Types of Fractions

Types of Fractions, deals with various concepts which are as under:-

Proper Fraction
Improper Fraction
Mixed Fraction
– Convert Improper Fraction to Mixed Fraction
– Convert Mixed Fraction to Improper Fraction

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Fraction:

Fraction is a part of whole number.
In generalise form for any two natural numbers ‘a’ and ‘b’ fraction is:
$\cfrac{a}{b}$

Where,
a = Numerator
b = Denominator

Example 1

Write down the Numerator and Denominator of the Fraction:

$\cfrac{4}{3}$

Explanation

Numerator is the upper part (Number on Top) of the Fraction

So, the Numerator of $\cfrac{4}{3}$ is 4

Denominator is the lower number ( Number at Bottom) of the Fraction
So, the Denominator of $\cfrac{4}{3}$ is 3

Example 2

Write down the Numerator and Denominator of the Fraction:
$\cfrac{5}{6}$

Explanation

Numerator is the upper part (Number on Top) of the Fraction
So, the Numerator of $\cfrac{5}{6}$ is 5

Denominator is the lower number ( Number at Bottom) of the Fraction
So, the Denominator of $\cfrac{5}{6}$ is 6

Proper Fraction

Proper fraction is a fraction which represents the part of whole number. In proper fraction numerator is always less than its denominator.

In generalise form for any two integer ‘a’ and ‘b’

$\cfrac{a}{b}$ where (a < b)

i.e Numerator < Denominator

Example 1

Is $\cfrac{2}{3}$ is a proper fraction?

Explanation

Proper fraction is a fraction which represents the part of whole number. In proper fraction numerator is always less than its denominator.

In generalise form for any two integer ‘a’ and ‘b’

$\cfrac{a}{b}$ where (a < b)

i.e Numerator < Denominator

Numerator = 2

Denominator = 3

Here 2 < 3

i.e, Numerator < Denominator

Hence, $\cfrac{2}{3}$ is a proper fraction

Example 2

Is $\cfrac{7}{5}$ is a proper fraction?

Explanation

Proper fraction is a fraction which represents the part of whole number. In proper fraction numerator is always less than its denominator.

In generalise form for any two integer ‘a’ and ‘b’

$\cfrac{a}{b}$ where (a < b)

i.e Numerator < Denominator

Numerator = 7

Denominator = 5

Here 7 > 5

i.e, Numerator > Denominator

Hence, $\cfrac{7}{5}$ is not a proper fraction

Improper Fraction

Improper fractions are the combination of whole number and a proper fraction. Improper fraction is opposite of proper fraction, since in improper fraction numerator is greater than its denominator

In generalise form for any two integer ‘a’ and ‘b’

$\cfrac{a}{b}$ where (a > b)

i.e Numerator > Denominator

Example 1

Is $\cfrac{17}{9}$ is a improper fraction?

Explanation

Improper fractions are the combination of whole number and a proper fraction. Improper fraction is opposite of proper fraction, since in improper fraction numerator is greater than its denominator

In generalise form for any two integer ‘a’ and ‘b’

$\cfrac{a}{b}$ where (a > b)

i.e Numerator > Denominator

Numerator = 17

Denominator = 9

Here, 17 > 9

i.e, Numerator > Denominator

Hence, $\cfrac{17}{9}$ is an improper fraction.

Example 2

Is $\cfrac{7}{10}$ is a improper fraction?

Explanation

Improper fractions are the combination of whole number and a proper fraction. Improper fraction is opposite of proper fraction, since in improper fraction numerator is greater than its denominator

In generalise form for any two integer ‘a’ and ‘b’

$\cfrac{a}{b}$ where (a > b)

i.e Numerator > Denominator

Numerator = 7

Denominator = 10

Here, 7 < 10

i.e, Numerator < Denominator

Hence, $\cfrac{7}{10}$ is not an improper fraction.

Mixed Fraction

Mixed Fraction is a sum of whole number and proper fraction. Improper fraction can be converted into mixed fraction and mixed fraction can be converted into improper fraction with the help of simple multiplication, division and addition.

Convert Improper Fraction to 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 + $\cfrac{Remainder}{Divisor}$ )

Example 1

Convert $\cfrac{3}{2}$ into Mixed Fraction.

Explanation

Given Fraction:

$\cfrac { 3 }{ 2 }$

Divide the Numerator by the Denominator

On dividing 3 by 2

We get Quotient = 1

Remainder = 1

For a Mixed Fraction we have to write ( Quotient + $\cfrac{Remainder}{Divisor}$ )

So, the Mixed Fraction is ( 1 + $\cfrac{1}{2}$ ) = $1\cfrac { 1 }{ 2 }$

Example 2

Convert $\cfrac{5}{3}$ into Mixed Fraction.

Explanation

Given Fraction:

$\cfrac { 5 }{ 3 }$

Divide the Numerator by the Denominator
On dividing 5 by 3
We get Quotient = 1
Remainder = 2

For a Mixed Fraction we have to write ( Quotient + $\cfrac{Remainder}{Divisor}$ )

So, the Mixed Fraction is ( 1 + $\cfrac{2}{3}$ ) = $1\cfrac { 2 }{ 3 }$

Convert Mixed Fraction to 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.

Example 1

Convert the Fraction $2\cfrac { 2 }{ 3 }$ into an Improper Fraction

Explanation

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

Here,

Mixed Fraction = $2\cfrac { 2 }{ 3 }$

Whole Number Part = 2

Numerator = 2

Denominator = 3

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

2 x 3 = 6

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

2 + 6 = 8

Write the sum as the numerator and denominator would remain the same, as in the Mixed Fraction.
$\cfrac { 8 }{ 3 }$

Hence, $2\cfrac { 2 }{ 3 }$ = $\cfrac { 8 }{ 3 }$

Example 2

Convert the Fraction $3\cfrac { 1 }{ 2 }$ into an Improper Fraction

Explanation

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

Here,

Mixed Fraction = $3\cfrac { 1 }{ 2 }$

Whole Number Part = 3

Numerator = 1

Denominator = 2

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

3 x 2 = 6

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

1 + 6 = 7

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

$\cfrac { 7 }{ 2 }$

Hence, $3\cfrac { 1 }{ 2 }$ = $\cfrac { 7 }{ 2 }$

Types of Fractions | Proper | Improper | Mixed Fraction

Fraction: