NEETClass 11thClass 12thClass 12th PlusJEEClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thOnline CoursesDistance LearningInternational OlympiadNEETClass 11thClass 12thClass 12th PlusJEE (Main+Advanced)Class 11thClass 12thClass 12th PlusJEE MainClass 11thClass 12thClass 12th PlusClass 6-10Class 6thClass 7thClass 8thClass 9thClass 10thKCET/MHT-CETKCETMHT-CETNEET20262025202420232022JEE20262025202420232022Class 6-1020262025JEE MainPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DatePercentile PredictorAnswer KeyCounsellingEligibilityExam PatternJEE MathsJEE ChemistryJEE PhysicsJEE AdvancedPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateAnswer KeyEligibilityExam PatternRank PredictorNEETPrevious Year PapersSample PapersMock TestResultAnalysisSyllabusExam DateCollege PredictorAnswer KeyRank PredictorCounsellingEligibilityExam PatternBiologyNCERT SolutionsClass 6Class 7Class 8Class 9Class 10Class 11Class 12TextbooksCBSEClass 12Class 11Class 10Class 9Class 8Class 7Class 6SubjectsSyllabusNotesSample PapersQuestion PapersICSEClass 10Class 9Class 8Class 7Class 6State BoardBiharKarnatakaMadhya PradeshMaharashtraTamilnaduWest BengalUttar PradeshOlympiadMathsScienceEnglishSocial ScienceNSOIMONMTCTALLENTEXASATInstant Online ScholarshipAIOT(NEET)ALLEN for SchoolsAbout ALLENBlogsNewsCareersRequest a call backBook a demo
CBSE Notes Class 7 Maths Chapter 4 Expressions Using Letter-Numbers
This chapter introduces students to algebra, where letters are used along with numbers to form expressions. These letters are called variables and represent unknown values.
Students learn how to form algebraic expressions and understand their meaning. For example, instead of writing “a number plus 5,” we can write “x + 5.” This makes mathematical expressions shorter and easier to use.
The chapter also explains how to evaluate expressions by substituting values for variables. Students learn to simplify expressions and understand their practical use.This chapter builds the foundation for algebra and helps students develop problem-solving skills.
1.0Download CBSE Class 7 Maths Chapter 4 Notes: Free PDF
To learn the basics of algebra and how to make expressions, download the CBSE Class 7 Maths notes Chapter 4—Expressions Using Letter-Numbers Notes PDF. The notes make it easy to understand variables, terms, and how to simplify things. Helps you get a good start in algebra.
2.0The Notion of Letter–Numbers Class 7 Maths Chapter 4 - Revision Notes
Chapter Summary: This chapter introduces the concept of letter-numbers (variables) as mathematical helpers used to represent unknown quantities, construct algebraic expressions, solve real-world problems, and express repeating sequence patterns.
Key Concepts to Remember
- Unknowns in Mathematics: Quantities whose values are not immediately known in a given problem or situation are referred to as unknowns.
- Letter-Numbers (Variables): A symbol or letter from the English alphabet (such as x,y,z,a,b,c) assigned to represent an unknown quantity or a value that can change depending on the problem.
- Algebraic Expression: A mathematical phrase constructed by combining letter-numbers and numerical constants using signs of arithmetic operations (+,-,,).
- Terms of an Expression: The individual constants, letter-numbers, or products of constants and letter-numbers that are separated by addition or subtraction signs.
- Regular Polygons: Polygons in which all side lengths and interior angles are equal, allowing their perimeters to be expressed as a product of the number of sides and the side length a.
- Pattern Sequences: Numerical or geometric arrangements where the position of an element in a repeating cycle can be generalized using an algebraic expression involving the position number n.
- Grid and Array Algebra: Systematic row-and-column arrangements where position values can be modeled algebraically based on row number r and column number c.
- Origins of Algebra: The word algebra originates from the foundational 9th-century book "Al-jabr wa'l muqabalah" written by the Persian mathematician Muhammad ibn Musa al-Khwarizmi.
Concept of Unknowns & Letter-Numbers
- Defining Letter-Numbers: Instead of using fixed numbers or visual symbols, letters like x,y,z or a,b,c are used for convenience to represent unknown quantities.
- Dynamic Values: Unlike fixed numerical values, the value of a letter-number changes based on the constraints of the specific problem.
- Translating Words to Algebraic Phrases:
- 7 less than x is expressed as (x-7).
- 5 subtracted from x is expressed as (x-5).
Perimeter Rules of Regular Polygons
- Regular Heptagon Perimeter: A regular heptagon has 7 equal sides. If the side length is a, the perimeter is 7a.
- Regular Nonagon Perimeter: A regular nonagon has 9 equal sides. If the side length is a, the perimeter is 9a.
Formulating Expressions from Real-Life Word Problems
- Printing Press Warm-Up: If a press takes 15 seconds to warm up and 5 seconds per page, the total time for p pages is 15+5p seconds.
- Ribbon Length: If Anita has 12 meters of ribbon and buys an additional ribbon of length r meters, her total ribbon length is (12+r) meters.
- Fruit Stall Revenue: Selling apples at price a and bananas at price b over 3 days (Monday: 6a+10b, Tuesday: 8a+12b, Wednesday: 5a+9b) gives a total revenue of 19a+31b.
- Bicycle and Helmet Rentals: Renting m bicycles at ₹60 each and n helmets at ₹20 each with refunds of ₹15 per bicycle and ₹5 per helmet results in a net cost of (60m+20n)-(15m+5n)=45m+15n.
- Monkey Climbing Path: A monkey climbing x meters and slipping y meters down each half-hour covers a net distance of k(x-y) meters after k periods.
Number Machines and Function Rules
- Machine Rule Type 1: A machine taking inputs a and b and returning "two times the sum of inputs" operates under the formula 2(a+b).
- Machine Rule Type 2: A machine returning "three times the first input plus the second input" operates under the formula 3a+b.
- Machine Rule Type 3: A machine taking inputs A and B and giving output 11,10,13 operates under the formula 2A+B.
Repeating Sequence Positions & Grid Patterns
3-Element Repeating Tile Pattern:
- Blue Diamond (positions 1, 4, 7): Appears at position (3n-2).
- Orange Diamond (positions 2, 5, 8): Appears at position (3n-1).
- Red Circle (positions 3, 6, 9): Appears at position 3n.
4-Element Colour Block Sequence:
- Red Block (positions 1, 5, 9): General formula (4n-3).
- Yellow Block (positions 2, 6, 10): General formula (4n-2).
- Green Block (positions 3, 7, 11): General formula (4n-1).
- Pink Block (positions 4, 8, 12): General formula 4n.
- Endless 5-Column Grid: Numbers arranged sequentially across 5 columns have the general term formula 5(r-1)+c, where r is the row number and c is the column number.
3.0Important Formulas: The Notion of Letter–Numbers
- Perimeter of a Regular Polygon: Perimeter=na (where n is the number of equal sides and a is the side length).
- Subtraction Translation Rule: "k less than x" (x-k).
Number Machine Formulas:
- Double the sum of inputs: Output=2(a+b)
- Three times first input plus second: Output=3a+b
- Double first input plus second: Output=2A+B
Repeating 3-Sequence Formulas:
- Position for 1st item: (3n-2)
- Position for 2nd item: (3n-1)
- Position for 3rd item: 3n
Repeating 4-Sequence Formulas:
- Position for 1st item: (4n-3)
- Position for 2nd item: (4n-2)
- Position for 3rd item: (4n-1)
- Position for 4th item: 4n
- Endless 5-Column Grid Position Formula: Value=5(r-1)+c
4.0Learning Guide for Class 7 Maths The Notion of Letter–Numbers – Chapter 4
- Seating Plan Roll Number Grid: In a 2 × 3 block of desks where roll numbers increase by 1 left-to-right and by 6 top-to-bottom, if the bottom-right seat is r, the other seats are (r-8), (r-7), (r-6) in the top row, and (r-2), (r-1), r in the bottom row.
- Book Fair Bookmark Distribution: If p people visit only science, q people visit only fiction, and r people visit both sections receiving a bookmark at each section, total bookmarks distributed =p+q+2r.
- June 2025 Calendar Diagonal Pattern Activity: In any 2 × 2 square on a calendar with bottom-right number a, the 4 entries are (a-8), (a-7), (a-1), and a. The sum of both diagonals is identical: (a-8)+a=(a-7)+(a-1)=2a-8.
- Determining Grid Positions via Division: To find the row and column of a number like 123 in a 5-column grid, divide 123 by 5: quotient =24, remainder =3. Thus, r-1=24r=25 and column c=3.
- Revision Tip for Expression Building: Always identify the fixed part (constant) and the changing part (product of rate and letter-number) before combining them into a final algebraic expression.
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 4: Expressions Using Letter-Numbers
- An introduction to algebra: It uses letters (variables) to stand in for numbers in expressions.
- Algebraic Expressions: Defines terms, factors, and coefficients.
- Forming Expressions: Shows you how to turn word problems into algebraic equations.
- Simplifying Expressions: Teaches how to combine terms that are the same.
- Use in Problem Solving: Uses algebra in real life and in patterns.
- Foundation for Algebra: Lays the groundwork for equations and more advanced maths.