Synopses & Reviews
Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: NINE. Curious properties of the number nine, and numerical tricks with it, are given and explained by many writers; among them Dr. Edward Brooks, in his Philosophy of Arithmetic. Of all such properties, perhaps the most practical application is the check on division and multiplication by casting out nines, the Hindu check as it is called. Next might come the bookkeeper's clue to inverted numbers. In double-entry book-keeping, if there has been inversion (e. g., $4.83 written in the debit side of one account, and $4.38 in the credit side of another) and no other mistake, the trial balance will be off by a multiple of nine. It can also be seen in what columns the transposition was made. Recently suggested, and of no practical interest, is another property of the magic number, easily explained, like the rest, but at first glance curious: invert the figures of any three-place number; divide the difference between the original number and the inverted number by nine; and you may read the quotient forward or backward. More- 845 over the figure that occurs in the quotient 548 is the difference between the first and last 9)297 figures of the number taken. Explanation: 33 Let a, b, c be the hundreds, tens, units figures respectively of any three-place number. Then the number is lOOa + 0b + c, and the number inverted is 00c+10b + a. (100a + 10 b+c) - (lOOc+10 b+a) 99 (a-c) 9 9 = 11 (a-c) The product of 11 and any one-place number will have both figures alike, and may be read either way. Better known are the following three?all old and all depending on the principle, that the remainder, after dividing any number by 9, is the same as the remainder after dividing the sum of its digits by 9. 1. Find the difference betweeen a number of two figures and the number ma...
Synopsis
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