Class 7 Maths Chapter 4 Expressions Using Letter-Numbers Infographic | NCF 2023 Ganita Prakash

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✦ NCF 2023 GANITA PRAKASH • GRADE 7 SERIES ✦

Chapter 4: Expressions Using Letter-Numbers

Algebraic Foundations: Letter-Numbers, Like & Unlike Terms, Pattern Modeling & Calendar Proofs

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📖 Core Foundations

Letter-Numbers

Letters used in place of numbers to show general relationships (e.g., Aftab's age 'a', Shabnam's age s = a + 3).

Skipping × Sign

Standard shorthand: 4 × n is written as 4n. Number is written first, followed by letter.

Like vs Unlike Terms

Like terms share identical letter-numbers (5c + 3c = 8c). Unlike terms cannot combine (18c + 11d).

✂️ Simplification Laws

1. Distributive Addition:

Add numbers in front of matching letters:
• 5c + 3c + 10c = (5 + 3 + 10)c = 18c
• 4(x + y) − y = 4x + 4y − y = 4x + 3y

2. Bracket Sign Flipping:

Minus outside flips all signs inside:
• (40x + 75y) − (6x + 10y)
= 40x − 6x + 75y − 10y = 34x + 65y

🧩 General nth Formulations

Matchstick L-Pattern:

For n L-shapes: Total = 2n matchsticks

Triangle Chain Pattern:

Step y: 3 + 2(y − 1) = 2y + 1 matchsticks

Square Chain (w squares):

4 + 3(w − 1) = 3w + 1 matchsticks

📅 Visual Calendar & Grid Proofs

Why Calendar Math Works: Moving 1 step Right adds +1 day; moving 1 step Down adds +7 days (full week)!

2×2 Diagonal Square

a

a + 1

a + 7

a + 8

Diag 1: a + (a+8) = 2a + 8
Diag 2: (a+1) + (a+7) = 2a + 8
Result: Diagonals always match!

Calendar Plus (+) Shape

a − 7

a − 1

a

a + 1

a + 7

Sum = (a−7) + (a−1) + a + (a+1) + (a+7) = 5a
Result: Always 5× the center!

• Endless 4-Column Grid: For row r and column c, date formula = 4(r − 1) + c.

⚠️ Common Exam Traps

Trap 1: Digit Pasting Fallacy

If d = 6, then 3d = 3 × 6 = 18 (not 36!). If r = 8, 2r + 1 = 2×8 + 1 = 17 (not 29).

Trap 2: Structural Distinctions

5u (5 times u) ≠ 5 + u (5 more than u). Similarly, 10y − 3 ≠ 10(y − 3) because 10(y−3) expands to 10y − 30.

Designed by Akash Srivastva | Mathematics Hub • NCF 2023 Visual Learning Series

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