Topics
Number System
Rational Numbers
- Concept of 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
Squares and Square Root
Cubes and Cube Roots
Playing with Numbers
Sets
Ratio and Proportion
Percent and Percentage
Profit, Loss and Discount
Interest
Direct and Inverse Variations
Algebra
Algebraic Expressions
- Algebraic Expressions
- Degree of Polynomial
- Product , Factor and Coefficient
- Like and Unlike Terms
- 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
Factorisation
Linear Equations in One Variable
Linear Inequations
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 Angles of 60°,30°,90° and 45°
- Construction of Bisector of a Line
- Drawing the Perpendicular Bisector of a Line Segment
- Construction of Parallel Lines
- Constructing a Quadrilateral
- Construction of Parallelograms
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Construction of Square
- Concept of Reflection Symmetry
Representing 3-D in 2-D
Mensuration
Area of a Trapezium and a Polygon
Surface Area, Volume and Capacity
Data Handling (Statistics)
Data Handling
Probability
notes
Divisibility by 11:
To check the divisibility of a number by 11, the rule is, find 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) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.
Number |
Sum of the digits (at odd places) from the right |
Sum of the digit (at even places) from the right |
Difference |
308 |
8 + 3 = 11 |
0 |
11 – 0 = 11 |
1331 |
1 + 3 = 4 |
3 + 1 = 4 |
4 – 4 = 0 |
61809 |
9 + 8 + 6 = 23 |
0 + 1 = 1 |
23 – 1 = 22 |
We observe that in each case the difference is either 0 or divisible by 11. All these numbers are also divisible by 11.
For the number 5081, the difference of the digits is (5+ 8) – (1 + 0) = 12which is not divisible by 11. The number 5081 is also not divisible by 11.
More Examples:
Is the number 2547039 divisible by 11?
First, find the difference between the sum of its digits at odd and even places.
(Sum of digits at odd places) - (Sum of digits at even places)
= (9 + 0 + 4 + 2) - (3 + 7 + 5)
= 15 - 15 = 0
The number is 0, so the number 2547039 is divisible by 11.
Is the number 13165648 divisible by 11?
(Sum of digits at odd places) - (Sum of digits at even places)
= (8 + 6 + 6 + 3) - (4 + 5 + 1 + 1)
= 23 - 11 = 12
The number is 12, so the number 13165648 is not divisible by 11.