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For division of bigger numbers with 2 and 3 digit numbers, the essential procedure is same. For division where the divisor has more than 1 digit, the process of division becomes simpler if the multiplication table for the divisor is written down in advance. Chapter 12.16 gives a quick procedure for this with an example.
The following chapters 12.13, 12.14 & 12.15 give detailed work-outs and explanations of various levels of division, starting with 1d by 1d going up to long division.
Confusion caused by language in long division or larger numbers
In this way of thinking about the division process, for dividends greater than ten thousand, the day-to-day language used in naming the rupee notes creates confusion. Consider an amount of Rs 56,478. There is no confusion till we proceed to from 8 (1 rupees) to 6 which mean 6 Thousand Rupee notes. But 5 is not called as 5 Ten Thousands but seen as part of 56 thousand.
In the process outlined above, we need to think of 56 thousand as 5 Ten Thousands & 6 One Thousand. The sharing will start from the Ten thousand-rupee notes and then progressively proceed to the lower denominations.
Zeros in the quotient
The issue of whether or not a 0 needs to be inserted in the quotient, is always a confusing issue in the division process. The method described above clears the confusion. At any point in the algorithm, we are clear about the denomination of the notes that we are planning to share.
If in any point in the algorithm, if there are not enough rupee notes of a particular denomination to be shared, then it means that 0 quantity of those rupee notes (of a particular denomination) would be present in the quotient.
If the number of ten thousand-rupee notes are not sufficient to be distributed one each, then each share does not have any ten thousand rupee note and hence we have to imagine a 0 in the ten thousand’s place. This is also done with the other denominations.
Direction of Division
There is a doubt in the minds of many students as to why division starts with the highest denomination (from left) whereas multiplication starts from the lowest denomination (from right).
As we have seen from the above process, sharing any higher denomination can generate smaller denominations when the remainder is converted to the lower denomination. If we share the rupees in a lower denomination and proceed to the next higher denomination (to the left), that can once again create lower denominations causing confusion. Hence it makes more sense to start from the right.
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