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example 6. 341 ÷ 9 = ? example 8. 63 ÷ 9 = ?

Solution. Solution. Quotient = 6 + 1 = 7
Remainder = 6 + 3 – 9 = 0
9 ) 341 (
Case 2: When a three-digit number is
Dividend = 341
divisible by 9
Quotient = 3 | (3 + 4) = 37
Remainder = 3 + 4 + 1 = 8 H T O
All the above examples are true as long a b c
as the sum of the digits is less than 9. Quotient = a | a + b + 1, where a is in

Now let us take the case of division by 9, the tens place, a + b + 1 is in the ones
when the sum of the digits in the dividend place.
Remainder = a + b + c – 9
is greater than or equal to 9.
The two cases for two- and three-digit example 9. Divide 225 by 9
dividends are illustrated below. Solution. Since 2 + 2 + 5 = 9 is divisible
by 9 .
Let us take some examples to make it Quotient = 2 tens and 2 + 2 + 1 = 5 ones = 25
clear.
Remainder = 2 + 2 + 5 – 9 = 0
Case 1: When a two-digit number is example 10. 459 ÷ 9 = ?
divisible by 9 Solution.

T O Quotient = 4 tens and 4 + 5 + 1 = 10 ones or
a b 1 ten = 50
Remainder = 4 + 5 + 9 – 9 = 9
Quotient = a + 1, Remainder = a + b – 9 Since the remainder = 9, we need to

subtract 9 again and 1 will in due course
example 7. 45 ÷ 9 = ? be added to the quotient
Solution. Quotient = 4 + 1 = 5 Quotient = 50 + 1 = 51

Remainder = 4 + 5 – 9 = 0 Remainder = 9 – 9 = 0

78 Mathematics 4