Class 9 Mathematics Chapter 7 Fractions Previous Year Questions: Complete PYQ Bank with Solutions

Students often spiral into re-reading NCERT chapters, hoping retention improves. Research shows this passive review yields minimal gains. Previous year questions train your brain to recognise question patterns, time management, and the exact reasoning examiners expect. For Chapter 7 (Fractions), past papers reveal: • 1-mark questions almost always test: identifying like/unlike fractions, finding equivalent forms, or spotting errors in simplification. • 3-mark questions focus: comparing fractions using cross-multiplication or common denominators, performing mixed operations, ordering fractions on a number line. • 5-mark questions demand: multi-step fraction operations, proof-style reasoning, or real-world word problems involving fractional quantities. When you solve a PYQ, you're not just practising arithmetic—you're learning the examiner's language. You internalise which steps earn marks, where students typically lose points, and which shortcuts are safe. This meta-awareness translates to higher scores on unfamiliar questions too. Plus, PYQs expose gaps in your understanding that rereading would miss. A student might 'understand' equivalent fractions in theory, but solving 5 past paper questions in a row reveals whether they can reliably apply the concept under time pressure.

These five questions represent the most common 1-mark patterns. They test quick recall and conceptual clarity. **Q1: Identify Like Fractions** Which pair represents like fractions? (a) 3/5 and 7/5 (b) 2/7 and 2/9 (c) 1/3 and 3/1 (d) 4/6 and 5/7 **Answer:** (a) 3/5 and 7/5 **Explanation:** Like fractions have the same denominator. Both 3/5 and 7/5 have denominator 5. --- **Q2: Simplify to Lowest Terms** Express 24/36 in simplest form. (a) 2/3 (b) 4/6 (c) 8/12 (d) 12/18 **Answer:** (a) 2/3 **Explanation:** HCF(24, 36) = 12. Dividing both: 24÷12 = 2, 36÷12 = 3. Thus 24/36 = 2/3. --- **Q3: Identify Equivalent Fractions** Which fraction is equivalent to 5/8? (a) 10/16 (b) 5/16 (c) 15/24 (d) Both (a) and (c) **Answer:** (d) Both (a) and (c) **Explanation:** 5/8 × 2/2 = 10/16; 5/8 × 3/3 = 15/24. Both are equivalent. --- **Q4: Compare Using >, <, or =** Compare: 7/9 ___ 5/7 (a) > (b) < (c) = (d) Cannot compare **Answer:** (a) > **Explanation:** Cross-multiply: 7 × 7 = 49 and 9 × 5 = 45. Since 49 > 45, then 7/9 > 5/7. --- **Q5: Decimal Representation** Which fraction equals 0.75? (a) 3/4 (b) 7/10 (c) 3/5 (d) 2/5 **Answer:** (a) 3/4 **Explanation:** 3 ÷ 4 = 0.75. Also, 0.75 = 75/100 = 3/4 (after simplification).

These questions require multi-step reasoning and are worth practising thoroughly. --- **Q1: Order Fractions and Represent on Number Line** Arrange 2/3, 5/6, 1/2 in ascending order. Also, represent them on a number line. **Solution:** Find LCM of denominators 3, 6, 2 = 6. Convert: 2/3 = 4/6, 5/6 = 5/6, 1/2 = 3/6. Ascending order: 3/6 < 4/6 < 5/6, i.e., 1/2 < 2/3 < 5/6. [Number line from 0 to 1 with marks at 1/2, 2/3, 5/6] **Marks Distribution:** Conversion (1 mark) + Ordering (1 mark) + Number line representation (1 mark). --- **Q2: Operations on Unlike Fractions (Addition/Subtraction)** Add: 3/4 + 5/6 – 1/3 **Solution:** LCM(4, 6, 3) = 12. 3/4 = 9/12, 5/6 = 10/12, 1/3 = 4/12. 9/12 + 10/12 – 4/12 = (9 + 10 – 4)/12 = 15/12 = 5/4. **Marks:** LCM identification (1 mark) + Conversion (1 mark) + Final answer (1 mark). --- **Q3: Multiplication of Fractions** Simplify: 8/15 × 25/16 × 3/5 **Solution:** = (8 × 25 × 3)/(15 × 16 × 5) = 600/1200 = 1/2 (after simplification). Alternatively, cancel before multiplying: 8/16 = 1/2, 25/5 = 5, 3/15 = 1/5. = (1/2) × 5 × (1/5) = 1/2. **Marks:** Cancellation strategy (1 mark) + Multiplication (1 mark) + Simplified answer (1 mark). --- **Q4: Division of Fractions** Divide: 7/8 ÷ 3/4 **Solution:** 7/8 ÷ 3/4 = 7/8 × 4/3 (reciprocal of divisor). = (7 × 4)/(8 × 3) = 28/24 = 7/6. **Marks:** Reciprocal application (1 mark) + Multiplication (1 mark) + Simplification (1 mark). --- **Q5: Word Problem Involving Fractions** Ravi ate 2/5 of a pizza, and Priya ate 1/3 of the remaining pizza. What fraction of the pizza remained? **Solution:** Ravi ate: 2/5. Remaining after Ravi: 1 – 2/5 = 3/5. Priya ate: 1/3 of 3/5 = 1/3 × 3/5 = 1/5. Total eaten: 2/5 + 1/5 = 3/5. Remaining: 1 – 3/5 = 2/5. **Marks:** First fraction subtraction (1 mark) + Computing Priya's portion (1 mark) + Final remainder (1 mark).

These questions test integration of multiple concepts and demand clear, step-by-step reasoning. --- **Q1: Complex Fraction Operations with Simplification** Simplify: (3/4 + 5/8) × (2/3 – 1/6) ÷ 7/12 **Full Solution:** Step 1: Simplify the first bracket (3/4 + 5/8). LCM(4, 8) = 8. 3/4 = 6/8. 6/8 + 5/8 = 11/8. [1 mark] Step 2: Simplify the second bracket (2/3 – 1/6). LCM(3, 6) = 6. 2/3 = 4/6. 4/6 – 1/6 = 3/6 = 1/2. [1 mark] Step 3: Multiply the results. 11/8 × 1/2 = 11/16. [1 mark] Step 4: Divide by 7/12. 11/16 ÷ 7/12 = 11/16 × 12/7 = (11 × 12)/(16 × 7) = 132/112. Step 5: Simplify to lowest terms. HCF(132, 112) = 4. 132 ÷ 4 = 33, 112 ÷ 4 = 28. Answer: 33/28. [2 marks for division and simplification] --- **Q2: Comparing and Ordering Fractions with Justification** Arrange these fractions in descending order: 7/9, 11/15, 4/5, 13/18. Justify your answer using a common denominator or cross-multiplication. **Full Solution:** Step 1: Find LCM of 9, 15, 5, 18. 9 = 3² 15 = 3 × 5 5 = 5 18 = 2 × 3² LCM = 2 × 3² × 5 = 90. [1 mark] Step 2: Convert all fractions to denominator 90. 7/9 = 70/90 11/15 = 66/90 4/5 = 72/90 13/18 = 65/90 [2 marks] Step 3: Compare numerators. 72 > 70 > 66 > 65. So: 72/90 > 70/90 > 66/90 > 65/90. [1 mark] Step 4: Write in original form. Descending order: 4/5 > 7/9 > 11/15 > 13/18. [1 mark] --- **Q3: Real-World Problem Combining Multiple Operations** A baker has 5 kg of flour. On Monday, she used 2/5 of the flour for bread. On Tuesday, she used 1/3 of the remaining flour for cakes. On Wednesday, she used 3/4 of what remained after Tuesday for pastries. How much flour is left? Also express this as a decimal. **Full Solution:** Step 1: Calculate flour used on Monday. Used = 2/5 × 5 = 2 kg. Remaining after Monday = 5 – 2 = 3 kg. [1 mark] Step 2: Calculate flour used on Tuesday. Used = 1/3 × 3 = 1 kg. Remaining after Tuesday = 3 – 1 = 2 kg. [1 mark] Step 3: Calculate flour used on Wednesday. Used = 3/4 × 2 = 3/2 = 1.5 kg. Remaining after Wednesday = 2 – 1.5 = 0.5 kg. [1 mark] Step 4: Express as a fraction. 0.5 kg = 1/2 kg. [1 mark] Step 5: Verification. Total used = 2 + 1 + 1.5 = 4.5 kg. Total remaining = 5 – 4.5 = 0.5 kg = 1/2 kg. ✓ [1 mark] **Answer:** 1/2 kg or 0.5 kg of flour remains.

Examiners are gradually introducing skill-based and reasoning-heavy questions. Observe these emerging trends: **1. Reduced Rote Memorisation, Increased Justification** Older papers often asked: 'Simplify 15/25.' New pattern asks: 'Explain why 15/25 and 3/5 are equivalent using the definition of equivalent fractions.' Students must articulate reasoning, not just compute. **2. Integration with Decimals and Percentages** Older: 'Convert 3/4 to decimal.' New: 'A shopkeeper offers a discount of 1/4 on an item. If the original price is ₹800, calculate the sale price and express the discount as a decimal and percentage.' Fractions now sit within multi-concept problems. **3. Number Line Representations as Primary Tool** Recent papers emphasise visual reasoning. Expect questions like: 'Shade the region representing 2/5 + 1/3 on a number line and verify your answer algebraically.' Drawing and calculating are equally weighted. **4. Word Problems with Real-World Contexts** Abstract operations are giving way to scenarios: recipe adjustments, distance/time fractions, financial literacy (loans, investments). CBSE is aligning with NEP 2020's emphasis on practical mathematics. **5. Higher-Order Thinking (HOT) Questions** New papers occasionally include: 'Prove that between any two fractions, infinitely many fractions exist. Provide three examples.' Such questions test conceptual depth, not speed. **Preparation Strategy:** Don't rely solely on old 1-mark tricks. Instead, after solving a PYQ, ask yourself: 'Why does this work? Can I explain it to someone else?' This meta-cognitive habit prepares you for newer question designs. At cbsetutor.ai, our AI tutors adapt practice problems dynamically based on these shifting patterns, ensuring your preparation stays ahead of the curve.

When you encounter a fractions question in the exam, follow this 4-step attack plan: **Step 1: Classify the Question Type (15 seconds)** Read the question and label it: • Simplification? (Reduce to lowest terms.) • Comparison? (Use cross-multiplication or common denominator.) • Operation? (Identify +, –, ×, ÷.) • Word problem? (Identify what fraction of what, then translate.) • Number line? (Plot positions, check ordering.) Classification primes your brain to use the right algorithm. --- **Step 2: Write the Setup Clearly (30–60 seconds)** Don't skip the "working." Write: • LCM (if unlike fractions) • Conversion step • The operation in expanded form Marks are awarded for process, not just the final answer. A correct setup with an arithmetic error often scores 80% of marks; no setup scores zero. --- **Step 3: Perform One Operation at a Time** Resist the urge to combine steps mentally. For 3/4 + 5/8 – 1/6: • Convert to 18/24 + 15/24 – 4/24 (show this line). • Add: (18 + 15)/24 = 33/24 (show this line). • Subtract: (33 – 4)/24 = 29/24 (show this line). • Simplify: Check HCF(29, 24) = 1, so 29/24 is final. This linear approach minimizes careless errors. --- **Step 4: Verify Using an Alternative Method** For comparison questions, if you used cross-multiplication, verify by converting to common denominator. For operations, estimate using benchmarks (e.g., 3/4 ≈ 0.75) and check if your answer is reasonable. Spending 20 seconds here can save you from a ½-mark loss. --- **Time Allocation for Different Question Lengths:** • 1-mark: 1.5–2 minutes (classify + compute + verify). • 3-mark: 4–5 minutes (setup + step-by-step + one check). • 5-mark: 8–10 minutes (careful setup + multi-step reasoning + full verification). If stuck after 60% of allocated time, move on and return later. --- **Common Pitfalls to Avoid:** 1. **Forgetting to simplify final answers.** Always check if HCF > 1. 2. **Mixing up reciprocals in division.** Remember: a/b ÷ c/d = a/b × d/c (flip the divisor). 3. **Careless LCM errors.** Double-check by verifying each fraction's conversion. 4. **Skipping the common denominator step.** Never add/subtract unlike fractions directly. Start a 3-day free trial at cbsetutor.ai to access interactive fraction problem-sets with instant feedback and step-by-step video solutions tailored to your pace.