March 09, 2026

Class 6 Maths Chapter 7 Fractions – NCERT Ganita Prakash Complete Explanation with Solutions

Introduction

In daily life we often share things equally. For example, if a roti is shared between two children, each child gets half of the roti. Mathematics uses fractions to represent such equal parts of a whole.

A fraction represents a part of a whole quantity.

Example
If one roti is divided among 2 children:

1/2 roti each

If one roti is divided among 4 children:

1/4 roti each

Clearly,

1/2 > 1/4

because fewer people sharing means a bigger share.

Fractions help us represent equal sharing, measurements, and comparisons.

7.1 Fractional Units and Equal Shares

When a whole object is divided into equal parts, each part is called a fractional unit.

Examples of fractional units:

1/2
1/3
1/4
1/5
1/6

These are also called unit fractions because the numerator is 1.

Example Problems

Question 1

Three guavas together weigh 1 kg.
Each guava weighs?

Solution

Total weight = 1 kg
Number of guavas = 3

Weight of each guava

1 ÷ 3 = 1/3 kg

Answer

1/3 kg

Question 2

1 kg rice is packed into 4 equal packets.

Weight of each packet?

Solution

1 ÷ 4 = 1/4 kg

Answer

1/4 kg

Question 3

4 friends share 3 glasses of juice equally.

Each friend gets:

3 ÷ 4 = 3/4 glass

Answer

3/4 glass

Question 4

Big fish weight = 1/2 kg
Small fish weight = 1/4 kg

Total weight?

Solution

1/2 + 1/4

Convert to common denominator

1/2 = 2/4

2/4 + 1/4 = 3/4

Answer

3/4 kg

7.2 Fraction as Part of a Whole

A fraction also represents part of a whole object.

Example

A chikki divided into 6 equal pieces

Each piece =

1/6

Even if the shapes of pieces are different, if they are equal in size, they represent the same fraction.

7.3 Measuring Using Fractional Units

Fractions can measure length.

Suppose a paper strip represents 1 unit length.

If we fold it into 2 equal parts:

Each part = 1/2

If folded into 4 equal parts:

Each part = 1/4

2 × 1/4 = 2/4
3 × 1/4 = 3/4

Example

5 × 1/4

= 5/4

= 1 1/4

Reading Fractions

Example

5/6

5 = Numerator
6 = Denominator

Numerator → number of parts taken
Denominator → total equal parts

7.4 Fractions on the Number Line

Fractions can also be represented on a number line.

Between 0 and 1 we can divide the segment into equal parts.

Example

If divided into 2 equal parts

Midpoint represents

1/2

Insert Image Here

7.5 Mixed Fractions

Fractions greater than 1 can be written as mixed numbers.

Example

3/2

= 1 + 1/2

= 1 1/2

Another example

5/2

= 2 + 1/2

= 2 1/2

Convert Improper Fraction to Mixed Fraction

Example

8/3

Divide numerator by denominator

8 ÷ 3 = 2 remainder 2

8/3 = 2 2/3

7.6 Equivalent Fractions

Fractions representing the same value are called equivalent fractions.

Example

1/2 = 2/4 = 4/8

All represent the same portion.

Example

Are 1/3 and 2/6 equivalent?

Multiply numerator and denominator of 1/3 by 2

1 × 2 / 3 × 2

= 2/6

Yes, they are equivalent.

Simplest Form of Fractions

A fraction is in simplest form if numerator and denominator have no common factor.

Example

16/20

Common factor = 4

Divide

16 ÷ 4 = 4
20 ÷ 4 = 5

Simplest form

4/5

7.7 Comparing Fractions

To compare fractions:

Step 1
Convert them to the same denominator.

Step 2
Compare numerators.

Example

Compare

4/5 and 7/9

Find common denominator

4/5 = 36/45
7/9 = 35/45

36/45 > 35/45

Therefore

4/5 > 7/9

7.8 Addition of Fractions

Same Denominator

Example

2/5 + 1/5

= (2+1)/5

= 3/5

Different Denominators

Example

1/4 + 1/3

Common denominator = 12

1/4 = 3/12
1/3 = 4/12

Add

3/12 + 4/12 = 7/12

Answer

7/12

Subtraction of Fractions

Example

3/4 − 2/3

Convert to common denominator

3/4 = 9/12
2/3 = 8/12

Subtract

9/12 − 8/12 = 1/12

Answer

1/12

History of Fractions

Fractions were known in ancient India as Bhinna, which means broken part.

Indian mathematicians like:

Aryabhata
Brahmagupta
Mahaviracharya

developed rules for fraction operations.

Even today we use Brahmagupta's method for adding and subtracting fractions.

Key Points Summary

• Fraction represents equal parts of a whole
• Numerator shows number of parts taken
• Denominator shows total parts
• Fractions can be shown on number line
• Equivalent fractions represent same value
• Improper fractions can be written as mixed numbers
• Fractions can be added or subtracted using common denominators

Practice Questions

1 Compare
3/4 and 5/6

2 Write 9/2 as mixed fraction

3 Simplify
18/24

4 Add
2/3 + 5/6

5 Subtract
7/8 − 3/4

Conclusion

Fractions are an important concept in mathematics. They help us understand equal sharing, measurements, and comparisons. By learning fractions clearly in Class 6, students build a strong foundation for algebra, ratios, percentages, and many advanced topics in higher classes.