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:

 D183 ÷× d36 == q618

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

Example:

 D3056 ÷×× d565 === q63030

Let us have a quick review of what we have learnt about division. Division is splitting into equal parts or groups. It is the result of “fair sharing”.

If 5 friends want to share 15 chocolates. How many chocolates will each of them get? Let us divide the chocolates equally amongst them.

15 divided by 5 is 3. They get 3 each.

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