Notes For All Chapters – Ganita Prakash Class 7th
Expressions using Letter-Numbers
1. What is an Algebraic Expression?
- An algebraic expression is a combination of letter-numbers and mathematical operations (+, –, ×, ÷).
- Example: If a is Aftab’s age, and Shabnam is 3 years older, then Shabnam’s age = a + 3.
2. What are Letter-Numbers?
- Letters like x, y, a, b are used to represent unknown or changing numbers.
- Example: n can be the number of matchstick patterns. If each pattern uses 2 sticks, total sticks = 2n.
3. Writing Expressions for Real-Life Situations
Example 1: Cost of c coconuts and j kg jaggery = 35c + 60j
Example 2: Perimeter of square with side q = 4q
Example 3: Matchsticks for n L-shaped patterns = 2n
4. Arithmetic Rules Used in Expressions
Expressions can be simplified using arithmetic rules:
Swap: a + b = b + a
Group: (a + b) + c = a + (b + c)
Distributive: a × (b + c) = ab + ac
Brackets can be removed using signs:
-(a + b) = -a – b
5. Simplifying Expressions
Like terms: Same letter-number part → Can be added.
Example: 3x + 5x = 8x
Unlike terms: Cannot be added.
Example: 3x + 4y → Cannot be simplified
6. Perimeter Expressions
Rectangle: If length = l, breadth = b
Perimeter = 2l + 2b
7. Common Mistakes in Simplification
3s – 2 = 15 → If s = 7, correct value: 3×7 – 2 = 21 – 2 = 19
Be careful with brackets and signs while evaluating.
8. Patterns and Formulas
Sequences:
Multiples of 4: 4, 8, 12, 16…
nth term = 4n
Matchstick Pattern (triangles):
Step y = 2y + 1 matchsticks
9. Calendar Patterns
For a 2×2 square: Diagonal sums are always equal → 2a + 8
Helps explain mathematical truths in a simple way.
10. Position Patterns
In saree borders or design patterns:
Design C at positions: 3, 6, 9, 12 → 3n
Design B: One before → 3n – 1
Design A: Two before → 3n – 2
11. Word Problems as Expressions
Train with stops: Time = 3t + 6 if t = time between stations
Flags distributed: Customers = p + q + r if r bought both items
12. Expression Building
“5 more than a number x” → x + 5
“13 less than 2 times a number y” → 2y – 13
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