Topics
Number System(Consolidating the Sense of Numberness)
Number System
Estimation
Ratio and Proportion
Algebra
Numbers in India and International System (With Comparison)
Geometry
Place Value
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
Data Handling
Negative Numbers and Integers
Number Line
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Sets
Ratio
Proportion (Including Word Problems)
Unitary Method
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
Percent (Percentage)
Idea of Speed, Distance and Time
Fundamental Concepts
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
- Introduction
- Solving Equations of Common Forms
- Solving Using Transposition
- Solving Using Multiple Properties
- Real-Life Examples
- Key Points Summary
Introduction
Solving Equations of Common Forms
1. Equation of the form x + a = b
Example:
x + 3 = 10
⇒ x + 3 − 3 = 10 − 3
⇒ x = 7
2. Equation of the form x - a = b
Example:
x − 5 = 2
⇒ x - 5 + 5 = 2 + 5
⇒ x = 7
3. Equation of the form ax = b
Example:
2x = 6
⇒ x = `6/2` = 3
4. Equation of the form `x/a` = b
Example:
`y/2` = 5 ⇒ `y/2` × 2 = 5 × 2
⇒ y = 10
Solving Using Transposition
Transposition means moving a term from one side to another by changing its sign.
| Equation | Step | Answer |
|---|---|---|
| (x + 5 = 32) | (x = 32 – 5) | (x = 27) |
| ( y - 4 = 3 ) | ( y = 3 + 4 ) | ( y = 7 ) |
| ( 3z - 1 = 8 ) | (3z = 8 + 1 = 9), then divide. | (z = 3) |
| (`x/5` + 4 = 2) | (`x/5` = 2 – 4 = –2 ), then ×5 | (x = –10) |
Solving Using Multiple Properties
(i) 3x + 8 = 14
⇒ 3x + 8 − 8 = 14 − 8 [Subtracting 8 from both sides]
⇒ 3x = 6
⇒ `"3x"/3` = `6/3`
⇒ x = 2
(ii) `m/3` + 7 = 11
⇒ `m/3` + 7 − 7 = 11 − 7
⇒ `m/3` = 4
⇒ `m/3` × 3 = 4 × 3
⇒ m = 12
(iii) 2 + `"5x"/3` = x + 6
⇒ 2 + `"5x"/3` − 2 = x + 6 − 2
⇒ `"5x"/3` = x + 4
⇒ `"5x"/3` − x = x + 4 − x
⇒ `"5x"/3` − x = 4
⇒ `"5x"/3` × 3 − x × 3 = 4 × 3
⇒ 5x - 3x = 12
⇒ 2x = 12
⇒ x = 6
Real-Life Examples
Example: Pocket Money
You have some money x. You spend ₹20 and have ₹80 left.
Equation:
⟹x − 20 = 80
⟹ x = 80 + 20 (Transposition Method)
Key Points Summary
Method 1: Balancing
- Rule: Do the same thing to BOTH sides.
- Uses: Addition/Subtraction/Multiplication/Division.
Method 2: Transposition
- Rule: Change the sign (+ becomes -, - becomes +).
Final Step: Simplify to find the value of the variable.
