ARITHMETIC. 
each product under the figure of the multi- 
plier from which it arises; then add the 
product, y 
Example. 
7329 
93956 
365 
8704 
36645 
375824 
43974 
657692 
21987 
751648 
2675085 
817793024 
A number which caimot be produced by 
the multiplication of two others, is called a 
prime number; as 3, 5, 7, 11, and many 
others. A number which may be produced 
by the multiplication of two or more smaller 
ones, is called a composite number. For 
example, 27, which arises from the multi- 
plication of 9 by 3; and these numbers 
(9 and 3) are called the component parts 
of 27. 
1. If the multiplier be a composite num- 
ber, we may multiply successively by the 
component parts. 
Example. 
7638 
by 45, or 5 times 9 7638 
45 
9 
38190 
68742 
30552 
5 
343710 
343710 
Because the second product is equal to 
five-times the first, and the first is equal to 
nine-times the multiplicand, it is obvious 
that the second product must be five-times- 
nine, or forty-five-times as great as the mul- 
tiplicand. 
2. If the multiplier be 5, which is the half 
of 10, we may annex a cypher, and divide 
by 2. If it be 25, which is the fourth part 
of 100, we may annex two cyphers, and 
divide by 4. Other contractions of the like 
kind will readily occur to the learner. 
3. To multiply by 9, which is one less 
than 10, we may annex a cypher, and sub- 
tract the multiplicand from the number it 
composes. To multiply by 99,999, or any 
number of 9’s, annex as many cyphers, and 
substract the multiplicand. The reason is 
obvious; and a like rule may be found, 
though the unit place be different from 9. 
Multiplication is proved by repeating the 
operation, using the multiplier for the mul- 
tiplicand, and the multiplicand for the mul- 
tiplier. It may also be proved by division, 
«r by casting out the 9’s ; of which after- 
wards; and an account, wrought by any 
contraction, may be proved by performing 
the operation at large, or by a different con- 
traction. 
The following examples will serve to ex- 
ercise a learner in this rule. 
1. Multiply 
87945 by 
2 
2 
947321 by 
3 
3 
7914735 by 
4 
4 
49782147 by 
5 
5 
5721321 by 
6 
6 
4794321 by 
7 
7 
7654319 by 
8 
8 
3721478 by 
9 
9 
4783219 by 
It 
10 
4733218 by 
12 
11 
4783882 by 
21 
12 
2179929 by 
32 
13 .* .. ... 
921577394 by 
84 
14 
217431473 by 
132 
15 
47314796 by 
144 
16 
217932173 by 
96 
17 
314731271 by 
121 
18 
4796427 by 
238 
19 
470621472 by 
432 
20 
479621473 by 
453 
21 
479632179 by 
473 
22 
473457896 by 
963 
23 
943446788 by -987 
24 
49416739 by 
298 
25 
479327 by 
403 
26 
4932149 by 3028 
27. .. 
4731214 by 3008 
28 
49496 by 4009 
29 
97213217 by 
904 
30 
49321729 by 
706 
31 
4932920 by 
720 
32 
493679310 by 
970 
33 
7893470 by 
760 
34 
479379340 by 
900 
COMPOUND MULTIPLICATION. 
I. If the multiplier do not exceed 12, 
the operation is performed at once, begin- 
ning at the lowest place, and carrying ac- 
cording to the value of the place. 
Examples. 
£. s. d. 
cwt. qr. ft). 
13 .. 6 .. 7 
12 .. 2 .. 8 
9 
5 
119 .. 19 .. 3 
62 .. 3 .. 12 
A. R. P. 
ftb. oz. dwt. 
13 .. 3 .. 18 
7.. 5.. 9 
6 
12 
83 .. 0 .. 28 
89 .. 5 .. a 
