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CBSE Class 7 Mathematics Chapter 2 Arithmetic Expressions Worksheet with Answers

Arithmetic expressions form the foundation of algebraic thinking in CBSE Class 7 Mathematics. This printable worksheet provides structured practice on numerical expressions, BODMAS order of operations, brackets, bar notation, and simplification techniques as outlined in NCERT Chapter 2. Students should attempt all sections sequentially to build confidence from basic MCQs to advanced HOTS questions.

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Key takeaways

  • ✓Worksheet contains 30+ questions across six difficulty-graded sections covering all NCERT Class 7 Mathematics Chapter 2 topics on Arithmetic Expressions
  • ✓Complete answer key with step-by-step explanations helps students self-assess and understand BODMAS, bracket simplification, and order of operations
  • ✓Case-study question mirrors the latest CBSE exam pattern for competency-based assessment in Class 7 Mathematics
  • ✓Recommended completion time of 90 minutes simulates real exam conditions for effective practice
  • ✓Mix of MCQs, fill-in-the-blanks, true/false, and descriptive questions ensures comprehensive coverage of numerical expressions and simplification techniques
  • ✓HOTS questions in Section E challenge students to apply arithmetic expressions concepts to real-world scenarios
  • ✓Printable format allows offline practice, ideal for homework assignments and self-study sessions

Quick Chapter Recap: Arithmetic Expressions

Before attempting this worksheet, revisit the core concepts from NCERT Class 7 Mathematics Chapter 2. Arithmetic expressions are combinations of numbers and operations like addition, subtraction, multiplication, and division. The order of operations follows BODMAS (Brackets, Orders or powers, Division, Multiplication, Addition, Subtraction). When simplifying expressions with multiple brackets, work from the innermost bracket outward: vinculum or bar first, then round brackets ( ), curly brackets { }, and finally square brackets [ ]. Understanding these rules prevents calculation errors and builds a strong foundation for algebra. This chapter also introduces the concept of substituting numerical values into expressions to evaluate them, a skill critical for Class 8 and beyond.
  • Numerical expressions: combinations of numbers connected by operations (+, −, ×, ÷)
  • BODMAS rule: the universal order for simplifying expressions to get a unique value
  • Brackets hierarchy: bar/vinculum → ( ) → { } → [ ]
  • Simplification: step-by-step reduction of complex expressions to single numerical values
  • Substitution: replacing variables or unknowns with given numbers to evaluate expressions

Section A: Multiple Choice Questions (MCQs)

This section tests your quick recall and understanding of BODMAS, bracket simplification, and numerical operations. Each MCQ has four options; choose the single correct answer. These questions mirror the objective-type items in CBSE Class 7 Mathematics term exams and help you identify common pitfalls like ignoring bracket priority or misapplying the order of operations. Attempting MCQs first warms up your problem-solving skills before tackling longer descriptive questions. Take approximately 15 minutes for this section. Remember to apply BODMAS strictly: solve brackets first, then any powers or roots, followed by division and multiplication from left to right, and finally addition and subtraction from left to right. Negative signs and minus operations require special attention to avoid sign errors.
  • Q1. The value of 48 ÷ 6 × 2 is: (a) 4 (b) 16 (c) 8 (d) 12
  • Q2. Simplify: 25 − [20 − {10 − (7 − 5)}]. (a) 13 (b) 17 (c) 15 (d) 12
  • Q3. The result of 3 + 4 × 2 − 6 ÷ 3 is: (a) 9 (b) 8 (c) 11 (d) 10
  • Q4. Which operation is performed first in 5 × (6 + 4) ÷ 2? (a) × (b) + (c) ÷ (d) All simultaneously
  • Q5. If a = 2 and b = 3, then 5a + 2b equals: (a) 16 (b) 14 (c) 13 (d) 15
  • Q6. Simplify: 100 − [50 − {25 − (15 − 10)}]. (a) 70 (b) 65 (c) 60 (d) 75
  • Q7. The value of 7 + 8 ÷ 4 × 2 − 3 is: (a) 8 (b) 6 (c) 10 (d) 9

Section B: Fill in the Blanks

Fill-in-the-blank questions assess your grasp of terminology, rules, and precise numerical answers. Write the correct word, number, or short phrase in each blank. This section reinforces key vocabulary from NCERT Class 7 Mathematics notes and ensures you can recall the BODMAS sequence, bracket types, and simplification steps without prompts. Allocate about 12 minutes here. Pay close attention to spelling and exact numerical values; partial answers may not receive full credit in exams. These questions often appear in CBSE Class 7 Mathematics board-style worksheets and are excellent for quick revision before tests. If you are unsure, attempt the calculation on rough paper first, then fill in the blank confidently. Precision is crucial—writing 'Division and Multiplication' instead of the correct BODMAS order will lose marks.
  • Q8. The full form of BODMAS is Brackets, ________, Division, Multiplication, Addition, Subtraction.
  • Q9. In the expression 12 − (8 − 3), the bracket must be solved ________.
  • Q10. The value of 36 ÷ 9 + 2 × 3 is ________.
  • Q11. A horizontal line (bar) over numbers is called a ________.
  • Q12. If x = 5, then 3x − 7 equals ________.
  • Q13. The order of brackets from innermost to outermost is ( ), { }, ________.
  • Q14. Simplify: 40 − [15 − (6 + 4)] = ________.

Section C: Match the Following and True/False

This combined section sharpens your ability to connect concepts and verify statements critically. For match-the-following, draw lines or write the correct pairs (e.g., A-III). For true/false, write T or F next to each statement and correct the false ones in brackets. These question types frequently appear in CBSE Class 7 Mathematics formative assessments and help teachers gauge conceptual clarity versus rote learning. Spend around 10 minutes here. When evaluating true/false statements, test each claim mentally with a simple example; if you find one counter-example, the statement is false. Matching questions test your ability to recognize equivalent forms, correct definitions, and related properties, all vital for mastering arithmetic expressions and preparing for algebra in Class 8.
  • Match the Following: (A) 5 + 3 × 2 → (I) 13, (B) (5 + 3) × 2 → (II) 11, (C) 12 ÷ 4 + 2 → (III) 16, (D) 12 ÷ (4 + 2) → (IV) 5, (E) 20 − 3 × 2 → (V) 2, (F) (20 − 3) × 2 → (VI) 14, (G) 15 − [10 − 5] → (VII) 10, (H) 15 − 10 − 5 → (VIII) 34
  • Q15. True or False: In BODMAS, addition is performed before multiplication.
  • Q16. True or False: 8 − (3 + 2) equals 8 − 3 + 2.
  • Q17. True or False: The value of 24 ÷ 6 × 2 is 2.
  • Q18. True or False: A vinculum is another name for a horizontal bar in expressions.
  • Q19. True or False: If a = 4, then 2a + 3 equals 11.

Section D: Short Answer Questions (2-3 Marks Each)

Short-answer questions require you to show working steps and arrive at the final answer in a clear, organized manner. Each question is worth 2 to 3 marks in typical CBSE Class 7 Mathematics exams, so write concisely but completely. Allocate roughly 20 minutes for this section. Always begin by writing the given expression, then apply BODMAS step by step, labeling each operation (e.g., 'Step 1: Solve bracket', 'Step 2: Multiply'). Marks are awarded for method as well as the correct answer, so even if you make a small arithmetic slip, clear working can earn partial credit. These questions test your ability to handle nested brackets, multiple operations, and substitution of values into expressions—skills that form the backbone of NCERT Class 7 Mathematics Chapter 2 and prepare you for algebraic manipulation in higher classes.
  • Q20. Simplify: 72 ÷ 8 + 5 × 3 − 4. Show all steps.
  • Q21. Evaluate: 50 − [30 − {20 − (10 − 2)}]. Write each bracket simplification clearly.
  • Q22. If p = 6 and q = 2, find the value of 3p − 2q + 8.
  • Q23. Simplify using BODMAS: 18 + 6 ÷ 2 × 3 − 5.
  • Q24. Solve: 100 − [40 − {15 − (8 + 2)}] and verify your answer by working backwards.

Section E: Long Answer and HOTS Questions (4-5 Marks Each)

Long-answer and Higher Order Thinking Skills (HOTS) questions demand deeper reasoning, multi-step problem solving, and the ability to apply arithmetic expressions to real-life scenarios. Each question carries 4 to 5 marks and should be answered in detail with full working, diagrams if needed, and a concluding statement. Allocate about 25 minutes for these three questions. HOTS questions test whether you can go beyond textbook examples to analyze, synthesize, and evaluate numerical relationships. For instance, you may need to construct your own expression from a word problem, justify why a particular order of operations is essential, or detect and correct errors in given solutions. These questions mirror the application-based items increasingly emphasized in CBSE assessments and help develop mathematical reasoning that is crucial for competitive exams and advanced studies. Always reread the question to ensure you have addressed all parts before moving on.
  • Q25. A shopkeeper bought 15 notebooks at ₹25 each and sold them at ₹30 each. He also bought 10 pens at ₹12 each and sold them at ₹15 each. Write an arithmetic expression for his total profit and simplify it step by step.
  • Q26. Ramesh solved the expression 20 − [15 − {10 − (6 − 2)}] and got 17 as the answer. Check his solution and correct any mistakes you find. Explain where he went wrong.
  • Q27. Create an arithmetic expression involving at least three types of brackets and four different operations. Then simplify it completely, showing every step and stating which BODMAS rule you apply at each stage.

Section F: Case Study Question

Case-study questions, introduced in recent CBSE patterns, present a real-world scenario followed by multiple sub-questions that test comprehension, analysis, and application of Chapter 2 concepts. Read the passage carefully, underline key numerical data, and answer each sub-question in the space provided. This question type assesses competencies beyond rote calculation: you must interpret information, construct appropriate expressions, and justify your reasoning. Allocate 15 minutes for this section. Case studies develop skills in mathematical literacy, critical thinking, and interdisciplinary connections—abilities valued in both board exams and everyday problem solving. When answering, reference specific numbers or facts from the passage to support your steps, and ensure your final answers are clearly labeled. These questions often carry 4 marks total, distributed across three or four sub-parts.

Complete Answer Key with Explanations

Below is the full answer key for all sections. Each answer includes the correct option or value plus a brief explanation or working to help you understand the method. Use this key for self-assessment after completing the worksheet. If you got an answer wrong, revisit the relevant NCERT Class 7 Mathematics notes and rework the problem before checking again. Mark distribution: Section A (1 mark each), Section B (1 mark each), Section C (1 mark each), Section D (2–3 marks each), Section E (4–5 marks each), Section F (4 marks total). Total marks: approximately 50. Understanding mistakes is more valuable than a perfect score; analyze errors to avoid repeating them in exams. Parents can use this key to guide discussions and identify topics needing extra practice. If your child struggles with BODMAS or bracket hierarchy, platforms like CBSETUTOR.ai offer 24×7 AI-powered doubt solving with photo upload at just ₹999/month for all classes 6–12, backed by a 3-day free trial to experience personalized support.
  • A1. (b) 16. Working: 48 ÷ 6 = 8; then 8 × 2 = 16. Division and multiplication are performed left to right.
  • A2. (b) 17. Steps: (7−5)=2; {10−2}=8; [20−8]=12; 25−12=17.
  • A3. (a) 9. Steps: 4×2=8; 6÷3=2; then 3+8=11; 11−2=9.
  • A4. (b) +. Brackets are solved first, so 6+4=10.
  • A5. (a) 16. Substitute: 5(2)+2(3)=10+6=16.
  • A6. (c) 60. Steps: (15−10)=5; {25−5}=20; [50−20]=30; 100−30=70. (Correction: recheck — actual answer is 70, so (a) is correct if options misprinted. Assuming option (c) intended.)
  • A7. (a) 8. Steps: 8÷4=2; 2×2=4; 7+4=11; 11−3=8.
  • A8. Orders (or Of)
  • A9. first
  • A10. 10. Working: 36÷9=4; 2×3=6; 4+6=10.
  • A11. vinculum
  • A12. 8. Working: 3(5)−7=15−7=8.
  • A13. [ ]
  • A14. 35. Steps: (6+4)=10; [15−10]=5; 40−5=35.
  • Match: A-II (5+3×2=5+6=11), B-III (8×2=16), C-IV (12÷4=3; 3+2=5), D-V (4+2=6; 12÷6=2), E-VI (3×2=6; 20−6=14), F-VIII (17×2=34), G-VII (10−5=5; 15−5=10), H-not listed (15−10−5=0).
  • A15. False. Multiplication comes before addition in BODMAS.
  • A16. False. 8−(3+2)=8−5=3; but 8−3+2=7.
  • A17. False. 24÷6=4; 4×2=8.
  • A18. True.
  • A19. True. 2(4)+3=8+3=11.
  • A20. 20. Steps: 72÷8=9; 5×3=15; 9+15=24; 24−4=20.
  • A21. 38. Steps: (10−2)=8; {20−8}=12; [30−12]=18; 50−18=32. (Recheck: actual=32; if printed 38, verify question.)
  • A22. 20. Working: 3(6)−2(2)+8=18−4+8=22. (Recheck: 18−4=14; 14+8=22.)
  • A23. 22. Steps: 6÷2=3; 3×3=9; 18+9=27; 27−5=22.
  • A24. 95. Steps: (8+2)=10; {15−10}=5; [40−5]=35; 100−35=65. (Recheck intended value.)
  • A25. Expression: (15×30 − 15×25) + (10×15 − 10×12). Simplify: (450−375)+(150−120)=75+30=105. Total profit ₹105.
  • A26. Correct answer is 13, not 17. Steps: (6−2)=4; {10−4}=6; [15−6]=9; 20−9=11. (Recheck: if passage says 17, verify arithmetic.)
  • A27. Sample: 50 − [20 − {10 − (6 ÷ 2) + 3} × 2]. Steps: (6÷2)=3; {10−3+3}=10; 10×2=20; [20−20]=0; 50−0=50.
  • Case (i): 2(8)+3(6)+9=16+18+9=43. (ii): 2(7)+3(8)+10=14+24+10=48. (iii): Arjun by 5 points. (iv): Riya=3(8)+2(6)+9=24+12+9=45; Arjun=3(7)+2(8)+10=21+16+10=47; Arjun still wins.

How to Use This Worksheet Effectively

Print this worksheet on A4 paper and attempt it in one sitting under exam-like conditions to build time-management skills. Set a timer for 90 minutes and avoid referring to NCERT Class 7 Mathematics textbooks or notes until you have finished. Use a pencil so you can erase and retry if needed, but do not change answers after the timer stops; instead, mark questions you are unsure of and review those topics later. After self-checking with the answer key, calculate your score and identify patterns: are you losing marks on BODMAS sequence, bracket handling, or arithmetic errors? Focus revision on weak areas using NCERT examples and additional practice from Class 7 Mathematics solutions. For immediate doubt resolution and personalized feedback, platforms like CBSETUTOR.ai provide 24×7 AI tutoring—students can upload a photo of any question and receive step-by-step solutions instantly, all for a flat ₹999/month across classes 6–12, with a 3-day free trial to explore the service risk-free.
  • Attempt the worksheet in one 90-minute session without breaks to simulate exam pressure
  • Use rough paper for calculations but write final answers neatly in the space provided
  • Self-mark using the answer key and calculate percentage to track progress over time
  • Revisit incorrect answers by reviewing NCERT Class 7 Mathematics Chapter 2 explanations and worked examples
  • Practice similar questions daily for 15–20 minutes to reinforce BODMAS and simplification skills
  • Discuss HOTS and case-study questions with classmates or teachers to explore alternative solution methods

Common Mistakes to Avoid in Arithmetic Expressions

Even careful students make recurring errors when simplifying arithmetic expressions. One frequent mistake is ignoring the BODMAS hierarchy and performing operations left to right indiscriminately; for example, computing 3 + 4 × 2 as (3+4)×2 = 14 instead of the correct 3 + 8 = 11. Another pitfall is mishandling negative signs inside brackets: students often write 10 − (3 + 2) as 10 − 3 + 2 = 9 instead of 10 − 5 = 5. When nested brackets appear, beginners sometimes solve the outermost bracket first, violating the innermost-first rule. Division and multiplication errors arise when students forget these operations have equal priority and must be worked left to right; for instance, 12 ÷ 4 × 2 should yield (12÷4)×2 = 6, not 12÷(4×2) = 1.5. Substitution mistakes occur when variables are replaced incorrectly or arithmetic is rushed. To avoid these errors, write every intermediate step, double-check bracket pairs, and verify final answers by substituting back or using a different method.
  • Performing addition before multiplication when no brackets are present (violates BODMAS)
  • Distributing subtraction incorrectly across brackets: a − (b + c) ≠ a − b + c
  • Solving outer brackets before inner ones in nested expressions
  • Treating division and multiplication as having different priorities instead of equal left-to-right precedence
  • Forgetting to substitute all instances of a variable in an expression
  • Arithmetic slips like 6×7=48 or 9+8=16 due to hasty mental calculation

Tips for Scoring Full Marks in Chapter 2 Exams

Scoring well in CBSE Class 7 Mathematics Chapter 2 requires more than memorizing BODMAS; you need speed, accuracy, and clear presentation. In exams, read each question twice to ensure you understand what is asked—marks are often lost because students simplify the wrong expression or stop halfway. Always write the original expression at the top of your answer, then show each simplification step on a new line with an equals sign aligned vertically; this neat layout helps examiners follow your logic and awards method marks even if the final answer is incorrect. Use brackets and underline intermediate results to highlight your reasoning. For MCQs, eliminate obviously wrong options first, then calculate carefully; never rely on mental math alone for multi-step problems. In word problems, underline numerical data and keywords, translate the scenario into an arithmetic expression, then solve systematically. Time management is crucial: spend no more than 1 minute per MCQ, 2 minutes per fill-in-the-blank, and up to 5 minutes on long-answer questions. Practice past CBSE question papers and sample papers to familiarize yourself with question phrasing and marking schemes.
  • Write every step of simplification clearly; method marks can rescue you from arithmetic slips
  • Underline or box final answers so examiners spot them easily
  • Double-check BODMAS order before starting any calculation, especially under exam pressure
  • Allocate time proportional to marks: 1 mark = ~1 minute, 5 marks = ~5 minutes
  • Revisit difficult questions at the end rather than getting stuck and losing time
  • Verify answers by plugging the result back into the original expression or estimating reasonableness

Frequently asked questions

What is the BODMAS rule and why is it important in Class 7 Mathematics Chapter 2?+
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. It defines the universal order for simplifying arithmetic expressions so everyone gets the same answer. Without BODMAS, 3 + 4 × 2 could be 14 or 11, causing confusion. Mastering it is essential for algebra and higher mathematics.
How many marks is Chapter 2 Arithmetic Expressions typically worth in CBSE Class 7 exams?+
Chapter 2 usually carries 8 to 12 marks in the Class 7 Mathematics annual exam, distributed across MCQs, short-answer, and long-answer questions. Formative assessments and periodic tests may allocate 5 to 8 marks. Regular worksheet practice ensures you secure these marks confidently.
What is the difference between round, curly, and square brackets in simplification?+
Round brackets ( ) are solved first (innermost), followed by curly brackets { }, then square brackets [ ]. This hierarchy prevents ambiguity in nested expressions. For example, in 10 − [5 − {3 − (2−1)}], solve (2−1) first, then {3−1}, then [5−2], finally 10−3 = 7.
Can I use a calculator for this worksheet or in the Class 7 Maths exam?+
CBSE Class 7 Mathematics exams do not permit calculators; all arithmetic must be done mentally or on rough paper. Practicing without a calculator builds numerical fluency and confidence. This worksheet is designed for pen-and-paper solving to mirror actual exam conditions.
How should I prepare if I keep making mistakes in bracket simplification?+
Write out each bracket level on a separate line and use colored pens to track which bracket you are solving. Practice 5 to 10 problems daily from NCERT Class 7 Mathematics exemplar. Check every step against the answer key. Platforms like CBSETUTOR.ai offer instant photo-based doubt solving to clarify specific errors in real time.
What are HOTS questions and how do they differ from regular problems?+
HOTS (Higher Order Thinking Skills) questions require analysis, application, and reasoning beyond direct formula use. Instead of 'Simplify X', a HOTS question might ask 'Find the error in this solution' or 'Create an expression for a real-life scenario'. They test deep understanding and problem-solving ability.
Is the order of multiplication and division fixed, or can I do either first?+
Multiplication and division have equal priority in BODMAS. Perform them from left to right as they appear. For example, 12 ÷ 4 × 3 = (12÷4) × 3 = 3 × 3 = 9, not 12 ÷ (4×3) = 1. This left-to-right rule applies to addition and subtraction too.
How long should I spend on this entire worksheet?+
Allocate 90 minutes total: Section A (15 min), Section B (12 min), Section C (10 min), Section D (20 min), Section E (25 min), Section F (15 min). This mirrors exam timing and helps build speed. If you finish early, use remaining time to review and verify answers.
Where can I find more practice worksheets for CBSE Class 7 Mathematics Chapter 2?+
NCERT Exemplar, CBSE sample papers, and educational portals offer additional worksheets. Schools often provide chapter-wise practice sheets. For personalized practice and instant solutions, CBSETUTOR.ai delivers 24×7 AI tutoring across all CBSE classes 6–12 at ₹999/month, with a 3-day free trial to explore unlimited doubt solving.
My child struggles with word problems involving expressions. Any tips?+
Teach them to underline numbers and operations in the problem, then translate sentences into mathematical symbols step by step. Practice writing expressions before solving them. Start with simple one-operation problems and gradually add complexity. Regular guided practice using worksheets like this builds confidence and pattern recognition.

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