Quick Eight Times (II)

The digits in the number we selected, however, were even. If we select a number with some of its digits odd, do you think this method would need any modifications?

Since, in finding out eight times of any number we do not require to find half of any number, it is clear that no modification in the method will be necessary. Whatever subtraction procedure we follow for the number with even digits the same will be applicable for the number with odd digits.

There is another way we can manage eight times of a number maintaining the same logic. In the new method subtraction can be accomplished using complementary method of subtraction. Although the complementary subtraction is discussed earlier let us try it here with some more examples and refresh our logic.

Let us subtract 2863 from 3751 using the method of complementary subtraction.

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Now, check your answer by using any method you wish. You will find that the answer is correct indeed!

The whole process works correctly, as in finding the complement of the subtrahend you subtract the same from 10,000. The obtained difference you then add to the minuend. From this sum you again subtract 10,000 (Because, you have taken these extra earlier) to get back your true answer.

Go through the steps given below to have abundant clarity about the way complementary subtraction works. .

The beauty of this method lies in the fact that the subtraction involved here is always very easy. The digit is to be subtracted either from ten or nine. The only digit you subtract from 10 is the one in the units place. In the example above you have subtracted 3 from 10. All other digits are always to be subtracted from 9. Thus, in the example above we have subtracted 6, 8 and 2 from 9.

Try the following subtraction quickly and mentally using the logic mentioned here:

(a) 100 - 68 (b) 1000 - 389 (c) 1000 - 127 (d) 1000 -935

I hope you have managed all these subtractions getting complementary number of the number being subtracted.

Since, in our method of finding eight times of any number quickly we have to manage same subtraction twice; we must think of a way to manage the required subtractions using complementary method.

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