amount.

ing long columns is to set down the result of each column on some waste spot, observing to place the numbers successively a place further to the left each time, as in putting down the product figures in multiplication; and afterward add up the In this way if the operator lose his count, he is not compelled to go back to units, but only to the foot of the column on which he is operating. It is also true that the brisk accountant, who thinks on what he is doing, is less liable to err than the dilatory one who allows his mind to wander. Practice too will enable a person to read amounts without naming each figure, thus instead of saying 8 and 6 are 14, and 7 are 21 and 5 are 26, it is better to let the eye glide up the column, reading only 8, 14, 21, 26, etc.; and, still further, it is quite practicable to accustom one's self to group 87 the figures in adding, and thus proceed very rap- 23 idly. Thus in adding the units' column, instead 45 of adding a figure at a time, we see at a glance 62 that 4 and 2 are 6, and that 5 and 3 are 8, then 24 6 and 8 are 14; we may then, if expert, add constantly the sum of two or three figures at a time, and with practice this will be found highly advantageous in long columns of figures; or two or three columns may be added at a time, as the practiced eye will see that 24 and 62 are 86 almost as readily as that 4 and 2 are 6.

Teachers will find the following mode of match ing lines for beginners very convenient, as they can inspect them at a glance:

In placing the above the lines are matched in pairs, the digits constantly making 9. In the above, the first and fourth, second and fifth are matched; and the middle is the key line, the result being just like it, except the units' place, which is as many less than the units in the key line as there are pairs of lines; and a similar number will occupy the extreme left. Though sometimes used as a puzzle, it is chiefly useful in teaching learners; and as the location of the key line may be changed in each successive example, if necessary, the artifice could not be detected. The number of lines is necessarily odd.

B*

RULE.-Set down the smaller factor under the larger, units under units, tens under tens. Begin with the unit figure of the multiplier, multiply by it, first the units of the multiplicand, setting the units of the product, and reserviny the tens to be added to the next product; now multiply the tens of the multiplicand by the unit figure of the multiplier, and the units of the multiplicand by tens figure of

he multiplier; add these two products together, setting down the units of their sum, and reserving the tens to be added to the next product; now multiply the tens of the multiplicand by the tens figure of the multiplier, and set down the whole amount. This will be the complete product.

Remark.-Always add in the tens that are reserved as soon as you form the first product.

EXAMPLE 1.-EXPLANATION.

24

31

1. Multiply the units of the multiplicand by the unit figure of the multiplier, thus: 1X4 is 4; set the 4 down as in example. 2. Multiply the tens in the multiplicand by 744 the unit figure in the multiplier, and the units in the multiplicand by the tens figure in the multiplier, thus: 1×2 is 2; 3×4 are 12, add these two products together, 2+12 are 14, set the 4 down as in example, and reserve the 1 to be added to the next product. 3. Multiply the tens in the multiplicand by the tens figure in the multiplier, and add in the tens that were reserved, thus: 3×2 are 6, and 6+1=7; now set down the whole amount, which is 7.

EXAMPLE 2.-EXPLANATION.

1. Multiply units by units, thus: 4×3 are 12, set down the 2 and reserve the 1 to carry. 2. Multiply tens by units, and units by tens, and add in the one to carry on the

53

84

4452

nrst product, then add these two products together, thus: 4×5 are 20+1 are 21, and 8×3 are 24, and 21+24 are 45, set down the 5 and reserve the 4 to carry to the next product. 3. Multiply tens by tens, and add in what was reserved to carry. thus: 8×5 are 40+4 are 44, now set down the whole amount, which is 44.

EXAMPLE 3.-EXPLANATION.

43

25

5X3 are 15, set down the 5 and carry the 1 to the next product; 5X4 are 20=1 are 21; 23 are 6, 21+6 are 27, set down the 7 and carry the 2; 2×4 are 8+2 are 1075 10; now set down the whole amount.

When the multiplicand is composed of three fig. ures, and there are only two figures in the multiplier, we obtain the product by the following

RULE.--Set down the smaller factor under the larger, units under units, tens under tens; now multiply the first upper figure by the unit figure of the multiplier, setting down the units of the product, and reserving the tens to be ad led to the next product; now multiply the second upper by units, and the first upper by tens, add these two products together, setting down the units figure of their sum, and reserv ing the tens to carry, as before; now multiply the third upper by units, and the second upper by tens, add these two products together, setting down the units figure of their sum, and reserving the tens to