131
2160; then multiply the unit 2 by S, makes 16, added to 2160 equals 2176.
Example III.—Multiply 38 by 76.
| 38 | Add 76 to 8 is 84, multiplied by 3 is 232, the difference between the 3 of 38 and the 7 of 76 is 4, by which figure multiply the 8 of 38, making 32, added to 252 is 284, join an 0, is 2840, next multiply 8 by 6 is 48, added to 2840 equals 2888. | |
| 76 | ||
| 2888 |
| 76 + 8 = 84 | ||
| 84 × 3 = 252 | ||
| The difference between 3 and 7 is 4 |
4 x 8 + 252 = 284 join an 0 = 2840 | |
| 8 × 6 + 2840 = 2888 |
A different mode may be adopted, by making the lesser number the multiplier, and proceed as in this Example:—
| 42 | Add 28 to 2 is 30, which multiplied by the 2 of 28 is 60, then subtracting the 2 of 28 from the 4 of 42 leaves 2, by which figure multiply 28, making 56, which added to 60 is 116, next join an O is 1160, multiply the units 8 by 2, is 16, plus 1160, equals 1176. | |
| 28 | ||
| 1176 |
Those two modes embrace all figures between 12 and 100, another arrangement is now submitted, which is in many instances superior.
Rule.—When the figures in the tens places are alike, and the figures in the units places by being added together, make 10; the figure in the tens place of the multiplicand must be increased 1; (which 1 ten is the sum of the units) then multiply them in the usual manner, putting down each product without any other combination.
Thus to multiply 27 by 23; the multiplicand 27 must be viewed as if it were 37.
