As done earlier for multiplication we should have ways to manage multiplication and subtraction on a single digit of the dividend at a time. Then only we can overcome writing of many smaller steps which could be managed at the mental level.
To achieve this let us go through a simple division; viz. 389 ÷ 12 =?
The normal way we solve the example is shown here. Now we can think each step critically and decide which way it is possible to minimize writing by retaining part of the operations in our mind. In the present example, since the first left- hand digit of the dividend (3) was not divisible by 12 we had to take the next digit in the dividend and use it along with the first digit (3). Thus, we had 38 to divide by 12. We then went to find out which multiple of 12 can be subtracted from 38 leaving a remainder of less than 12.
Let us see if this simple step can be further broken up into smaller steps.
We will focus only on the first left-hand digit of the dividend (389), i.e. 3. Similarly we will take only the first left-hand digit of the divisor (12), i.e. 1. This is shown here:
In order to find out the first left-hand digit of the quotient (or answer), we simply solve 3 ÷ 1 =? We have the answer 3. We note it down the answer. In our mind we find out '3 times 12', which equals 36. Therefore, we subtract 3 from 3, getting 0. We ignore this 0, as it indicates no value.
Since we have to deal with the 6 from 36, which is '3 times 12' we go to the next digit in the dividend. This digit is 8. Therefore, we subtract 6 from 8. The remainder we have now is 2, which we consider in the further part of the division. Here, we complete partial division related to single digit of the quotient. It means, we will be repeating the steps discussed in the earlier paragraph and this paragraph for each next digit of the quotient (or answer) till all the digits in the dividend are considered.
In order to find out the second left-hand digit of the quotient (which is the answer), we simply solve 2 ÷ 1 =? Since, the 2 we are using is the one obtained in the earlier step and is not part of the dividend, it is shown in color.
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