Learn to Divide
The division is a mathematical operation, of elementary Arithmetic, inverse of the multiplication and can also be considered as a repeated subtraction.
It consists of finding out how many times a number (36) contains to another number (9). Its representation is : 36 : 9 = 4.
The first number (36) is called Dividend, the second (9) Divider and the obtained result (4) is called Quotient.
In order to verify that the division is well done, we multiply the quotient by the divider and it must give the dividend to us: (9 x 4 = 36).
If the division is not exact, that is to say, the dividend does not contain an exact number of times to the divider, the operation will have a remainder, and then it is had to fulfill that: dividend = divider x quotient + remainder
To divide two numbers we placed to the left the dividend and in the same line, leaving a space, the divider within which we call "box of the division.".
Later we will be making successive partial divisions that we will place, gradually, underneath the dividend.
Let's see an example of division by a divider of two digits:
- The first partial division is 256 : 34 (we have taken 256 because 25 is less than 34). Now we divide
25 : 3 = 8, but as when multiplying 8 by 34 it gives us 272, that is greater than 256, we subtract a unit to 8 and we have 7, that is the first digit of the quotient.
We multiply 7 x 34 = 238 and we placed it under the partial dividend, to subtract, 256 - 238 = 18 and this is the first partial remainder.
- To the right of this remainder, we placed "down" the next digit (7) and we make the second partial division 187 : 34.
We divide 18 : 3 = 6, but as when multiplying 6 by 34 it gives us 204,
that is greater than 187, we subtract a unit to 6 and we have 5, the second digit of the quotient. We multiply 5 x 34 = 170 and we placed it under the partial dividend to subtract,
187 - 170 = 17 and this is the second partial remainder.
- To the right of this remainder we placed "down" the next digit (2) and we make the third partial division 172 : 34. We divide 17 : 3 = 5, as when multiplying 5 by 34 it gives us 170,
that is less than 172 then 5 is the third digit of the quotient. We multiply 5 x 34 = 170 and we placed it under the partial dividend to subtract,
172 - 170 = 2 and this is the third partial remainder.
- To the right of this remainder we placed "down" the next digit (9), but we cannot divide 29 between 34 (because it is smaller), then put a "zero to the quotient" (0 the fourth digit of the quotient)
and "down the next digit" (8). Now we can make the fourth partial division 298 : 34. We divide 29 : 3 = 9, but as when multiplying 9 by 34 it gives us 306 that is greater than 298, we subtract a unit to 9 and we have 8,
that is the fifth digit of the quotient. We multiply 8 x 34 = 272 and we placed it under the partial dividend to subtract, 298 - 272 = 26 and as no longer they are more digits of the dividend,
we have finished the division, being 26 the rest of the same, that always must be smaller than the divider.