 | Robert Johnston (F.R.G.S.) - 1872 - 342 pages
...and 6. NOTES. — 1. The method of proof (vi.) depends on a property of the number 9, riz. : — ' any number divided by 9 will leave the same remainder as the sum of il» figures divided by 9.' 2. The explanation of the annexed example in multiplication will be found... | |
 | Joseph Ray - 1856 - 400 pages
...consequently, the excess in this instance, is 3. All the methods of proof are founded on this PRINCIPLE.— Any number divided by 9 will leave the same remainder as the sum of its digits divided by 9 For example, take 3456. f3000=3(1000)=3x(999+l)=3x 999+3 400= 4(100)= 4X(99+1)=... | |
 | Robert Johnston (F.R.G.S.) - 1879 - 320 pages
...3, 4, and 6. NOTES. — 1. The method of proof (vt) depends on a property of the number 9, viz.: — 'any number divided by 9 will leave the same remainder as the sum of its figures divided by 9.' ÍÍ. The explanation of the annexed example in multiplication will be found useful.... | |
 | Joseph Ray - Arithmetic - 1880 - 420 pages
...3 + 4 + 5 are 12; drop the 9; the excess is 3. The 9 in the number was not counted. PRINCIPLE. — Any number divided by 9, will leave the same remainder as the sum of its digits divided by 9. ILLUSTRATION. 700000 = 7 X 100000 = 7 X ( 99999 + 1 ) = 7 X 99999 + 7 60000 =... | |
 | H. Bryant - 1881 - 574 pages
...PECULIAR NUMBERS. 188, 1. Nine. — The relation of the number 9 in the decimal system of notation is such that any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. The remainder in this case is called the excess of nines. Thus 75 -H 9 =8, Rem.... | |
 | James Bates Thomson - Arithmetic - 1882 - 416 pages
...rejecting 9 from 14 leaves 5, the excess required. 875. Hence we derive this property of the number 9: Any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. NOTES.—1. It will be observed that the excess of 9's in any two digits is always... | |
 | James Bates Thomson - Business mathematics - 1884 - 344 pages
...3313 3319 3323 3329 8331 3343 3347 3359 3361 3371 3373 3389 3391 3407 698. Property of the number 9: Any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. 1. Let it be required to find the excess of 9's in 7548467. Adding 7 to 5, the... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...its digits is divisible by r — 1. 83. By taking r = 10 we learn from the above proposition that a number divided by 9 will leave the same remainder as the sum of its digits divided by 9. The rule known as " casting out the nines " for testing the accuracy of multiplication... | |
 | Book-keeping and business man's magazine - 1904 - 190 pages
...above 9; 2 and 4 are 6; 6 is the sum of the digits above a certain numbet of 9's. Proposition. — Any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. To illustrate this we will take the number 36745. 36745= 3C000=3C10(100) = 6000=6(... | |
| |
... any number divided by 9, will leave the same remainder as the sum of its figures, or digits, divided by 9, which may be thus demonstrated. 
