Triks With Figures

VARIETY is also the spice of figures. If numbers seem dull, very likely you have approached them in the same unvaried way too long. Try these strategic attacks.

In multiplying by five perhaps you subconsciously annex a cipher and then divide by two. But do you know that to multiply by 25 you may add two ciphers and divide by four; to to multiply by 125 you add three ciphers and divide by eight?

To multiply by 11, annex a cipher and add the original to the newly formed. Or put down the last digit of the original number, then to the left place the sum of each digit plus the one to its left, setting down each time only the unit figure, and carrying the figure representing the tens. Multiplying by 111 can be done in a similar manner. (See below.)

To multiply by nine, place a cipher before and after the number. Now subtract each figure from that to the right of it, taking care to borrow when the next fig-use is too small.

At times, multiplying is an easy way of dividing. Just as to divide by five you may multiply by two and set off the last figure by a decimal point, to divide by 25 you can and tell you in which of these columns it may be found. Add the numbers at the heads of the columns he designates and you get his number. (From "Mathematical Recreations," by Maurice Kraitchik; W. W. Norton & Co., New York) multiply by four and set off two figures. Similarly, to divide by 125, multiply by eight and set off three places.

Figures are fun, too. Let a friend choose a number.

In adding, attack a double column on the left flank instead of the right. Add the figures on the left, put down that representing the tens in your total; to that representing units, annex a cipher and add the figures in the right column. Put the results to the right of the figure already set down.

The same left-flank approach can be made to subtraction. Keep glancing ahead one column to allow for borrowing. Subtracting 72931 from 89068, take 7 from 8; then 2 from 8 (since one must be saved for borrowing); 9 from 10; and so on.

To divide by 125, multiply by eight and set off three places. To multiply by III, set down the last digit, then the sum of the last two, that of the last three, then the next three, and so on.