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.
3rd grade math class
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