NCERT Solutions for Class 7th Maths Chapter 4 Expressions using Letter-Numbers
Updated on 2026-09-19
About this chapter
A letter used in place of a number is a letter-number ; an expression built from letter-numbers and numbers is an algebraic expression . The multiplication sign is dropped: 4 × n is written 4n, with the number first. Swapping, grouping, opening brackets and the distributive property work exactly the same for algebraic expressions as for arithmetic ones. Like terms (5c, 3c, 10c) can be added into one term; unlike terms (18c, 11d) cannot. Expressions let us describe patterns — matchstick steps, calendar squares, saree borders, traffic signals — and, more importantly, prove that the pattern always holds. A formula is read both ways: from a situation to an expression, and from an expression back to a situation.
- The Notion of Letter-Numbers
- Revisiting Arithmetic Expressions
- Omission of the Multiplication Symbol
- Simplification of Algebraic Expressions
- Pick Patterns and Reveal Relationships
- Algebraic Expressions to Describe Patterns
- Patterns in a Calendar
- Matchstick Patterns
Quick revision
| Idea | What it means | Example from the chapter | Key result |
|---|---|---|---|
| Letter-number | A letter standing for a number | a = Aftab's age | s = a + 3 |
| Algebraic expression | Numbers + letter-numbers joined by operations | c × 35 + j × 60 | Cost of c coconuts and j kg jaggery |
| Dropping × | Write the number first, then the letter | 4 × n | 4n |
| Value of an expression | Replace the letter by a number | 5m + 3, m = 2 | 13 |
| Like terms | Same letter-numbers | 5c, 3c, 10c | 18c |
| Unlike terms | Different letter-numbers | 18c and 11d | Cannot be added |
| Distributive property | A multiple of a sum is the sum of multiples | 4v + 3v | 7v |
| Opening a bracket with – | Change the sign of every term inside | (40x + 75y) – (6x + 10y) | 34x + 65y |
| Perimeter formulas | Sides written with a letter | square side q, rectangle l and b | 4q, 2l + 2b |
| Pattern formula | nth step of a growing pattern | matchstick triangles | 2y + 1 |
| Calendar 2 × 2 square | Top-left a, then a+1, a+7, a+8 | diagonal sums | Both are 2a + 8 |
| Position formula | Which item sits at position n | saree designs A, B, C | 3n – 2, 3n – 1, 3n |
Exercises
- In-text Questions — The Notion of Letter-Numbers Page 81
- In-text Questions — The Notion of Letter-Numbers Page 82
- In-text Questions — The Notion of Letter-Numbers Page 83
- Figure it Out — The Notion of Letter-Numbers Page 84–85
- In-text Questions — Revisiting Arithmetic Expressions Page 85–86
- Mind the Mistake, Mend the Mistake — Omission of the Multiplication Symbol Page 87
- In-text Questions — Simplification of Algebraic Expressions Page 88–90
- In-text Questions — Simplification of Algebraic Expressions Page 91–93
- Figure it Out — Simplification of Algebraic Expressions Page 93–94
- Mind the Mistake, Mend the Mistake — Simplification of Algebraic Expressions Page 94–95
- Formula Detective — Pick Patterns and Reveal Relationships Page 95–96
- Algebraic Expressions to Describe Patterns — In-text Questions Page 96–97
- Patterns in a Calendar — In-text Questions Page 97–99
- Matchstick Patterns — In-text Questions Page 100–101
- Figure it Out — Pick Patterns and Reveal Relationships Page 102–105