Types of Fraction | Proper | Improper | Mixed Fraction

Types of Fraction:

• Proper Fraction
• Improper Fraction
• Mixed Fraction
  – Convert Improper Fraction To Mixed Fraction
  – Convert Mixed Fraction To Improper Fraction

Fraction:

• A fraction is a part of the whole number.
• In generalising form for any two natural numbers ‘a’ and ‘b’ fraction is:
• a/b

Where,

• a = Numerator
• b = Denominator

Example 1

Write down the Numerator and Denominator of the Fraction:

4/3

Explanation

The numerator is the upper part (Number on Top) of the Fraction

So, the Numerator of 4/3 is 4

The denominator is the lower number ( Number at Bottom) of the Fraction
So, the Denominator of 4/3 is 3

Example 2

Write down the Numerator and Denominator of the Fraction:

5/6

Explanation

The numerator is the upper part (Number on Top) of the Fraction
So, the Numerator of 5/6 is 5

The denominator is the lower number ( Number at Bottom) of the Fraction
So, the Denominator of 5/6 is 6

TYPES OF FRACTION

Types of Fraction – Proper Fraction

• A proper fraction is a fraction which represents the part of the whole number. In a proper fraction, the numerator is always less than its denominator.
• In generalising form for any two integers ‘a’ and ‘b’
• a/b where (a < b)
• i.e Numerator < Denominator

Example 1

Is 2/3 is a proper fraction?

Explanation

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

• In generalise form for any two integer ‘a’ and ‘b’
• a/b where (a < b)
• i.e Numerator < Denominator
• Numerator = 2
• Denominator = 3
• Here 2 < 3
• i.e, Numerator < Denominator
• Hence, 2/3 is a proper fraction

Example 2

Is 7/5 is a proper fraction?

Explanation

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

• In generalising form for any two integers ‘a’ and ‘b’
• a/b where (a < b)
• i.e Numerator < Denominator
• Numerator = 7
• Denominator = 5
• Here 7 > 5
• i.e, Numerator > Denominator
• Hence, 7/5 is not a proper fraction

Types of Fraction – Improper Fraction

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

• In generalising form for any two integers ‘a’ and ‘b’
• a/b where (a > b)
• i.e Numerator > Denominator

Example 1

Is 17/9 is an improper fraction?

Explanation

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

• In generalising form for any two integers ‘a’ and ‘b’
• a/b where (a > b)
• i.e Numerator > Denominator
• Numerator = 17
• Denominator = 9
• Here, 17 > 9
• i.e, Numerator > Denominator
• Hence, 17/9 is an improper fraction.

Example 2

Is 7/10 is an improper fraction?

Explanation

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

• In generalising form for any two integers ‘a’ and ‘b’
• a/b where (a > b)
• i.e Numerator > Denominator
• Numerator = 7
• Denominator = 10
• Here, 7 < 10
• i.e, Numerator < Denominator
• Hence, 7/10 is not an improper fraction.

Types of Fraction – Mixed Fraction

Mixed Fraction is a sum of a whole number and a proper fraction. An improper fraction can be converted into a mixed fraction and mixed fraction can be converted into an 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.

Example 1

Convert 3/2 into Mixed Fraction.

Explanation

Given Fraction:

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

Example 2

Convert 5/3 into Mixed Fraction.

Explanation

Given Fraction:

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

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

Explanation

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

• 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.
  8/3

Example 2

Explanation

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

• 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.
• 7/2

Learn More..

• Types of Fractions | Proper | Improper | Mixed Fraction
• Equivalent Fractions Examples
• Fraction in Simplest Form
• Like Fractions and Unlike Fractions
• Comparing Fractions
• Adding Fractions
• Subtracting Fractions
• Multiplying Fraction
• Dividing Fractions