanation :__

In the given Fraction, Numerator = 5

The Denominator = 4

Here 5 > 4

i.e, Numerator > Denominator

Hence, is not a Proper Fraction.

#### Fraction For Class 4 – Like Fractions | Unlike Fractions

**Like Fractions**

Fractions having the same denominators are called Like Fractions.

For example are Like Fractions.

**Unlike Fractions**

Fractions having different denominators are called Unlike Fractions.

For example are Unlike Fractions.

__Question 5__

Are the following Fractions are Like Fractions or Unlike Fractions?

, and

__Explanation :__

In case of Like Fraction, the denominator of the Fractions are the same.

While, In case of Unlike Fraction denominator of the Fractions are not same.

In the present case, the given Fractions are

, and

Since, the Denominator in the present cases is 3 , which is the same for all Fractions, the given Fractions are Like Fractions

__Question 6__

Are the following Fractions are Like Fractions or Unlike Fractions?

, and

__Explanation :__

In case of Like Fraction, the denominator of the Fractions are the same.

While, In case of Unlike Fraction denominator of the Fractions are different.

In the present case, the given Fractions are

, and

Since the Denominator in the present cases are 6 , 3 , 5 , which are not same, the given Fractions are Unlike Fractions

#### Fraction For Class 4 – Fraction in Simplest Form

Fraction in Simplest Form – A Fraction is said to be in simplest form when the** numerator** and **denominator** of a fraction has **only common factor **i.e, **1**

In other words, To simplify a fraction in simplest form we **divide** the** numerator** and **denominator** of a fraction **by their H.C.F** ( Highest Common Factor ).

__Question 7__

Convert into its Simplest Form?

__Explanation :__

Finding HCF of **15** and **45**.

Factors of 15 are **3**, **5**

Factors of 45 are **5**, **3**, 3

HCF of **15** and **45** = 3 x 5 = **15**

Divide Numerator and Denominator by their HCF i.e, **15**

Hence, is the simplest form of

#### Fraction For Class 4 – Equivalent Fraction

#### Equivalent Fraction

Equivalent Fractions are Fractions that represent the same amount or same Fractions.

__Question 8__

Check whether and are Equivalent Fractions ?

__Explanation :__

If two fractions are equivalent, on cross multiplication, their Products will be the same

Cross multiplying and

we get,

2 x 9 = 18

and

6 x 3 = 18

Since, the products are same

Hence, and are Equivalent Fractions.

__Question 9__

Check whether and are Equivalent Fractions ?

__Explanation :__

If two fractions are equivalent, on cross multiplication, their Products will be the same

Cross multiplying and

We get,

5 x 16 = 80

and

10 x 9 = 90

Since, the products are not same

Hence, and are not Equivalent Fractions.

#### Finding Equivalent Fraction with given Numerator

__Question 10__

Write an equivalent Fraction of with Numerator 12 .

__Explanation :__

Let,

=

In order to obtain an equivalent fraction, we need to multiply the Numerator and Denominator of a given number , by same digit

To get 12 as Numerator, we have to multiply 2 by 6

In order to get an equivalent Fraction, we have to multiply the Denominator by the same number, i.e, 6

i.e,

=

#### Finding Equivalent Fraction with given Denominator

__Question 11__

Write an equivalent Fraction of with denominator 4 .

__Explanation :__

Let,

=

In order to obtain an equivalent fraction, we need to divide the Numerator and Denominator of a given number , by same digit

To get 4 in the denominator, we need to divide 12 by 3

So, in order to get an equivalent Fraction, we have to divide the Numerator also by 3

i.e,

=

Hence, is an equivalent Fraction of with denominator 4

#### Fraction For Class 4 – Conversion of Mixed Fraction into an Improper Fraction

To Convert Mixed Fraction into Improper Fraction, we follow the steps given below:-

**Step 1**: Multiply the Whole Number Part and Denominator of the Mixed Fraction

**Step 2**: Add the Numerator to the product obtained in Step 1

**Step 3**: Write the sum as the numerator and denominator would remain the same, as in the Mixed Fraction.

__Question 12__

Convert the Fraction into an Improper Fraction

__Explanation :__

A combination of Whole Number and a Proper Fraction is called a Mixed Fraction

Here,

Mixed Fraction =

Whole Number Part = 2

Numerator = 1

Denominator = 2

Step 1 : Multiply the Whole Number Part and Denominator of the Mixed Fraction

2 x 2 = 4

Step 2 : Add the Numerator to the product obtained in Step 1

1 + 4 = 5

Write the sum as the numerator and denominator would remain the same , as in the Mixed Fraction.

Hence, =

#### Fraction For Class 4 – Conversion of Improper Fraction into Mixed Fraction

To Convert Improper Fraction into Mixed Fraction, we follow the steps given below:-

**Step I**: Divide the Numerator by the Denominator.

**Step II**: Write the Mixed Fraction as: ( Quotient + )

__Question 13__

Convert into Mixed Fraction.

__Explanation :__

Given Fraction:

Divide the Numerator by the Denominator

On dividing 4 by 3

We get Quotient = 1

Remainder = 1

For a Mixed Fraction we have to write ( Quotient + )

So, the Mixed Fraction is 1 + = 1

#### Fraction For Class 4 – Comparing Fractions

**Comparing Fractions can be divided in two categories:**

- Comparison of Like Fractions
- Comparison of Unlike Fractions

First Method : By Converting Given Fractions into Like Fractions

Second Method : By Cross Multiplication Method

**COMPARISION OF LIKE FRACTION**

__Question 14__

Compare

__Explanation :__

are Like Fraction as Denominator of both the Fractions is same i.e, 3

In case of Like Fraction, the Fraction with the higher numerator is Higher

On Comparing the Numerators, we find

7 > 4

Hence,

**COMPARISON OF UNLIKE FRACTION**

__Question 15__

Compare

__Explanation :__

are Unlike Fractions as Denominator of both the Fractions is different i.e, 3 and 2

To compare Unlike Fractions we have two methods:

__First Method : By Converting Given Fractions into Like Fractions__

Given Fractions :

and

Taking LCM of the Denominator of both the Fractions.

i.e, LCM of 3 and 2 is 6

To change the Unlike Fractions into Like Fractions

We have to multiply the Numerator and Denominator of the Given Fraction by a number such that the Denominator of the given Fraction becomes equal to its LCM i.e, 6

We have to multiply Numerator and Denominator of by 2

=

We have to multiply Numerator and Denominator of by 3

=

Now the Given Fractions are Like Fraction as their Denominator become same.

On Comparing their Numerators, we find

4 > 3

Therefore, >

Hence, >

__Second Method : By Cross Multiplication Method __

On Cross multiplying and

In Cross Multiplication Method we multiply the Numerator of First Fraction namely 2 by the Denominator of Second Fraction namely 2 i.e,

2 x 2 = 4

Then, we multiply the Numerator of Second Fraction namely 1 by the Denominator of First Fraction namely 3 i.e,

1 x 3 = 3

Since, 4 > 3

Therefore, >

#### Fraction For Class 4 – Addition of Like Fractions and Unlike Fractions

To add **Like Fractions**, we add the numerators and write the sum over the same denominator.

To add **Unlike Fractions**, first we have to change the Unlike Fractions, into equivalent Like Fractions, and then add the two equivalent Like Fractions

**Example on Addition of Like Fractions**

__Question 16__

Find the sum of and and reduce to its lowest term.

__Explanation :__

Sum of Like Fraction =

Sum of Like Fraction =

Sum of Like Fraction =

Hence, the sum of and is

Simplifying further,

HCF of 12 and 14 is 2

Dividing both Numerator and Denominator by their HCF i.e,

=

Hence, the sum of and =

**Example on Addition of Unlike Fractions**

__Question 17__

Find the sum of and and reduce to its lowest term.

__Explanation :__

In order to add Unlike Fraction

Firstly, we have to change the Unlike Fraction, into equivalent Like Fractions, and then add the two equivalent Like Fractions

Take LCM of 3 and 4 is 12

Converting the Unlike Fraction into Equivalent Like Fraction

We have to multiply , both the numerator and denominator of by 4

=

We have to multiply , both the numerator and denominator of by 3

=

Now + =

Simplifying further,

HCF of 10 and 12 is 2

Dividing both Numerator and Denominator by their HCF i.e,

=

Hence, the sum of and =

#### Fraction For Class 4 – Subtraction of Like Fractions or Unlike Fractions

To subtracts **Like Fractions**, we subtract the numerators and write the difference over the same denominator.

To subtracts **Unlike Fractions**, first we have to change the Unlike Fractions, into equivalent Like Fractions, and then subtract the two equivalent Like Fractions

**Example on Subtraction of Like Fractions**

__Question 18__

Find the difference of and and reduce to its lowest term.

__Explanation :__

Difference of Like Fraction =

Difference of Like Fraction =

Difference of Like Fraction =

Simplifying further,

HCF of 4 and 8 is 4

Dividing both Numerator and Denominator by their HCF i.e,

=

Hence, the difference of and =

**Example on Subtraction of Unlike Fractions**

__Question 19__

Find the difference of and and reduce to its lowest term.

__Explanation :__

To find the difference of Unlike Fraction

Firstly, we have to change the Unlike Fraction into equivalent Like Fraction, and then subtract the two equivalent Like Fraction

Take LCM of 2 and 4 is 4

Converting the Unlike Fraction into Equivalent Like Fraction

We have to multiply Numerator and Denominator of by 2

=

We have to multiply Numerator and Denominator of by 1

=

Now – =

Hence, the difference of and =

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