 | James Bates Thomson - 1860 - 440 σελίδες
...its multiple, or its product by any whole number. 15. Any number expressed by the decimal notation, divided by 9, will leave the same re/mainder, as the sum of its figures or digits divided by 9. Demonstration. — Take any number, as 6357 ; now separating it into... | |
 | Robert Johnston (F.R.G.S.) - 1863 - 254 σελίδες
...3, 4, and 6. NOTES—l. The method of proof (vi.) 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.' 2. The explanation of the annexed example in multiplication will be found useful.... | |
 | John Groesbeck - 1867 - 226 σελίδες
...part of a thousand when its three right-hand figures may be thus divided. Any number divided by 3 or 9 will leave the same remainder as the sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9.... | |
 | John Groesbeck - 1868 - 350 σελίδες
...part of a thousand when its three right-hand figures may be thus divided. Any number divided by 3 or 9 will leave the same remainder as» the sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9.... | |
 | John Groesbeck - 1871 - 370 σελίδες
...part of a thousand when its three right-hand figures may be thus divided. Any number divided by 3 or 9 will leave the same remainder as the sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9.... | |
 | Henry Beadman Bryant, Emerson Elbridge White, Corydon Giles Stowell - 1872 - 576 σελίδες
...NUMBERS. 188. 1. Nine. — The relation of the number 9 in the decima 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 -=-9 =8, Rem. 3, and... | |
 | Robert Johnston (F.R.G.S.) - 1872 - 342 σελίδες
...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... | |
 | John Groesbeck - 1872 - 374 σελίδες
...part of a thousand when its three right-hand figures may be thus divided. Any number divided by 3 or 9 will leave the same remainder as the sum of its digits divided by 3 or 9. Th« difference between any number and the sum of its digits is a multiple of 9.... | |
 | Joseph Ray - 1856 - 400 σελίδες
...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)= 4x99+4... | |
 | Robert Johnston (F.R.G.S.) - 1879 - 320 σελίδες
...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... | |
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... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. 
