 | William Vogdes - 1849 - 134 pages
...method depends upon a property of the number 9, which, except 3, belongs to no other digit whatever ; that any number divided by 9, will leave the same...as the sum of its figures, or digits, divided by 9, which may be thus demonstrated. DEMONSTRATION. — Let there be any number, as 8467, this, separated... | |
 | George Roberts Perkins - Arithmetic - 1849 - 356 pages
...follows that 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... | |
 | Rufus Putnam (of Salem, Mass.) - Arithmetic - 1849 - 174 pages
...depends upon a property that is peculiar to the numbers 3 and 9, viz., that any number divided by 3 or 9 will leave the same remainder as the sum of its figures divided by 3 or 9. Thus the number 87145 divided by 3 leaves a remainder of 1, and divided by 9 leaves... | |
 | Charles Guilford Burnham - 1850 - 350 pages
...method of proof depends upon a property of the number 9, which belongs to no other digit but 3 ; — namely, that any number divided by 9 will leave the...as the sum of its figures, or digits, divided by 9 237456 467892 736345 849213 EXAMPLES. 478145 956736 202379 698783 Sum, 2290906 Sum, 2336043 632891... | |
 | George Roberts Perkins - Arithmetic - 1850 - 356 pages
...follows that 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... | |
 | Sarah Porter - Arithmetic - 1852 - 286 pages
...leave the same 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... | |
 | James B. Dodd - Arithmetic - 1852 - 410 pages
...the methods 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... | |
 | John Fair Stoddard - Arithmetic - 1852 - 320 pages
...is equal to the excess of 9's in the total product, the work is considered light. REMARK. — This method of proof depends on a property of the number 9 which is explained in my Philosophical Arithmetic. Take for illustration the preceding example OPERATION.... | |
 | James B. Dodd - 1853 - 398 pages
...the methods 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... | |
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... any number divided by 9, will leave the same remainder as the sum of its figures or digit: divided by 9 ;" which may bt demonstrated in this manner. 
