NCERT / CBSE NOTES : Chapter Summary


Playing with Numbers

General Form of Numbers

Various types of numbers such as Natural numbers, Whole numbers, Integers, Rational numbers and the various properties such as closure, associative, commutative and distributive.

2-digit number
The number in the general form can be written as for example 26 = 2 x 10 + 6. General Form of a 2-digit Number 10 × a + 1 × b
  1. The sum of a 2-digit number and the number obtained by interchanging its digits is always divisible by 11.
  2. The difference between a 2-digit number and the number obtained by interchanging its digits is always divisible by 9.


Assume ab is a 2-digit number.
   •  a is the tens digit
   •  b is the ones digit

ab = 10 × a + 1 × b.

3-digit number
General form of a 3-digit number is 100 × a + 10 × b + 1 × c.

  1. The difference between a 3-digit number and a number obtained by reversing its digits is always divisible by 99.


Assume abc is a 3-digit number, where:
     •  a is the hundreds digit
     •  b is the tens digit
     •  c is the ones digit

abc = 100 × a + 10 × b + 1 × c

Letters for digits
Assume that each letter in a puzzle stands for just one digit and each digit is represented by a one letter, so it is like cracking a code. Here problems of addition and multiplication to solving puzzles.
Get to know about Playing with Numbers (Ncert / Cbse Solutions & Revision Notes), Chapter Summary, CBSE / NCERT Revision Notes, CBSE NCERT Class VIII (8th) | Mathematics, CBSE NCERT Solved Question Answer, CBSE NCERT Solution.
For example, eighty one will be written as 81 not as 081 or 0081.

Tests of Divisibility

The tests of divisibility with 10, 5, 2, 3, 6, 4, 8, 9 and 11. In this, learn why the numbers are divisible by 10, 5, 2, 3, 6, 4, 8, 9 and 11.
A number is said to be divisible by another number, when the remainder is zero.

     •  A number is divisible by 10, if its ones digit is 0.

     •  A number is divisible by 5, if its ones digit is 0 or 5.

     •  A number is divisible by 2, if its ones digit is 0, 2, 4, 6 or 8.

     •  If a number is divisible by 10, then the number is also divisible by 2 and 5.

     •  A number is divisible by 9, if the sum of its digits is divisible by 9.

     •  A number is divisible by 3, if the sum of its digits is divisible by 3.

     •  If a number is divisible by 9, then the number is also divisible by 3.

     •  If a number is divisible by 3, then it may not necessarily be divisible by 9.

     •  If a number is divisible by 6, then the number is divisible by 2 as well as 3.

     •  If a number is divisible by 11, then the difference of its digits in odd places and the sum of its digits in    
        even places is either 0 or a multiple of 11.

 •  If a number is divisible by 4, then the number formed by its digits in units and tens places is divisible by 4.

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