CBSE Class 7 Maths
NCERT Ganita Prakash • Chapter-wise Theory • Questions • Solutions
Explore Class 7 Mathematics through chapter-wise theory, clear explanations, worked examples, practice questions and step-by-step solutions based on the official NCERT Ganita Prakash Grade 7 curriculum for the 2026–27 academic session.
What is CBSE Class 7 Maths?
CBSE Class 7 Maths is the Grade 7 middle-school mathematics curriculum based on the official NCERT textbook Ganita Prakash Grade 7. Designed under NEP 2020 and NCF-SE 2023, the curriculum is divided into two comprehensive volumes: Part I (8 chapters) and Part II (7 chapters), containing 15 chapters in total. It cultivates mathematical reasoning, geometric proofs, algebraic formulation using letter-numbers, integer operations, statistical data interpretation, and hands-on tilings while building an intuitive foundation for Computational Thinking.
Class 7 Maths Overview
Grade 7 Mathematics takes students deeper into the middle school journey started in Grade 6. Grounded in the vision of NCF-SE 2023 and NEP 2020, the two-part Ganita Prakash textbook encourages students to discover mathematical concepts through curiosity and collaborative exploration. Instead of expecting blind execution of mechanical procedures, the curriculum weaves storytelling, hands-on paper folding, puzzles, and discussions to help learners understand what it means to prove mathematical assertions, analyze invariants, and connect patterns across daily life and computing.
Chapter-Wise Theory
In-depth explanations of Grade 7 mathematical concepts organized chapter-by-chapter across Part I and Part II.
Worked Examples
Step-by-step mathematical walkthroughs showing how logical deduction and rigorous reasoning are applied.
Interactive Practice
Multiple-choice conceptual questions with immediate evaluation, hints, and complete step-by-step solutions.
Mathematical Reasoning
Problems that encourage students to identify patterns, formulate conjectures, and justify conclusions with proofs.
Geometry & Construction
Interactive visual learning for transversals, triangles, congruence criteria (SSS, SAS, ASA, RHS), constructions, and tilings.
Computational Thinking Bridge
Connecting arithmetic algorithms, parity invariants, parse trees, and variable abstractions to computer science.
Class 7 Maths Chapters
Part I
8 Chapters • Ganita Prakash Grade 7 Part I (pp. 1–200)
Large Numbers Around Us
Lakhs, Crores, Millions, Billions & Number Magnitude
Explores large numbers encountered in the real world—from national census figures and cosmic distances to state budgets. Introduces place-value conventions across the Indian system (lakhs, crores) and International system (millions, billions), alongside estimation, rounding, and order-of-magnitude reasoning.
- •Indian place value system: Ones, Thousands, Lakhs, and Crores with comma grouping
- •International place value system: Ones, Thousands, Millions, and Billions
- •Conversion rules between systems (1 million = 10 lakhs; 1 crore = 10 millions; 1 billion = 100 crores)
- •Magnitude estimation and sensible rounding strategies in real contexts
Arithmetic Expressions
Multiple Operations, Precedence Rules & Disambiguation with Brackets
Investigates expressions containing multiple arithmetic operations (+, −, ×, ÷) and examines how ambiguities arise when rules of priority are not defined. Establishes conventions of operator precedence, the role of brackets as grouping devices, and expression tree representations.
- •Understanding ambiguity in sequential calculations without standard rules
- •Operator precedence conventions: Multiplication and Division take priority over Addition and Subtraction
- •Left-to-right evaluation among operators of equal precedence
- •Using parentheses and brackets ( ) to override default precedence and group terms
A Peek Beyond the Point
The Decimal Point, Tenths, Hundredths & Addition/Subtraction
Extends the base-10 positional notation beyond whole numbers into fractional parts using the decimal point. Explores tenths, hundredths, and thousandths through grid models, metric measurements, the history of decimal coinage in India (1957), and column addition and subtraction of decimals.
- •The decimal point as a marker separating whole units from sub-unit tenths and hundredths
- •Place values beyond the point: Tenths (1/10), Hundredths (1/100), and Thousandths (1/1000)
- •Interconverting terminating fractions and decimal numbers
- •Historical context: The 1957 transition from annas/pies to decimal coinage (Naya Paisa) in India
Expressions using Letter-Numbers
Letter-Numbers, Variables, Algebraic Formulation & Substitution
Introduces students gently into the world of algebra. Builds on arithmetic expressions by treating letters as placeholder numbers that can vary or represent unknowns. Explores algebraic terms, coefficients, forming expressions from verbal descriptions, and substituting numerical values.
- •The concept of 'letter-numbers' as numbers whose values can vary (variables)
- •Distinction between fixed numerical constants and flexible variables
- •Forming algebraic expressions from word statements (e.g., '5 more than twice a number' = 2n + 5)
- •Structure of expressions: Terms, variables, and numerical coefficients
Parallel and Intersecting Lines
Transversals, Alternate Angles, Linear Pairs & Geometric Proofs
Investigates the geometric behavior of intersecting and parallel lines in a plane through hands-on paper folding and deductive reasoning. Explores vertically opposite angles, linear pairs, transversal intersections, alternate interior angles, corresponding angles, and co-interior angle sums.
- •Intersecting lines, adjacent angles, and the linear pair property (angles sum to 180°)
- •Proof that vertically opposite angles formed by intersecting lines are equal
- •Parallel lines as coplanar lines that maintain constant perpendicular distance and never meet
- •Transversal lines crossing pairs of lines
Number Play
Parity Invariants, Virahāṅka Sequences, Cryptarithms & Logic Puzzles
A rich computational thinking laboratory exploring mathematical puzzles, invariants, parity (odd/even behavior under addition and multiplication), the recursive Virahāṅka-Fibonacci sequence, alphametics/cryptarithms, and structured deduction strategies.
- •The concept of mathematical invariants: What remains constant across transformations?
- •Parity analysis: Odd and even properties (odd + odd = even, odd × odd = odd)
- •The Virahāṅka-Fibonacci sequence (1, 2, 3, 5, 8, 13, 21...) and Sanskrit poetic meters
- •Alphametic puzzles / cryptarithms where unique letters represent distinct digits (0–9)
A Tale of Three Intersecting Lines
Triangles, Angle Sum Property, Exterior Angles & Triangle Inequality
Explores triangles as the closed 2D figures formed when three non-concurrent lines intersect. Investigates striking fundamental properties: the angle sum theorem (180°), exterior angle relationships, classification by sides and angles, and the triangle inequality theorem.
- •Formation of triangles from three mutually intersecting lines
- •Classification of triangles by side lengths (scalene, isosceles, equilateral) and angles (acute, right, obtuse)
- •Angle Sum Property of a triangle: The sum of the three interior angles is always 180°
- •Exterior Angle Theorem: An exterior angle of a triangle equals the sum of its two interior opposite angles
Working with Fractions
Multiplication, Division, Brahmagupta's Rules & Reciprocals
Deepens fractional understanding by mastering multiplication and division of fractions. Connects fraction multiplication to scaling and area of sub-unit grids, explores reciprocals (multiplicative inverses), and introduces Brahmagupta's historic 628 CE procedures for dividing fractions.
- •Multiplication of fractions as finding a 'fraction of a fraction' and unit-square grid subdivision
- •Rule for fraction multiplication: (a/b) × (c/d) = (a × c) / (b × d)
- •Concept of reciprocal (multiplicative inverse) where (a/b) × (b/a) = 1
- •Division of fractions as multiplication by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c)
Part II
7 Chapters • Ganita Prakash Grade 7 Part II (pp. 1–191)
Geometric Twins
Congruence of Plane Figures, Triangle Criteria (SSS, SAS, ASA, RHS) & CPCTC
Introduces the foundational concept of congruence—plane figures having identical shape and identical size that coincide exactly through superposition. Develops rigorous triangle congruence criteria (SSS, SAS, ASA, and RHS) and uses corresponding parts of congruent triangles (CPCTC) in deductive proofs.
- •The definition of congruence (≅): Exact match of shape and size via rigid superposition
- •Congruence of basic objects: Line segments (equal length), angles (equal measure), and circles (equal radius)
- •Corresponding vertices, sides, and angles in congruent triangles
- •SSS (Side-Side-Side) Congruence Criterion
Operations with Integers
Multiplication & Division of Integers, Sign Rules & Brahmagupta's Laws
Deepens arithmetic beyond whole numbers into multiplication and division of positive and negative integers. Discovers why the product of two negative numbers is positive using patterns, establishes algebraic properties (closure, commutative, associative, distributive), and applies Brahmagupta's classic laws.
- •Multiplying a positive integer by a negative integer as repeated addition in the negative direction
- •Pattern-based proof showing why (−a) × (−b) = +(a × b)
- •Properties of integer multiplication: Closure, Commutative, Associative, and Distributive over addition
- •Multiplicative identity (1) and multiplication by zero (a × 0 = 0)
Finding Common Ground
Common Factors, Common Multiples, Prime Factorization, HCF & LCM
Explores prime factorizations to reveal common structures shared by numbers. Develops systematic methods for determining the Highest Common Factor (HCF) and Lowest Common Multiple (LCM), verifies the relationship HCF(a, b) × LCM(a, b) = a × b, and solves periodic synchronization problems.
- •Review of factors, multiples, and the fundamental theorem of arithmetic (unique prime factorization)
- •Finding common factors and identifying the Highest Common Factor (HCF / GCD)
- •Finding common multiples and identifying the Lowest Common Multiple (LCM)
- •Using prime factorization factor trees and division grids for systematic computation
Another Peek Beyond the Point
Multiplication & Division of Decimals, Power of 10 Shifts & Practical Scaling
Takes decimals to higher operational fluency with systematic multiplication and division. Teaches students how multiplying or dividing by powers of 10 (10, 100, 1000) shifts the decimal point, how to determine decimal places in products, and how to convert decimal divisors into whole numbers.
- •Multiplying decimals by powers of 10 (10, 100, 1000) as place value shifting to the right
- •Multiplying two decimal numbers: Product of whole values followed by counting total decimal places
- •Dividing decimals by powers of 10 as place value shifting to the left
- •Dividing a decimal by a whole number through standard long division
Connecting the Dots...
Central Tendency, Arithmetic Mean, Median, Mode & Data Interpretation
Introduces statistical measures of central tendency to represent and compare data collections meaningfully. Investigates the Arithmetic Mean (fair share average), Median (middle positional value in ordered datasets), Mode (most frequent observation), range, and when each measure is most appropriate.
- •Need for representative values to summarize large collections of quantitative data
- •Arithmetic Mean: Sum of all observations divided by total number of observations (Mean = Σx / n)
- •Range: Difference between the highest and lowest observations (Range = Maximum − Minimum)
- •Median: The exact middle observation when data is arranged in ascending or descending order
Constructions and Tilings
Practical Triangle Constructions, Plane Tilings, Tessellations & Vertex Angle Sums
Combines precision geometric construction with the artistic beauty of tilings and tessellations. Teaches step-by-step compass-and-ruler construction of triangles using congruence conditions (SSS, SAS, ASA, RHS) and investigates why certain regular polygons tile a flat floor without gaps.
- •Constructing a line parallel to a given line through an external point using alternate interior angles
- •Constructing triangles given three sides (SSS condition)
- •Constructing triangles given two sides and included angle (SAS condition)
- •Constructing triangles given two angles and included side (ASA condition)
Finding the Unknown
Linear Equations, The Balance Scale Model, Transposition & Real-Life Solutions
A thrilling introduction to solving linear equations in one variable. Treats equations as balanced scales where equality is maintained by applying identical arithmetic operations to both sides. Develops the method of transposition, verifies candidate roots, and applies algebraic models to solve real-life riddles.
- •The concept of an equation as a condition of balance on a variable
- •The balance scale analogy: Adding, subtracting, multiplying, or dividing both sides by the same non-zero quantity preserves equality
- •Solving simple equations by inverse operations step-by-step
- •The transposition technique: Moving a term across the equals sign changes its sign (+ becomes −, × becomes ÷)
Class 7 Maths Theory
Select any chapter across Part I and Part II below to inspect its core mathematical foundations, textbook terminology, and pedagogical connections:
Large Numbers Around Us
Explores large numbers encountered in the real world—from national census figures and cosmic distances to state budgets. Introduces place-value conventions across the Indian system (lakhs, crores) and International system (millions, billions), alongside estimation, rounding, and order-of-magnitude reasoning.
Comprehensive Concepts in this Chapter:
Fixed-width integer encoding, magnitude scaling, scientific notation, and large dataset indexing.
Class 7 Maths Questions & Solutions
Test your understanding of Grade 7 Mathematics concepts through chapter-based questions, instant feedback, hints and step-by-step explanations across both Part I and Part II:
How many lakhs are equivalent to 10 million in the International system of numeration?
Evaluate the arithmetic expression: 24 − 4 × (2 + 3) + 8 ÷ 2
What is the result of subtracting 4.78 from 12.5?
If n represents the number of boxes, which expression represents '7 less than 4 times n', and what is its value when n = 6?
Two parallel lines are intersected by a transversal. If one interior angle is 65°, what is the measure of the consecutive interior angle on the same side of the transversal?
If three integers a, b, and c are all odd, which of the following expressions will always result in an EVEN number?
Which of the following sets of three line segment lengths CANNOT form a triangle?
Evaluate: (5/8) ÷ (15/16)
If ΔABC ≅ ΔXYZ under the correspondence A ↔ X, B ↔ Y, and C ↔ Z, which angle corresponds to ∠BCA?
Evaluate the expression: (−8) × (−5) − (−24) ÷ (+6)
The HCF of two numbers is 12 and their LCM is 180. If one of the numbers is 36, what is the other number?
What is the value of 0.25 × 0.08?
The scores of 7 students in a quiz are: 6, 8, 4, 9, 8, 7, 14. What are the Median and Mean of this dataset?
Why can regular hexagons tile a flat floor seamlessly without gaps, while regular pentagons cannot?
Solve the linear equation for x: 5x − 7 = 3x + 11
Mathematics and Computational Thinking
As emphasized in the Foreword and pedagogy of Ganita Prakash, Grade 7 mathematics is an invitation to think systematically. Discovering parity invariants, constructing expression parse trees, manipulating symbolic variables, and executing geometric tiling algorithms build the direct cognitive foundation for Computational Thinking and Artificial Intelligence.
Investigating large magnitudes, rational fractions, transversals, and triangle congruence.
Reasoning why parity holds, verifying triangle inequalities, and proving angle theorems.
Operator precedence trees, Euclidean GCD procedures, variable substitution, and tilings.
Data measures of central tendency (mean, median), constraint solving, and predictive models.
Practice Computational Thinking with Class 7 Maths
After mastering the Grade 7 mathematical concepts, explore structured problem decomposition, logic puzzles, and Python algorithmic thinking on TeacherColab's dedicated Class 7 CT & AI platform.
Practice Class 7 Computational Thinking Questions →