We have already learned division by repeated subtraction, equal sharing/distribution and by short division method. Now, we will read some facts about division to learn long division.
1. If the dividend is ‘zero’ then any number as a divisor will give the quotient as ‘zero’.
Example: If ‘zero’ sweets are to be distributed among 8 children, naturally no one will get any sweets.
2. If the divisor is ‘1’ then any dividend will have the quotient equal to itself.
Example: There are 15 sweets; each child is to get 1 sweet. How many children get the sweets?
3. The product of the divisor and the quotient added to the remainder is always equal to the dividend.
(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.
4. 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).
5. 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.
6. The quotient and the divisor are always the factors of the dividend, if there is no remainder.
Example:
D 18 3 
÷ × 
d 3 6 
= = 
q 6 18 
7. The dividend is always a multiple of the quotient and divisor, if there is no remainder.
Example:
D 30 5 6 
÷ × × 
d 5 6 5 
= = = 
q 6 30 30 
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