NCERT Solutions for Class 6 Maths: Complete Chapter by Chapter Guide (2026)

This chapter takes students from the thousands they already know to the lakhs and crores. It covers the Indian and International number systems, comparing and ordering large numbers, estimation, and using brackets.

Key concepts to master:

• Place value up to crores
  - Indian system (lakhs, crores) vs International system (millions, billions)
  - Rounding off to the nearest tens, hundreds, and thousands
  - Use of commas in both systems

Common mistake: Students often confuse the comma placement between the two systems. Make sure they practice writing the same number in both formats. For example, 23,47,896 in Indian vs 2,347,896 in International.

This chapter introduces zero and the concept of whole numbers. It covers the number line, properties of whole numbers (closure, commutative, associative, distributive), and patterns in numbers.

Key concepts to master:

• Difference between natural numbers and whole numbers
  - The number line and what it represents
  - Properties: If $a$ and $b$ are whole numbers, then $a + b$ is also a whole number (closure)
  - Distributive property: $a \times (b + c) = a \times b + a \times c$

Common mistake: Students forget that division is NOT closed for whole numbers. $5 \div 2 = 2.5$ which is not a whole number.

This is one of the most important chapters in Class 6 because it introduces factors, multiples, HCF, and LCM. These concepts come back in Class 8 and even in Class 10 Real Numbers.

Key concepts to master:

• Factors and multiples of a number
  - Prime and composite numbers
  - Tests of divisibility (by 2, 3, 4, 5, 6, 8, 9, 10, 11)
  - Prime factorisation
  - HCF and LCM using prime factorisation

Important relationship: For any two numbers $a$ and $b$:

Common mistake: Mixing up HCF and LCM. Remember, HCF is always smaller than or equal to both numbers, and LCM is always larger than or equal to both numbers.

This chapter covers points, lines, line segments, rays, curves, polygons, angles, and triangles. It is mostly about understanding definitions and recognizing shapes.

Key concepts to master:

• Difference between a line (extends infinitely), ray (one endpoint), and line segment (two endpoints)
  - Types of curves: open and closed
  - Interior and exterior of closed curves
  - Parts of a triangle and quadrilateral (vertices, sides, angles, diagonals)

Tip for parents: Use real objects around the house to explain these concepts. The edge of a ruler is a line segment. A torch beam is a ray. This makes the abstract ideas much easier to grasp.

This chapter goes deeper into measurement of line segments, angles, perpendicular lines, and classifying triangles and quadrilaterals.

Key concepts to master:

• Measuring angles with a protractor
  - Types of angles: acute (less than $90°$), right ($90°$), obtuse (between $90°$ and $180°$), straight ($180°$), reflex (between $180°$ and $360°$)
  - Classification of triangles by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse)
  - Types of quadrilaterals: rectangle, square, parallelogram, rhombus, trapezium

Common mistake: Students often forget that a square is also a rectangle, a rhombus, and a parallelogram. Understanding the hierarchy of quadrilaterals saves confusion later.

Welcome to negative numbers! This chapter introduces integers, the number line with negatives, and operations on integers.

Key concepts to master:

• What integers are: ..., $-3, -2, -1, 0, 1, 2, 3$, ...
  - Ordering integers on the number line
  - Addition and subtraction of integers using the number line
  - Additive inverse: The additive inverse of $a$ is $-a$

Common mistake: When subtracting a negative number, students get confused. Remember: $5 - (-3) = 5 + 3 = 8$. Subtracting a negative is the same as adding a positive.

Fractions are introduced or revised in Class 6 with a focus on proper, improper, and mixed fractions, equivalent fractions, and basic operations.

Key concepts to master:

• Types of fractions: proper ($\frac{3}{7}$), improper ($\frac{9}{4}$), mixed ($2\frac{1}{4}$)
  - Finding equivalent fractions by multiplying or dividing numerator and denominator by the same number
  - Simplest form of a fraction
  - Comparing fractions by cross multiplication or by converting to like fractions
  - Addition and subtraction of fractions with the same and different denominators

Common mistake: When adding fractions like $\frac{2}{3} + \frac{1}{4}$, students sometimes add both numerators and denominators separately. You need to find the LCM of 3 and 4 first, which is 12, and then convert: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$.

Decimals are closely related to fractions and the place value system. This chapter covers reading, writing, comparing, and basic operations with decimals.

Key concepts to master:

• Place value in decimals: tenths, hundredths, thousandths
  - Converting between fractions and decimals
  - Comparing decimals
  - Addition and subtraction of decimals

Tip: Line up the decimal points vertically when adding or subtracting. This simple habit prevents most calculation errors.

This chapter teaches students to collect, organize, and represent data using pictographs and bar graphs.

Key concepts to master:

• Collecting and organizing data into a table
  - Drawing and reading pictographs (each symbol represents a fixed number)
  - Drawing and reading bar graphs
  - Interpreting data from graphs

Tip: Practice drawing bar graphs neatly with a ruler. In exams, neat presentation of graphs matters. Always label both axes and give the graph a title.

Perimeter and area are introduced here. These formulas come back in every class after this.

Key formulas:

• Perimeter of a rectangle: $P = 2(l + b)$
  - Area of a rectangle: $A = l \times b$
  - Perimeter of a square: $P = 4s$
  - Area of a square: $A = s^2$
  - Area of a triangle: $A = \frac{1}{2} \times b \times h$

Common mistake: Confusing perimeter (total boundary length, measured in cm or m) with area (surface covered, measured in $\text{cm}^2$ or $\text{m}^2$). Always check your units.

This is the first real introduction to algebra. Students learn to use letters to represent unknown numbers and write simple expressions and equations.

Key concepts to master:

• Using variables: if Ravi's age is $x$, his father's age might be $3x + 5$
  - Writing algebraic expressions from word problems
  - Evaluating expressions by substituting values
  - Simple equations like $x + 5 = 12$, solved by trial or inspection

Why this matters: Algebra is the language of all higher mathematics. Building comfort with variables in Class 6 makes everything from Class 7 onwards much easier.

Ratios and proportions are used everywhere in real life and in maths. This chapter builds the foundation.

Key concepts to master:

• Ratio: comparing two quantities, written as $a : b$ or $\frac{a}{b}$
  - Simplest form of a ratio (divide both by their HCF)
  - Proportion: when two ratios are equal, $a : b :: c : d$, meaning $\frac{a}{b} = \frac{c}{d}$
  - Unitary method: finding the value of one unit first

Common mistake: Writing ratio in the wrong order. "Ratio of boys to girls" means boys first, girls second. Order matters!

This chapter covers line symmetry and reflective symmetry. It is mostly visual and fun to learn.

Key concepts: A figure has line symmetry if one half is the mirror image of the other half. The line dividing them is the line of symmetry. A circle has infinite lines of symmetry. A regular polygon with $n$ sides has $n$ lines of symmetry.

This chapter teaches students to use a ruler, compass, and protractor to construct basic geometric figures.

Key constructions to master:

• Drawing a circle with a given radius
  - Drawing a line segment of given length
  - Constructing a copy of a line segment
  - Drawing perpendiculars and perpendicular bisectors
  - Constructing angles of $60°$, $90°$, $120°$, and bisecting an angle

Tip: Constructions need practice with actual instruments. You cannot master this chapter just by reading. Get a geometry box and practice each construction at least 3 times.