We have already learned division by repeated subtraction, equal division / distribution, and by the short division method. Now we are going to read some facts about division to learn long division.

1. If the dividend is ‘zero’, then every number as a divisor gives the quotient as ‘zero’.

Example: If “zero” sweets are to be distributed to 8 children, of course nobody gets sweets.

2. If the divisor is ‘1’, each dividend has the quotient equal to itself.

Example: There are 15 candies; each child receives 1 candy. How many children will the candy be given?

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, then add the rest. (This helps us to check whether the split is correct or not.)

Example: Divide 23 by 7

Verification:

(d × q) + r = D

(7 × 3) + 2 = 23

21 + 2 = 23

23 = 23

So the division is correct.

4th With a division sum, the remainder is always smaller than the divisor.

Example:

In the last example we can clearly see that the remainder (2) is smaller than the divisor (7).

5. Each dividing factor has two multiplication factors to verify it.

Example:

When dividing 12 ÷ 6 = 2, there are two multiplication factors 2 × 6 = 12 and 6 × 2 = 12.

6th The quotient and divisor are always the factors of the dividend when there is no remainder.

Example:

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

Example:

 D. 30th 5 6th ÷ × × d 5 6th 5 = = = q 6th 30th 30th

Let’s have a quick look back at what we’ve learned about the division. Division is the division into equal parts or groups. It is the result of “fair sharing”.

When 5 friends want to share 15 chocolates. How many chocolates do each of them get? Let’s divide the chocolates evenly among them.

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

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