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Dealing with Subtraction(II)

© Vidya Narayan Wadadekar

We have seen in last article, how decomposition simplifies subtraction. Let us now see some more examples of decomposition, presented in figure 1.

How could a child solve this mentally? Let us see an example. In the first example “81 – 64” child’s mental steps would be, ‘4 from 1, I can’t. Borrow 10 from tens column. One ten from eight tens leaves seven tens. 4 units from 11 = 7, 6 from 7 = 1’ For the remaining examples similar method should be followed.

Let us see how the other procedure, that is ‘equal additions’ work. However, let us first learn the vocabulary related to subtraction. Minuend is the number, which is decreased. Subtrahend is the number, by which we decrease the given number. Remainder is the sum, which remains i.e. we get as an answer as a result of subtraction. Thus, in the figure 1; 81 is the minuend, 64 is the subtrahend, and the answer 17 is the remainder.

Equal Additions: This procedure is also called additive or complementary subtraction method. In order to subtract using this method, both the minuend and subtrahend are increased by the same number. Here we actually apply the principle of compensation – adding the same number to both the minuend and subtrahend does not change the difference. The process is illustrated in figure 2.

In the figure above we added ten ones to the minuend and one ten to the subtrahend, thus we have added equal numbers, that is ten ones and one tens, to both the minuend and subtrahend.

Let us take the next example, which is presented in figure 3.

In this example 110 is added to both the minuend and subtrahend; however, ten ones and ten tens are added to minuend, while one tens and one hundred are added to subtrahend.

Although, the decomposition method appears to be more rationalized as well as natural for use, research by Murray¹ gave unexpected findings. The research involved children between the ages of 8 and 9 years (in 55 different schools) and 10 and 11 years (in 54 different schools). He studied their accuracy and speed on subtraction using both these methods. His research showed that the decomposition method was decidedly inferior to the equal additions method with both groups of children and for both speed and accuracy. However, there are evidences from the interviews with children and from the diaries of the teachers participating in the Brownell and Moser’s ² experiment to show that the equal additions method was more difficult to explain to children. This was mainly due to the fact that it involves a new principle, namely that the relative values of numbers are not changed if we add the same amount to each. But once children acquire it, and it can be acquired by children of all intellectual levels, it results in superior subtraction ability.

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