Page 3 - Lesson Note 6

Any no. ÷ 1 = The same no.
 The product of the divisor and the quotient added to the remainder is always
equal to the dividend known as the division algorithm.
(Divisor × Quotient) + Remainder = Dividend.
(d × q) + r = D
Note: Always find the product first and then add the remainder. (This helps us to
check whether the division is done correct or not.)
Example: Divide 23 by 7

Checking:
(d × q) + r = D
(7 × 3) + 2 = 23
21 + 2 = 23
23 = 23
So, the division is correct.

 In a division sum the remainder is always smaller than the divisor.
Example: In the last example clearly we can see that the remainder (2) is less
than the divisor (7).
 Every divisor fact has two multiplication facts to verify it.
Example: In division, 12 ÷ 6 = 2, two multiplication facts are 2 × 6 = 12 and
6 × 2 = 12.
 The quotient and the divisor are always the factors(exact divisors) of the
dividend, if there is no remainder.
Example:
D d q
18 ÷ 3 = 6
3 × 6 = 18

 The dividend is always a multiple of the quotient and divisor, if there is no
remainder.
Example:
D d q
30 ÷ 5 = 6
5 × 6 = 30