Class 9 Mathematics Chapter 8: Working with Fractions MCQ Quiz with Answers

The 2024–25 CBSE rationalized curriculum emphasises objective, time-efficient assessment. Multiple-choice questions serve three pedagogical goals: they force you to discriminate between plausible distractors (deepening conceptual grip), they reduce marking ambiguity, and they align with competitive entrance exams like JEE and NEET. For Chapter 8, MCQs are particularly powerful because fraction operations involve common procedural errors—multiplying denominators instead of cancelling common factors, or inverting the dividend instead of the divisor in division problems. A well-designed MCQ with four trap options exposes these misunderstandings instantly. Research shows that students who solve 15–20 MCQs on a topic achieve 30% higher conceptual retention than those who solve the same number of free-response questions. The CBSE Class 9 mathematics board paper now allocates 25–30% weightage to MCQs, making systematic practice non-negotiable.

**Q1.** What is 3/5 × 2/7? (A) 6/35 (B) 5/12 (C) 6/12 (D) 10/35 **Answer: (A) 6/35** *Reason: Multiply numerators and denominators separately: (3×2)/(5×7) = 6/35.* **Q2.** Find the reciprocal of 4/9. (A) 4/9 (B) 9/4 (C) 1/4 (D) 4/1 **Answer: (B) 9/4** *Reason: Reciprocal swaps numerator and denominator: reciprocal of a/b is b/a.* **Q3.** What is 7/8 ÷ 2/3? (A) 14/24 (B) 21/16 (C) 7/16 (D) 14/16 **Answer: (B) 21/16** *Reason: Division flips the divisor: 7/8 × 3/2 = 21/16.* **Q4.** Simplify 6/12. (A) 1/2 (B) 1/3 (C) 2/3 (D) 3/4 **Answer: (A) 1/2** *Reason: GCD(6,12) = 6; divide both by 6 to get 1/2.* **Q5.** Which fraction is larger: 3/4 or 2/3? (A) 3/4 (B) 2/3 (C) Equal (D) Cannot compare **Answer: (A) 3/4** *Reason: Cross-multiply: 3×3 = 9 > 2×4 = 8, so 3/4 > 2/3.* **Q6.** What is 5/6 × 1? (A) 6/5 (B) 5/6 (C) 1 (D) 0 **Answer: (B) 5/6** *Reason: Any fraction multiplied by 1 (the multiplicative identity) equals itself.* **Q7.** Find 3/4 × 4/3. (A) 1 (B) 12/12 (C) 7/7 (D) 3/4 **Answer: (A) 1** *Reason: When a fraction is multiplied by its reciprocal, the product is always 1.* **Q8.** What is 1/2 ÷ 1/2? (A) 1/4 (B) 1 (C) 2 (D) 0 **Answer: (B) 1** *Reason: 1/2 × 2/1 = 2/2 = 1; dividing a number by itself gives 1.* **Q9.** Multiply 2/5 × 5/8. (A) 10/40 (B) 1/4 (C) 2/8 (D) 10/13 **Answer: (B) 1/4** *Reason: (2×5)/(5×8) = 10/40 = 1/4 after cancelling the common factor 10.* **Q10.** Divide 9/10 ÷ 3/5. (A) 3/2 (B) 27/50 (C) 3/5 (D) 15/10 **Answer: (A) 3/2** *Reason: 9/10 × 5/3 = 45/30 = 3/2 after simplification.*

**Q11.** A recipe requires 3/4 cup of sugar. If you triple the recipe, how much sugar is needed? (A) 1 1/4 cups (B) 2 1/4 cups (C) 9/12 cups (D) 3/4 cups **Answer: (B) 2 1/4 cups** *Reason: 3 × 3/4 = 9/4 = 2 1/4; word problems often require converting improper fractions to mixed numbers.* **Q12.** Simplify (5/6 × 2/3) ÷ 1/9. (A) 10/18 (B) 5 (C) 18/10 (D) 90/18 **Answer: (B) 5** *Reason: First multiply: 5/6 × 2/3 = 10/18 = 5/9; then divide: 5/9 ÷ 1/9 = 5/9 × 9 = 5.* **Q13.** A tank is 2/3 full. If 1/4 of the full tank's capacity is drained, what fraction remains? (A) 1/6 (B) 5/12 (C) 2/3 (D) 11/12 **Answer: (B) 5/12** *Reason: Drained amount = 1/4 of full = 1/4; remaining = 2/3 − 1/4 = 8/12 − 3/12 = 5/12.* **Q14.** What is the product of 7/12 and the reciprocal of 7/12? (A) 49/144 (B) 1 (C) 14/24 (D) 7/12 **Answer: (B) 1** *Reason: A number multiplied by its reciprocal always equals 1 (multiplicative inverse property).* **Q15.** If 2/5 of a number is 20, what is the number? (A) 8 (B) 50 (C) 40 (D) 25 **Answer: (B) 50** *Reason: Let the number be x. Then 2/5 × x = 20 → x = 20 ÷ 2/5 = 20 × 5/2 = 50.* **Q16.** Compute (3/5 ÷ 2/3) × 5/2. (A) 9/20 (B) 9/4 (C) 45/20 (D) 30/30 **Answer: (B) 9/4** *Reason: 3/5 × 3/2 = 9/10; then 9/10 × 5/2 = 45/20 = 9/4.* **Q17.** A rope of length 5 1/2 metres is cut into pieces of 1/2 metre each. How many pieces are there? (A) 5 (B) 10 (C) 11 (D) 22 **Answer: (C) 11** *Reason: Convert to improper fraction: 5 1/2 = 11/2; divide: 11/2 ÷ 1/2 = 11/2 × 2 = 11.* **Q18.** Which pair of fractions are reciprocals of each other? (A) 2/3 and 3/2 (B) 1/4 and 1/4 (C) 5/7 and 5/7 (D) 2/5 and 5/2 **Answer: (A) 2/3 and 3/2** or **(D) 2/5 and 5/2** *Reason: Reciprocals are pairs where one is the inverted form of the other; both (A) and (D) satisfy this (accept either as correct in class context).* **Q19.** Simplify 4/7 × 14/16 × 2/3. (A) 112/336 (B) 1/3 (C) 2/3 (D) 28/336 **Answer: (B) 1/3** *Reason: Cancel common factors: 4 and 16 → 1/4; 14 and 7 → 2; result: 1/4 × 2/1 × 2/3 = 4/12 = 1/3.* **Q20.** A gardener uses 3/8 kg of fertilizer per plant. For 24 plants, how much fertilizer is needed? (A) 8 kg (B) 9 kg (C) 3 kg (D) 72/8 kg **Answer: (B) 9 kg** *Reason: 24 × 3/8 = 72/8 = 9 kg; real-world scaling problems require multiplying whole numbers by fractions.*

**Q21.** **Assertion (A):** When you divide a fraction by another fraction, you must invert the divisor and multiply. **Reason (R):** Division is the inverse operation of multiplication, and inverting a fraction gives its multiplicative inverse. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) A is false; R is true **Answer: (A) Both A and R are true; R explains A** *Reason: The assertion is a procedural fact; the reason provides the conceptual justification (multiplicative inverse).* **Q22.** **Assertion:** If a/b × c/d = 1, then c/d is the reciprocal of a/b. **Reason:** Two fractions are reciprocals if their product equals 1. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: The reason is the definition of reciprocals, and it directly justifies why the assertion holds.* **Q23.** **Assertion:** 2/3 × 1 = 2/3, but 2/3 ÷ 1 = 2/3 as well. **Reason:** 1 is both the multiplicative and divisive identity for fractions. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (B) Both A and R are true; R does not explain A** *Reason: The assertion is correct, but the reason uses imprecise language ('divisive identity' is not standard); 1 is the multiplicative identity, and dividing by 1 preserves the value, but that is distinct from identity property.* **Q24.** **Assertion:** For any non-zero fraction a/b, a/b × b/a = 1. **Reason:** The product of a fraction and its reciprocal is always 1. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: b/a is indeed the reciprocal of a/b, so the reason justifies the assertion fully.* **Q25.** **Assertion:** 3/4 ÷ 2/5 = 3/4 × 5/2. **Reason:** Dividing by 2/5 is equivalent to multiplying by its reciprocal, 5/2. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: This is the core inversion rule; the reason is the definition behind it.* **Q26.** **Assertion:** If 2/5 of a work is completed in 4 hours, then the full work will take 10 hours. **Reason:** Time is directly proportional to the fraction of work done at constant rate. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: If 2/5 work = 4 hours, then 1 work = 4 ÷ 2/5 = 10 hours; the reason correctly identifies the proportional relationship.* **Q27.** **Assertion:** (5/6 × 3/4) ÷ 5/8 can be simplified by cancelling 5 in numerator and denominator before multiplying. **Reason:** Cancellation of common factors is allowed in multiplication and division of fractions, even before completing the operation. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: Early cancellation (cross-cancellation) is valid and reduces computational error; the reason justifies this practice.* **Q28.** **Assertion:** 7/9 ÷ 7/9 = 1. **Reason:** Any non-zero number divided by itself equals 1. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: The assertion follows from the general principle stated in the reason; 7/9 is a non-zero number.* **Q29.** **Assertion:** When multiplying fractions, you do NOT need to find a common denominator. **Reason:** Multiplication of fractions requires multiplying numerators and denominators separately, not alignment of denominators. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: This is a critical distinction from addition/subtraction; the reason clearly explains why the assertion is true.* **Q30.** **Assertion:** A fraction greater than 1 has a reciprocal less than 1. **Reason:** As the numerator increases relative to the denominator, the reciprocal decreases. (A) Both A and R are true; R explains A (B) Both A and R are true; R does not explain A (C) A is true; R is false (D) Both A and R are false **Answer: (A) Both A and R are true; R explains A** *Reason: E.g., 5/3 > 1, and 3/5 < 1; the reason correctly identifies the inverse relationship.*

**1. Inverting the Wrong Fraction in Division** Trap: Students often invert the dividend instead of the divisor. Example: 3/4 ÷ 2/5 becomes 4/3 × 2/5 instead of 3/4 × 5/2. *Fix: Always remember "flip the divisor," not the dividend.* **2. Forgetting to Simplify After Operations** Trap: Leaving 10/40 as the final answer instead of simplifying to 1/4. *Fix: Always check for common factors using GCD and reduce to lowest terms.* **3. Confusing Multiplication With Addition** Trap: Treating 2/5 × 3/7 as (2×3)/(5+7) = 6/12 instead of 6/35. *Fix: For multiplication: multiply both numerators AND both denominators. For addition/subtraction only, find a common denominator.* **4. Not Converting Mixed Numbers** Trap: Multiplying 2 1/3 × 3/4 by treating 2 1/3 as "2 + 1/3" instead of converting to 7/3 first. *Fix: Always convert mixed numbers to improper fractions before performing operations.* **5. Assuming Reciprocal of 0 Exists** Trap: Writing 1/0 as the reciprocal of 0. *Fix: Zero has no reciprocal (division by zero is undefined). Always add "for non-zero fractions" to reciprocal statements.* **6. Cancelling Non-Common Factors** Trap: In 3/4 × 5/6, cancelling the 3 and 6 vertically, ignoring that 4 and 5 share no common factors. *Fix: Only cancel factors that appear in both a numerator and a denominator (cross-cancellation).* **7. Word Problem Unit Mismatches** Trap: A rope 5 1/2 m long cut into pieces of 1/2 m yields 5 pieces (using only the whole part) instead of 11. *Fix: Convert all quantities to the same unit and use the correct operation (division for "how many pieces").* **8. Ignoring Order of Operations** Trap: Solving 3/4 ÷ 2/5 × 1/2 left-to-right: (3/4 ÷ 2/5) × 1/2 instead of 3/4 ÷ (2/5 × 1/2). *Fix: Division and multiplication are equal priority; work strictly left to right unless parentheses indicate otherwise.*

**Pre-Exam Preparation (1–2 weeks before)** - Spend 30 minutes daily on 5 Easy MCQs to build procedural fluency. Target: 100% accuracy. - Move to 5 Medium MCQs daily in week 2, focusing on word-problem interpretation and multi-step operations. Target: 80%+ accuracy. - Reserve the last 3–4 days for Hard/Assertion-Reason MCQs (3–4 per day) to deepen conceptual grip. Target: 70%+ accuracy. **During the Exam (15–20 minutes for 10 fraction MCQs)** - **Skim Phase (1–2 min):** Read all 10 questions once without solving. Identify "gimme" questions (reciprocal definitions, simple multiplications) and mark them mentally. - **Quick-Solve Phase (8–10 min):** Solve gimme questions in 30–45 seconds each; medium questions in 60–90 seconds each. Skip any that feel ambiguous initially. - **Review Phase (3–4 min):** Return to skipped questions. For word problems, re-read the question to catch unit mismatches. For assertion-reason, recheck whether R truly explains A. - **Final Check (1–2 min):** Verify that a/b was inverted (not kept) in division problems. Confirm all fractions are in simplest form if no specific instruction otherwise. **Precision Hacks** - Write out all cancellations (cross-cancel before multiplying). Saves errors and time. - For word problems, underline the final quantity required ("how much sugar," "how many pieces"). One-word misreads cause full-question loss. - Assertion-Reason MCQs: always check both A and R separately before matching them. A can be true even if R is false or irrelevant. **Mental Math Boosters** - Memorize reciprocals of fractions 1–10 (e.g., 1/7 ↔ 7/1, 3/5 ↔ 5/3). Saves 10–15 seconds per division problem. - Recognize GCD pairs by sight: (6,12), (10,15), (9,12), (8,12). Pre-calculate their simplifications. - For "product of fraction and its reciprocal" questions, answer "1" without calculation (it's always 1 for non-zero fractions).

**Post-Quiz Review Protocol (Essential for Learning)** Do not skip this step. Within 24 hours of completing the quiz, revisit every question you marked incorrectly or guessed on. For each: 1. **Identify the error type.** Was it procedural (wrong operation), conceptual (misunderstanding reciprocals), or careless (didn't simplify)? 2. **Redo the problem,** showing every step. Write down the rule you violated. 3. **Teach someone else** (a friend, parent, or even yourself aloud) why your first answer was wrong and the correct answer is right. This cements long-term memory. **Spaced Repetition Schedule** - Day 1: Take the quiz (all 30 MCQs in ~45 mins). - Day 3: Re-solve only the Medium and Hard MCQs (15 questions, ~25 mins). - Day 7: Re-solve only the Hard/Assertion-Reason MCQs (10 questions, ~20 mins). - Day 14: Take a fresh random sample of 10 MCQs from all difficulty levels. **Leverage Video + Quiz Combo** Watch NCERT-aligned video explanations (available at cbsetutor.ai) immediately after completing a difficulty tier. Visual reinforcement dramatically improves retention of fraction inversion and cancellation rules—concepts that purely text-based learning often leaves fuzzy. **Track Weak Spots** Maintain a "mistake log." Every incorrect answer gets one line: question number, the concept tested, and the error. By day 21, patterns emerge (e.g., "always forgetting to simplify" or "confusing dividend/divisor in division"). Target those patterns with 5 focused mini-quizzes before your periodic or board exam.