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:

18 3 |
÷ × |
3 6 |
= = |
6 18 |

**7.** The dividend is always a multiple of the quotient and
divisor, if there is no remainder.

Example:

30 5 6 |
÷ × × |
5 6 5 |
= = = |
6 30 30 |

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