Chapter 4: Expressions using Letter-Numbers
Letters can stand for numbers. In this chapter we write rules like "Meher's age = Kabir's age + 4" as k + 4, find the values of such expressions, simplify them by combining like terms, and use them to describe patterns and even prove that a pattern always holds.
In this chapter you will
- write relationships using letter-numbers
- find the value of an expression for given values
- simplify expressions by combining like terms
- describe and explain patterns with expressions
Topics
- The Notion of Letter-Numbers NCERT 4.1
A letter-number stands for a number; an expression like k + 4 is algebraic.
- Revisiting Arithmetic Expressions NCERT 4.2–4.3
4n means 4 × n: write the number first and leave out the × sign.
- Simplification of Algebraic Expressions NCERT 4.4
Add like terms by adding their numbers (5c + 3c = 8c); unlike terms stay separate.
- Pick Patterns and Reveal Relationships NCERT 4.5
Describe a pattern in words first, then as an expression (C at 3n, B at 3n − 1, …).
Key words
- Letter-number
- a letter that stands for a number
- Algebraic expression
- an expression with letter-numbers, like 2l + 2b
- Formula
- a general rule written with letter-numbers
- Like terms
- terms with the same letter-number (5c, 3c)
- Unlike terms
- terms with different letter-numbers (18c, 11d)
- Simplify
- rewrite an expression in its shortest equal form
Summary
- Letter-numbers turn rules into expressions: k + 4, 2n, c × 35 + j × 60.
- 4n means 4 × n; to evaluate, put the number in brackets in place of the letter.
- Combine like terms (5c + 3c = 8c); open brackets with the usual sign rules.
- Expressions describe and prove patterns: matchsticks 2y + 1, calendar diagonals 2a + 8.