CBSE Class 6 Mathematics Chapter 7: Fractions NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Mathematics Chapter 7: Fractions NCERT Solutions introduces students to the fundamental concepts of fractions. This chapter focuses on understanding how to represent fractions visually, identifying shaded portions of figures, and coloring parts of figures based on given fractions. It also covers identifying errors in fraction representations, which is essential for building a solid understanding of parts of a whole. Working through these exercises helps students develop their ability to interpret and manipulate fractions, laying a crucial groundwork for more advanced mathematical concepts. These solutions are designed to facilitate clear comprehension and effective preparation for examinations, ensuring students grasp the core ideas of fractions thoroughly.

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BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 7: Fractions

Chapter summary

Chapter 7 of the Class 6 NCERT Mathematics textbook introduces the concept of fractions. This section provides solutions for exercises that focus on representing fractions visually, identifying shaded and unshaded parts of figures, and coloring figures based on given fractional values. It also includes problems that require identifying potential errors in fraction representations. These exercises are fundamental for grasping the basic principles of fractions as parts of a whole.

Learning outcomes

  • Understand the concept of a fraction as a part of a whole.
  • Represent fractions visually by identifying shaded portions.
  • Color parts of a figure to represent a given fraction.
  • Identify and correct errors in the representation of fractions.

Topics covered

Paper topics

  • Introduction to Fractions
  • Representing Fractions
  • Shaded Portions
  • Coloring Fractions
  • Identifying Errors in Fractions

Important topics

  • Visual Representation of Fractions
  • Numerator and Denominator
  • Fractions as Parts of a Whole
  • Identifying Shaded Parts

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Questions and Solutions

Question 1

Write the fraction representing the shaded portion for each of the given figures.

The figures provided are:

(i) A circle divided into 2 equal parts, with 1 part shaded.

(ii) A square divided into 4 equal parts, with 3 parts shaded.

(iii) A rectangle divided into 7 equal parts, with 3 parts shaded.

(iv) A triangle divided into 4 equal parts, with 1 part shaded.

(v) A circle divided into 4 equal parts, with 2 parts shaded.

(vi) A rectangle divided into 8 equal parts, with 4 parts shaded.

(vii) A square divided into 9 equal parts, with 4 parts shaded.

(viii) A circle divided into 4 equal parts, with 1 part shaded.

(ix) A rectangle divided into 10 equal parts, with 10 parts shaded.

(x) A circle divided into 8 equal parts, with 4 parts shaded.

Solution:

To find the fraction representing the shaded portion, we count the number of shaded parts (which becomes the numerator) and divide it by the total number of equal parts in the figure (which becomes the denominator).

  1. Figure (i): 1 shaded part out of 2 total parts. Fraction = \frac{1}{2}
  2. Figure (ii): 3 shaded parts out of 4 total parts. Fraction = \frac{3}{4}
  3. Figure (iii): 3 shaded parts out of 7 total parts. Fraction = \frac{3}{7}
  4. Figure (iv): 1 shaded part out of 4 total parts. Fraction = \frac{1}{4}
  5. Figure (v): 2 shaded parts out of 4 total parts. Fraction = \frac{2}{4}
  6. Figure (vi): 4 shaded parts out of 8 total parts. Fraction = \frac{4}{8}
  7. Figure (vii): 4 shaded parts out of 9 total parts. Fraction = \frac{4}{9}
  8. Figure (viii): 1 shaded part out of 4 total parts. Fraction = \frac{1}{4}
  9. Figure (ix): 10 shaded parts out of 10 total parts. Fraction = \frac{10}{10}
  10. Figure (x): 4 shaded parts out of 8 total parts. Fraction = \frac{4}{8}

Question 2

Colour the part according to the given fraction for each figure.

The figures and fractions are:

(i) A circle divided into 6 equal parts. Colour \frac{1}{6}.

(ii) A square divided into 4 equal parts. Colour \frac{1}{4}.

(iii) A rectangle divided into 3 equal parts. Colour \frac{1}{3}.

(iv) A rectangle divided into 4 equal parts. Colour \frac{3}{4}.

(v) A square divided into 9 equal parts. Colour \frac{4}{9}.

Solution:

To colour the part according to the given fraction, we need to identify the total number of equal parts (denominator) and the number of parts to be coloured (numerator). Then, we colour the specified number of parts.

  1. For \frac{1}{6}, colour 1 part out of the 6 equal parts in the circle.
  2. For \frac{1}{4}, colour 1 part out of the 4 equal parts in the square.
  3. For \frac{1}{3}, colour 1 part out of the 3 equal parts in the rectangle.
  4. For \frac{3}{4}, colour 3 parts out of the 4 equal parts in the rectangle.
  5. For \frac{4}{9}, colour 4 parts out of the 9 equal parts in the square.

The figures would show the specified number of parts coloured accordingly.

Question 3

Identify the error, if any, in the given representations of fractions.

The representations shown are:

Figure 1: A rectangle divided into 4 equal parts, with 3 parts shaded. It is labelled "This is 3/4".

Figure 2: A rectangle divided into 4 equal parts, with 1 part shaded. It is labelled "This is 1/4".

Figure 3: A rectangle divided into 2 equal parts, with 1 part shaded. It is labelled "This is 1/2".

Solution:

Let's examine each representation:

  1. The first figure shows a rectangle divided into 4 equal parts, and 3 of these parts are shaded. The label "This is 3/4" correctly represents this situation, as the numerator (3) is the number of shaded parts, and the denominator (4) is the total number of equal parts. There is no error here.
  2. The second figure shows a rectangle divided into 4 equal parts, with 1 part shaded. The label "This is 1/4" correctly represents this situation. The numerator (1) is the number of shaded parts, and the denominator (4) is the total number of equal parts. There is no error here.
  3. The third figure shows a rectangle divided into 2 equal parts, with 1 part shaded. The label "This is 1/2" correctly represents this situation. The numerator (1) is the number of shaded parts, and the denominator (2) is the total number of equal parts. There is no error here.

Based on the visual representations and the labels provided, there are no errors in any of the given fractions.

Common mistakes

  • Incorrectly counting the total number of parts in a figure.
  • Misidentifying the number of shaded or required parts.
  • Confusing the numerator and denominator.
  • Errors in coloring the correct number of parts for a given fraction.

Revision tips

  • Practice drawing and shading figures to represent various fractions.
  • Pay close attention to the total number of parts and the number of shaded parts in each figure.
  • Review the definitions of numerator and denominator to avoid confusion.
  • Work through the exercises multiple times to solidify understanding.

Practice MCQs

Q1. What fraction represents the shaded portion in a figure with 4 equal parts, where 2 are shaded?

Q2. If a figure is divided into 6 equal parts and 1 part is shaded, what fraction represents the shaded portion?

Q3. To represent the fraction 3/4, how many parts should be colored in a figure divided into 4 equal parts?

Q4. In the fraction 4/9, what does the number 9 represent?

Q5. Which fraction is incorrectly represented if a figure shows 1 shaded part out of 2 equal parts?

Frequently asked questions

What is a fraction?

A fraction represents a part of a whole. It is written as a ratio of two numbers, where the top number (numerator) is the number of parts considered, and the bottom number (denominator) is the total number of equal parts the whole is divided into.

How do I represent a fraction visually?

To represent a fraction visually, draw a shape (like a circle or rectangle), divide it into the number of equal parts indicated by the denominator, and then shade or color the number of parts indicated by the numerator.

What is the difference between the numerator and the denominator?

The numerator is the top number in a fraction and tells us how many parts of the whole are being considered. The denominator is the bottom number and tells us the total number of equal parts the whole is divided into.

How can these NCERT solutions help with exam preparation?

These solutions provide clear, step-by-step explanations for each problem, helping students understand the concepts of fractions thoroughly. Practicing with these rewritten solutions aids in building confidence and accuracy for exams.

What kind of errors can occur when representing fractions?

Common errors include miscounting the total number of parts, incorrectly identifying the number of shaded parts, or confusing the numerator with the denominator when writing or interpreting a fraction.

Important links

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