Class 7 | Ganita Prakash | Chapter 4
๐ค Expressions Using Letter-Numbers
Variables ยท Algebra ยท Simplification ยท Patterns
๐ค 4.1 โ Letter-Numbers (Variables)
What is a Letter-Number (Variable)?
When a number is unknown or can change, we use a letter!
When a number is unknown or can change, we use a letter!
- Perimeter of a square with side s = 4 ร s = 4s
- Cost of n pens at โน5 each = 5 ร n = 5n
- If Arun has x marbles and gets 3 more = x + 3
@edugrown
Important Vocabulary:
| Term | Meaning |
|---|---|
| Variable | Letter representing unknown number |
| Constant | Fixed number (e.g., 5, 100) |
| Coefficient | Number in front of variable (3 in 3x) |
| Expression | Combination of variables and constants |
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ข 4.2 โ Arithmetic Expressions Revisited
Evaluating expressions by substituting values:
If x = 5, then:
3x + 2 = 3(5) + 2 = 15 + 2 = 17
xยฒ โ x = 25 โ 5 = 20
If x = 5, then:
3x + 2 = 3(5) + 2 = 15 + 2 = 17
xยฒ โ x = 25 โ 5 = 20
Rules for Letter-Numbers:
- x + x = 2x (not xยฒ!)
- x ร x = xยฒ (x squared)
- 3x + 5x = 8x (add like terms!)
- 3x + 5y = 3x + 5y (can't combine different letters!)
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ 4.3 โ Algebraic Expressions
Types of Algebraic Expressions:
| Type | Terms | Example |
|---|---|---|
| Monomial | 1 term | 3x, 5yยฒ, 7 |
| Binomial | 2 terms | 3x + 2, a โ b |
| Trinomial | 3 terms | xยฒ + 2x + 1 |
| Polynomial | Many terms | xยณ + 3xยฒ โ 2x + 5 |
๐ฏ Algebra is about PATTERNS!
Number of toothpicks for n triangles = 2n + 1
For 1 triangle: 2(1)+1 = 3 โ
For 5 triangles: 2(5)+1 = 11 โ
ONE FORMULA works for ALL cases! ๐
Number of toothpicks for n triangles = 2n + 1
For 1 triangle: 2(1)+1 = 3 โ
For 5 triangles: 2(5)+1 = 11 โ
ONE FORMULA works for ALL cases! ๐
ใฐ๏ธใฐ๏ธใฐ๏ธ
โ๏ธ 4.4 โ Simplification
@edugrown
Combining Like Terms:
Like terms = terms with same variable and power
5x + 3x = 8x โ (same variable x)
7y โ 2y = 5y โ
3xยฒ + 4x = 3xยฒ + 4x โ (DIFFERENT โ can't combine!)
Steps:
Like terms = terms with same variable and power
5x + 3x = 8x โ (same variable x)
7y โ 2y = 5y โ
3xยฒ + 4x = 3xยฒ + 4x โ (DIFFERENT โ can't combine!)
Steps:
Remove brackets using distributive law
Group like terms together
Add/subtract like terms
Examples:
3(x + 2) + 2x = 3x + 6 + 2x = 5x + 6
4(2x โ 1) โ 3x = 8x โ 4 โ 3x = 5x โ 4
3(x + 2) + 2x = 3x + 6 + 2x = 5x + 6
4(2x โ 1) โ 3x = 8x โ 4 โ 3x = 5x โ 4
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ 4.5 โ Patterns & Relationships
@edugrown
๐ข Amazing Number Patterns!
37 ร 3 = 111
37 ร 6 = 222
37 ร 9 = 333
โ Pattern: 37 ร (3n) = nnn for n = 1 to 9!
37 ร 3 = 111
37 ร 6 = 222
37 ร 9 = 333
โ Pattern: 37 ร (3n) = nnn for n = 1 to 9!
Odd and Even Patterns:
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd
- Even ร anything = Even
- Odd ร Odd = Odd
ใฐ๏ธใฐ๏ธใฐ๏ธ
๐ Quick Cheatsheet
Variable = unknown
e.g. x, y, n
changes value
e.g. x, y, n
changes value
Like terms = same
variable & power
3x + 5x = 8x โ
variable & power
3x + 5x = 8x โ
x+x = 2x โ
xรx = xยฒ โ
xยฒ + x โ 2xยณ โ
xรx = xยฒ โ
xยฒ + x โ 2xยณ โ
Substitute to
evaluate:
x=3 โ 2x=6
evaluate:
x=3 โ 2x=6
๐ Chapter 4 Complete! ๐
Made with โค๏ธ by @edugrown
Made with โค๏ธ by @edugrown