RBSE Class 8 Maths Notes Chapter 16 Playing with Numbers

These comprehensive RBSE Class 8 Maths Notes Chapter 16 Playing with Numbers will give a brief overview of all the concepts.

RBSE Class 8 Maths Chapter 16 Notes Playing with Numbers

→ Numbers in General Form:

• 2-digit Number, ab = 10 × a + b = 10a + b
  ba = 10 × b + a = 10b + a
• 3-digit Number, abc = 100 × a + 10 × b + c = 100a +10b + c
  bca = 100b + 10c + a
  cab = 100c + 10a + b

2. The sum of two digit number and its reversing number is always a multiple of 11.
(10a + b) + (10b + a) = 11a + 11b = 11(a + b)

→ The difference of a two-digit number and its reversing no. is always a multiple of 9.
If a > b, then (10a + b) - (10b + a)
= 10a + b - 10b - a = 9a - 9b
= 9 (a - b)

• If b > a, then (10b + a) - (10a + b) = 9(b - a)
• If a = b, then (10a + b) - (10b - a) = 0

Thus, the quotient is divisible by 9 and remainder is zero.

→ Subtraction of 3-digit number from its reversed number is a multiple of 99.

• If a > c, then (100a + 10b + c) - (100c + 10b + a) = 99(a - c)
• If c > a, then (100c + 10b + a) - (100a + 10b + c) = 99(c - a)
• If a = c, the difference is zero.

→ (abc + bca + cab) is divisible by 37 with no Remainder.
Here a, b and c are digits of the number.

→ Divisibility rule:

• For 2: One’s digit is 0, 2, 4, 6 or 8 i.e., (even number)
• For 3: Sum of its digits is divisible by 3.
• For 9: Sum of its digits is divisible by 9.
• For 5: One’s digit must be 0 or 5.
• For 10: One’s digit must be 0.
• For 4: The number formed by last two digits is divisible by 4.
• For 6: If the number is divisible by both 2 and 3.
• For 9: If the sum of the number’s digit is divisible by 9.
• For 11: If the difference of the sum of digits in odd places and the sum of digits in even places is either 0 or a multiple of 11.