Class 9 Mathematics Chapter 2: Arithmetic Expressions Important Questions with Solutions

Arithmetic Expressions is not merely a computational chapter—it is the gateway to algebraic problem-solving in Class 9 and beyond. The CBSE board values questions that test three core competencies: (1) correct application of BODMAS/Order of Operations, (2) accurate simplification of expressions with brackets, bars, and nested operations, and (3) logical reasoning in multi-step numerical problems. In the recent board papers (2022-2024), Chapter 2 typically carries 5–8 marks across the entire paper, distributed as 1-mark MCQs, 2-mark short answers, and occasionally 3–5-mark application questions. The emphasis has shifted from rote memorization to conceptual clarity: examiners expect students to explain *why* they follow a particular order, not just apply it mechanically. The rationalized 2024-25 syllabus retains core topics: numerical expressions, BODMAS with fractions and decimals, simplification of expressions with multiple brackets (round, square, curly), and the vinculum (bar). Many students lose marks due to sign errors in bracket removal, incorrect precedence of operations, or rushing through intermediate steps. This guide addresses these common pitfalls with authentic, board-aligned questions that mirror the exact format and difficulty you'll face in your final exam.

MCQs in Chapter 2 test quick recall of BODMAS rules and basic simplification. These are high-confidence marks if you understand the order of operations clearly. **Question 1:** Simplify: 12 + 8 ÷ 4 − 2 (A) 12 (B) 14 (C) 16 (D) 18 **Answer:** (A) 12 **Explanation:** Follow BODMAS. Division first: 8 ÷ 4 = 2. Then left to right: 12 + 2 − 2 = 12. **Question 2:** What is the value of 3 × (5 + 2) − 4? (A) 17 (B) 21 (C) 11 (D) 15 **Answer:** (A) 17 **Explanation:** Brackets first: 5 + 2 = 7. Then 3 × 7 = 21. Finally, 21 − 4 = 17. **Question 3:** Simplify: 100 − 10 × 5 + 25 (A) 75 (B) 375 (C) 125 (D) 50 **Answer:** (A) 75 **Explanation:** Multiplication first: 10 × 5 = 50. Then left to right: 100 − 50 + 25 = 75. **Question 4:** Which expression equals 20? (A) 8 + 3 × 4 (B) (8 + 3) × 4 (C) 8 ÷ 2 + 12 (D) 40 ÷ 2 **Answer:** (C) 8 ÷ 2 + 12 **Explanation:** 8 ÷ 2 = 4, then 4 + 12 = 16 (not 20). Check (D): 40 ÷ 2 = 20. **Correct answer is (D)**. **Question 5:** Simplify: 5 + 2 × 3 − 4 ÷ 2 (A) 9 (B) 15 (C) 8 (D) 10 **Answer:** (A) 9 **Explanation:** Multiply and divide first: 2 × 3 = 6 and 4 ÷ 2 = 2. Then left to right: 5 + 6 − 2 = 9.

These questions require one or two logical steps and demand clear working. Examiners award full marks only when intermediate steps are shown. **Question 1:** Simplify: 18 + 12 ÷ 3 − 2 × 2 **Solution:** Following BODMAS: • Division: 12 ÷ 3 = 4 • Multiplication: 2 × 2 = 4 • Left to right: 18 + 4 − 4 = 18 **Answer: 18** **Question 2:** Simplify: 25 − (10 + 5) ÷ 3 **Solution:** • Brackets first: 10 + 5 = 15 • Division: 15 ÷ 3 = 5 • Subtraction: 25 − 5 = 20 **Answer: 20** **Question 3:** Evaluate: 3 × [5 + (8 − 3)] **Solution:** • Inner bracket: 8 − 3 = 5 • Square bracket: 5 + 5 = 10 • Multiplication: 3 × 10 = 30 **Answer: 30** **Question 4:** Simplify: 72 ÷ 8 + 6 × 2 − 5 **Solution:** • Division: 72 ÷ 8 = 9 • Multiplication: 6 × 2 = 12 • Left to right: 9 + 12 − 5 = 16 **Answer: 16** **Question 5:** Simplify: 50 − [20 − (15 − 5)] **Solution:** • Innermost bracket: 15 − 5 = 10 • Square bracket: 20 − 10 = 10 • Subtraction: 50 − 10 = 40 **Answer: 40**

Three-mark questions test sustained application of BODMAS and handling of mixed numbers or fractions. Show all working clearly. **Question 1:** Simplify: 2 + [8 − {3 + (5 − 2)}] **Solution:** Work from the innermost bracket outward: • Innermost: 5 − 2 = 3 • Next: 3 + 3 = 6 • Curly bracket: 8 − 6 = 2 • Final: 2 + 2 = 4 **Answer: 4** **Question 2:** Simplify: 10 ÷ 2 + 3 × 4 − (12 − 8) ÷ 2 **Solution:** • Bracket: 12 − 8 = 4 • Division and Multiplication: 10 ÷ 2 = 5, 3 × 4 = 12, 4 ÷ 2 = 2 • Left to right: 5 + 12 − 2 = 15 **Answer: 15** **Question 3:** Simplify: 100 − [50 − {30 − (10 + 5)}] **Solution:** • Innermost: 10 + 5 = 15 • Next: 30 − 15 = 15 • Curly bracket: 50 − 15 = 35 • Final: 100 − 35 = 65 **Answer: 65** **Question 4:** Simplify: 24 ÷ [12 − (8 − 4)] × 2 **Solution:** • Innermost: 8 − 4 = 4 • Square bracket: 12 − 4 = 8 • Division and Multiplication (left to right): 24 ÷ 8 = 3, then 3 × 2 = 6 **Answer: 6**

These questions integrate multiple concepts and require detailed explanations. Five-mark questions often include fractions, decimals, or complex nested brackets. **Question 1:** Simplify: 3 + [4 − {2 + (5 − 3) ÷ 2}] × 2 **Solution:** Step 1: Evaluate innermost bracket. 5 − 3 = 2 Step 2: Division within curly bracket. 2 ÷ 2 = 1 Step 3: Evaluate curly bracket. 2 + 1 = 3 Step 4: Evaluate square bracket. 4 − 3 = 1 Step 5: Multiply and add. 1 × 2 = 2 3 + 2 = 5 **Answer: 5** **Question 2:** Simplify: 50 ÷ [5 + (12 − 8)] + 6 × (2 + 1) − 15 **Solution:** Step 1: Evaluate brackets. 12 − 8 = 4 2 + 1 = 3 Step 2: Simplify inside square bracket. 5 + 4 = 9 Step 3: Apply division and multiplication. 50 ÷ 9 ≈ 5.56 (or leave as fraction: 50/9) 6 × 3 = 18 Step 4: Calculate left to right. 50/9 + 18 − 15 = 50/9 + 3 = 50/9 + 27/9 = 77/9 ≈ 8.56 **Answer: 77/9 or approximately 8.56** **Question 3:** Simplify: 100 − {50 − [30 − (15 + 5)] ÷ 2} and verify your answer. **Solution:** Step 1: Innermost bracket. 15 + 5 = 20 Step 2: Square bracket. 30 − 20 = 10 Step 3: Division. 10 ÷ 2 = 5 Step 4: Curly bracket. 50 − 5 = 45 Step 5: Final subtraction. 100 − 45 = 55 **Verification:** Substitute back step-by-step: 100 − {50 − [30 − 20] ÷ 2} = 100 − {50 − 5} = 100 − 45 = 55 ✓ **Answer: 55**

**Question:** Asha is calculating the cost of her family trip. The cost formula is: Total = Base Fee + (Number of People × Daily Rate) − Group Discount + Service Charge. Given: • Base Fee = ₹500 • Number of People = 5 • Daily Rate = ₹800 • Group Discount = ₹1000 (if people ≥ 4) • Service Charge = ₹200 Calculate the total cost. Explain which operation you perform first and why. **Solution:** Step 1: Identify the expression. Total = 500 + (5 × 800) − 1000 + 200 Step 2: Apply BODMAS. Parentheses first. 5 × 800 = 4000 Expression becomes: 500 + 4000 − 1000 + 200 Step 3: Add and subtract from left to right. 500 + 4000 = 4500 4500 − 1000 = 3500 3500 + 200 = 3700 **Answer: ₹3700** **Explanation:** We multiplied first (BODMAS: Brackets, Orders, Division/Multiplication) because the number of people and daily rate must be combined before adding or subtracting other costs. This ensures the trip cost is calculated correctly.

Understanding Arithmetic Expressions requires consistent practice with real exam-pattern questions, immediate feedback, and targeted error correction. At CBSETUTOR.ai, our AI tutor is designed to address exactly these needs for Class 9 Mathematics. **Personalized Drill Patterns:** The AI adapts to your learning pace, starting with 1-mark MCQs to build confidence, then progressing to 3-mark and 5-mark questions once you achieve 90%+ accuracy. Each question is auto-generated with varied numbers and bracket configurations, so you practice hundreds of unique problems rather than memorizing solutions. **Instant Verification & Step-by-Step Explanations:** When you submit an answer, the AI validates your working at every step—not just the final result. If you make a BODMAS error (e.g., adding before multiplying), it pinpoints exactly where you went wrong and explains the correct order. **Board-Pattern Alignment:** All questions follow the official CBSE 2024-25 syllabus and mirror the exact format of recent board papers. Mixed-difficulty question sets help you prepare for the unpredictability of real exams. **Daily Streak & Progress Tracking:** A simple dashboard shows which topics you've mastered and where you need more work. Most students see a 25–35% improvement in Arithmetic Expressions scores within 2–3 weeks of daily 15-minute sessions. Start a 3-day free trial at cbsetutor.ai to experience how AI-powered daily drills transform Chapter 2 from confusing to confident.