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CBSE Notes Class 7 Maths Chapter 2 Arithmetic Expressions
Arithmetic expressions are combinations of numbers and mathematical operations like addition, subtraction, multiplication, and division. This chapter helps students understand how to solve these expressions correctly. Students learn about the order of operations, which specifies the correct sequence for evaluating expressions. For example, multiplication and division are done before addition and subtraction.
The chapter explains how to solve expressions step by step and how to avoid common mistakes. Students also learn how to simplify complex expressions by breaking them into smaller parts.
This chapter helps students develop logical thinking and improve their calculation skills. It also prepares them for algebra in higher classes.
1.0Download CBSE Class 7 Maths Chapter 2 Notes: Free PDF
To learn how to simplify expressions using BODMAS rules, download the CBSE Class 7 Maths Notes Chapter 2—Arithmetic Expressions Notes PDF. The notes give examples and explain step-by-step methods to help you understand better. A helpful tool for getting better at maths and getting ready for tests.
2.0An Arithmetic Expression Class 7 Maths Chapter 2 - Revision Notes
An arithmetic expression combines numbers using operations to represent a single value. This chapter covers evaluating, comparing, grouping, and altering terms within expressions using core algebraic properties and bracket rules.
Key Concepts to Remember
- Arithmetic Expression: A mathematical phrase built using numbers and operational signs (+, −, ×, ÷) that evaluates to a single numerical value.
- Value of an Expression: The final single number obtained after carrying out all mathematical operations in an expression (e.g., the value of 13 + 2 is 15).
- Terms in an Expression: Individual numbers or multiplied/divided groups separated by addition (+) signs, where subtraction is treated as adding a negative number.
- Commutative Property of Addition: The rule stating that changing the order of terms being added does not change the total sum (a+b=b+a).
- Associative Property of Addition: The rule stating that changing the grouping of terms being added does not change the total sum ((a+b)+c=a+(b+c)).
- Removing Brackets Preceded by a Plus Sign: When brackets are preceded by a plus sign (+), the brackets can be removed directly without changing any signs inside.
- Removing Brackets Preceded by a Minus Sign: When brackets are preceded by a minus sign (−), removing the brackets requires changing every sign inside the bracket to its opposite (plus becomes minus, and minus becomes plus).
- Distributive Property of Multiplication: Multiplying a number by a sum or difference inside brackets is equal to multiplying that number by each term individually and then adding or subtracting the products (a(b+c)=(ab)+(ac)).
- Tinkering Terms: Changing or adjusting a term in an expression directly affects the total value of the expression depending on the magnitude and sign of the change.
- Inverse Operations: Addition and subtraction are inverse operations that undo each other, meaning adding a number and then subtracting the same number leaves the value unchanged.
Understanding Arithmetic Expressions & Values
- Nature of Expressions: An expression represents a specific quantity or value. For example, 15+9 evaluates to 24.
- Context & Structure: When an expression lacks clear order, brackets are used to clarify which operations must be solved first (e.g., 25+(63)=25+18=43).
Terms in an Expression & Subtraction as Addition of Negatives
- Identifying Terms: Terms are parts of an expression separated by addition signs.
- Handling Subtraction: Subtraction is written as the addition of a negative number. For example, 30-10+5 is written as 30+(-10)+5, making the terms 30, -10, and 5.
- Multiplication Groups as Single Terms: Two numbers multiplied together form a single term because they are not separated by a + sign (e.g., in 7+48, the terms are 7 and 48).
Commutative, Associative & Distributive Properties
- Swapping Order (Commutative): Changing the order of terms in addition or multiplication does not change the result (e.g., 13+2=2+13=15).
- Grouping Terms (Associative): Grouping numbers differently in addition or multiplication yields the same total (e.g., [(-3)+(-4)]+7=-3+[(-4)+7]=0).
- Multiplying Across Brackets (Distributive): Multiplying a sum by a number is equal to multiplying each part separately: 3(15+10)=(315)+(310)=45+30=75.
Bracket Removal Rules & Changing Signs
- Preceded by Plus Sign (+): Removing brackets keeps all internal signs unchanged: 42+(38-12)=42+38-12=68.
- Preceded by Minus Sign (-): Removing brackets flips every internal sign to its opposite: 200-(40+3)=200-40-3=157 and 20-(5-9)=20-5+9=24.
Comparing Expressions & Tinkering with Terms
- Comparing Without Full Calculation: Analyze terms directly instead of finding full totals. For example, 415-122 and -122+415 have identical terms (+415 and -122), making them equal.
- The 4 Rules of Tinkering Terms:
- Rule 1: If a term becomes larger, the overall total becomes larger.
- Rule 2: If a term becomes smaller, the overall total becomes smaller.
- Rule 3: If a negative term becomes less negative (closer to zero), the overall total increases.
- Rule 4: If a negative term becomes more negative (further from zero), the overall total decreases.
Order of Operations (BODMAS) & Historical Contribution of Brahmagupta
- Order of Operations: In multi-operation expressions without explicit brackets, evaluate terms with multiplication/division first before adding or subtracting.
- Brahmagupta's Legacy (c. 598–668 CE): In his treatise Brahmasphutasiddhanta (628 CE), ancient Indian mathematician Brahmagupta was among the first scholars to formalize systematic arithmetic rules for positive numbers, negative numbers, and zero (e.g., a+0=a, a0=0, 0-a=-a).
3.0Important Formulas and Rules: Working with Expressions
- Commutative Property: a+b=b+a
- Associative Property: (a+b)+c=a+(b+c)
- Distributive Property over Addition: a(b+c)=(ab)+(ac)
- Distributive Property over Subtraction: a(b-c)=(ab)-(ac)
- Bracket Removal Rule (Plus Sign): a+(b+c)=a+b+c and a+(b-c)=a+b-c
- Bracket Removal Rule (Minus Sign): a-(b+c)=a-b-c and a-(b-c)=a-b+c
- Inverse Operation Rule: a+b-b=a
- BODMAS Rule for Order of Operations: Brackets → Of (multiplication) → Division → Multiplication → Addition → Subtraction.
4.0Learning Guide for Class 7 Maths Working with Expressions – Chapter 2
- Rahul's Sandwich & Juice Change Problem: Rahul buys a sandwich for ₹30 and juice for ₹25, paying ₹70. Correct expression with brackets: 70-(30+25)=70-55=₹15.
- Anita's Phone Discount Problem: Anita has ₹700 and plans to buy a ₹400 phone with a ₹75 discount. Expression with brackets: 700-(400-75). Removing brackets with sign change: 700-400+75=375.
- Movie Theater Snacks (Distributive Property): 3 friends buy ₹15 popcorn and ₹10 drinks. Method 1: 3(15+10)=325=₹75. Method 2: (315)+(310)=45+30=₹75.
- Grouping Students for a Project: Group A has 6 students (2 sheets each), Group B has 4 students (2 sheets each). Expressed as: (6+4)2=(62)+(42)=20sheets.
- Fast Mental Math Shortcuts: Calculate 9835 by rewriting 98 as (100-2):
9835=(100-2)35=(10035)-(235)=3500-70=3430. - Revision Tip for Bracket Removal: Always remember: + before bracket = keep signs, - before bracket = flip signs.
5.0Explore Chapter-wise Class 7 Maths Notes
6.0Additional Study Materials for Class 7 Maths
7.0Find the Right Study Resources for Class 7
8.0Key Features of Chapter 2 Arithmetic Expressions
- Understanding Expressions: This explains how to make mathematical statements using numbers and operations.
- Order of Operations: Teaches rules like BODMAS and PEMDAS for getting the right answer to expressions.
- Simplification Techniques: Shows you how to break down complicated expressions into simpler parts.
- Use of Brackets: This shows how brackets change the order of operations.
- Practical Problem Solving: Uses expressions to figure out how to solve real-life maths problems.
- Development of Logical Thinking: Improves accuracy and the ability to solve problems in a structured way.