On this page, you will find Playing with Numbers Class 8 Notes Maths Chapter 16 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 16 Playing with Numbers will seemingly help them to revise the important concepts in less time.
CBSE Class 8 Maths Chapter 16 Notes Playing with Numbers
Playing with Numbers Class 8 Notes Conceptual Facts
1. Generalised form of a two-digit number if a is ten place digit and 6 is unit place digit.
a x 10 + b x 1 = 10a + b
2. Generalised form of a three-digit number if a is ten place digit and b is unit place digit.
a x 100 + b x 10 + c x 1 = 100a + 10b+ c
3. Two-digit original numbers = 10a + b
Number obtained by reversing the digits = 10b + a
Sum = 10a + b + 10b + a
= 11a + 11b – 11(a + b)
which is divisible by 11.
Difference = (10a + b) – (10b + a)
= 10a + 6 – 106 – a
= 9a -9b – 9(a – b)
which is divisible by 9.
4. Three-digit original number if a is hundred place digit and 6 is ten place digit and c is unit place digit.
= 100a + 10b + c
The number obtained by reversing the digits = 100c + 10b + a
Difference = (100a + 10b + c) – (100c + 10b + a)
= 100a + 10b + c – 100c – 10b – a
= 99a – 99c = 99(a – c)
which is divisible by 99.
5. Divisibility test by 2 – A number is divisible by 2 if its unit place is even.
For example: 24, 48, 56 and 76 etc.
6. Divisibility test by 3 – A number is divisible by 3 if the sum of all digits of the given number is also divisible by 3.
For example: 123 = 1 + 2 + 3 = 6÷3 = 2
528 = 5 + 2 + 8 = 15 ÷ 3 = 5
7. Divisibility test by 5 – If the unit place digit is either 0 or 5 then it is divisible by 5.
8. Divisibility test by 9 – A number is divisible by 9 if the sum of its digits is also divisible by 9.
For example:
225 =2+2+5=9÷ 9=1
684 = 6 + 8 + 4 = 18 ÷ 9 = 2
9. Letters for digits – There are two rules followed while doing such puzzles.
- The first digit cannot be zero.
- Each letter in the puzzle must stand for just one digit.