A single, long-form guide with chapter-wise concept notes, solved-answer frameworks, and smart revision tips — fully aligned to the latest NCERT textbooks and CBSE syllabus. Optimized for readability and Google Helpful Content, this page covers Ganita Prakash (New) and the complete Old Syllabus index in one place.
NCERT Solutions for Class 7 Maths help you learn the “why” behind every step. Written by experienced teachers, these solutions balance clarity with rigor: quick definitions, reasoning, small worked examples, and the exact presentation examiners expect. Whether you’re revising for unit tests or building a base for higher classes in science and maths, you’ll find concise explanations, sample papers pointers, and higher order thinking skill prompts. You can also download NCERT book for class 7 Maths and chapter-wise PDFs for offline study.
NCERT Solutions for Class 7 Maths
| Section | What’s Inside | Jump |
|---|---|---|
| Ganita Prakash – New Syllabus | 8 chapters with concept summaries, step patterns, mistakes to avoid, and “exam-style frames” | Open |
| Old Syllabus – Full Exercise Index | 15 chapters with exercise lists (Ex 1.1, 1.2 …), recap & strategy — perfect for extra practice | Open |
| Downloads | Free PDFs for books, solutions, notes, MCQs, extra questions | Go |
| FAQs | Common doubts about preparation, step marking, and the two syllabi | Read |
Ganita Prakash – Chapter-wise Solutions (New Syllabus)
Each chapter below follows the same student-friendly pattern: Concept Recap → Model Example → Textbook Exercise Approach → Common Errors → Exam-Style Answer Frame. Use the “View/PDF” buttons to open the full step-by-step solutions.
Chapter 1: Large Numbers Around Us
What you learn: Indian vs International place value, reading/writing large numbers, estimation, and operations in context (population, money, distances). Core ideas: Place value charts, rounding rules (to nearest 10/100/1000), word-problems that need sensible approximations.
Model idea: Rounding to nearest thousand — if last three digits are ≥ 500, add 1 to the thousands, else keep as is. Tip: Use mental estimation first to sense-check elaborate calculations. Exam Frame (2–3 marks): State place value → apply rounding rule → show one line of verification.
Chapter 2: Arithmetic Expressions
What you learn: Order of operations, brackets ((), {}, []), evaluating expressions, substituting given numbers. Core ideas: BODMAS/PEMDAS, nested brackets, substitution pitfalls (negative numbers!).
Model idea: Evaluate \( 7 – \{4 – (3 – 8)\} \) → inner first: \(3 – 8 = -5\); then \(4 – (-5) = 9\); finally \(7 – 9 = -2\). Common error: Dropping the sign during substitution. Exam Frame: Write the order used; compute step-by-step on separate lines; box the final value.
Chapter 3: A Peek Beyond the Point
What you learn: Decimals to thousandths, number line placement, addition/subtraction/multiplication/division of decimals, money/measurement problems. Core ideas: Place value alignment, converting to fractions for clarity in tricky steps.
Model idea: Align decimals in columns: to add \( 3.405 + 0.62 \), write \(0.620\). Equation check: \(3.405 + 0.620 = 4.025\). Exam Frame: “Given” table with place values → operation steps → units (₹, m, L) clearly noted.
Chapter 4: Expressions using Letter Numbers
What you learn: Variables, translating statements to expressions, combining like terms, simple evaluations. Core ideas: Difference between constants & variables, coefficient & term, writing rules in algebra (e.g., “three more than a number \(x\) is \(x+3\)”).
Model idea: “A number doubled and decreased by 5” → \(2x – 5\). For \(x=7\), value \(= 9\). Common error: Reversing “less than” expressions. Exam Frame: Statement → algebraic form → substitution table → final value.
Chapter 5: Parallel and Intersecting Lines
What you learn: Transversal angles (corresponding, alternate interior, co-interior), identifying parallelism through angle properties, basic reasoning. Core ideas: If lines are parallel, corresponding angles are equal; alternate interior angles are equal; co-interior angles are supplementary.
Mini-proof pattern: State the reason before the step (e.g., “Since \(l \parallel m\), ∠A = ∠B (corresponding angles)”). Exam Frame: Neat figure with labels → theorem used → numeric substitution → conclusion.
Chapter 6: Number Play
What you learn: Factors/multiples, prime vs composite, prime factorization, LCM & HCF with applications. Core ideas: Division tests, product of primes, word problems (synchronizing cycles, grouping items).
Model idea (HCF by prime factorization): \(60 = 2^2 \cdot 3 \cdot 5\), \(48 = 2^4 \cdot 3\) → HCF \(= 2^2 \cdot 3 = 12\). Exam Frame: List prime factors → pick common primes with minimum powers (HCF) / maximum powers (LCM) → one-line check.
Chapter 7: A Tale of Three Intersecting Lines
What you learn: Triangle basics, interior & exterior angle theorems, classification by sides/angles, angle sum \(= 180^\circ\). Core ideas: Exterior angle equals sum of opposite interior angles; linear pair idea to justify steps.
Model idea: If ∠1 and ∠2 are interior angles, exterior angle at the third vertex \(= ∠1 + ∠2\). Exam Frame: Draw triangle → mark angles → cite theorem → compute → state triangle type, if asked.
Chapter 8: Working with Fractions
What you learn: Like/unlike fractions, equivalent fractions, simplification, addition/subtraction/multiplication/division, mixed numbers. Core ideas: LCM for unlike denominators, cross-checking via estimation.
Model idea: \( \tfrac{3}{4} + \tfrac{5}{6} = \tfrac{9}{12} + \tfrac{10}{12} = \tfrac{19}{12} = 1 \tfrac{7}{12}\). Common error: Adding denominators directly. Exam Frame: Convert to like denominators → add numerators → reduce fraction → mixed form (if needed).
| Chapter | Open Solutions | Download PDF |
|---|---|---|
| 1. Large Numbers Around Us | View | |
| 2. Arithmetic Expressions | View | |
| 3. A Peek Beyond the Point | View | |
| 4. Expressions using Letter Numbers | View | |
| 5. Parallel and Intersecting Lines | View | |
| 6. Number Play | View | |
| 7. A Tale of Three Intersecting Lines | View | |
| 8. Working with Fractions | View |
Common Pitfalls (and Quick Fixes)
- Fractions/Decimals: Align place values and denominators; estimate first to catch impossible answers.
- Signs in substitution: Wrap negatives in brackets, e.g., \(a – (-3) = a + 3\).
- Geometry reasoning: Always name the theorem/law before using numbers. Neat figures fetch marks.
- LCM/HCF mix-ups: HCF → minimum powers of common primes; LCM → maximum powers across all.
NCERT Class 7 Maths – Old Syllabus (Full Exercise Index + Concept Pointers)
Schools still use the Old Syllabus for drills. Below, each chapter includes a one-paragraph concept refresher and the full exercise list so you can jump straight to practice PDFs.
Chapter 1: Integers
Focus: Number line, addition/subtraction with signs, multiplication/division rules, comparing integers. Trick: For \( (+a) + (-b) \), think “big minus small” and keep the bigger sign. Example: \( +5 + (-7) = -2 \).
Exercises: 1.1, 1.2, 1.3, 1.4 + Extra Questions
Chapter 2: Fractions and Decimals
Focus: Equivalent forms, operations, converting between fractions and decimals, real-life use (money, measures). Tip: For division by a decimal, move the decimal point to make the divisor a whole number and move the dividend point equally.
Exercises: 2.1 → 2.7 + Extra Questions
Chapter 3: Data Handling
Focus: Tally marks, bar graphs, double bar graphs, probability idea (simple). Exam habit: Proper titles, axis labels, uniform scales — presentation matters.
Exercises: 3.1 → 3.4 + Extra Questions
Chapter 4: Simple Equations
Focus: Translate statements into equations; solve by inverse operations; check your solution. Example: “Five more than twice a number is 17” → \(2x + 5 = 17\) → \(x = 6\).
Exercises: 4.1 → 4.4 + Extra Questions
Chapter 5: Lines and Angles
Focus: Adjacent angles, linear pair, vertically opposite angles, transversal properties. Proof habit: Draw, mark, reason, compute.
Exercises: 5.1, 5.2 + Extra Questions
Chapter 6: The Triangle and Its Properties
Focus: Angle sum property, exterior angle property, triangle inequality, medians/altitudes. Memory cue: Any exterior angle \(=\) sum of the two interior opposite angles.
Exercises: 6.1 → 6.5 + Extra Questions
Chapter 7: Congruence of Triangles
Focus: SSS, SAS, ASA, RHS congruence criteria; matching order of vertices is crucial. Tip: State criterion explicitly before concluding congruence.
Exercises: 7.1, 7.2 + Extra Questions
Chapter 8: Comparing Quantities
Focus: Percentage, profit & loss, discount, simple interest. Key formulae: \( \text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100\), \( \text{SI} = \frac{PTR}{100} \).
Exercises: 8.1 → 8.3 + Extra Questions
Chapter 9: Rational Numbers
Focus: Standard form, comparison, operations, closure properties. Note: Write in lowest terms with positive denominator.
Exercises: 9.1, 9.2 + Extra Questions
Chapter 10: Practical Geometry
Focus: Drawing triangles given SSS/SAS/ASA/RHS; perpendicular bisector and angle bisector constructions. Exam habit: Light pencil, accurate arcs, label all points.
Exercises: 10.1 → 10.5 + Extra Questions
Chapter 11: Perimeter and Area
Focus: Area/perimeter of rectangles, triangles, parallelograms; unit conversions. Formulae: \(A_{\triangle}=\frac{1}{2}bh\), \(A_{||gm}=bh\).
Exercises: 11.1 → 11.4 + Extra Questions
Chapter 12: Algebraic Expressions
Focus: Terms, coefficients, like/unlike terms, addition/subtraction, simple multiplication patterns. Memory: \((a+b)^2 = a^2+2ab+b^2\) (preview idea for later classes).
Exercises: 12.1 → 12.4 + Extra Questions
Chapter 13: Exponents and Powers
Focus: Laws of exponents: \(a^m\cdot a^n=a^{m+n}\), \(\frac{a^m}{a^n}=a^{m-n}\), \((a^m)^n=a^{mn}\), \(a^0=1\) (for \(a\neq0\)). Care: Negative powers and reciprocals.
Exercises: 13.1 → 13.3 + Extra Questions
Chapter 14: Symmetry
Focus: Lines of symmetry, rotational symmetry, practical recognition in patterns. Tip: Count axes carefully; some shapes have none.
Exercises: 14.1 → 14.3 + Extra Questions
Chapter 15: Visualising Solid Shapes
Focus: Nets, views (top/front/side), 2D–3D mapping. Habit: Sketch lightly, label edges/faces, check counts (e.g., cube has 6 faces, 12 edges, 8 vertices).
Exercises: 15.1 → 15.4 + Extra Questions
Answer-Writing System (Score Booster)
Line 2 (To Find): Name the exact quantity asked.
Line 3 (Working): Show steps with reasons (theorem/law), then a boxed final answer. This mirrors step-marking in board exams.
Downloads & Quick Links
| Resource | Details | Action |
|---|---|---|
| NCERT Class 7 Maths – Ganita Prakash (Textbook PDF) | Latest edition by National Council of Educational Research and Training, aligned to CBSE syllabus. | Download Book |
| Chapter-wise NCERT Solutions – Ganita Prakash (New) | Precise steps, solved examples, and printable PDFs; great for exam preparation. | Download All |
| Old Syllabus – Exercise-wise Solutions | Integers to Visualising Solid Shapes; indexes with Ex 1.1, 1.2… + Extra Questions. | Open |
| Class 7 Maths — Extra Questions, MCQs, Notes | Targeted practice to build speed and accuracy for tests. | Open Sets |