Class 7 Maths Chapter 4 Expressions using Letter-Numbers: Step-by-Step NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 4 Expressions using Letter-Numbers (2025-26)

1. Answer the following questions as given in the chapters and exercises:

Example 1: Shabnam is 3 years older than Aftab. When Aftab's age is 10 years, Shabnam’s age will be 13 years. Now Aftab’s age is 18 years, what will Shabnam’s age be?

Answer: Shabnam’s age will be 18 + 3 = 21 years.

Given Aftab’s age, how will you find out Shabnam’s age?

Answer: Add 3 to Aftab’s age to get Shabnam’s age.

Write an expression for Shabnam’s age in terms of Aftab’s age.

Answer: If Aftab’s age is denoted by a, then Shabnam’s age = a + 3.

Given the age of Shabnam, write an expression to find Aftab’s age.

Answer: Aftab’s age = Shabnam’s age – 3. If s is Shabnam’s age, then a = s – 3.

Find Aftab’s age if Shabnam’s age is 20.

Answer: a = 20 – 3 = 17 years.

Example 2: How many matchsticks are needed to make 5 L’s?

Answer: 5 × 2 = 10 matchsticks.

How many matchsticks are needed to make 7 L’s?

Answer: 7 × 2 = 14 matchsticks.

How many matchsticks are needed to make n L’s? What is the expression?

Answer: Number of matchsticks = 2 × n. Expression: 2n.

Example 3: Write an algebraic expression to find the total amount to be paid for c coconuts at ₹35 each and j kg jaggery at ₹60 each.

Answer: Total cost = c × 35 + j × 60.

Use this expression to find the amount for 7 coconuts and 4 kg jaggery.

Answer: Total cost = (7 × 35) + (4 × 60) = 245 + 240 = ₹485.

Example 4: The perimeter of a square is 4 times the length of its side. Express this algebraically, if the side length is q.

Answer: Perimeter = 4 × q.

What is the perimeter if the side length is 7 cm?

Answer: Perimeter = 4 × 7 = 28 cm.

Figure it Out: Write formulas for the perimeter of:

• Triangle with all sides equal: 3 × a (where a is the side length).
• Regular pentagon: 5 × p (where p is the side length).
• Regular hexagon: 6 × h (where h is the side length).

Munirathna has a 20 m long pipe. He joins another pipe of some length k. Give the expression for the combined length.

Answer: Combined length = 20 + k metres.

What is the total amount Krithika has, if she has x notes of ₹100, y notes of ₹20, and z notes of ₹5?

Answer: Total amount = (x × 100) + (y × 20) + (z × 5)

Venkatalakshmi owns a flour mill. It takes 10 seconds to start. Each kg takes 8 seconds to grind. Which expression shows total time to grind y kg of grain starting from off?

• (a) 10 + 8 + y
• (b) (10 + 8) × y
• (c) 10 × 8 × y
• (d) 10 + 8 × y
• (e) 10 × y + 8

Answer: (d) 10 + 8 × y

Write algebraic expressions using letters:

• 5 more than a number x: x + 5
• 4 less than a number x: x – 4
• 2 less than 13 times a number x: 13x – 2
• 13 less than 2 times a number x: 2x – 13

Describe situations corresponding to the following algebraic expressions:

• 8 × x + 3 × y: The total cost if x items cost ₹8 each and y items cost ₹3 each.
• 15 × j – 2 × k: The total marks if j answers earn 15 marks each and k answers lose 2 marks each (or similar problem).

In a calendar month, any 2 × 3 grid full of dates: Write expressions for the dates in blank cells if the bottom middle cell has date 'w'.

Answer: For example, one step up: w – 7, one step left: w – 1, one step right: w + 1, etc. (Actual layout depends on question illustration.)

4.2 Revisiting Arithmetic Expressions: Simplify the following:

1. 23 – 10 × 2 = 23 – 20 = 3
2. 83 + 28 – 13 + 32 = 111 – 13 + 32 = 98 + 32 = 130
3. 34 – 14 + 20 = 20 + 20 = 40
4. 42 + 15 – (8 – 7) = 42 + 15 – 1 = 57 – 1 = 56
5. 68 – (18 + 13) = 68 – 31 = 37
6. 7 × 4 + 9 × 6 = 28 + 54 = 82
7. 20 + 8 × (16 – 6) = 20 + 8 × 10 = 20 + 80 = 100

4.3 Omission of the Multiplication Symbol: Fill in the blanks.

1. If a = –4, then 10 – a = 10 – (–4) = 14
2. If d = 6, then 3d = 3 × 6 = 18

4.4 Simplification of Algebraic Expressions: For example, simplify 2d – d – c – c:

Answer: 2d – d – c – c = (2d – d) + (–c – c) = d – 2c

4.5 Pick Patterns and Reveal Relationships:

The formula for the number machine above (two times the first number minus the second number):

Answer: 2a – b

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Key Concepts of Expressions using Letter-Numbers

Mastering Expressions using Letter-Numbers in Class 7 Maths is vital for building strong algebraic thinking. This chapter introduces concise ways of expressing relationships and patterns, which is a foundation for higher-level problem-solving in mathematics.

Practicing NCERT Solutions for Class 7 Maths Chapter 4 (2025-26) ensures you understand algebraic expressions, formulas, and pattern-based questions. Use clear step-by-step approaches for all exercise types—this strengthens both your understanding and exam confidence.

Regular revision of exercise-based answers will help you tackle MCQs and reasoning questions more efficiently. Focus on applying the core concepts to different scenarios to improve your performance and boost your maths score.