 | George Roberts Perkins - Arithmetic - 1850 - 356 pages
...any number being diminished by the sum of its digits, will become divisible by 9. Also, any number divided by 9, will leave the same remainder as the sum of its digits when divided by 9. The above properties belong to the digit 3, as well as to that of 9, since... | |
 | John Bonnycastle - 1851 - 314 pages
...before added upwards; in which case, if the two sums agree, it may be presumed that the work is right. divided by 9 will leave the same remainder as the sum of its figures, or digits, divided by 9; which may be shown thus: Let there be any number, as 3467; which, being separated into its several... | |
 | James B. Dodd - Arithmetic - 1852 - 410 pages
...of proving Addition. Subtraction, &c., by the following Property of the Number 9. § 311. Any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. Take any number, as 345, which is 300+40+5. 300=3 XlOO=3x(99+l)=3X99+3; and 40=4X... | |
 | Sarah Porter - Arithmetic - 1852 - 286 pages
...remamder as , or as J y n \ I [ ir | t\ ~ , then it is probable the work is right. Since any number divided by 9 will leave the same remainder as the sum of its digits divided by 9, it follows that the sum of two or more numbers divided by 9 will leave the same... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 476 pages
...depends on a property of the number 9, which belongs to no other digit, except 3. It is this : any number divided by 9 will leave the same remainder as the sum of its figures or digits divided by 9. For take the number 563, for instance, which is equal to 500 •+• CO + 3. Now 500 = 5 X 100 = 5... | |
 | James B. Dodd - 1853 - 398 pages
...of proving Addition. Subtraction, &c., by the following Property of the Number 9. § 311. Any number divided by 9 will leave the same remainder as the sum of its digits divided by 9. Take any number, as 345, which is 300+40+5300=3 X100=3X(99+l)=3X99+3; and 40=4X... | |
 | Thomas H. Palmer - Arithmetic - 1854 - 356 pages
...number diminished by the sum of its digits will become divisible by 9 and also by 3. Why ? Any number divided by 9 will leave the same remainder as the sum of its digits when divided by 9. Why ? The same remark also applies to 3. Why ? 10. The sum of any number,... | |
 | Thomas H. Palmer - Arithmetic - 1854 - 368 pages
...number diminished by the sum of its digits will become divisible by 9 and also by 3. Why ? Any number divided by 9 will leave the same remainder as the sum of its digits when divided by 9. Why ? The same remark also applies to 3. Why ? 12. Any prime number (greater... | |
 | 1856 - 418 pages
...multiple, or its product by any wluile number. 15. Any number expressed by the decimal notation, di\ ided by 9, will leave the same remainder, as the sum of its figures or digits divided by 9. For Example. — Take any number, as C357 ; now separating it into its several parts, it become? 6000+300+50+... | |
 | Charles Guilford Burnham - Arithmetic - 1857 - 328 pages
...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.... | |
| |
... 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. 
