मराठी

Methods of Solving Linear Equations

Topics

Number System
Number System(Consolidating the Sense of Numberness)
- Comparing Numbers
- To Form The Smallest and The Greatest Numbers Using Given Digits
- Operations on Larger Numbers
Number System (Including Estimation and Approximation)
Theme 1 : Numbers
Estimation
- Basic Concept of Estimation and Approximation of Numbers
- Rounding off a Number
- Estimation in Basic Operations
Numbers in Indian and International Systems (With Comparison)
Theme 2 : Ratio, Proportion and Arithmetic Problems
Ratio and Proportion
Numbers in India and International System (With Comparison)
- Concept of Unit, Number, Numeral and Numeration
- Hindu-Arabic (Indian) System of Numeration
- International System of Numeration
- Indian vs. International Place Value System
Theme 3 : Algebra
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Algebra
Negative Numbers and Integers
Place Value
- Concept of Place Value
- Largest and Smallest Numbers
Theme 4 : Geometry
Geometry
Theme 5 : Mensuration
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
- Natural Numbers
- Whole Numbers
- Successor and Predecessor of Whole Number
- Properties of Whole Numbers
- Mathematical Patterns
- Patterns in Whole/Natural Numbers
- Magic Square
- Matchstick Pattern
Sets
Data Handling
Negative Numbers and Integers
- Concept of Negative Numbers
- Integers
- Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Integers
Theme 6 : Statistics
Fractions
Number Line
- Number Line
- Representation of Natural numbers, Whole Numbers and Integers On Number Line
- Comparing Numbers
- Addition and Subtraction on a Number Line
Decimal Fractions
Playing with Numbers (Including H.C.F. and L.C.M.)
HCF and LCM
- Factors and Common Factors
- Prime and Composite Numbers
- Eratosthenes’ Method of Finding Prime Numbers
- Prime Factorisation
- Highest Common Factor (HCF)
- Methods of Finding HCF
- Multiples and Common Multiples
- Lowest Common Multiple
- Methods of Finding LCM
Ratio and Proportion (Including Unitary Method)
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
Percent (Percentage)
Sets
- Concept of Sets
- Representation of a Set
- Types of Sets
- Cardinality of a Set
Idea of Speed, Distance and Time
Ratio
- Quantitative Comparison Using Basic Operations
- Ratio
- Simplifying Ratios
- Problems based on Ratio
- All About Ratios: Dividing, Comparing, and Modifying Quantities
Proportion (Including Word Problems)
- Proportion
- Concept of Continued Proportion
Fundamental Concepts (With operations on Algebraic Expressions)
Framing Algebraic Expressions (Including Substitution and Linear Equations)
Unitary Method
- Unitary Method
- Types of Variation
Fundamental Concepts (Including Angles and their Properties)
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
Triangles (Including Types and Properties of Triangles)
Decimal Fractions
- The Decimal Number System
- Like and Unlike Decimal Numbers
- Conversion between Decimal Fraction and Common Fraction
- Addition of Decimal Fraction
- Subtraction of Decimal Numbers
- Multiplication of Decimal Numbers
- Division of Decimal Numbers
- Application of Decimals in Real Life
- Word Problems based on Decimals
Percent (Percentage)
- Basic Concept of Percentage
- Conversion between Percentage and Fraction or Decimal
- Expressing Quantities as Percentages
- Increase or Decrease in Percent
- Percentage Problems Related to Environment
Quadrilaterals
Circles
Idea of Speed, Distance and Time
- Speed, Distance and Time
- Uniform Speed, Variable Speed, and Conversions
Constructions
Symmetry
Fundamental Concepts
- Introduction to Algebra
- Constants and Variables in Mathematics
- Classification of Terms in Algebra
- Algebraic Expressions
- Factors and Common Factors
- Powers and Exponents
- Basic Concept of Polynomial and its Degree
Fundamental Operations (Related to Algebraic Expressions)
- Addition of Like and Unlike Terms
- Subtraction of Like and Unlike Terms
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Algebraic Expressions
- Division of Algebraic Expressions
Recognition of Solids
Substitution (Including Use of Brackets as Grouping Symbols)
- Basic Concept of Substitution
- Brackets in Mathematics
Framing Algebraic Expressions (Including Evaluation)
- Algebraic Expressions
- Evaluation of Algebraic Expressions
Perimeter and Area of Plane Figures
Simple (Linear) Equations (Including Word Problems)
- Concept of Linear Equations
- Rules for Solving a Linear Equation
- Methods of Solving Linear Equations
- Word Problems on Linear Equations
Data Handling (Including Mean and Median)
Fundamental Concepts
- Fundamentals of Geometrical Concepts
- Concept of Points
- Concept of Lines
- Rays
- Line Segments
- Mathematical Concept of Surface
- Planes
- Parallel Lines
- Intersecting Lines
- Concept for Open and Closed Figures
- Plane Closed Figures
- The Perpendicular
- The Perpendicular Bisector
Angles (With Their Types)
- Concept of Angle
- Angle and Its Formation
- Measuring Angles
- Types of Angles
- Concept of Pairs of Angles
- The Sum of the Angles Around a Point is Always 360°
Properties of Angles and Lines (Including Parallel Lines)
- Properties of Adjacent and Vertically Opposite Angles
- Parallel Lines
- Concept of Transversal Lines
- Construction of an Angle
- Drawing a Perpendicular to a Line
Triangles (Including Types, Properties and Constructions)
- Basic Concepts of Triangles
- Exterior Angle of a Triangle and Its Property
- Classification of Triangles based on Angles
- Classification of Triangles based on Sides
- Altitudes of a Triangle
- Median of a Triangle
- Construction of Triangles
Quadrilateral
- Quadrilaterals
- Angle sum Property of Quadrilateral
- Types of Quadrilaterals
Polygons
- Basic Concept of Polygons
- Sum of Interior Angles of a Polygon
- Sum of Exterior Angles of a Polygon
- Basic Concept of Regular Polygon
The Circle
- Basic Concept of Circle
- Secant and Tangent
- Arc of the Circle
- Sector of a Circle
- Segment of a Circle
- The Interior and the Exterior of a Circle
- Circumcircle of a Triangle
- Incircle of a Triangle
Symmetry (Including Constructions on Symmetry)
- Concept of Symmetry
- Reflection Symmetry in 2-D Shapes
- Construction of Symmetric Points and Lines
Recognition of Solids
- Identification of 3-d Shapes
- Faces, Edges and Vertices of Polyhedron
- Nets of 3D Figures
- Oblique Sketches of 3D Shapes
Perimeter and Area of Plane Figures
- Basic Concepts in Mensuration
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of an Equilateral Triangle
- Problems based on Perimeter
- Shapes with the Same Perimeter
- Concept of Area
- Area of Rectangle
- Area of Square
- Problems based on Area
Data Handling (Including Pictograph and Bar Graph)
- Mathematical Data Collection and Organisation
- Frequency Distribution and Its Applications
- Pictographs
- Bar Graphs
Mean and Median
- Concept of Mean (Average)
- Basic Concept of Median

Introduction
Solving Equations of Common Forms
Solving Using Transposition
Solving Using Multiple Properties
Real-Life Examples
Key Points Summary

CISCE: Class 6

Introduction

An equation is like a perfect balance. It has two sides (the Left Hand Side and the Right Hand Side) separated by an equals sign (=).

Solving a linear equation means finding the value of the unknown number that makes the equation true.

We are going to learn two helpful methods to find that missing numbe!

CISCE: Class 6

Solving Equations of Common Forms

1. Equation of the form

Example:
x + 3 = 10
⇒ x + 3 − 3 = 10 − 3
⇒ x = 7

2. Equation of the form

Example:
x − 5 = 2
⇒ x - 5 + 5 = 2 + 5
⇒ x = 7

3. Equation of the form

Example:

4. Equation of the form

Example:
`y/2` = 5 ⇒ `y/2` × 2 = 5 × 2
⇒ y = 10

CISCE: Class 6

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)

CISCE: Class 6

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

CISCE: Class 6

Real-Life Examples

Example: Pocket Money

You have some money $x$ . You spend ₹20 and have ₹80 left.
Equation:

$⟹ x = 100$

CISCE: Class 6

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.

Test Yourself

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Methods of Solving Linear Equations

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Topics

Number System

Number System(Consolidating the Sense of Numberness)

Number System (Including Estimation and Approximation)

Theme 1 : Numbers

Estimation

Numbers in Indian and International Systems (With Comparison)

Theme 2 : Ratio, Proportion and Arithmetic Problems

Ratio and Proportion

Numbers in India and International System (With Comparison)

Theme 3 : Algebra

Natural Numbers and Whole Numbers (Including Number Line and Patterns)

Algebra

Negative Numbers and Integers

Place Value

Theme 4 : Geometry

Geometry

Theme 5 : Mensuration

Mensuration

Natural Numbers and Whole Numbers (Including Patterns)

Sets

Data Handling

Negative Numbers and Integers

Theme 6 : Statistics

Fractions

Number Line

Decimal Fractions

Playing with Numbers (Including H.C.F. and L.C.M.)

HCF and LCM

Ratio and Proportion (Including Unitary Method)

Playing with Numbers

Percent (Percentage)

Sets

Idea of Speed, Distance and Time

Ratio

Proportion (Including Word Problems)

Fundamental Concepts (With operations on Algebraic Expressions)

Framing Algebraic Expressions (Including Substitution and Linear Equations)

Unitary Method

Fundamental Concepts (Including Angles and their Properties)

Fractions

Triangles (Including Types and Properties of Triangles)

Decimal Fractions

Percent (Percentage)

Quadrilaterals

Circles

Idea of Speed, Distance and Time

Constructions

Symmetry

Fundamental Concepts

Fundamental Operations (Related to Algebraic Expressions)

Recognition of Solids

Substitution (Including Use of Brackets as Grouping Symbols)

Framing Algebraic Expressions (Including Evaluation)

Perimeter and Area of Plane Figures

Simple (Linear) Equations (Including Word Problems)

Data Handling (Including Mean and Median)

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

Test Yourself

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