NCERT Solutions for Class 7 Mathematics Chapter 4: Expressions using Letter-numbers

This worksheet focuses on the fundamental concepts of algebraic expressions involving letter-numbers (variables), designed to help students in Grade 7 grasp algebra's core principles. Students will learn how to represent numbers and real-world situations using algebraic symbols, simplifying expressions and solving problems. This chapter is essential because it lays the groundwork for future algebraic studies and problem-solving in mathematics. The worksheet contains complete and accurate NCERT Solutions for each question, following the prescribed guidelines from the NCERT textbook. Download the worksheet and practice alongside the solutions for better clarity. Book a free trial now to get expert guidance.

Chapter summary: stories, poems & themes

This chapter does not feature stories or poems but instead provides a series of problems that require students to use algebraic expressions and apply them to real-world situations. It includes activities like writing formulas for geometric shapes, solving word problems involving costs and quantities, and representing situations with variables. The focus is on mathematical operations, simplifying expressions, and creating algebraic formulas to represent everyday life situations.

What this NCERT chapter covers?

- Writing formulas for perimeters of polygons like triangles, pentagons, and hexagons.
- Formulating algebraic expressions to represent various situations, such as adding lengths or calculating costs.
- Learning to simplify algebraic expressions by combining like terms.
- Solving word problems using algebraic expressions, including those involving costs, distances, and time.
- Understanding how to represent real-life scenarios using algebraic formulas.

How to use these NCERT solutions?

- Start by attempting the questions on your own to build your problem-solving skills.
- After attempting, compare your solutions with the NCERT-aligned answers provided in this worksheet.
- Parents and teachers can use these solutions to guide students step by step, reinforcing the correct approach to each problem.
- These solutions follow the exact order of the worksheet, making it easy to follow and use for revision and practice.

Student tips & learning tricks

- Carefully read each problem and identify the key elements like variables and constants before writing down an expression.
- For word problems, translate the information into an algebraic expression step by step.
- Simplify expressions by grouping like terms together to make calculations easier.
- Double-check the signs (positive or negative) when performing algebraic operations to avoid mistakes.
- For activities that involve representing real-life situations, ensure you correctly identify what each variable represents.
- Practice similar problems to gain confidence and improve speed.

Why NCERT solutions are important?

NCERT Solutions provide a clear, structured approach to learning mathematical concepts. These solutions help students build a strong foundation in algebra by following the NCERT standards, ensuring that they are well-prepared for exams. The detailed, step-by-step solutions improve conceptual understanding and boost students' confidence. Using these solutions ensures that students are practicing the correct methods and techniques for solving mathematical problems.

Complete answer key – NCERT solutions

1. Write formulas for the perimeter of:
- a) Triangle with all sides equal: Perimeter of Triangle = 3a units
- b) Regular Pentagon: Perimeter of Regular Pentagon = 5a units
- c) Regular Hexagon: Perimeter of Regular Hexagon = 6a units

2. Munirathna has a 20 m long pipe. 
Expression for the combined length of the pipe = (20 + k) meters

3. What is the total amount Krithika has, if she has the following numbers of notes of ₹100, ₹20, and ₹5? 
Expression and total amount = 30 * 100 + 5 * 20 + 6 * 5 = ₹965

4. Venkatalakshmi owns a flour mill. 
Expression for the time taken to grind ‘y’ kg of grain = 10 + 8 * y

5. Write algebraic expressions using letters of your choice: 
- a) 5 more than a number = d + 5 
- b) 4 less than a number = d - 4 
- c) 2 less than 13 times a number = 13 * d - 2 
- d) 13 less than 2 times a number = 2 * d - 13

6. Describe situations corresponding to the following algebraic expressions: 
- a) A shopkeeper sells a pen for ₹x and a notebook for ₹y. Abha buys 8 pens and 3 notebooks. 
Expression = 8 * x + 3 * y 
- b) A factory makes 15 chairs every day. If the factory works for ‘j’ days, the number of chairs made is 15 * j. If 2 chairs break every day for ‘k’ days, the number of good chairs remaining is: 
Expression = 15 * j - 2 * k

7. In a calendar month, if any 2 × 3 grid full of dates is chosen as shown in the picture**, the expressions for the dates in the blank cells are: 
Expression = w, w + 1, w + 2, etc.

8. Simplify the following expressions: 
- a) 4p + 5b + 10 
- b) a - 13b - 16 
- c) 12x + 6 
- d) 6x + 15

9. Add and subtract the following expressions as instructed: 
- a) 13d + c – 2 + 7f + 4s – 4 = 13d + 7f + c + 4s – 6 
- b) -3a + 15b – 32 - (16y + 18x – 23) = -3a + 15b - 32 - 16y - 18x + 23

10. Describe situations corresponding to the following algebraic expressions: 
Expression = 8x + 3y 
Example: A fruit seller sells mangoes at ₹8 each and bananas at ₹3 each. If a customer buys ‘x’ mangoes and ‘y’ bananas, the total cost would be: 
8x + 3y

11. Imagine a straight rope. If it is cut once as shown, we get 2 pieces. If the rope is folded once and then cut, we get 3 pieces. The number of pieces when the rope is folded ‘r’ times and cut is: 
Expression = r + 2

12. Look at the matchstick pattern below. To make ‘w’ squares, the number of matchsticks required is: 
Expression = 4 + 3(w - 1)

13. Use expressions to find the number of squares and matchsticks as required.

14. In a traffic signal, find the expression for positions of each colour (Red, Green, Yellow). 
Expression for the position of Red = 4n - 3, Green = 4n - 1, Yellow = 2n

15. Numbers in a 4-column grid are represented as: 
Formula = 4(r – 1) + c 
Row and column for number 124 = r = 31, c = 4

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