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Dealing with Subtraction(I)

© Vidya Narayan Wadadekar

Before finding out many more interesting ways to simplify multiplication, let us deal with a third arithmetic operation, subtraction, which we need quite often. And if we use this in combination with simple multiplication we can manage complicated multiplication quickly and accurately.

Subtraction means to take a number or quantity away from another number or quantity. The concept of subtraction should be developed progressively from active and concrete experiences. We should use objects easily available in the child's environment while teaching subtraction. Then, we can give them practice in finding out answers for the basic subtraction facts shown in figure 1.

While finding out the answers for these basic subtraction facts, children may use cards with dots, as explained in article Visualizing the Numbers (Part IV) in this series.

Once children develop facility with given subtraction facts they should be given practice in the slightly higher-level subtraction facts given in figure 2. In these cases, too, children should be encouraged to use the cards, as these help their visualizing ability.

Before proceeding to the subtraction of larger numbers we should make them understand how the basic subtraction facts are used in carrying out subtraction involving larger numbers. This is brought out in figure 3.

By using all the figures above children can discover many important facts. For example, if the child knows 14 - 6 is 8, s/he may learn to reason that 14 - 5 is 9, since subtracting five gives an answer greater than subtracting six. The child also knows that if 14 - 6 is 8, then 15 - 6 is 9. Because subtracting from 15 gives an answer greater than subtracting from 14. All such observations help chidren to think with proper reasoning and arrive at the correct answer.

From there on children could be taught the written presentation of subtraction.

As seen in the example above, in subtractions such as 23 - 4 where a change of form is required, decomposition and equal additions are two common methods for performing the operations. The technique of decomposition is common in use. However, teachers should understand both, as there is a possibility that they might come across some children who use the other method.

Let us see here the technique of decomposition in detail.

Decomposition: This is also known as the method of borrowing. In this case, if the number from which you are subtracting is not larger than the one your are subtracting from it, you borrow one unit from the next immediate left-hand digit (that is, the one with the immediate higher-place value). This allows you to add ten to the digit from which you were trying to subtract.

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