Topics
Number System
Rational Numbers
- Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers on a Number Line
- Inserting Rational Numbers Between Two Given Rational Numbers
- Method of Finding a Large Number of Rational Numbers Between Two Given Rational Numbers
Exponents
- Concept of Exponents
- Law of Exponents (For Integral Powers)
- Negative Integral Exponents
- More About Exponents
Squares and Square Root
- Concept of Square Roots
- Finding Square Root by Division Method
- Finding Square Root Through Prime Factorisation
- To Find the Square Root of a Number Which is Not a Perfect Square (Using Division Method)
- Properties of Square Numbers
Cubes and Cube Roots
Playing with Numbers
- Arranging the Objects in Rows and Columns
- Generalized Form of Numbers
- Some Interesting Properties
- Letters for Digits (Cryptarithms)
- Divisibility by 10
- Divisibility by 2
- Divisibility by 5
- Divisibility by 3
- Divisibility by 6
- Divisibility by 11
- Divisibility by 4
Sets
- Concept of Sets
- Representation of a Set
- Cardinality of a Set
- Types of Sets
- Subset
- Proper Subset
- Super Set
- Universal Set
- Complement of a Set
- Difference of Two Sets
- Distributive Laws
- Venn Diagrams
Ratio and Proportion
Percent and Percentage
Profit, Loss and Discount
- Overhead Expenses
- To Find S.P., When C.P. and Gain (Or Loss) Percent Are Given
- To Find C.P., When S.P. and Gain (Or Loss) Percent Are Given
- Concept of Discount
Interest
- Calculation of Interest
- Concept of Compound Interest
- To Find the Principle (P); the Rate Percent (R) and the Time
- Interest Compounded Half Yearly
- Applications of Compound Interest Formula
Direct and Inverse Variations
- Types of Variation
- Unitary Method
- Concept of Arrow Method
- Time and Work
Algebra
Algebraic Expressions
- Algebraic Expressions
- Degree of Polynomial
- Factors and Common Factors
- Classification of Terms in Algebra
- Combining like Terms
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Polynomial
- Multiplying a Polynomial by a Polynomial
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Simplification of Expressions
Identities
- Algebraic Identities
- Product of Sum and Difference of Two Terms
- Expansion Form of Numbers
- Important Formula of Expansion
- Cubes of Binomials
- Application of Formulae
Factorisation
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Grouping
- Factorisation by Difference of Two Squares
- Factorisation of Trinomials
- Factorising a Perfect Square Trinomial
- Factorising Completely
Linear Equations in One Variable
Linear Inequations
- Pair of Linear Equations in Two Variables
- Replacement Set and Solution Set
- Operation of Whole Numbers on Number Line
- Concept of Properties
Geometry
Understanding Shapes
Special Types of Quadrilaterals
Constructions
- Introduction of Constructions
- Construction of an Angle
- To Construct an Angle Equal to Given Angle
- To Draw the Bisector of a Given Angle
- Construction of an Angle Bisector: 30°, 45°, 60°, 90°
- Construction of Bisector of a Line
- The Perpendicular Bisector
- Construction of Parallel Lines
- Constructing a Quadrilateral
- Construction of Parallelograms
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Square: Properties and Construction
- Reflection Symmetry (Mirror Symmetry)
Representing 3-D in 2-D
- 2dimensional Perspective of 3dimensional Objects
- Concept of Polyhedron
- Faces, Edges and Vertices of Polyhedron
- Euler's Formula
- Concept of Polyhedron
- Nets of 3D Figures
Mensuration
Area of a Trapezium and a Polygon
Surface Area, Volume and Capacity
Data Handling (Statistics)
Data Handling
- Mathematical Data Collection and Organisation
- Frequency
- Raw Data, Arrayed Data and Frequency Distribution
- Cumulative Frequency and Cumulative Frequency Table
- Frequency Distribution Table
- Class Intervals and Class Limits
- Frequency Distribution and Its Applications
Probability
- Rule
- Step-by-Step Explanation
- Examples
- Real-Life Application
- Key Points Summary
CISCE: Class 6
Rule
A number is divisible by 11 if the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) is either 0 or a multiple of 11.
CISCE: Class 6
Step-by-Step Explanation
CISCE: Class 6
Example
1.90816
- Odd places (from right): 6 + 8 + 9 = 23
- Even places: 1 + 0 = 1
- Difference = 23 − 1 = 22
22 ÷ 11 = 2
90816 is divisible by 11.
2. 1,27,446
- Odd places: 6 + 4 + 2 = 12
- Even places: 4 + 7 + 1 = 12
- Difference = 12 − 12 = 0
1,27,446 is divisible by 11.
CISCE: Class 6
Real-Life Applications
Suppose your school bus ticket number is 41273.
- Odd places: 3 (1st) + 2 (3rd) + 4 (5th) = 9
- Even places: 7 (2nd) + 1 (4th) = 8
- Difference: 9 – 8 = 1
- Is 1 a multiple of 11? No
- So, 41273 is not divisible by 11.
CISCE: Class 6
Key Points Summary
- Always start counting digit places from the right.
- Odd and even places matter!
- Subtract sums. Ignore minus signs.
- If the result is 0 or a multiple of 11, it works!
Test Yourself
Shaalaa.com | To Check Whether Any Number Is Divisible By 11 Or Not.
to track your progress
Series: Divisibility by 11
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