# NCERT Class 6 Mathematics Chapter 7 Fractions: Summary, Concepts, and Revision Notes | SwaVid

This chapter introduces the fundamental concept of fractions, which are numbers representing parts of a whole. Children will learn to identify, represen...

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# Fractions

## Concepts in this chapter

## The ideas this chapter keeps returning to

## Where this chapter usually trips people up

## Find the gaps before this chapter finds them for you.

## Related chapters

### What is a Fraction?

Chapter 7 · Class 6 Mathematics

This chapter introduces the fundamental concept of fractions, which are numbers representing parts of a whole. Children will learn to identify, represent, compare, and perform basic operations with fractions, building a crucial foundation for advanced mathematical concepts. The chapter begins with relatable examples of sharing to make the idea of 'parts of a whole' intuitive.

Your study route

Key topics

A fraction is a number that represents a part of a whole. The 'whole' can be a single object or a group of objects. It consists of a numerator (the number of parts taken) and a denominator (the total number of equal parts the whole is divided into).

Example

The chapter introduces fractions with examples like dividing a cake into 2 equal parts, where each part is 1/2. It defines 1/2, 1/4, 3/4 as fractions, clearly labeling the numerator and denominator (Page 108).

Watch out

Children might confuse the numerator and denominator, or think that a fraction like 1/2 means one out of two separate items, rather than one part of a single divided item.

A fraction is a number that represents a part of a whole. The 'whole' can be a single object or a group of objects. It consists of a numerator (the number of parts taken) and a denominator (the total number of equal parts the whole is divided into).

Tap the card for an example

Example

The chapter introduces fractions with examples like dividing a cake into 2 equal parts, where each part is 1/2. It defines 1/2, 1/4, 3/4 as fractions, clearly labeling the numerator and denominator (Page 108).

Why it matters

Fractions are essential for understanding sharing, division, and measurement in everyday life, from cooking recipes to understanding statistics.

Watch out

Children might confuse the numerator and denominator, or think that a fraction like 1/2 means one out of two separate items, rather than one part of a single divided item.

Ask at home

Ask your child to divide a piece of paper or a fruit into equal parts and tell you the fraction each part represents. For example, 'If I cut this apple into 4 equal pieces, what fraction is one piece?'

Chapter 7, 'Fractions', from Ganita Prakash, Class 6 Mathematics, systematically introduces students to the world of fractions. It starts by defining a fraction as a part of a whole, explaining the roles of the numerator and denominator. Students learn to represent fractions visually and on a number line. The chapter then delves into different types of fractions: proper, improper, and mixed, along with methods for converting between improper and mixed forms. A significant portion is dedicated to understanding equivalent fractions and simplifying fractions to their lowest terms. Crucially, students are taught various techniques for comparing fractions, including those with like and unlike denominators. Finally, the chapter covers the addition and subtraction of both like and unlike fractions, emphasizing the importance of finding common denominators for unlike fractions. This comprehensive approach ensures a solid understanding of fractional concepts.

Chapter summary

Chapter 7, 'Fractions', from Ganita Prakash, Class 6 Mathematics, systematically introduces students to the world of fractions. It starts by defining a fraction as a part of a whole, explaining the roles of the numerator and denominator. Students learn to represent fractions visually and on a number line. The chapter then delves into different types of fractions: proper, improper, and mixed, along with methods for converting between improper and mixed forms. A significant portion is dedicated to understanding equivalent fractions and simplifying fractions to their lowest terms. Crucially, students are taught various techniques for comparing fractions, including those with like and unlike denominators. Finally, the chapter covers the addition and subtraction of both like and unlike fractions, emphasizing the importance of finding common denominators for unlike fractions. This comprehensive approach ensures a solid understanding of fractional concepts.

What you should learn

Keep these close

A fraction represents a part of a whole, with a numerator (parts taken) and a denominator (total equal parts).

Fractions can be visually represented and accurately placed on a number line.

Proper fractions have a numerator smaller than the denominator (e.g., 1/2).

Improper fractions have a numerator greater than or equal to the denominator (e.g., 5/3).

Mixed fractions combine a whole number and a proper fraction (e.g., 1 2/3).

Improper fractions can be converted to mixed fractions and vice-versa.

Equivalent fractions represent the same value (e.g., 1/2 = 2/4).

To find equivalent fractions, multiply or divide both numerator and denominator by the same non-zero number.

A fraction is in its simplest form when its numerator and denominator have no common factor other than 1.

To compare unlike fractions, convert them to equivalent like fractions using a common denominator (LCM).

To add or subtract like fractions, operate on the numerators and keep the denominator same.

To add or subtract unlike fractions, first convert them to like fractions, then perform the operation.

Common confusions

It is easy to think

When adding or subtracting fractions, children might incorrectly add or subtract both the numerators and the denominators.

The clearer idea

Only the numerators are added or subtracted. The denominators must be the same (like fractions) and remain unchanged. If denominators are different, they must first be converted to a common denominator.

It is easy to think

Children often believe that a fraction with a larger denominator is always a larger fraction.

The clearer idea

For fractions with the same numerator, a larger denominator means the whole is divided into more parts, making each part smaller. For example, 1/5 is smaller than 1/2.

It is easy to think

When simplifying a fraction, children might divide by any common factor but not necessarily the greatest one, leaving the fraction not fully simplified.

The clearer idea

To simplify a fraction to its *simplest form*, both the numerator and denominator must be divided by their Greatest Common Factor (GCF) until no common factors other than 1 remain.

It is easy to think

Children may struggle with the concept that improper fractions are valid numbers and can be greater than one whole.

The clearer idea

Improper fractions represent quantities equal to or greater than one whole. They are perfectly valid and often more convenient for calculations than mixed fractions. For example, 5/4 means five quarters, which is more than one whole.

Before you push ahead

Most stuck chapters trace back to one earlier idea. Check the prerequisites first, or let SwaVid adapt this chapter to the way your child learns.

Keep exploring Class 6

Source

- Understand what a fraction is, identifying its numerator and denominator, and represent it as a part of a whole.
- Represent proper, improper, and mixed fractions on a number line.
- Differentiate between proper, improper, and mixed fractions, and convert improper fractions to mixed fractions and vice-versa.
- Identify and generate equivalent fractions, and reduce fractions to their simplest form.
- Compare and order fractions using appropriate methods for like and unlike denominators.
- Perform addition and subtraction of like and unlike fractions.
- Understand what a fraction is, identifying its numerator and denominator, and represent it as a part of a whole.
- Represent proper, improper, and mixed fractions on a number line.
- Differentiate between proper, improper, and mixed fractions, and convert improper fractions to mixed fractions and vice-versa.
- Identify and generate equivalent fractions, and reduce fractions to their simplest form.
- Compare and order fractions using appropriate methods for like and unlike denominators.
- Perform addition and subtraction of like and unlike fractions.
- NCERT Class 6 Mathematics textbook: Ganita Prakash : Chapter 7: Fractions

## Key Links

- [NCERT Mathematics](https://swavid.com/maths)
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- [Start with concepts](https://swavid.com/maths/class/6/chapter/fractions)
- [Check a prerequisite](https://swavid.com/learning-debt-identifier)
- [Concepts](https://swavid.com/maths/class/6/chapter/fractions)
- [Practice](https://swavid.com/maths/class/6/chapter/fractions/practice-questions)
- [NCERT Solutions](https://swavid.com/maths/class/6/chapter/fractions/ncert-solutions)
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- [All Class 6 chapters](https://swavid.com/maths/class/6)
- [6 Perimeter and Area Understanding Perimeter · Perimeter of a Rectangle Open chapter](https://swavid.com/maths/class/6/chapter/perimeter-and-area)
- [8 Playing with Constructions Drawing a Circle · Copying a Given Line Segment Open chapter](https://swavid.com/maths/class/6/chapter/playing-with-constructions)
- [5 Prime Time Factors and Multiples · Prime and Composite Numbers Open chapter](https://swavid.com/maths/class/6/chapter/prime-time)
- [NCERT Class 6 Mathematics textbook: Ganita Prakash](https://ncert.nic.in/textbook/pdf/fegp107.pdf)