 # NCERT SOLUTIONS FOR CLASS 6

## Introduction about NCERT Solutions for Class 6 Maths

NCERT solutions for class 6 Maths provide complete and thorough knowledge about various topics in an easy and simple way. It includes solutions to all the questions provided in NCERT textbooks as per the latest syllabus of 2020-21. All the solutions of class 6 NCERT are prepared by our experienced subject experts in a well-structured format. All the solutions are curated in such a way that students will find it extremely easy to understand and it will encourage students to think logically and will improve their reasoning skills as well. This will also build a strong foundation of all these concepts for the higher level.

## Why students prefer NCERT Solutions for Class 6 Maths

Mathematics is one of the most important subjects for students of any field. Class 6th mathematics is cornerstone for developing interest towards the subject. Most students who ignores mathematics in lower classes finds the subject tough and boring in higher classes, that is why class 6 NCERT is important for beginners to help them in developing basic knowledge for the subject. Students prefer NCERT solutions for their home work, mock tests and final exam.

## Topics Covered in NCERT Solutions for Class 6 Maths & Brief Detail About Them

NCERT Solutions of class 6 maths contains all chapter solutions in pdf. Solutions can be downloaded chapter-wise. NCERT solutions for class 6 cover all the chapters including Knowing Our Numbers, Whole Numbers, Playing with Numbers, Basic Geometrical Ideas, Understanding Elementary Shapes, Integers, Fractions, Decimals, Data Handling, Mensuration, Algebra, Ratio and Proportion, Symmetry, Practical Geometry.

These all the chapters are fully comprehensive well explained. It can really help you with your exams, providing you with the easiest and fastest method to solve the question, additionally, the concept of solutions has kept so simple and easy to understand so that it can be remembered for a lifetime to students hence it will also help you cracking other higher-level exams.

## 14 Chapters of Maths NCERT Solutions for Class 6 with Free PDF Download

NCERT Solutions for Class 7 Maths are given below for all chapters.

### Chapter 1 – Knowing Our Numbers

1. Comparing Numbers – Numbers are compared to check which one is higher/smaller than others. Given two numbers, one with more digits is the greater number. If the number of digits in two given numbers is the same, that number is larger, which has a greater  leftmost digit.
2. Large numbers in practice – Large numbers are technically described as numbers bigger than what is used in daily life. The numbers are separated into groups: the ones, tens, hundreds, thousands, millions, and so on. Each group is home to three subdivision : ones, tens, and hundreds. When reading or writing a large number begins at the left with the latest group and proceeds to the right. It also includes the estimation of numbers approximately to an accuracy required.
3. Using Brackets – Brackets are used to avoid confusion during addition, subtraction, multiplication, and division. Different types of brackets are used to perform arithmetic operations.
4. Roman Numerals – One of the oldest systems of writing numbers is the Roman numeral system. Roman numbers are used in many places like in clocks or as symbols for indicating chapter numbers in a book. Some of the symbols used in this system are I, V, X, L, C, D, M.

### Chapter 2 – Whole Numbers

1. Whole Numbers – The naturals numbers along with zero forms the collection of whole numbers. The sequence of whole numbers is 0, 1, 2, 3, 4, 5…….
2. The Number Line –A pictorial representation of numbers evenly marked on a straight line is known as a number line. We take a line, mark a point on it and label it 0, we then mark out points to the right of 0 at equal intervals. We can easily perform the number operations of addition, subtraction, and multiplication on the number line.
3. Properties of Whole Numbers–Whole numbers are closed under addition, subtraction, multiplication, and division, this property is known as closure property. There are also some other properties like commutative property, associative property, distributive property of multiplication over addition, and identity property.
4. Patterns in Whole Numbers – Patterns in whole numbers can be made by arranging numbers in fundamental shapes using dots. Four shapes line, triangle, square, and rectangle are used and no other shape is allowed. With the help of patterns, we can easily simplify our calculations.

### Chapter 3 – Playing with Numbers

1. Factors and Multiples – A factor of a number is an exact divisor of that number. A multiple is a number that can be divided by another number a certain number of times without a remainder.
2. Prime and Composite Numbers – The numbers other than 1 whose only factor is 1 and the number itself are called prime numbers.
3. Tests for Divisibility of Numbers – It is for testing the divisibility of numbers without actually dividing them, we will study various divisibility rues of 10, 5, 2, 3, 8, 9 and 11
4. Common Factors and Common Multiples – A factor is said to be a common factor of given numbers if it is a factor of all the given numbers. A multiple is said to be a common multiple of given numbers if it is a multiple of the given numbers.
5. Some More Divisibility Rules – There are some more divisibility rules and properties of factors and multiples of a number like if a number is divisible by another number, then it is divisible by each of the factors of that number and if a number is divisible by two co-prime numbers then it is divisible by their product also, etc.
6. Prime Factorisation – A number is said to be factorized if it is expressed as a product of its factors.
7. Highest Common Factor – The highest (or greatest) of the common factors of the given two or more number is known as the Highest Common Factor(HCF) or Greatest Common Divisor (GCD), we can calculate HCF by prime factorization method.
8. Lowest Common Multiple – The Least Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples.
9. Some Problems on HCF and LCM– LCM of two co-prime numbers ‘a’, ‘b’ will be the product of ‘a’ and ‘b’ and if one number is the multiple of the other number, then greater number will be the LCM of two given numbers.

### Chapter 4 – Basic Geometrical Ideas

1. Points – A point determines a location, it is usually denoted by a capital letter. A point is used to represent any specific location or position. It has neither any size nor dimensions such as length and breadth.
2. A line segment – A line segment corresponds to the shortest distance between two points. The line segments joining points A and B are denoted and denote the same line segment. Points A and B are called the endpoints of the line segment.
3. A line – A line is obtained when a line segment is extended on both sides indefinitely, it is denoted by or sometimes by a single small letter like l, m, n, etc. A line contains countless points, a line can be fixed by any two points.
4. Intersecting Lines – Two distinct lines meeting at a point are called intersecting lines. Two lines cannot intersect more than one point and more than two lines can intersect at one point.
5. Parallel Lines – Two lines in a plane are said to be parallel if they do not meet, however far they are extended.
6. Ray – A ray is a portion of a line whose one endpoint is fixed (called starting point) and going in one direction endlessly. It is denoted as.
7. Curves – Any drawing made without lifting the pencil from the paper and without using a ruler is called a curve. In mathematics, a line is also a curve. There are three types of curves simple, closed, and open curves.
8. Polygons – It is a closed figure made by using straight lines, So we can say that a figure is a polygon if it is a simple closed figure made up entirely of line segments.
9. Angles – An angle is made up of two rays starting from a common endpoint. The two rays forming the angle are called arms or sides of the angle. The common endpoint is the vertex of the angle.
10. Triangles – A triangle is a three-sided polygon. It is the polygon with the least number of sides. Triangle XYZ is written as.
11. Quadrilaterals – A four-sided polygon is a quadrilateral. It has four sides, four angles, four vertices, and two diagonals.
12. Circles – A circle is a simple closed curve that is not a polygon. When we trace any round shape like a bangle, we get the shape of a circle. There are many parts of the circle like center, radius, diameter, chord, arc.

### Chapter 5 – Understanding Elementary Shapes

1. Measuring Line Segments – A line segment is a fixed portion of a line. The measure of a line segment is a unique number, which we call, the ‘length’ of the line segment. Length of a line segment means the distance between the endpoints of the line segment. For measuring the length, we use a divider and ruler. We can compare two lengths by observation and tracing, by using a ruler and a divider.
2. Angles – There are different types of angles as acute, obtuse, or reflex, right and straight. An angle smaller than a right angle is called an acute angle, if an angle is greater than a right angle and is smaller than the straight angle is called an obtuse angle, and an angle larger than a straight angle is called a reflex angle.
3. Measuring Angles – We use a protractor to measure an angle. One complete revolution of a clock is divided into 360 equal parts and each part is called a degree. The unit of measurement for an angle is a degree (°). The angle name for one complete revolution is complete angle and it measures 360°.
4. Perpendicular Lines – Two lines in a plane, which intersect each other and form an angle of 90° are called perpendicular lines. The adjacent edges of a book, the line segment that forms the letter L are models for perpendicular lines.
5. Classification of Triangles – Triangles can be classified in two ways:
6. According to the length or measure of their sides like scalene, isosceles and equilateral triangle.
7. According to the measures of its angles like the acute, right, and obtuse angle.
8. Quadrilaterals– A quadrilateral is a polygon that has four sides. There are five types of quadrilateral like rectangle, square, rhombus, trapezium, and parallelogram.
9. Polygons – A figure is a polygon if it is a closed figure, formed entirely of line segments. Polygons are named according to the number of the sides three-sided polygon is called triangle and four-sided polygon is called quadrilateral and so on.
10. Three Dimensional Shapes – Plane figures have two dimensions i.e. length and breadth. The object which cannot be confined to a plane surface is called a solid and it is also called a three-dimensional object as it has three-dimensions i.e. length, breadth, and height. Example cuboid, cone, etc. We see around in our daily lives different types of 3-D shapes.

### Chapter 6 – Integers

1. Integers – Group of whole numbers and negative numbers is called integers, integers are denoted by the letter An integer number line starts from zero and is extended in both the directions, on the right side of zero it consists of positive integers and on the left side of the zero it consists of negative integers. -1 is the greatest negative integer.
2. Addition of Integers – In addition to integers when we add two positive integers we get a positive integer and when we add two negative integers we get a negative integer. When one positive and one negative integer are added we subtract them as whole numbers by considering the numbers without their sign and then put the sign of the bigger number with the subtraction obtained. Similarly, the addition of integers can be done on a number line.
3. Subtraction of Integers with the help of a Number Line– The subtraction of an integer is the same as the addition of its additive inverse. To subtract an integer from another integer, it is enough to add the additive inverse of the integer that is being subtracted to the other integer.

### Chapter 7 – Fractions

1. A Fraction – A fraction is a selected part out of an equal number of parts of a whole. The whole may be an object or a group. It has two parts numerator and denominator. Example: is defined as 4 parts out of 5 equal parts. Here 4 is the numerator and 5 is the denominator.
2. Fraction on the Number Line – Fraction can be shown on a number line. Every fraction has a point associated with it on the number line.
3. Proper Fractions – A proper fraction is a number that represents part of a whole. In this type of fraction, the denominator shows the number of parts to which the whole is divided and the numerator shows the number of parts we have taken out. Therefore in a proper fraction, the numerator is always less than the denominator.
4. Improper and Mixed Fractions – The fractions where the numerator is greater than the denominator are called improper fractions. An improper can be written as a combination of a whole and a part and such fractions are then called mixed fractions. All improper fractions can be written in the form of mixed fractions and every mixed fraction can be written as an improper fraction.
5. Equivalent Fractions – Two or more fractions having the same value or representing the same part of a whole are called equivalent fractions.
6. Simplest form of a Fraction – A fraction is said to be in the simplest form if its numerator and denominator have no common factor except 1. A given fraction is expressed in its simplest form by dividing the numerator and denominator by their HCF.
7. Like Fractions – Fractions with the same denominator are called fractions and fractions with different denominators are called, unlike fractions.
8. Comparing Fractions – When we compare fractions then only numerators are compared because the denominators are the same in like fractions. When we compare unlike fractions, firstly we try and make the denominator the same, and then we compare.
9. Addition and Subtraction of Fractions – We add and subtract like fractions and unlike fractions using the concept of Lowest Common Multiple.

### Chapter 8 – Decimals

1. Tenths – When one unit divided into 10 equal parts, each part is called (one-tenth) of the unit. To understand the part of one whole we represent a unit by a block, the block is divided into 10 equal parts to understand 0.1 decimal notation.
2. Hundredths – When one unit divided into 100 equal parts, each part is called (one-hundredth) of the unit.  The block is divided into 100 equal parts to understand 0.01 decimal notation.
3. Comparing Decimals – The decimals to be compared should first be changed into like decimals. The whole number part and decimals part would be compared, the decimal number with the smaller whole number would be smaller.
4. Using Decimals – Often decimals are used to represent units or fractions of money, length, and weight.
5. Addition of Numbers with Decimals – The decimals to be added would first be written as like decimals and then these decimals would be arranged in such a way that the decimal point of all the decimals to be added falls in a vertical line.
6. Subtraction of Decimals –The decimals to be subtracted would first be written as like decimals and then these decimals would be arranged in such a way that the decimal point of all the decimals to be subtracted falls in a vertical line.

### Chapter 9 – Data Handling

1. Recording Data – The collection of facts from which a conclusion may be drawn is called data. The information collected can be visually represented, which can help us to draw conclusions. Data that is not arranged in a systematic order is called ungrouped or raw data. There are two types of data primary data and secondary data.
2. Organisation of Data – The data can be organized in many ways, the arrangement of observations in an increasing or decreasing order is called an array. Tally marks are a quicker way of keeping track of numbers in a group of five.
3. Pictograph – A pictograph represents data in form of pictures, objects, or part of objects or in other words we can say that pictorial representation of numerical data is called pictograph.
4. Interpretation of Pictograph – a pictograph uses pictures to represent statistical information. Pictographs should be properly titled and labeled so as to convey to the reader what they are about.
5. Drawing of Pictograph – All the pictorial representations of the data are called pictograms, the title or heading at the top of a pictograph tells us what a pictograph represents. Labels of the pictograph tell us the item represented by each row and symbols in a pictograph represent the number of items.
6. A Bar Graph – A bar graph is the pictorial representation of the numerical data by a number of bars(rectangles) of uniform width erected horizontally or vertically with equal spacing between them. In a bar graph, each rectangle or bar represents only one value of the numerical data and so there are as many bars as the number of values of numerical data.

### Chapter 10 – Mensuration

1. Perimeter – Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once. The perimeter of any closed figure which is entirely made of line segments is the sum of the length of all its sides.
2. Area – The amount of surface enclosed by a closed figure is called its area. The area of the square is an area of a rectangle is.

### Chapter 11 – Algebra

1. Matchstick Patterns – Matchsticks are used to learn patterns of making letters and other shapes. With the help of this, we learn how to write the general relation between the number of matchsticks required for repeating a given shape
2. The Idea of a Variable – A variable takes on different values, its value is not fixed. The length of the square can have many values as it is a variable, but the number of angles of a triangle has a fixed value of 3, it is not a variable. We may use any letter l, m, n, o, p, etc to show a variable, a variable allow us to express relations in any practical situation.
3. More Matchstick Patterns – Matchstick patterns are used for a better understanding of variables.
4. More Examples of Variables – variables are numbers although their value is not fixed still we can perform the operations of addition, subtraction, multiplication, and division on them just as in the case of fixed numbers.
5. Use of Variables in Common Rules – Variables allow us to express many common rules in both geometry and arithmetic in a general way. For example, the rule of the sum of two numbers remains the same if the order in which the number is taken is reversed can be expressed as here the variables a and b stands for any number.
6. Expression with Variables – Using operations of addition, subtraction, multiplication, and division on variables, expressions like etc can be formed.
7. Using Expressions Practically – choose a variable to represent the unknown, from given situation determine the operations, and then by using operations, write an expression according to the given situation.
8. What is an Equation – An equation is a condition on a variable. It is expressed by saying that an expression with a variable is equal to a fixed number. An equation has two sides LHS and RHS between the is the equal(=) sign.
9. Solution of an Equation – The value of the variable in an equation that satisfies the equation is called a solution of the equation. We can solve equation using various methods like Hit and Trial method or Trial and Error method.

### Chapter 12 – Ratio and Proportion

1. Ratio – A comparison between quantities can also be made by using division i.e. comparing the two quantities in terms of “how many times”, this comparison is known as the ratio. The order in which quantities are considered to express their ratio is important.
2. Proportion –If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’ to equate the two ratios. In proportion four quantities involved when taken in order are known as respective terms as A:B::C:D. A and D are called the extreme terms, and B and C are known as the middle terms.
3. Unitary Method – The method in which the value of one unit is found first and then the value of the required number of units is known as the unitary method or in other words we can say that the stepwise solving of the problem, where to find a unit’s value and then calculate the total value of all the units, is called unitary method.

### Chapter 13 – Symmetry

1. Making Symmetric Figures: Ink-blot Devils – Figures with evenly balanced proportions are called symmetrical figures. If a figure is folded in half such that its left and right halves match exactly each other then the figure is said to have a line symmetry
2. Figures with Two Lines of Symmetry – A figure has line symmetry if a line can be drawn dividing the figure into two identical parts, this line is called the line of symmetry. Figures can have more than one line of symmetry, they can have vertical, horizontal, or diagonals lines of symmetry. In figures, rectangles and rhombus have two lines of symmetry and in letters H, X, I.
3. Figures with Multiple (more than two) Lines of Symmetry – Figures which have more than two lines of symmetry are called figures with multiple lines of symmetry. Figures like an equilateral triangle, regular pentagon, hexagon, etc.
4. Reflection and Symmetry – The line symmetry is closely related to mirror reflection. The image is the reflection of the object in the mirror line. The mirror image is symmetrical to the object with reference to the mirror line. In mirror reflection, the left and right positions are reversed. When an object is reflected there is no change in the lengths and angles.

### Chapter 14 – Practical Geometry

1. The Circle – A circle is a closed round plane figure, each point on it is at the same distance from its center. We can construct a circle when its radius is known using a ruler and compass. A radius is a segment with one endpoint on the center of the circle and other on its circumference.
2. A Line Segment – A line segment is a portion of a line with fixed endpoints. To construct a line segment, we require a compass, pencil, and a ruler we can also construct a copy of a given length.
3. Perpendiculars – Two lines are said to be perpendicular if the angle between them measures 90°. We can draw perpendiculars to a line through a point on it and through a point, not on it, we can also construct a perpendicular bisector of a line segment using a ruler and compass.
4. Angles – We can draw angles of different measures by using a protractor, a compass, and a scale. We can construct different measures like 30°, 60°, 90°, 45°, 120°,135° and can also construct a copy of an angle of unknown measure and bisector of an angle.

## Benefit of NCERT Solutions for Class 6 Maths

NCERT solutions for class 6 Maths will create better and effective learning for students. It will help in building a strong foundation of all the concepts for higher-level classes and also for competitive exams.

NCERT Class 6 Maths solutions will help students to clear their doubts by offering an in-depth understanding of the concepts. It will also help students to apply these concepts in their real-life as well.

• It is very easy for students to access the solutions for every application from the chapters available.
• There are graphs and illustrations provided to students that help them understand the concepts better and retain them.
• These solutions are prepared by an expert team of Fliplearn that focuses on accuracy.
• The study material helps students to bridge the knowledge gap with the exercises and solutions.
• Simple and easily understandable solutions are provided.
• Detailed study material is available for class 6 students

Fliplearn is here to simplify your problems and make learning easy and enjoyable. Download the Fliplearn app to find more help and a personalized experience.

## Frequently Asked Questions About NCERT Solutions for Class 6

### Which chapters in NCERT Solutions for class 6th Maths require more practice?

The chapter based on numbers, integers, fractions, decimals, algebra, and geometry are very important as these concepts would be important in higher levels of education. Students must understand these concepts and work on them on a regular basis to score well in the annual exams. The important formulae and shortcut tips explained in these chapters must be remembered to understand the complex topics in further classes.

### Is it necessary to use the NCERT solutions for class 6 Maths PDFs?

The NCERT solutions for class 6 Maths are designed by the team of Fliplearn after conducting vast research on each concept. Students having doubts during class hours can download the solution PDFs available on Fliplearn and learn the concepts efficiently. The solutions are present in both chapter-wise and exercise-wise format to help the students ace the exam without fear.

### Is it required to solve each and every problem of NCERT Solutions for Class 6 Maths?

In the CBSE board, each and every problem irrespective of their understanding level are important for the exam. So the students are recommended to solve the NCERT textbook on a daily basis to gain a grip on the fundamental concepts. By regular practice, students will be able to analyze their areas of weakness and work on them for a better academic score. The step-wise explanation under each problem will help students to perform well in the annual exams.

### NCERT Solutions for other Classes

NCERT Solutions is also available for other classes. Students preparing for class 7th, 8th, 9th, 10th, 11th, and 12th will find it the best way to score good marks. NCERT Solutions for class 7th, 8th, 9th, 10th, 11th, and 12th provides a plethora of study material and references that help students trust it the most.