NCERT Solutions for Class 6 Maths provide comprehensive answers to all the questions in the new NCERT Book for Class 6 Maths 'Ganita Prakash', replacing the older version of the book of Mathematics according to NEP 2020 recommendations. This guide includes all the solutions to the problems of the NCERT Maths textbook, which consists of 10 chapters. NCERT Math Solutions Class 6 are developed according to the CBSE syllabus. It can be a great resource for solving homework questions or getting ready for exams. Here is the NCERT Maths book class 6 solutions PDF free download link:
Chapter No. | Chapter-wise NCERT Class 6 Maths Solutions |
1 | Patterns in Mathematics |
2 | Lines and Angles |
3 | Number Play |
4 | Data Handling |
5 | Prime Time |
6 | Perimeter and Area |
7 | Fractions |
8 | Playing with Constructions |
9 | Symmetry |
10 | The Other Side of Zero |
The NCERT Solutions for Class 6 Maths MCQs Free Download link is highly popular among students because they enjoy learning the full concept. Chapter-wise NCERT Math Solutions Class 6 MCQs PDF link is provided below:
Chapter No. | Class 6 Maths Ganita Prakash MCQs |
1 | Patterns in Mathematics MCQs |
2 | Lines and Angles MCQs |
3 | Number Play MCQs |
4 | Data Handling MCQs |
5 | Prime Time MCQs |
6 | Perimeter and Area MCQs |
7 | Fractions MCQs |
8 | Playing with Constructions MCQs |
9 | Symmetry MCQs |
10 | The Other Side of Zero MCQs |
Class 6 Mathematics Ganita Prakash NCERT Solutions Chapter 1 introduces you to the amazing world of mathematical patterns. Class 6 Maths NCERT solutions Chapter 1 lays the foundation of your ability to reason logically and mathematically, as it helps you to identify, continue, and create patterns in numbers and shapes. The class 6 maths chapter 1 solutions teach you how to recognise patterns, understand repeated patterns, and see that mathematics itself is all about patterns.
Number sequences and series
Patterns in odd and even numbers
Triangular and square numbers
Shape-based patterns
Patterns in addition and multiplication tables
Topic | Type of Pattern | Example |
Counting numbers | Linear sequence | 1, 2, 3, 4, 5 |
Odd numbers | Skip pattern | 1, 3, 5, 7, 9 |
Even numbers | Skip pattern | 2, 4, 6, 8, 10 |
Triangular numbers | Additive growth | 1, 3, 6, 10, 15 |
Square numbers | Quadratic growth | 1, 4, 9, 16, 25 |
Powers of 2 | Doubling pattern | 1, 2, 4, 8, 16 |
Virahanka numbers | Sum of the previous two | 1, 1, 2, 3, 5, 8 |
Therefore, it is recommended that the students draw various figures, employ dot patterns, and even create tables so that it becomes easier for them to visualise the growth of these number patterns. For example, the triangle numbers can easily be visualised by drawing triangles through the use of dots, and from this process, it is possible to realise that the number that is being added increases by 1 in every subsequent step.
NCERT Solutions for Class 6 Maths Chapter 2 consists of concepts that focus on the study of lines and angles in geometry. The chapter discusses the concepts associated with learning and identifying various types of lines and angles with the help of rulers and protractors. The chapter forms the basis of all geometry-related chapters in the future.
Point, line, line segment, and ray
Intersecting and parallel lines
Types of angles: acute, obtuse, right, straight, reflex, and complete
Measuring angles using a protractor
Adjacent angles, linear pairs, and vertically opposite angles
Angle Type | Measure | Example |
Acute Angle | Between 0° and 90° | 45°, 60° |
Right angle | Exactly 90° | Corner of a book |
Obtuse angle | Between 90° and 180° | 120°, 135° |
Straight angle | Exactly 180° | A straight line |
Reflex angle | Between 180° and 360° | 270° |
Complete angle | Exactly 360° | Full rotation |
Line Type | Description |
Line segment | Has two fixed endpoints |
Ray | Has one endpoint, extends infinitely in one direction |
Line | Extends infinitely in both directions |
Intersecting lines | Two lines that meet at a point |
Parallel lines | Two lines that never meet |
Perpendicular lines | Two lines that meet at 90° |
In the NCERT solution class 6 maths book, there is a specific chapter that explains to students the usage of the protractor and the proper way of representing angles (∠ABC). The students can calculate the answers of complementary and supplementary angles (90° and 180° respectively) through simple equations.
The subject matter covered in the NCERT Solutions for Class 6 Maths Chapter 3 is the interesting part of numbers. Here, the class 6 maths NCERT solutions are not confined only to calculations but seek to develop an understanding of numbers through some interesting activities. Chapter 3 has been authored considering the joyful learning approach adopted under NEP 2020.
Supercells and number placement puzzles
Palindromes in numbers
Divisibility rules (2, 3, 4, 5, 6, 8, 9, 10)
Number patterns in grids
Estimation and approximation
Mental math strategies
Divisible By | Rule |
2 | Last digit is 0, 2, 4, 6, or 8 |
3 | Sum of digits divisible by 3 |
4 | Last two digits divisible by 4 |
5 | Last digit is 0 or 5 |
6 | Divisible by both 2 and 3 |
8 | Last 3 digits must be divisible by 8 |
9 | The sum of digits must be divisible by 9 |
10 | Last digit is 0 |
In the NCERT Solutions for Class 6 Maths Chapter 3, some exercises encourage the practice of experimenting with numbers using trial and error, identifying patterns by using grids, and applying the tests of divisibility in different cases. These practices are meant to develop mental math skills.
NCERT solutions for class 6 maths chapter four give an introduction to statistics using data handling and visualisation. The solutions to class six maths chapter four give students guidance on how to handle and visualise data in table and graph forms.
Collection and organisation of raw data
Tally marks and frequency tables
Pictographs and their interpretation
Bar graphs: drawing and reading
Choosing an appropriate scale
Drawing inferences from data
Method | Best Used For | Key Features |
Tally Marks | Counting and recording data | Groups of 5 for easy counting |
Frequency table | Organising data | Shows count for each category |
Pictograph | Simple Comparisons | Uses symbols to represent quantity |
Bar graph | Comparing categories | The height of the bar shows the value |
NCERT Solutions for Class 6 Maths Chapter 4 deals with the procedures of preparing the frequency table from raw data and graphing the information using the proper labelling on square paper. Some of the other key features are scale choice for constructing bar graphs, problem-solving using graphs, and distinguishing between pictographs and bar graphs according to circumstances.
The topic discussed in the NCERT solutions for class 6 maths chapter 5 is based on prime numbers, factors and multiples. Chapter 5 is considered one of those chapters which consist of the maximum number of topics that can be understood. NCERT solutions of class 6 maths can prove to be extremely useful in this regard.
Factors and multiples
Prime and composite numbers
The Sieve of Eratosthenes
Prime factorization
Highest Common Factor (HCF)
Lowest Common Multiple (LCM)
Co-prime numbers
Type | Definition | Example |
Prime | Exactly 2 factors: 1 and itself | 2, 3, 5, 7, 11, 13, 17, 19… |
Composite | More than 2 factors | 4, 6, 8, 9, 10, 12, …. |
Special case | Neither prime nor composite | 1 |
The NCERT solutions for Class 6 Maths Chapter 5 use factor trees and prime factorisation in order to facilitate easy calculation of HCF and LCM by students. HCF multiplied by LCM equals the product of two numbers, which is yet another vital formula to be learned by students.
In the NCERT Solutions for class 6 maths chapter 6, measurement geometry is taught to help students calculate the perimeter and area of different shapes. These NCERT class 6 maths solutions of chapter 6 involve real-life applications like fencing of a garden, flooring of the house, and so forth.
Perimeter of triangles, rectangles, and squares
Perimeter of irregular shapes
Area of rectangles and squares
Area of irregular figures using grid/graph paper
Relationship between perimeter and area
Units of measurement for length and area
Shape | Perimeter formula | Area formula |
Square | 4x sides | side x side |
Rectangle | 2 x (length + breadth) | length x breadth |
Triangle | Sum of all three sides | ½ × base × height |
Irregular shape | Sum of all sides | Count unit squares on graph paper |
From | To | Multiply By |
cm | mm | 10 |
m | cm | 100 |
Km | m | 1000 |
cm² | mm² | 100 |
m² | cm² | 10,000 |
Class 6 math NCERT solution for chapter 6 employs calculations with formulas and estimation through grids. The learners are taught to choose the correct units based on the situation (millimetres, centimetres, or meters) and that it is possible for the perimeters to be equal, but the areas not to be.
Fractions are an essential topic amongst several topics covered in class 6. The NCERT Solutions for Class 6 Maths Chapter 7 provide complete knowledge about the concept of fractions, along with the operations that can be carried out on them.
Review of basic fractions (numerator and denominator)
Proper, improper, and mixed fractions
Equivalent fractions
Simplest form / lowest terms
Comparing and ordering fractions
Addition and subtraction of fractions
Fractions on a number line
Type | Definition | Example |
Proper fraction | Numerator < Denominator | 3/5 |
Improper Fraction | Numerator > Denominator | 7/4 |
Mixed Fraction | Whole number + Proper fraction | 2¾, 5⅓ |
Equivalent Fraction | Same value, different form | 1/2 = 2/4 = 4/8 |
Like Fraction | Same denominator | 3/7 and 5/7 |
Unlike fractions | Different denominators | 1/3 and 2/5 |
Operation | Like Fractions | Unlike Fractions |
Addition | Add numerators directly | Find the LCM of denominators, convert, and then add |
Subtraction | Subtract numerators directly | Find the LCM of denominators, convert, and then subtract |
Comparison | Compare numerators | Convert to like fractions or use cross-multiplication |
The NCERT class 6 maths solutions chapter 7 involves both visual methods, such as the use of fraction bars and number lines, as well as numeric solutions. In problems related to the addition and subtraction of unlike fractions, children get to learn the way of finding the LCM of the denominators first.
NCERT Solutions for Class 6 Maths Chapter 8 is an applicable chapter wherein students practice making geometrical shapes using only a ruler and a compass. Class 6th Maths NCERT solutions chapter 8 are based on the application aspect to develop precision and a good sense of space.
Drawing circles of a given radius using a compass
Constructing the perpendicular bisector of a line segment
Constructing angles of specific measures (60°, 90°, 120°)
Bisecting a given angle
Drawing parallel lines
Constructing basic geometric shapes (equilateral triangle, square)
Tools | Purpose |
Ruler | Drawing straight lines and line segments |
Compass | Drawing circles, arcs, and measuring equal lengths |
Protractor | Measuring and drawing angles |
Divider | Comparing and transferring lengths |
In the NCERT Class 6 textbook, Chapter 8 deals with the construction problems, which consist of numbered instructions and verbal explanations of the diagram. Pupils must avoid applying too much pressure on the compass while drawing and sharpen their pencils, as well as writing the point names.
Symmetry is discussed in shapes, nature, and the arts in Chapter 9. The NCERT Solutions for Class 6 Maths Chapter 9 help students understand how to identify the line of symmetry and reflection, along with the concept of rotational symmetry in mathematics.
Line of symmetry (axis of symmetry)
Lines of symmetry in regular polygons
Reflection and mirror image
Rotational symmetry
Order of rotational symmetry
Symmetry in alphabets and real-life objects
Shape | Number of Lines of Symmetry |
Equilateral Triangle | 3 |
Square | 4 |
Regular Pentagon | 5 |
Regular Hexagon | 6 |
Circle | Infinite |
Rectangle | 2 |
Isosceles triangle | 1 |
Scalene triangle | 0 |
Chapter 9 in NCERT Class 6 Maths Solutions deals with the concept of symmetry, which is explained to the children via an activity using the paper-folding technique. This method involves the children finishing off the figures on the basis of reflection with respect to the mirror line, counting the number of lines of symmetry by rotating the figure mentally and also finding out rotational symmetry.
One of the topics in the NCERT Solutions for Class 6 Maths Chapter 10 that holds utmost importance compared to other topics of mathematics for Class 6 is 'negative numbers'. By means of NCERT class 6 maths solutions for chapter 10, students learn about integers and how to perform basic operations on them.
The need for numbers less than zero (context: temperature, floors below ground, bank accounts)
Integers: positive integers, zero, and negative integers
The number line is extended to negative numbers
Ordering and comparing integers
Addition and subtraction of integers
Introduction to opposite numbers
Category | Examples | Position on Number Line |
Positive integers | 1,2, 3, 4 | To the right of zero |
Zero | 0 | Centre |
Negative integers | -1, -2, -3, -50 | To the left of zero |
NCERT Class 6 Maths Chapter 10 highly relies on the use of the number line for visual representation. The learners are expected to translate problems in real life, which have temperatures below zero or elevators going below the ground, into integers and represent the same on the number line. After that, they learn addition and subtraction through the number line.
NCERT solutions for class 6 maths include every topic from the book 'Ganita Prakash' and can be used by students as a guide during the entire school year in order to develop an advanced level of understanding and solve questions precisely.
Study Strategy | How to Implement |
Read the chapter first | Go through the textbook before looking at solutions |
Attempt questions independently | Try each exercise question on your own first |
Use solutions for verification | Compare your method and answer with the solution |
Focus on steps, not just answers | Marks are awarded for the process, not just the final answer |
Revise regularly | Revisit completed chapters once a week during exam preparation |
Practice construction chapters with tools | Keep compass, ruler, and protractor handy for Chapters 2 and 8 |
Solution of NCERT for Class 6 Mathematics comprises stepwise solutions to all the questions present in the NCERT book. The solutions include all 14 chapters. The solutions have been prepared by expert teachers.
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