 | Joseph Ray - 1880 - 420 σελίδες
...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 = 6X 10000... | |
 | H. Bryant - 1881 - 574 σελίδες
...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. 3, and... | |
 | 1883 - 536 σελίδες
...the respective rates of 7 and 8 miles an hour ? 15. Prove that any number when divided by 9 leaves the same remainder as the sum of its digits when divided by 9 leaves. Show how this property of the number 9 can be used to test the correctness of the operation... | |
 | James Bates Thomson - 1882 - 416 σελίδες
...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 equal... | |
 | Leonard Marshall - 1883 - 198 σελίδες
...- 1 pan, and 32, 1 in the other. 3)4, 1 1, 1 7. (i.) Any number in the scale of r divided by r—l will leave the same remainder as the sum of its digits when divided by r—1. r—1 - [See § 10, p. 2.] Therefore any number in the scale of r is divisible by r — 1 if... | |
 | Leonard Marshall - 1883 - 212 σελίδες
...form a number divisible by 8. The proof is similar to (ii.) (v.) Any number, when divided by 9, leaves the same remainder as the sum of its digits when divided by 9. Therefore a number is divisible by 9 if the sum of its digits is divisible by 9. [See § 7 (i.).] (vi.)... | |
 | Leonard Marshall - 1883 - 184 σελίδες
...1 pan, and 32, 1 in the other. 3)4, 1 1, 1 7. (i.) Any number in the scale of r divided by r — 1 will leave the same remainder as the sum of its digits when divided byr-1. For r—l r—1 _ Integer +aLtj-V_+ft +*4 [See § 10, p. 2.] Therefore any number in the scale... | |
 | James Bates Thomson - 1884 - 344 σελίδες
...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 sum is... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - 1891 - 606 σελίδες
...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... | |
 | 1904 - 190 σελίδες
...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( 1000)... | |
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... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. 
