Class 7 Maths Ch 4: Expressions Using Letter‑Numbers – learn basic algebra with variables, write and simplify expressions from real‑life patterns and formulas, with notes, solved examples, extra questions and quiz for CBSE Exam

Chapter at a Glance – Expressions Using Letter-Numbers

This chapter introduces a concise way of expressing mathematical relations and patterns using letter-numbers (variables). It helps in thinking about relationships, explaining why they hold, and simplifying expressions.

Main Topics Covered

Notion of letter-numbers and algebraic expressions.
Forming expressions from real-life situations (ages, matchsticks, costs, perimeters).
Revisiting arithmetic expressions: swapping, grouping, brackets, distributive property.
Omission of multiplication symbol in algebraic expressions.
Simplification: like terms, unlike terms, brackets.
Patterns and relationships: number machines, saree borders, calendars, matchsticks.

Key Takeaways for Exams

Letter-Numbers

Letters representing numbers; e.g., s = a + 3.

Expressions

Concise way for relations; e.g., 2n for matchsticks.

Simplification

Combine like terms; e.g., 5c + 3c = 8c.

Patterns

Matchsticks: 2y + 1; Calendar: diagonal sums equal.

Key Concepts & Rules – Expressions Using Letter-Numbers

Important definitions, rules for letter-numbers, algebraic expressions, and simplification for quick reference.

Key Rules

Letter-number (variable): Represents any number.
Algebraic expression: Combination of numbers, variables, operations.
Omission of ×: Write coefficient before variable, e.g., 4n = 4 × n.
Like terms: Same variable, e.g., 5x, –2x.
Unlike terms: Different variables, e.g., 5x and 3y.
Simplification: Combine like terms, use distributive property.
Distributive property: a(b + c) = ab + ac.
Brackets with minus: –(p + q) = –p – q.

Pattern Examples

Pattern	Expression	Example
Matchstick Ls	2n	For 5 Ls: 10 matchsticks
Triangle Matchsticks	2y + 1 or 3 + 2(y–1)	For Step 5: 11 matchsticks
Calendar 2x2 Diagonal Sums	2a + 8	Equal for any a
Cross Shape Sum	5a	5 times center

Golden Lines for Exams

“Letter-numbers allow general expressions; Simplify by combining like terms.”

Concept Cards – Quick Explanations

Letter-Numbers (Variables)

Letters standing for unknown numbers; e.g., a for Aftab's age.

Exam Tip: Use to form general rules.

Algebraic Expressions

e.g., s = a + 3; a = s – 3.

Simplification

Combine like terms; Use distributive property.

Like/Unlike Terms

Like: Same variable; Unlike: Different.

Omission of ×

4n means 4 × n.

Patterns

Describe using expressions; e.g., matchsticks 2n.

Number Machines

Find formulas for outputs.

Examples + Solutions

Example 1: Ages of Shabnam and Aftab

Shabnam is 3 years older than Aftab.

Solution: Let a = Aftab's age. Then s = a + 3.

If a = 23, s = 26.

Aftab's age = Shabnam's age - 3: a = s - 3.

Example 2: Matchstick L Patterns

Each L uses 2 matchsticks.

Solution: For n Ls, number of matchsticks = 2n.

For 5 Ls: 10; 7 Ls: 14; 45 Ls: 90.

Example 3: Cost of Laddus

Coconuts ₹35 each, jaggery ₹60/kg.

Solution: Cost = 35c + 60j, where c = no. of coconuts, j = kg of jaggery.

For 10 coconuts, 5 kg: ₹650; 8 coconuts, 9 kg: ₹780; 7 coconuts, 4 kg: ₹485.

Example 4: Perimeters of Shapes

Square side q: Perimeter = 4q.

For q = 7 cm: 28 cm.

Example 5: Pencils and Erasers

Price per pencil c, eraser d.

Solution: Total earned = 18c + 11d.

Example 6: Area of Split Rectangle

Bigger area = 7v; Also 4v + 3v = 7v.

Another split: 12n - 4n = 8n.

Example 7: Renting Chairs and Tables

Pay 40x + 75y; Get back 6x + 10y.

Net paid = 34x + 65y.

Example 8: Quiz Scores

Scores: 7p - 3q, 8p - 4q, 6p - 2q.

Total: 21p - 9q.

Difference from Krishita's 23p - 7q: 2p - 2q.

Example 9: Simplify 4(x + y) - y

4x + 4y - y = 4x + 3y.

Example 10: 5u vs 5 + u

Not equal; Different values for u.

Example 11: Sum of Numbers in Picture

3 ways all give 2r + 2s + 24.

Example 12: Saree Border Patterns

Design C: 3n; B: 3n - 1; A: 3n - 2.

Position 122: Remainder 2 (divide by 3), Design A.

Figure it Out Solutions (All Solved)

Page 83-84

1. Perimeter Formulas

(a) 3a (equilateral triangle)

(b) 5a (regular pentagon)

(c) 6a (regular hexagon)

2. Pipe Length

20 + k meters.

3. Money Table

3: 695; 8,4,z: 800 + 80 + 5z; x,y,z: 100x + 20y + 5z.

4. Flour Mill Time

(d) 10 + 8 × y.

5. Expressions

(a) n + 5

(b) m - 4

(c) 13k - 2

(d) 2p - 13

6. Situations for Expressions

(a) e.g., 8 apples + 3 bananas cost.

(b) e.g., 15 books - 2 pens cost.

7. Calendar Grid

w-1, w; w-8, w-7.

Page 93

1. Add Numbers in Pictures

All methods give 2r + 2s + 24.

Page 102-103

1. Flower Sales

(a), (b).

2. Flower Customers

(a) p + q + r.

3. Snail Climb

(a) 10u - 10d.

(b) If d > u, snail moves down.

4. Radha Cycling

5*7 + (5+z)*7 + (5+2z)*7 = 105 + 21z.

5. Expression Paths

Fill blanks: 4w + 20 = w + 2 + 3w + 18, etc.

6. Train Stops

(a) 4*4 + 3*2 = 22 min.

(b) Diagram: 4t + 6.

7. Simplify Expressions

(a) 4a + 5b + 10

(b) a - 7b - 16

(c) 12x + 6

(d) 6x + 9

(e) 3h + 4

(f) 5m - 20n + 5

8. Add Expressions

(a) 13d - 3c + 18

(b) 7f + 11 - 20s

(c) -d + 2c - 2

(d) -5f + 3 + -4s

(e) 0

(f) 0

9. Subtract Expressions

(a) -3a + 15b - 32

(b) 18x - 2y - 23

(c) -27g + 10h - 2

(d) -3a + 15b - 32

(e) -13x + 13y - 6

(f) -16g - 3h + 30

10. Situations for Expressions

(a) 8 pens + 3 books cost.

(b) 15km - 2km distance.

11. Rope Folding

1 cut: 2 pieces; Fold 1: 3; Fold 10: 11.

Expression: r + 1.

12. Matchstick Squares

10 squares: 34 matchsticks; w squares: 3w + 1.

13. Traffic Colours

Remainder 0: Red, 1: Green, 2: Yellow.

90: Red, 190: Red, 343: Green.

14. Pattern of Squares

Step 4: 30; Step 10: 220; Step 50: 1275.

Formula: n(n+1)(2n+1)/6.

Vertices: 4 times squares.

15. Endless Grid

(a) Column 1: 4r - 3; 2: 4r - 2; 3: 4r - 1; 4: 4r.

(b) (i) Row 31 Column 4; (ii) Row 37 Column 1; (iii) Row 51 Column 1.

(c) 4(r-1) + c.

(d) Multiples of 3 in column 3 or 4r, etc.

Extra Practice Questions (Exam-Ready) – Chapter 4 Expressions Using Letter-Numbers

50+ Questions • Categorized by Marks • With Detailed Solutions • Difficulty Tags

1-Mark Questions (Very Short Answer)

1. What is a letter-number?

2. Write 4 × n without ×.

3. Simplify 5x + 3x.

4. Like terms in 2a + 3b - a.

5. Expand 3(x + 2).

2-Mark Questions (Short Answer)

6. Explain letter-numbers with age example.

7. Simplify 4(l + b).

8. Matchstick for 5 Ls.

9. Compare 5u and 5 + u.

10. Calendar diagonal sum expression.

3-Mark Questions (Reasoning / Explanation)

11. Why use algebraic expressions?

12. Simplify cost expression 35c + 60j.

13. Rope folding n times cut.

14. Traffic signal colour at 90.

15. Why 2y + 1 = 3 + 2(y-1).

4–5 Mark Questions (Application / Word Problems)

16. Pencils erasers total 18c + 11d.

17. Saree pattern position 122.

18. Endless grid number at row r column c.

19. Calendar cross sum 5a.

20. Matchstick triangles Step 33.

Common Mistakes & How to Avoid

Mistake 1: Not Combining Like Terms

5x + 3x = 5x3x (wrong).

Avoid: Add coefficients for same variable.

Mistake 2: Wrong Bracket Removal

-(p + q) = -p + q (wrong).

Avoid: Distribute minus sign.

Mistake 3: Mixing Like/Unlike

3x + 2y = 5xy (wrong).

Avoid: Unlike terms can't combine.

Mistake 4: Omission of × Confusion

4n = 4 + n (wrong).

Avoid: Remember coefficient means multiplication.

Mistake 5: Pattern Expressions

Matchsticks for n Ls = n + 2 (wrong).

Avoid: Verify with small n.

Quick Revision One-Pager & Mind Map

Concept	Key Points
Letter-Numbers	Variables for general rules.
Expressions	Numbers + variables + operations.
Simplification	Like terms, distributive, brackets.
Patterns	Describe, verify with expressions.

Mind Map

Central: Algebraic Expressions

Letter-Numbers: Represent unknowns.
Forming: From situations.
Simplifying: Rules from arithmetic.
Patterns: Calendars, matchsticks.

Interactive Quiz – 15 Questions

Test Your Knowledge!