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Let us now look at the procedure for Division.
Difficulty with Division
The division algorithm is considered a difficult one. This is because it appears like a series of steps with no logic. Hence, chances of going wrong in many "subtle" situations are very large. For example, where and when to insert a "0" in the quotient is something which can make many stumble.
One of the reasons is the procedure based on the idea of "repeated subtraction". This is actually a procedure and not a concept which can be related to a real-life situation. A procedure without a coherent story underpinning it is difficult to remember.
But the concept of "equal sharing" provides us with a coherent story which can make the division operation easy to remember and execute.
Division as "Equal Sharing"
The number to be divided (Dividend) is imagined as a sum of rupees to be divided into a fixed number (Divisor) of equal shares. In addition, the dividend is to be imagined as made only of rupee notes of dominations One, Ten, Hundred, Thousand, Ten Thousand only. Other denominations like two and five are not to be used. This is to mirror the place value system accurately.
The Quotient, which is normally the required answer, is the resulting magnitude of each share. The amount which is left over, as not shareable equally, is the Remainder. The Remainder will always be less than the Divisor. This implies that the Remainder is not even sufficient to be distributed in terms One Rupee each to each share.
Division Process (story) in Brief
In the above example, think of Rs 43 as being made of 4 ten-rupee notes and 3 one-rupee notes. We start from the highest denomination, here ten-rupee notes, and start sharing the amount equally.
We see that there are 4 ten-rupee notes, which, since there are only 3 sharers, can be shared 1(ten rupee note) each. (This is arrived at by reciting the multiplication table for the divisor 3). Hence in the quotient we write 1 in the ten's place, implying that each share gets one ten rupee note.
The remaining 1 ten-rupee note is not sufficient to be shared among 3. Hence, the 1 ten-rupee is converted to 10 one-rupee notes. With the already existing 3 one-rupee notes, we now have a total of 13 one-rupee notes. (This aspect of converting one ten-rupee note into ten one-rupee notes does not become explicit in the division process, where the remainder in the ten's place is 1 and becomes 13 when 3 is brought down)
If the 13 one-rupee notes are shared, each of the 3 shares will get 4 one-rupee notes. ((This is again arrived at by reciting the multiplication table for the divisor 3, until 3 X 4 =12 is reached). When 12 rupees are distributed out of 13, only one 1 rupee will remain undistributed.
So, each share gets Rs14 and Rs 1 is left over. I.e the Quotient is 14 and Remainder 1.
Interpreting the Remainder
Students may get confused with the idea of a remainder. The remainder in a division problem needs to be interpreted appropriately through many simple real life situations within their experience.
In some life situations, the remainder has to be left as it is. In some others, mathematically, they can be shared further.
If children are sharing some books among themselves, the remainder has to be left as it is. On the contrary if they are sharing some fruits, there is a possibility that the remaining fruit can also be shared. This can be done mathematically if the students understand fractions.
In such cases the decision depends on what the problem expects as the answer.
Hence it is important to comprehend the problem both in terms of the given data but also in terms of what is expected.
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