ARITHMETIC. 
amounts to, when reckoned as many times 
as there are units in the second. Thus 8 
multiplied by 5, or 5 times 8, is 40. The 
given numbers (8 and 5) are called factors ; 
the first (8) the multiplicand; the second 
(5) the multiplier; and the amount (40) the 
product. This operation is nothing else 
than addition of the same number several 
times repeated. If we mark 8 five times 
under each other, and add them, the sum is 
40 : but as this kind of addition is of fre- 
quent and extensive use, in order to shor- 
ten the operation, we mark down the num- 
ber only once, and conceive it to be re- 
peated as often as there are units in the 
multiplier. For this purpose, the learner 
must be thoroughly acquainted with the fol- 
lowing multiplication table, which is com- 
posed by adding each digit 12 times. 
Example. 
76859 multiplied by 4, 
4 
Ans. 307436 
or, 76859 added 4 times. 
76859 
76859 
76859 
Ans. 307 436 the same as before. 
TABLE. 
1 
2 1 3 
4 
6 
6 
7 
8 
9 
10 
11 
12 
2 
4 
6 
8 
ir 
12 
14 
16 
18 
20 
22 
24 
3 
6 
9 
12 
15 
18 
21 
24 
27 
30 
33 
36 
— 
— 
— 
— 
— 
— 
— 
— 
4 
812 
16 
20 
24 
28 
32 
36 
40 
44 
48 
5 
1015 
20 
25 
30 
35 
40 
45 
50 
55 
60 
— 
— 
— 
— 
— 
— 
— 
— 

6 
K ^ 
OO 
24 
30 
36 
42 
48 
54 
60 
66 
72 
— 

7 
14 21 
28 
35 
42 
49 
56 
63 
70 
77 
84 
8 
1624 
32 
40 
48 
56 
64 
72 
80 
88 
96 
S; 1 
SI 
36 
45 
54 
63 
72 
81 
90 
99 
108 
tojsoso 
40 
50 
60 
70 
80 
90 
100 
110 
120 
nhdss 
i i 
44 
55 
66 
77 
88 
99 
110 
121 
132 
12|g4|36 
48 
60 
72 
84 
96 
108 
120 
132 
144 
In this table the multiplicand figures are 
in the upper horizontal row ; the multipliers 
are in the left hand column, and the pro- 
ducts will be found under the multiplicand, 
and in the same row with the multiplier : 
thus 9 times 11 are 99 ; the 99 will be found 
in the column under the 11, and in the same 
horizontal row with the 9, among the mul- 
tipliers. 
If both factors be under 12, the table ex- 
hibits the product at once. If the multiplier 
only be under 12, we begin at the unit 
place, and multiply the figures in their or- 
der, carrying the tens to the higher place, 
as in addition. 
If the multiplier be 10, we annex a cy- 
pher to the multiplicand. If the multiplier 
be 100, we annex two cyphers ; and so on. 
The reason is obvious, from the use of cy- 
phers in notationX If the multiplier be any 
digit, with one or more cyphers on the right 
hand, wg multiply by the figure, and annex 
an equal number of cyphers to the pro- 
duct. y _ 
Thus, if it be required to multiply by 60, 
we first multiply by 6, and then annex a cy- 
pher. It is the same fifing as to add the 
multiplicand 60 times ; and this might be 
done by writing the account at large, di- 
viding the column into 10 parts of 6 lines, 
finding the sum of each part, and adding 
these ten sums together. If the multiplier 
consist of several significant figures, we mul- 
tiply separately by each, and add the pro- 
ducts. It is the same as if we divided a 
long account of Addition into parts corres- 
ponding to the figures of the multiplier. 
Example. 
To multiply 7329 by 365. 
7329 7329 7329 
5 60 300 
36645 439740 2198700 
36645 = 5 times. 
439740 60 times. 
2198700 = 300 times. 
2675085 = 365 times. 
It is obvious that 5 times the multiplicand 
added to 60 times, and to 300 times, the 
same must amount to the product required. 
In practice, we place the products at once 
under eacu other ; and as the cyphers arising 
from the higher places of the multiplier are 
lost m the addition, we omit them. Hence 
may be inferred the following 
/ Rule. Place the multiplier under the 
multiplicand, and multiply the latter suc- 
cessively by the significant figures of the 
tormer ; by placing the right hand figure of 
