Painless Nine Times (IV)


I am sure that many of you have successfully solved the problems given in the previous article. At the same time you may perhaps have thought that nine times of higher order numbers (3 or more digits) becomes painful instead of painless! Right?

Yes, to find out nine times of bigger numbers (like for problems No.6 to 10 given below), the subtraction gets complicated. Such subtractions would not be possible without paper-pencil. We must then have an easy method of subtraction to make the nine times of larger numbers painless.

In the earlier articles entitled Dealing With Subtraction... we have seen some methods of subtraction. However, none of these provides an easy and elegant way of finding answer for subtraction quickly and accurately. Besides these methods, there exists a method called "Complementary method of subtraction".

The complementary method of subtraction should not be confused with the complementary addition method discussed in the article Checking Subtraction (IV). The rationale of the complementary method of subtraction is based on the idea of the complement of a number.

The complement of a number is the difference between that number and the next higher power of 10. For example, the complement of six is (10 - 6) or 4. The complement of 64 is (100 - 64) or 36. Now could you think the complement of 1864? You are right! The complement of 1864 is (10000 - 1864) or 8136.

Let us see how the subtraction 10000 -1864 can be managed mentally, speedily, and accurately. This is shown in the figure to your left-hand side. If you repeat this procedure of finding out complement for many other numbers, you will soon realize that without arranging the minuend and the subtrahend in columns one below the other, you can find out the complement of any number. First, subtract its digit in the units place from ten and then all the other remaining digits from nine. This will be clear from the figure.

Let us take another example, 6832. The digit in the units place is 2. Subtracting 2 from 10 we get 8. Therefore, 8 will be in the units place of the answer. Now remaining digits, from ten's place to the leftmost place, subtract from 9 turn by turn. You get 6 in the tens place, 1 in the hundreds place, and 3 in the thousands place. Thus, complement of 6832 is (10000 - 6832) or 3168.

The copyright of the article Painless Nine Times (IV) in Math for Kids is owned by Vidya Narayan Wadadekar . Permission to republish Painless Nine Times (IV) in print or online must be granted by the author in writing.

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