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Class 7 → Mathematics → Chapter 2: Arithmetic Expressions
I. Chapter Summary:
The chapter Arithmetic Expressions introduces students to mathematical expressions formed using numbers and operations like addition, subtraction, multiplication, and division. It focuses on understanding how to simplify expressions using the correct order of operations (BODMAS rule). Students learn to evaluate expressions step-by-step, use brackets properly, and apply these concepts in real-life problem-solving situations.
II. Key Concepts Covered:
1. Arithmetic Expressions
A combination of numbers and operations ( +, −, ×, ÷ ).
2. Types of Expressions
- Simple expressions (single operation)
- Complex expressions (multiple operations)
3. Order of Operations (BODMAS Rule)
- B – Brackets
- O – Orders (powers, if any)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction
4. Use of Brackets
- Solve innermost brackets first
- Types: ( ), { }, [ ]
5. Simplification of Expressions
Step-by-step solving using correct order.
6. Real-Life Applications
Used in budgeting, shopping, and calculations.
III. Important Questions:
(A) MCQs (1 Mark):
- Which operation is performed first in BODMAS?
(a) Addition
(b) Division
(c) Brackets ✅
(d) Multiplication - Evaluate: 6 + 3 × 2
(a) 18
(b) 12 ✅
(c) 9
(d) 15 - Evaluate: (8 + 2) × 5
(a) 18
(b) 50 ✅
(c) 40
(d) 10 - Which is solved first?
(a) Multiplication
(b) Addition
(c) Brackets ✅
(d) Subtraction
(B) Short Answer Questions (2/3 Marks):
- What is an arithmetic expression? Give an example.
- State the BODMAS rule.
- Simplify: 12 + 6 ÷ 3
- Solve: (15 − 5) × 2
(C) Long Answer Questions (5 Marks):
- Explain the BODMAS rule with examples.
- Simplify complex expressions step-by-step.
- Solve expressions involving multiple brackets.
- Explain real-life applications of arithmetic expressions.
(D) HOTS Questions:
- Why is it important to follow the order of operations in mathematics?
- What errors can occur if BODMAS is not followed correctly?
IV. Key Formulas/Concepts:
BODMAS Rule (Order of Operations)
BODMAS: Brackets $text{BODMAS: Brackets} rightarrow text{Orders} rightarrow text{Division} rightarrow text{Multiplication} rightarrow text{Addition} rightarrow text{Subtraction}$ Subtraction}
BODMAS: $text{Brackets} rightarrow text{Orders} rightarrow text{Division} rightarrow text{Multiplication} rightarrow text{Addition} rightarrow text{Subtraction}$
Example 1:
$6 + 3 times 2 = 12$
Step: Multiplication first → 3 × 2 = 6
Then: 6 + 6 = 12
Example 2:
$(8 + 2) times 5 = 50$
Step: Brackets first → 8 + 2 = 10
Then: 10 × 5 = 50
V. Deleted Portions (CBSE 2025–2026):
No portions have been deleted from this chapter as per the rationalized NCERT textbooks.
VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):
| Unit/Chapter | Estimated Marks | Type of Questions Typically Asked |
|---|---|---|
| Arithmetic Expressions | 5–7 Marks | MCQs, Short Answer, Numerical-based |
Note: This is an estimate. Actual marks distribution may vary.
VII. Previous Year Questions (PYQs):
1 Mark:
- Evaluate: 5 + 2 × 3 (2019)
2/3 Marks:
- Simplify: (10 + 5) × 2 (2020)
- Evaluate: 20 − 4 ÷ 2 (2021)
5 Marks:
- Solve expressions using BODMAS rule. (2022)
VIII. Real-World Application Examples:
- Calculating total cost while shopping
- Budget planning
- Solving daily calculations
- Managing time and resources
IX. Student Tips & Strategies for Success:
Time Management:
- Practice daily for accuracy and speed.
Exam Preparation:
- Always follow BODMAS rule step-by-step.
- Avoid skipping steps.
Stress Management:
- Stay calm and double-check answers.
- Practice regularly to build confidence.
X. Career Guidance & Exploration:
- Science Stream: Engineering, Data Science
- Commerce Stream: Accounting, Banking
- Arts Stream: Statistics, Economics
Entrance Exams (Basic Awareness):
- JEE (Engineering)
- CA Foundation
XI. Important Notes:
- Follow BODMAS rule strictly.
- Practice more numerical problems.
- Avoid common calculation mistakes.
- Revise regularly.
- Refer to NCERT textbook for clarity.