Chapter 4 — Expressions using Letter-Numbers

Ganita Prakash • Grade 7 • Part I • 2026–27

🔤 Why use letters in mathematics?

Suppose one notebook costs ₹25. The cost of 2 notebooks is ₹50, of 5 is ₹125 and of 20 is ₹500. Instead of writing a new rule every time, let n represent the number of notebooks. Then the cost is 25n. A letter-number lets one mathematical rule describe many situations.

1. From words to expressions

The order of words matters. “5 less than x” means x − 5, not 5 − x.

2. Terms, coefficients and constants

In 7x + 4, the terms are 7x and 4. The coefficient of x is 7, and 4 is a constant. In 3a + 2b − 5, there are three terms: 3a, 2b and −5.

3. Substitution

If x = 6, then 2x + 7 = 2(6) + 7 = 19. Substitution means replacing the letter by its given value and then evaluating the expression.

4. Algebra describes patterns

The perimeter of a square of side s is s + s + s + s = 4s. If s = 6 cm, the perimeter is 24 cm. The expression 4s works for every possible side length.

5. Like and unlike terms

Terms with the same variable part can be combined: 3x + 2x = 5x. But 3x and 2y are unlike terms and cannot be combined as 5xy or 5x. This distinction is important when simplifying expressions.

🧠 Worked Examples

1. “7 more than twice n” → 2n + 7.
2. If n = 4, 2n + 7 = 8 + 7 = 15.
3. 3x + 5x = 8x.
4. For a rectangle of length l and breadth b, perimeter = 2l + 2b.

🎯 Think & Create

1. Create an expression for the cost of n pens at ₹12 each plus a fixed ₹20 delivery charge.
2. Explain the difference between 4x and x + 4 using x = 5.
3. Find two different word statements that can represent 3a + 2.

🧩 Concept MCQs

1. “4 more than x” is — A. x + 4 B. 4x C. x − 4 D. x/4
2. In 9y − 3, the coefficient of y is — A. 9 B. −3 C. y D. 6
3. If a = 5, 3a + 2 = — A. 15 B. 17 C. 12 D. 8
4. Which pair contains like terms? A. 3x and 5x B. 3x and 5y C. 3 and 5x D. x and y

Answers: 1-A, 2-A, 3-B, 4-A

📌 Case-based Challenge

A school charges ₹30 per student for a museum visit and a fixed bus charge of ₹1,200. Let n be the number of students.

1. Write an expression for the total cost.
2. Find the cost for 40 students.
3. What part of the expression remains unchanged when n changes?
4. Explain why the expression is more useful than making a separate calculation for every possible class size.

📝 Worksheet

1. Translate ten verbal statements into expressions.
2. Identify terms, coefficients and constants.
3. Evaluate expressions for given values.
4. Combine like terms in simple expressions.
5. Write algebraic rules for real-life patterns.

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