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