Class 9 Mathematics Chapter 8: Working with Fractions – Important Questions & Solutions

Chapter 8—Working with Fractions—is weighted heavily in board assessments because it bridges fundamental arithmetic and algebraic thinking. In the new rationalized CBSE curriculum, examiners focus on conceptual understanding rather than mechanical computation. The 2026-27 board will test your grasp of: (1) multiplication and division rules for fractions, (2) the relationship between a fraction and its reciprocal, (3) comparison of fractional operations to identify which yields larger or smaller results, and (4) multi-step word problems requiring fraction operations in practical contexts (recipes, distances, time, money). These skills are non-negotiable because they underpin higher algebra, ratio-and-proportion problems, and even geometry. Questions appear across all three answer formats: 1-mark MCQs (testing quick recall and common misconceptions), 2-mark short answers (checking procedural accuracy), 3-mark problem-solving, and 5-mark integrative questions combining multiple operations. By practising these curated questions, you'll internalize the patterns examiners expect and avoid costly errors on exam day.

MCQ questions test rapid recall, concept clarity, and common pitfalls. Here are 5 representative questions: **Q1:** If a/b is a fraction, its reciprocal is: (A) b/a (B) -a/b (C) a/(−b) (D) 1/(a/b) **Answer:** (A) b/a. The reciprocal of a/b is obtained by swapping numerator and denominator, yielding b/a (provided a ≠ 0). **Q2:** What is 3/4 × 8/9 ? (A) 24/36 (B) 2/3 (C) 11/13 (D) 3/4 **Answer:** (B) 2/3. Multiply: (3 × 8)/(4 × 9) = 24/36 = 2/3 (after cancelling common factors). **Q3:** Dividing 5/6 by 10/12 is the same as: (A) 5/6 × 10/12 (B) 5/6 × 12/10 (C) 6/5 × 10/12 (D) 5/6 ÷ 10/12 **Answer:** (B) 5/6 × 12/10. Division by a fraction equals multiplication by its reciprocal. **Q4:** Which is larger: 7/8 or 6/7? (A) 7/8 (B) 6/7 (C) Both equal (D) Cannot determine **Answer:** (A) 7/8. Compare: 7/8 = 49/56 and 6/7 = 48/56; 49/56 > 48/56. **Q5:** If 2/5 of a number is 16, the number is: (A) 32 (B) 40 (C) 6.4 (D) 20 **Answer:** (B) 40. Let the number be x; (2/5)x = 16 → x = 16 × (5/2) = 40.

These questions require concise calculation and explanation: **Q1:** Simplify: 4/5 × 15/16 ÷ 3/8 **Solution:** = (4/5 × 15/16) ÷ 3/8 = (60/80) ÷ 3/8 = (3/4) ÷ 3/8 [simplify 60/80] = (3/4) × (8/3) [divide = multiply by reciprocal] = 24/12 = 2 **Answer:** 2 **Q2:** A ribbon of length 45/2 metres is cut into pieces, each 9/4 metres long. How many pieces are obtained? **Solution:** Number of pieces = (45/2) ÷ (9/4) = (45/2) × (4/9) = (45 × 4)/(2 × 9) = 180/18 = 10 **Answer:** 10 pieces **Q3:** Find the reciprocal of 3 1/4 (3 and 1/4 as a mixed number). **Solution:** Convert to improper fraction: 3 1/4 = 13/4 Reciprocal = 4/13 **Answer:** 4/13 **Q4:** Simplify: (2/3 + 1/6) × 3/5 **Solution:** = (4/6 + 1/6) × 3/5 = (5/6) × 3/5 = 15/30 = 1/2 **Answer:** 1/2 **Q5:** If 3/8 of a tank holds 120 litres, what is the full capacity? **Solution:** Let capacity = x; (3/8)x = 120 x = 120 × (8/3) = 960/3 = 320 litres **Answer:** 320 litres

These require multi-step reasoning and application: **Q1:** A baker uses 2/3 kg of flour to bake one cake. She has 8 kg of flour. (a) How many complete cakes can she bake? (b) How much flour will remain? **Solution:** (a) Number of cakes = 8 ÷ (2/3) = 8 × (3/2) = 24/2 = 12 cakes (b) Flour used = 12 × (2/3) = 8 kg Flour remaining = 8 − 8 = 0 kg **Answer:** (a) 12 cakes (b) 0 kg (no flour remains) **Q2:** Compare 5/12 and 7/18 without converting to decimals. Which is larger? **Solution:** Find LCD of 12 and 18: 12 = 2² × 3; 18 = 2 × 3² LCD = 2² × 3² = 36 5/12 = 15/36; 7/18 = 14/36 Since 15/36 > 14/36, therefore 5/12 > 7/18 **Answer:** 5/12 is larger **Q3:** A recipe requires 3/4 cup of sugar. If you triple the recipe, how much sugar is needed? Express as a mixed number. **Solution:** Sugar needed = 3 × (3/4) = 9/4 = 2 1/4 cups **Answer:** 2 1/4 cups **Q4:** Simplify and verify: (4/9 × 3/8) ÷ (1/6). **Solution:** = (12/72) ÷ (1/6) = (1/6) ÷ (1/6) [simplify 12/72 to 1/6] = (1/6) × 6 = 1 **Verification:** (1/6) ÷ (1/6) = 1 ✓ **Answer:** 1

These questions combine multiple operations and require full justification: **Q1:** A water tank is 3/5 full. If 3/4 of the water in the tank is used, what fraction of the tank's capacity remains? **Solution:** Initial water = 3/5 of tank capacity Water used = (3/4) × (3/5) = 9/20 of tank capacity Water remaining = (3/5) − (9/20) Convert to LCD = 20: 3/5 = 12/20 Remaining = 12/20 − 9/20 = 3/20 of tank capacity **Answer:** 3/20 of the tank's capacity **Q2:** A student reads 2/5 of a book on Day 1 and 1/3 of the book on Day 2. (a) What fraction of the book is read in two days? (b) What fraction remains unread? (c) If the book has 300 pages, how many pages remain? **Solution:** (a) Fraction read = 2/5 + 1/3 LCD of 5 and 3 = 15 2/5 = 6/15; 1/3 = 5/15 Fraction read = 6/15 + 5/15 = 11/15 (b) Fraction unread = 1 − 11/15 = 15/15 − 11/15 = 4/15 (c) Pages unread = (4/15) × 300 = (4 × 300)/15 = 1200/15 = 80 pages **Answers:** (a) 11/15 (b) 4/15 (c) 80 pages **Q3:** Prove that (a/b) × (b/a) = 1 for any fraction a/b (where a ≠ 0 and b ≠ 0). Then use this to explain why multiplying a number by a fraction and then by its reciprocal returns the original number. **Solution:** (a/b) × (b/a) = (a × b)/(b × a) = ab/ab = 1 (provided a ≠ 0, b ≠ 0) Consider a number n. Multiply by fraction p/q, then by reciprocal q/p: n × (p/q) × (q/p) = n × [(p/q) × (q/p)] = n × 1 = n This shows that multiplication by a fraction and its reciprocal are inverse operations—they 'undo' each other and restore the original value. This principle underlies equation-solving in algebra. **Answer:** Proof shown; principle verified with example n × (3/5) × (5/3) = n.

**Case Study: Meal Planning with Fractions** A school cafeteria manager is planning a week-long meal programme. She buys 60 kg of rice. On Monday, she uses 2/5 of the rice. On Tuesday, she uses 1/3 of the *remaining* rice (not of the original 60 kg). On Wednesday, she decides to restock and buys 1/4 as much rice as she *used* on Monday. **Question:** (a) How much rice was used on Monday? (b) How much rice remained after Tuesday? (c) How much rice did she buy on Wednesday? (d) What is the total rice available on Wednesday evening after cooking? **Step-by-Step Solution:** (a) Rice used Monday = (2/5) × 60 = 24 kg (b) Rice remaining after Monday = 60 − 24 = 36 kg Rice used Tuesday = (1/3) × 36 = 12 kg [note: 1/3 of remaining, not original] Rice remaining after Tuesday = 36 − 12 = 24 kg (c) Rice bought Wednesday = (1/4) × 24 = 6 kg [1/4 of what was used Monday] (d) Total available Wednesday evening = 24 + 6 = 30 kg (before cooking) **Why this is HOTS:** This question requires careful reading (distinguishing 'remaining' from 'original'), multiple sequential operations, and referential fractions (e.g., "1/4 as much as used on Monday"). It tests real-world application and logical sequencing—skills essential for board success.

Conceptual mastery of Chapter 8 doesn't happen by reading solutions once—it requires deliberate, adaptive practice. CBSETUTOR.ai's AI tutor is designed to drill these exact question patterns daily in a way that personalizes to your learning pace. Each session presents randomized variations of the 18+ question types shown above: you solve a 2-mark short answer, get instant feedback with step-by-step corrections, then immediately encounter a similar problem to reinforce weak spots. The platform tracks which topics slow you down (e.g., reciprocals vs. division) and escalates difficulty only when you've internalized the fundamentals. Over 3 days of free use, you'll complete at least 6 full question sets covering multiplication, division, word problems, and comparison—the exact topics that appear on board exams. By exam day, these question patterns will feel familiar, reducing anxiety and careless errors. Start a 3-day free trial at cbsetutor.ai and see how adaptive learning transforms your fraction confidence.