Class 9 Mathematics Chapter 8: Working with Fractions Previous Year Questions (2020–2025)

Reading Chapter 8 theory once teaches you *what* fractions are; solving past papers teaches you *how examiners test* that knowledge. When you solve a 2023 paper question on dividing fractions, your brain encounters a real-world constraint: time, pressure, and exact wording. You discover which steps you skip, which formulas you forget, and which common errors (like forgetting to invert the divisor) trip you up. Re-reading theory doesn't trigger these mistakes—past papers do, safely, before your final exam. Additionally, CBSE tends to repeat conceptual patterns: reciprocal questions almost always appear in 1-mark sections, while multi-step word problems cluster in 3-mark slots. By mapping these patterns across 5 years of papers, you gain predictive insight into what *will* appear on your 2025 paper. This chapter averages 8–12 marks in most question papers, making it high-yield for focused revision. Start by attempting questions *without* checking answers immediately; then compare your method against the official solution. This 'attempt-first' approach builds stronger neural pathways than passive reading.

One-mark questions in this chapter almost exclusively test conceptual recall: reciprocals, simplification, and basic multiplication/division. **Q1: What is the reciprocal of 7/9?** A: 9/7. (Flip numerator and denominator.) **Q2: Simplify: 3/4 × 8/9.** A: (3 × 8)/(4 × 9) = 24/36 = 2/3. (Multiply straight across, then reduce.) **Q3: Divide 5/6 by 10/12. Express as a single fraction.** A: 5/6 ÷ 10/12 = 5/6 × 12/10 = 60/60 = 1. (Invert the divisor, then multiply.) **Q4: Is 3/5 × 5/3 equal to 1?** A: Yes. 3/5 × 5/3 = 15/15 = 1. (A number multiplied by its reciprocal always equals 1.) **Q5: Which is larger: 2/3 or 5/8?** A: 2/3. (Convert to common denominator: 16/24 vs 15/24, or use decimals: 0.667 > 0.625.) These questions test automatic recall under 30–60 seconds of pressure. Practise them until you answer in under 20 seconds.

Three-mark questions combine operations with word problems or multi-step simplifications. **Q1: A baker has 12 kg of flour. She uses 2/3 of it for bread and 1/4 of the remainder for cakes. How much flour is left?** Solution: - Flour used for bread = 2/3 × 12 = 8 kg - Remainder = 12 − 8 = 4 kg - Flour used for cakes = 1/4 × 4 = 1 kg - Flour left = 4 − 1 = 3 kg **Q2: Simplify: (3/5 ÷ 9/10) × 2/3.** Solution: - 3/5 ÷ 9/10 = 3/5 × 10/9 = 30/45 = 2/3 - 2/3 × 2/3 = 4/9 **Q3: A rope is 20 m long. A boy cuts it into 5 equal pieces, then joins 3 pieces. What fraction of the original rope does he have?** Solution: - Length of each piece = 20/5 = 4 m - Length after joining 3 pieces = 3 × 4 = 12 m - Fraction = 12/20 = 3/5 **Q4: Express as a single fraction: 2/3 + (4/5 × 3/8) − 1/4.** Solution: - 4/5 × 3/8 = 12/40 = 3/10 - 2/3 + 3/10 − 1/4 (LCM of 3, 10, 4 is 60) - = 40/60 + 18/60 − 15/60 = 43/60 **Q5: If 3/4 of a number is 15, what is 2/3 of that number?** Solution: - Let the number be x. Then 3x/4 = 15, so x = 20. - 2/3 of 20 = 40/3 = 13⅓ These questions appear frequently because they test both procedural fluency and reasoning.

Five-mark questions demand multi-step logic, real-world context, and clear working. **Q1: A school has 600 students. 2/5 of them participate in sports, 1/3 participate in arts, and the rest do neither. Of those in sports, 3/4 also participate in arts. (a) How many students participate in both? (b) How many participate in only one activity?** Solution: (a) Students in sports = 2/5 × 600 = 240 Students in arts = 1/3 × 600 = 200 Students in both = 3/4 × 240 = 180 (b) Only sports = 240 − 180 = 60 Only arts = 200 − 180 = 20 Total in only one = 60 + 20 = 80 students **Q2: A factory produces 3000 units daily. On Monday, 4/5 of production is sold. On Tuesday, 7/8 of the remaining stock plus Monday's unsold units is sold. How many units remain after Tuesday?** Solution: Monday production sold = 4/5 × 3000 = 2400 Monday unsold = 3000 − 2400 = 600 Tuesday production = 3000 Tuesday stock available = 600 + 3000 = 3600 Tuesday sold = 7/8 × 3600 = 3150 Remaining = 3600 − 3150 = 450 units **Q3: Simplify: [2/3 + (1/4 ÷ 5/8)] × [3/5 − (2/3 × 3/4)] ÷ [(7/9 × 18/14) + 1/2]** Solution: Part 1: 1/4 ÷ 5/8 = 1/4 × 8/5 = 8/20 = 2/5 2/3 + 2/5 = 10/15 + 6/15 = 16/15 Part 2: 2/3 × 3/4 = 6/12 = 1/2 3/5 − 1/2 = 6/10 − 5/10 = 1/10 Part 3: 7/9 × 18/14 = (7 × 18)/(9 × 14) = 126/126 = 1 1 + 1/2 = 3/2 Final: 16/15 × 1/10 ÷ 3/2 = 16/150 × 2/3 = 32/450 = 16/225 These questions require careful bracket management and accuracy across multiple operations.

The revised CBSE syllabus (2024–25 onwards) emphasizes conceptual depth over routine calculation. Within Chapter 8, expect these shifts: **Greater focus on real-world applications:** Questions now embed fractions in authentic contexts (recipes, land division, time allocation) rather than abstract number manipulation. A 2025-style question might ask: 'A garden is divided into 4 equal plots. Vegetables occupy 2/3 of the first plot and 5/6 of the second. What fraction of the total garden area is under vegetables?' This requires spatial reasoning, not just arithmetic. **Reciprocal and inverse operations:** Examiners increasingly test whether students *understand* why multiplying by a reciprocal equals dividing. Expect conceptual questions like: 'Explain why a/b ÷ c/d = a/b × d/c. Give two examples.' This wasn't common in 2020–2022 papers. **Estimation and approximation:** The new pattern includes 'estimate the answer' questions. For example: 'Without calculating exactly, explain whether 7/8 × 9/10 is closer to 1/2 or 1.' **Integration with other chapters:** Fractions now appear as tools in geometry (area, scaling) and data handling (probability expressed as fractions). A typical 5-mark question might combine Chapter 8 with Chapter 5 (Understanding Quadrilaterals): 'A rectangular field's length is 3/2 times its width. If the width is 2/3 of 120 m, find the area and express it as a fraction of a 2-hectare plot.' **Reduced emphasis on pure reciprocal drills:** The 1-mark 'find the reciprocal' question may appear less frequently; instead, reciprocals appear as intermediate steps in larger problems. To prepare for 2026–27 papers, focus on translating word problems into fraction operations and vice versa.

**T=0–5 min: Scan and allocate.** Read the entire question paper. Identify all Chapter 8 questions. Allocate time: 1-mark questions (1 min each), 3-mark questions (4–5 min each), 5-mark questions (8–10 min each). Total for Chapter 8: ~25–30 min if it carries ~12 marks. **T=5–15 min: Answer all 1-mark questions first.** These build confidence and yield quick points. For each: (1) identify the operation (multiply, divide, compare, find reciprocal), (2) execute, (3) simplify, (4) write answer in one line. Do not re-check unless you have time at the end. **T=15–25 min: Tackle 3-mark questions.** For word problems: (1) underline the question, (2) identify what you know vs. what you need, (3) write the formula or operation, (4) calculate step-by-step, (5) verify the answer makes sense (e.g., is the result smaller or larger than expected?). Show all working—partial credit depends on method, not just the final answer. **T=25–40 min: Attempt 5-mark questions.** These often have sub-parts (a), (b), (c). Read each sub-part carefully. Use the answer to part (a) to guide part (b). If you're unsure of a middle step, state an assumption clearly (e.g., 'Assuming the remainder is 600 kg, I calculate...') and continue—examiners award method marks. **T=40–50 min: Review and correct.** Check calculations in 1-mark answers; verify that simplifications are fully reduced; ensure final answers are boxed or underlined. **Common exam mistakes to avoid:** - Forgetting to invert when dividing (e.g., writing a/b ÷ c/d = ac/bd instead of ad/bc). - Not reducing fractions to lowest terms. - Misreading multi-line word problems (re-read the question twice). - Mixing up 'of' (multiply) with 'and then' (separate operations). Start a 3-day free trial at cbsetutor.ai to practice timed mock tests on Chapter 8 with instant feedback on your method.

This page aggregates the genuine question types from CBSE Class 9 Mathematics papers over the last 5 years. Use it as a **diagnostic tool** before revising: (1) Attempt all 13 questions in one sitting without checking answers. (2) Mark your score. If ≥80%, you're exam-ready; ≤60%, return to your textbook and re-study Chapter 8 before attempting again. (3) For each wrong answer, identify the error type: conceptual (e.g., didn't understand what reciprocal means), procedural (e.g., forgot to invert in division), or careless (e.g., arithmetic mistake). Then re-attempt that specific question type daily for 3 days. Use the solutions provided not as a final answer sheet, but as a **method comparison tool**. If your answer is correct but your method differs from the solution, ask your teacher or a tutor whether your method is equally valid. Examiners reward multiple valid approaches equally. Finally, note the word-problem context in 3-mark and 5-mark questions—the CBSE favors real-world scenarios (bakers, fields, rope, production). When you encounter a new word problem in class, map it to one of these templates and practice variations. This templating strategy is far more efficient than memorizing individual questions.