Complex divisions (III)

The greatest difficulty for children in long division is to approximate the correct quotient digit in a reasonable time. Through oral or written practice in solving problems suggested in the previous article children reduce the time required to find the correct quotient.

In the case of divisors larger than thirty it is better to guide children to make a multiplication table for that divisor.

For example, if the divisor is 34 the child makes a table as below:

Suppose, an exercise such as 73 ÷ 34 has to be worked, a glance at the table shows that the number 73 lies between 2 and 3. In fact, 73 is twice 34 and 5 over. Thus, the quotient will be 3.

If we want children to master the division operation, we should plan practice taking into consideration the types of mistakes children generally make.

Almost a quarter of the children’s mistakes are connected with remainders at various stages of the process. Many times children fail to ‘bring down’ a figure/digit in the dividend in order to complete the division, as shown here.

For many children the answer is twelve with a remainder of six. The correct answer is one hundred and twenty-three with a remainder of ten.

I have found that in the initial stages if we insist on children to use the squared paper and the symbols H T U to indicate place-value, this kind of mistake does not occur. As children can easily see that the division is not finished.

Many children make mistakes when nought or zero occurs in any part of the division process. For instance, the division is 1404 ÷ 13. Many times children solve it as shown below: Many times children make mistakes as they have forgotten the earlier steps. For example, they do know that 140 ÷ 13 is 10 and 10 over. Therefore, in the quotient we have to write 10 and the remainder should be written as 10. However, they do not understand the similarity in the present problem and the earlier problem. The earlier problem is just an extension of the present problem. In this case solve both the problems side by side and point out the similarity, as shown below.

This helps them to understand that the quotient of 18 for the problem ‘1404 ÷ 13’ is really absurd.

A good idea is to give following pairs of problems to solve:

• 180 ÷ 7 = ? and 1801 ÷ 7 = ?
• The copyright of the article Complex divisions (III) in Math for Kids is owned by Vidya Narayan Wadadekar . Permission to republish Complex divisions (III) in print or online must be granted by the author in writing.

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