 | Charles Guilford Burnham - 1857 - 342 σελίδες
...of the number nine, which belongs to no other digit but 3, which is a factor of 9 ; — namely, that any number divided by 9 will leave the same remainder as the sum of its digiU divided by 9. This peculiar property of the number 9 grows out of the decimal relation of place.... | |
 | Charles Guilford Burnham - 1859 - 338 σελίδες
...of the number nine, which belongs to no other digit but 3, which is a factor of 9 ; — namely, that any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. This peculiar property of the number 9 grows out of the decimal relation of place. Were the ratio of... | |
 | Robert Johnston (F.R.G.S.) - 1860 - 188 σελίδες
...MULTIPLICATION. 8. The method of proof (30, 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." 4. The following explanation of the annexed example in multiplication will be... | |
 | 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... | |
 | Daniel Adams - 1861 - 452 σελίδες
...contains 9 three times + 3 units, its simple value. Hence also, — Any number divided by 9 will have the same remainder as the sum of its digits divided by 9. On this principle is founded a method of proving Addition, Subtraction, Multiplication, and Division,... | |
 | 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. The difference... | |
 | 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. The difference... | |
 | 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. The difference... | |
 | 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 (7 + 5)-h9 =... | |
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... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. 
