Chapter focus
Letters can stand for numbers. Algebraic expressions describe calculations that work for many values, making patterns and relationships easier to express.
The chapter title in the current NCERT book is “Expressions using Letter-Numbers.” These original explanations and practice accompany the full textbook.
1. Variables, terms and coefficients
In 7n + 4, n is a variable, 7 is its coefficient, and 4 is a constant term. The expression has no equality sign, so it is not an equation. If n = 3, its value is 7 × 3 + 4 = 25.
A term is a number, a variable, or a product of numbers and variables. In 5x − 2y + 9, the terms are 5x, −2y and 9. The minus sign belongs to the term that follows it.
2. Like terms and simplification
Like terms have the same variable part and powers. Combine them by adding or subtracting their coefficients: 4a + 3a = 7a; 9p − 2p = 7p. Constants combine with constants. Unlike terms such as 3a and 3b cannot be combined.
Worked example: simplify 6x + 3 − 2x + 8
- Group like terms: (6x − 2x) + (3 + 8).
- Simplify each group: 4x + 11.
- If x = 2, the value is 4(2) + 11 = 19.
3. Subtract algebraic expressions
Subtracting a bracket changes the sign of every term inside it: A − (B + C) = A − B − C. This is because the subtraction applies to the whole expression, not only its first term.
Worked example: subtract 2x − 5 from 7x + 3
(7x + 3) − (2x − 5) = 7x + 3 − 2x + 5 = 5x + 8. Check with x = 1: the original values are 10 − (−3) = 13; the simplified expression is 5 + 8 = 13.
4. Describe number patterns with letters
If a pattern begins at 4 and increases by 3 each time, its first terms are 4, 7, 10, 13, … . The nth term can be written 3n + 1: for n = 1 it gives 4; for n = 2 it gives 7. Substituting several values checks the rule, while explaining why it works justifies the general form.
Common errors to avoid
- 4x means 4 × x, not 4 + x.
- Combine coefficients only for like terms.
- When subtracting a bracket, change the sign of every term inside.
- Keep the variable part when adding terms: 3x + 5x = 8x, not 8x².
Practice: simplify and explain
1. Simplify 8m − 3m + 4.
Answer: 5m + 4.
2. Evaluate 4a + 7 when a = 5.
Answer: 4(5) + 7 = 27.
3. Simplify (6x + 2) − (3x − 5).
Answer: 6x + 2 − 3x + 5 = 3x + 7.
4. Write an expression for “7 less than twice a number p.”
Answer: 2p − 7.
5. Find a rule for 5, 9, 13, 17, … using term number n.
Answer: 4n + 1. It gives 5 when n = 1 and increases by 4 for each next value of n.
Chapter summary
Letters represent numbers, and expressions use them to describe general calculations. Simplify by collecting like terms, substitute values to evaluate, and handle subtraction of brackets carefully. Check a proposed pattern rule with several terms.