Variables
Comprehensive notes, formulas, and practice questions for Variables.
Variables
Variables
What you'll learn
- What a variable is — a letter standing for an unknown or changing number.
- The difference between variable, constant, and numerical coefficient.
- How variables appear in patterns (matchstick triangles, calendar grids).
- Why algebra lets us describe rules that work for many numbers at once.
Key concepts
Level 1 — Letters for numbers
Verbal: A variable (often x, n, y) represents a quantity we do not know yet or that can change.
Symbolic: In n + 5, the letter n is the variable; 5 is a constant.
Visual (matchstick pattern):
| Triangles (n) | Matchsticks | Rule |
|---|---|---|
| 1 | 3 | 2×1 + 1 |
| 2 | 5 | 2×2 + 1 |
| 3 | 7 | 2×3 + 1 |
| n | 2n + 1 | general rule |
Constant vs variable: In 7y, 7 is fixed (coefficient); y varies.
Level 2 — Using variables in statements
Perimeter: Square side s → perimeter = 4s. Rectangle length l, breadth b → 2l + 2b.
Substitution: If n = 4, then 3n + 2 = 3(4) + 2 = 14.
| Term | Meaning | Example |
|---|---|---|
| Variable | Stands for a number | x in x − 7 |
| Constant | Fixed value | 7 in x − 7 |
| Expression | Combination without = sign | 2a + 5 |
NCERT link: Rules from "Maths Magic" patterns — chairs around tables, toothpick squares.
Worked example
A notebook costs ₹p. You buy 3 notebooks and pay ₹10 extra for a cover. Write the total cost.
Step 1 — Cost of notebooks: 3 × p = 3p
Step 2 — Add cover: 3p + 10
Step 3 — If p = 25: 3(25) + 10 = 75 + 10 = ₹85
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| x always means 10 | Roman numeral confusion | In algebra, x is a variable unless defined |
| 3n means 3 and n separately (add) | Missing multiplication convention | 3n means 3 × n |
| Confusing variable with label | n used as "number of" vs value | State what the letter represents |
| Treating a + b as ab | Concatenation habit | a + b means add; ab means a × b |
Quick check
- In 8 − 3m, identify the variable and the constant.
- Write an expression for "5 more than twice a number y."
- If side of a square is s, write its perimeter.
- For the matchstick rule 2n + 1, find matchsticks when n = 6.
Open the Practice tab for graded questions on Variables.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
Master this topic with Drishti OS
Get unlimited mock tests, AI-powered mentorship, and complete video courses when you join.
Start Free Practice