Topics
Rational Numbers
- Rational Numbers
- Closure Property of Rational Numbers
- Commutative Property of Rational Numbers
- Associative Property of Rational Numbers
- Distributive Property of Multiplication Over Addition for Rational Numbers
- Identity of Addition and Multiplication of Rational Numbers
- Negative Or Additive Inverse of Rational Numbers
- Concept of Reciprocals or Multiplicative Inverses
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
- Multiples and Common Multiples
Linear Equations in One Variable
- Constants and Variables in Mathematics
- Equation in Mathematics
- Expressions with Variables
- Word Problems on Linear Equations
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Solving Equations Having the Variable on Both Sides
- Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
- Reducing Equations to Simpler Form
- Equations Reducible to Linear Equations
Understanding Quadrilaterals
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Basic Concept of Polygons
- Classification of Polygons
- Properties of Quadrilateral
- Sum of Interior Angles of a Polygon
- Sum of Exterior Angles of a Polygon
- Quadrilaterals
- Properties of Trapezium
- Properties of Kite
- Properties of a Parallelogram
- Properties of Rhombus
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The adjacent angles in a parallelogram are supplementary.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Properties of Rectangle
- Properties of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.
Data Handling
Practical Geometry
- Geometric Tool
- Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
- Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
- Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
- Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
- Some Special Cases
Squares and Square Roots
- Concept of Square Number
- Properties of Square Numbers
- Some More Interesting Patterns of Square Number
- Finding the Square of a Number
- Concept of Square Roots
- Finding Square Root Through Repeated Subtraction
- Finding Square Root Through Prime Factorisation
- Finding Square Root by Division Method
- Square Root of Decimal Numbers
- Estimating Square Root
Cubes and Cube Roots
Comparing Quantities
- Ratio
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Basic Concepts of Profit and Loss
- Calculation of Interest
- Concept of Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula
Algebraic Expressions and Identities
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Classification of Terms in Algebra
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Monomial by a Trinomial
- Multiplying a Binomial by a Binomial
- Multiplying a Binomial by a Trinomial
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b) = a2-b2
- Expansion of (x + a)(x + b)
Mensuration
Exponents and Powers
Visualizing Solid Shapes
Direct and Inverse Proportions
Factorization
- Factors and Common Factors
- Factorising Algebraic Expressions
- Factorisation by Taking Out Common Factors
- Factorisation by Regrouping Terms
- Factorisation Using Identities
- Factors of the Form (x + a)(x + b)
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Concept of Find the Error
Introduction to Graphs
Playing with Numbers
- Rule
- Step-by-Step Explanation
- Examples
- Real-Life Application
- Key Points Summary
CISCE: Class 6
Rule
A number is divisible by 9 if the sum of all its digits is also divisible by 9.
Maharashtra State Board: Class 6
Step-by-Step Explanation
CISCE: Class 6
Example
Checking Divisibility by 9 Using the Sum of Digits:
| Number | Divide the number by 9. Is it completely divisible? |
Sum of the digits in the number |
Is the sum divisible by |
| 1980 | ✔ | 1 + 9 + 8 + 0 = 18 | ✔ |
| 2999 | X | 29 | X |
| 5004 | ✔ | 9 | ✔ |
| 13389 | X | 24 | X |
| 7578 | ✔ | 27 | ✔ |
| 69993 | ✔ | 36 | ✔ |
CISCE: Class 6
Real-Life Application
Suppose you are shopping and your bill shows ₹1,818. You want to check if this amount is likely to be divided equally among 9 friends.
Simply add 1+8+1+8 = 18.
Since 18 is a multiple of 9, 1,818 is divisible by 9!
CISCE: Class 6
Key Points Summary
- Add all the digits of the number.
- If their sum is a multiple of 9 (like 9, 18, 27…), then the number is divisible by 9.
- If not, the number isn’t divisible by 9.
Example Question 1
Check the divisibility of 21436587 by 9.
The sum of the digits of 21436587 is 2 + 1 + 4 + 3 + 6 + 5 + 8 + 7 = 36.
This number is divisible by 9 (for 36 ÷ 9 = 4).
We conclude that 21436587 is divisible by 9.
Example Question 2
Check the divisibility of 152875 by 9.
The sum of the digits of 152875 is 1 + 5 + 2 + 8 + 7 + 5 = 28.
This number is not divisible by 9.
We conclude that 152875 is not divisible by 9.
Example Question 3
If the three-digit number 24x is divisible by 9, what is the value of x?
Since 24x is divisible by 9, sum of its digits, i.e., 2 + 4 + x should be divisible by 9, i.e., 6 + x should be divisible by 9.
This is possible when 6 + x = 9 or 18, ....
But, since x is a digit, therefore, 6 + x = 9, i.e., x = 3.
Test Yourself
Shaalaa.com | To Check Whether Any Number Is Divisible By 9 Or Not.
to track your progress
