Checking Subtraction (IV)

Estimating by front end estimation

This method is not really a different one from the method of rounding we discussed in the previous article. It is generally useful when we have larger numbers. In this case, what we do is simply replace only the two end digits of the larger numbers with zeros. For example, we are estimating the answer for 3486 - 2857. We simply do 3400 - 2800, which gives 600. This is close to the actual answer, i.e.. 629.

By using the earlier method of estimation by rounding, we would have done 3000 - 2000 and gotten 1000 as the answer. This is too much larger than the actual answer.

Remember that most estimation is based on knowledge of the number system. So, unless children understand this we can not teach checking subtraction by estimation. Children must also recognize the extent to which we can approximate the minuend. If the minuend is approximated too much to the lower bound, the sum will naturally be underestimated. Similarly, if the minuend is approximated too much to the higher bound the sum will obviously be overestimated.

A better way to gain experience in making best approximation is to try different approximations of the numbers involved and compare the obtained answers with the actual answers, as shown here.

Complementary Addition Method is another method of subtraction. This can be used to carry out or to check subtraction. The "adding idea"- for examplem "What number added to 5 gives 9?"is called complementary addition or inverse addition and is really not subtraction.

This is shown in the figure below. Here the idea of "reverse process" is used. In effect, subtraction in this case is managed by means of addition. The arguments are like these: What must be added to 4 to make 13? Obviously, 9! In the addition 4 + 9 = 13 there is 1 to carry. Add it to the 2. Three and what make 6? Three. The complete answer states that 39 must be added to 24 to make 63, and hence 63 - 24 = 39. In short, this method is based on the checking notion that, whatever is the answer to the subtraction, this answer when added to 24 must make 63.

We had not discussed this method earlier, as the concept of complementary addition involved in this is difficult and much of the calculation must be done in the mind. Clearly it is a technique for a much later stage of development than the two described earlier. It is, of course, the principle of "making change" in the ordinary world of buying and selling. This method is used daily by bankers, accountants and, of course, shopkeepers, etc., when they give change to customers.

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