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CBSE Class 7 Mathematics Chapter 4 Expressions Using Letter-Numbers Worksheet with Answers

Expressions Using Letter-Numbers forms the foundation of algebra in the CBSE Class 7 Mathematics curriculum. This chapter introduces students to the powerful idea that letters can represent unknown or variable quantities, enabling them to write general rules and solve real problems. This worksheet has been carefully designed to align with NCERT Class 7 Mathematics Chapter 4, offering structured practice across all key concepts: variables and constants, forming algebraic expressions, identifying like and unlike terms, and substitution.

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Key takeaways

  • ✓Complete worksheet covering variables and constants, algebraic expressions, like and unlike terms, and substitution as per NCERT Class 7 Mathematics Chapter 4
  • ✓35+ practice questions across six difficulty-graded sections from MCQs to HOTS questions, designed for 60-minute sessions
  • ✓Full answer key with step-by-step explanations helps students verify their work and understand mistakes independently
  • ✓Case-study question connects real-world scenarios with algebraic expressions, reflecting current CBSE exam patterns
  • ✓Printable format allows offline practice, ideal for students preparing for unit tests and term exams without screen time
  • ✓Reinforces NCERT terminology verbatim—variables, constants, coefficients, terms—ensuring alignment with board exam language

Worksheet Information and Chapter Recap

This worksheet is designed at intermediate difficulty level and should take approximately 60 minutes to complete. Students are encouraged to attempt all sections in one sitting under exam-like conditions, then review their answers using the detailed answer key provided at the end. Chapter 4 of NCERT Class 7 Mathematics introduces students to algebraic thinking by using letters to represent numbers. A variable is a letter that can take different values, while a constant is a fixed number. An algebraic expression is formed by combining variables and constants using mathematical operations. Understanding like terms (terms with the same variable part) and unlike terms is crucial for simplification. Substitution means replacing the variable with a given value to find the numerical value of an expression. These concepts appear frequently in CBSE board exams and form the basis for more advanced algebra in Classes 8-10.
  • Difficulty Level: Intermediate
  • Suggested Time: 60 minutes
  • Total Questions: 35+
  • Format: Printable PDF-ready worksheet
  • Coverage: Complete NCERT Chapter 4 syllabus
  • Answer Key: Included with explanations

Section A: Multiple Choice Questions (MCQs)

This section contains six carefully crafted multiple-choice questions that test conceptual understanding of variables, constants, algebraic expressions, and like terms. Each question has four options with only one correct answer. MCQs are a staple of CBSE Class 7 Mathematics assessments and help students develop quick analytical skills. These questions cover the identification of variables and constants, recognition of like and unlike terms, coefficient identification, and basic substitution. Students should read each question carefully and eliminate obviously wrong options before selecting their answer. Mark your answers clearly and avoid spending more than 1 minute per question during timed practice.
  • Question 1: Which of the following is a variable? (a) 7 (b) x (c) 15 (d) 100
  • Question 2: In the expression 5x + 3y - 7, the constant term is: (a) 5x (b) 3y (c) -7 (d) 5
  • Question 3: Which pair represents like terms? (a) 3x and 3y (b) 5ab and 7ab (c) 2x and 2x² (d) 4p and 4
  • Question 4: The coefficient of y in the expression 9y - 4 is: (a) 9 (b) -4 (c) y (d) 9y
  • Question 5: If a = 2, then 4a + 5 equals: (a) 9 (b) 11 (c) 13 (d) 17
  • Question 6: How many terms are there in the expression 3x - 2y + 5z - 8? (a) 2 (b) 3 (c) 4 (d) 5

Section B: Fill in the Blanks

This section tests recall and application of key terminology from CBSE Class 7 Mathematics Chapter 4. Students must complete each sentence with the correct mathematical term, number, or expression. Fill-in-the-blank questions require precise knowledge of definitions and concepts such as variables, constants, coefficients, like terms, and algebraic expressions. Pay attention to spelling and mathematical notation. Write your answers clearly in the spaces provided. These questions reinforce NCERT Class 7 Mathematics vocabulary that appears repeatedly in board examinations and helps students communicate mathematical ideas accurately.
  • Question 7: A symbol which can take various numerical values is called a __________.
  • Question 8: In the term 7xy, the numerical factor is called the __________.
  • Question 9: Terms having the same algebraic factors are called __________ terms.
  • Question 10: The expression 2x + 3y has __________ terms.
  • Question 11: If m = 5, then 2m - 3 = __________.
  • Question 12: In the expression 4p² + 3p - 9, the constant is __________.

Section C: True or False with Correction

This section contains six statements about expressions using letter-numbers. Students must determine whether each statement is true or false. If the statement is false, students should rewrite it correctly. This exercise develops critical thinking and precise understanding of mathematical definitions. True/false questions often test common misconceptions about variables and constants, like and unlike terms, and the formation of algebraic expressions. Read each statement carefully—sometimes a single word makes the difference between true and false. This format appears regularly in CBSE Class 7 Mathematics assessments and requires students to justify their reasoning, a valuable skill for higher classes.
  • Question 13: All algebraic expressions must contain at least one variable. (True/False)
  • Question 14: The terms 5xy and 5x are like terms. (True/False)
  • Question 15: A constant can be any fixed number including zero. (True/False)
  • Question 16: In the expression 3a + 2b, there are three terms. (True/False)
  • Question 17: If x = 0, then any expression containing x will equal zero. (True/False)
  • Question 18: The coefficient of x in 'x + 5' is 0. (True/False)

Section D: Short Answer Questions (3 marks each)

This section contains five short-answer questions requiring students to show their working and provide brief explanations. Each question is worth 3 marks and should take 3-4 minutes to complete. These questions test application of concepts such as identifying variables and constants in expressions, combining like terms, forming algebraic expressions from word problems, and evaluating expressions through substitution. Students must write clear steps to earn full marks—partial credit is awarded for correct method even if the final answer contains a calculation error. These questions mirror the format commonly seen in CBSE Class 7 Mathematics term examinations and unit tests conducted by schools across India.
  • Question 19: Identify the variables, constants, and coefficients in the expression 7x - 3y + 9.
  • Question 20: Simplify by combining like terms: 5a + 3b - 2a + 7b.
  • Question 21: Form an algebraic expression for: 'Five times a number x increased by 8'.
  • Question 22: Find the value of 3p + 2q - 5 when p = 4 and q = 3.
  • Question 23: Write three different algebraic expressions, each having two unlike terms.

Section E: Long Answer and HOTS Questions (5 marks each)

This section presents three challenging long-answer and Higher Order Thinking Skills questions that require deeper analysis and multi-step solutions. Each question carries 5 marks and should take approximately 6-8 minutes. These questions test students' ability to apply multiple concepts from NCERT Class 7 Mathematics Chapter 4 simultaneously, form expressions from complex verbal statements, perform substitution with multiple variables, and analyze patterns in algebraic expressions. HOTS questions prepare students for competitive examinations and Olympiads. Full marks require complete working, clear reasoning, and accurate final answers. These questions develop problem-solving abilities that extend beyond rote learning and are increasingly emphasized in the revised CBSE curriculum.
  • Question 24: The perimeter of a rectangle is given by the expression 2(l + b), where l is the length and b is the breadth. If l = 12 cm and b = 8 cm, find the perimeter. Also, find the perimeter when l = 15 cm and b = 10 cm. What pattern do you observe?
  • Question 25: Rohit has x marbles, Sohan has 5 more marbles than Rohit, and Mohan has twice as many marbles as Sohan. Write algebraic expressions for the number of marbles each person has. If x = 10, how many marbles does each person have? Find the total number of marbles.
  • Question 26: Consider the expression 4a + 3b - 2c. Find its value when: (i) a = 2, b = 3, c = 1, (ii) a = 0, b = 5, c = 4, (iii) a = -1, b = 2, c = -3. Explain why the value changes when the variables change.

Section F: Case-Study Based Question

This case-study question reflects the latest CBSE examination pattern where real-world scenarios are connected to mathematical concepts. Students must read the situation carefully, extract relevant information, and answer sub-questions that test comprehension and application of expressions using letter-numbers. Case studies develop the ability to translate practical problems into mathematical language, a critical 21st-century skill. This question is worth 4 marks total (1 mark per sub-question) and should take approximately 8-10 minutes. Read the case study thoroughly before attempting the questions, and refer back to it as needed. Such questions have become standard in CBSE Class 7 Mathematics papers from 2020 onwards.

Complete Answer Key with Explanations

This comprehensive answer key provides correct answers and brief explanations for every question in the worksheet. Students should attempt all questions independently before consulting this section. When checking answers, pay attention to the method and reasoning, not just the final answer. If you made an error, identify where your thinking went wrong and rework the problem. The explanations use the same terminology as NCERT Class 7 Mathematics to ensure consistency. For numerical questions, verify each calculation step. For conceptual questions, compare your reasoning with the explanation provided. This answer key serves as a self-study tool, allowing students to learn from mistakes and reinforce correct understanding. Parents can use this section to guide their children without needing deep mathematical expertise themselves.
  • Section A Answers: 1(b), 2(c), 3(b), 4(a), 5(c), 6(c)
  • Section B Answers: 7-variable, 8-coefficient, 9-like, 10-two, 11-seven, 12-negative nine or -9
  • Section C Answers: 13-True, 14-False (different variable parts), 15-True, 16-False (two terms), 17-False (depends on other terms), 18-False (coefficient is 1)
  • Detailed solutions for Sections D, E, and F follow below with complete working

Detailed Solutions for Section D (Short Answer)

Question 19: In 7x - 3y + 9, variables are x and y (letters representing numbers), constants are 9 (fixed number), coefficient of x is 7, coefficient of y is -3. Question 20: Combine like terms: 5a - 2a = 3a and 3b + 7b = 10b. Final answer: 3a + 10b. Question 21: 'Five times a number x' translates to 5x, 'increased by 8' means adding 8. Expression: 5x + 8. Question 22: Substitute p = 4, q = 3 into 3p + 2q - 5: 3(4) + 2(3) - 5 = 12 + 6 - 5 = 13. Question 23: Sample answers: (i) 3x + 5, (ii) 2a - 7b, (iii) 4p + 9q (any expressions with two terms having different variable parts are acceptable).

Detailed Solutions for Section E (Long Answer & HOTS)

Question 24: When l = 12, b = 8: Perimeter = 2(12 + 8) = 2(20) = 40 cm. When l = 15, b = 10: Perimeter = 2(15 + 10) = 2(25) = 50 cm. Pattern: As dimensions increase, perimeter increases proportionally. Question 25: Rohit = x, Sohan = x + 5, Mohan = 2(x + 5) = 2x + 10. When x = 10: Rohit = 10, Sohan = 15, Mohan = 30. Total = 10 + 15 + 30 = 55 marbles. Question 26: (i) When a = 2, b = 3, c = 1: 4(2) + 3(3) - 2(1) = 8 + 9 - 2 = 15. (ii) When a = 0, b = 5, c = 4: 4(0) + 3(5) - 2(4) = 0 + 15 - 8 = 7. (iii) When a = -1, b = 2, c = -3: 4(-1) + 3(2) - 2(-3) = -4 + 6 + 6 = 8. The value changes because variables represent different numbers in each case, demonstrating that expressions give different results for different variable values.

Detailed Solutions for Section F (Case Study)

Question 27(a): Monday's sales = (5 kg tomatoes × ₹x per kg) + (3 kg potatoes × ₹y per kg) = 5x + 3y rupees. Question 27(b): Tuesday's sales = (4 kg tomatoes × ₹x per kg) + (6 kg potatoes × ₹y per kg) = 4x + 6y rupees. Question 27(c): Substitute x = 40, y = 30 into Monday's expression: 5(40) + 3(30) = 200 + 90 = ₹290. Question 27(d): Monday = 5(40) + 3(30) = 290. Tuesday = 4(40) + 6(30) = 160 + 180 = 340. Wednesday = 7(40) + 2(30) = 280 + 60 = 340. Tuesday and Wednesday both had highest sales of ₹340 (accept either or both as correct with proper working).

How CBSETUTOR.ai Supports Algebraic Thinking

Mastering expressions using letter-numbers requires practice, immediate feedback, and personalized doubt-clearing—exactly what CBSETUTOR.ai delivers. Students can photograph any problem from this worksheet or their textbook and receive step-by-step solutions within seconds. The AI tutor available 24×7 explains variable identification, like term combination, and substitution methods in simple language, adapting to each student's pace. Unlike generic video lectures, the platform responds to your specific doubt at the exact moment confusion arises. At just ₹999 per month for all subjects across Classes 6-12, it eliminates the need for expensive coaching classes. The 3-day free trial allows students to experience how instant doubt resolution builds confidence in algebra. Parents across metros and Tier-2 cities report that their children develop genuine understanding rather than memorizing formulas when they have access to on-demand, personalized support. For Chapter 4 specifically, students can practice unlimited variations of expression problems and receive tailored hints that guide without simply giving away answers, fostering true mathematical thinking.
  • Photo-upload doubt solving works perfectly for algebraic expression problems
  • Instant step-by-step explanations for substitution and simplification
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Frequently asked questions

What is the difference between a variable and a constant in CBSE Class 7 Mathematics Chapter 4?+
A variable is a symbol (usually a letter like x, y, or z) that can take various numerical values, while a constant is a fixed number that does not change. For example, in the expression 5x + 7, x is the variable and both 5 and 7 are constants.
How do I identify like terms and unlike terms in an algebraic expression?+
Like terms have exactly the same variable part with the same powers. For example, 3xy and 7xy are like terms because both have 'xy'. Unlike terms have different variable parts, such as 3xy and 5x or 2a and 2b. Only like terms can be combined through addition or subtraction.
What is substitution and how do I use it to find the value of an expression?+
Substitution means replacing each variable in an expression with a given numerical value, then performing the calculations. For example, to find the value of 2x + 3 when x = 5, substitute 5 for x: 2(5) + 3 = 10 + 3 = 13. Always follow BODMAS rules when calculating.
How much time should my child spend on this CBSE Class 7 Mathematics Chapter 4 worksheet?+
This worksheet is designed for 60 minutes of focused practice. Students should attempt all sections in one sitting under exam-like conditions, then spend an additional 20-30 minutes reviewing answers and understanding mistakes using the detailed answer key provided.
Can this worksheet be used for both CBSE school exams and competitive exam preparation?+
Yes, absolutely. The worksheet covers all NCERT Class 7 Mathematics Chapter 4 topics tested in school unit tests and term exams. The HOTS questions and case study also prepare students for competitive exams like NTSE, Olympiads, and scholarship tests that require deeper algebraic thinking.
My child struggles with forming algebraic expressions from word problems. Which section will help?+
Section D question 21, Section E question 25, and the entire case study in Section F specifically focus on translating verbal statements into algebraic expressions. These questions build the language-to-algebra translation skill through progressive difficulty. Practice these repeatedly, and consider using CBSETUTOR.ai for instant doubt clearing on specific word problems.
Are the answers provided in this worksheet sufficient for my child to self-study?+
Yes, the answer key includes not just correct answers but brief explanations and complete working for every question. Students can independently verify their solutions, understand where they went wrong, and learn the correct approach. For deeper doubts, the 24×7 AI tutor at CBSETUTOR.ai provides personalized explanations.
How does this worksheet align with the latest CBSE Class 7 Mathematics exam pattern?+
This worksheet mirrors current CBSE assessment formats including MCQs (for objective sections), short-answer questions (3 marks), long-answer questions (5 marks), and a case-study question reflecting the competency-based pattern introduced from 2020 onwards. The difficulty distribution matches typical school examination papers.
What should my child do if they score poorly on this worksheet?+
First, review NCERT Class 7 Mathematics Chapter 4 thoroughly, focusing on definitions of variables, constants, and like terms. Then rework this worksheet section-by-section, checking answers immediately after each section. Identify specific weak areas—substitution, forming expressions, or identifying terms—and practice additional problems on those topics. CBSETUTOR.ai offers unlimited practice problems with instant feedback.
Can I print this worksheet for classroom use or tuition purposes?+
This worksheet is designed as a printable resource for individual student practice. Teachers and tutors may use it for non-commercial classroom purposes. For bulk distribution or commercial use, please contact the content provider. The format is optimized for A4 printing with clear question numbering and adequate space for student responses.

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