The rule by which the multiplier is discovered (but which we do not attempt to explain) is this: Multiply the last figure (the 9) of the multiplicand by the figure of which you wish the product to be composed, and that number will be the required multiplier. Thus, when it was required to have the product composed of 2, the 2 multiplied by 9 gives 18, the multiplier: 3 multiplied by 9 gives 27, the multiplier to give the product in 3; &c.
If a figure, with a number of ciphers attached to it, be divided by 9, the quotient will be composed of one figure only, namely, the first figure of the dividend, as—
9)600,000 9)40,000
————— ————
66,666–6 4,444–4
{ 9)549
If any sum of figures can be divided by 9 as, {———
{ 61
the amount of these figures, when added together, can be divided by 9:—thus, 5, 4, 9, added together, make 18, which is divisible by 9. If the sum 549 is multiplied by any figure, the product can also be divided by 9, as—
| } | { | 3 | ||
| 549 | } | { | 2 | |
| 6 | } | { | 9 | |
| ——— | } | And the amount of the figures of | { | 4 |
| 9)3294 | } | the product can also be divided by | { | —— |
| ——— | } | 9, thus, | { | 2)18 |
| 366 | } | { | —— | |
| } | { | 9 |
To multiply by 9, add a cipher, and deduct the sum that is to be multiplied: thus,
| 43,260 | } | { | 4,326 | |
| 4,326 | } | Produces the same result as | { | 9 |
| —— | } | { | —— | |
| 38,934 | } | { | 38,934 |
In the same manner, to multiply by 99, add two ciphers; by 999, three ciphers, &c. These properties of the figure 9 will enable the young arithmetician to perform an amusing trick, quite sufficient to excite the wonder of the uninitiated.