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" An integer is divisible by 3 if the sum of its digits is divisible by 3. An integer is divisible by 9 if the sum of its digits is divisible by 9. "
Buker-Felter Arithmetics - Page 18
by Eva F. Buker - 1915
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Mathematical Problems and Examples, Arranged According to Subjects, from the ...

Mathematics - 1836 - 366 pages
...metre which is one ten-millionth part of a fourth of its circumference. 237. A number is divisible by 9, if the sum of its digits is divisible by 9 ; and by 1 1, if the sum of the 1st, 3rd, 5th .... digits is equal to the sum of the 2nd, 4th, 6th,...
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A Treatise on Arithmetic, Combining Analysis and Synthesis: Adapted to the ...

James Stewart Eaton - Arithmetic - 1857 - 376 pages
...-f- 4 -f- 3 is the sum of the digits which express the number 5G43 ; hence any number is divisible by 9 if the sum of its digits is divisible by 9. • If the sum of the digits of a number divided by 9 give a remainder, then the number itself divided...
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The Progressive Higher Arithmetic, for Schools, Academies, and Mercantile ...

Horatio Nelson Robinson - Arithmetic - 1860 - 444 pages
...sum, or the entire number, is divisible_by the same power of 5, (135, II). IX. A number is divisible by 9 if the sum of its digits is divisible by 9. For, if any number, as 7245, be separated into its parts, 7000 + 200 + 40+5, and each part be divided...
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Mathematical Exercises ...

Samuel H. Winter - 1864 - 348 pages
...shot in the bottom course. 11. Solve the equations i.ax ~,„ ~ 12. Prove that a number is divisible by 9, if the sum of its digits is divisible by 9. 13. Find the present value of £1 due 12 years hence, money bearing 4£ per cent. compound interest....
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A Written Arithmetic, for Common and High Schools: To which is Adapted a ...

George Augustus Walton - Arithmetic - 1864 - 376 pages
...number. Thi> following principles are derived directly from Art 511 : — «512. Any number is divisible by 9, if the sum of its digits is divisible by 9. •5 1 Νν . If any number is divided by 9, the remainder is equal to the remainder when the sum of...
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A Written Arithmetic, for Common and High Schools: To which is Adapted a ...

George Augustus Walton - Arithmetic - 1864 - 364 pages
...number. The following principles are derived directly from Art. 511 : — 513. Any number is divisible by 9, if the sum of its digits is divisible by 9. •113. If any number is divided by 9, the remainder is equal to the remainder when the sum of its...
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Help to Arithmetic ...

Howard Candler - 1868 - 130 pages
...further object in view of explaining the principle of the " chain rule." NOTE D. A number is divisible by 9, if the sum of its digits is divisible by 9. Take the numbers 45678. 45678 = 40000 4- 5000 + 600 + 70 + 8 = 4 (9999 + i) + 5 (999 + i) + 6 (99 +...
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The science and art of arithmetic, by A. Sonnenschein and H.A. Nesbitt.d Pt.1

Adolf Sonnenschein - 1873 - 194 pages
...divisible by 9. Note that 27 = the sum of the digits in 153576. Learn by heart : A number is divisible by 9 if the sum of its digits* is divisible by 9. (/) Eeasoning analogous to that just given shews that any number is an exact number of nines + the...
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The Complete Arithmetic: Oral and Written

Daniel W. Fish - Arithmetic - 1874 - 542 pages
...are ciphers, or express a number divisible by 8. Thus, 3000, 2728, and 10576 are divisible by 8. 7. By 9, if the sum of its digits is divisible by 9. Thus, 217683 and 401301 are divisible by 9. 8. By 10, if it ends with one or more ciphers. Thus, 40,...
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The Progressive Higher Arithmetic: For Schools, Academies, and Mercantile ...

Horatio Nelson Robinson - Arithmetic - 1875 - 468 pages
...sum, or the entire number, is divisible by the same power of 5, (135, II). IX. A number is divisible by 9 if the sum of its digits is divisible by 9. For, if any number, as 7245, be separated into its parts, 7000 + 200 +40+5, and each part be divided...
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