212 On. Arillmetical Complements. ~ 
. 
' MULTIPLICATION. 
. Supposing the multiplier an abstract number, multiply thé 
affirmative part of the proposed number by the multiplier, and 
only set down as many of the right figures as are in the number 
to be multiplied; then deduct the number formed by the re~ 
maining figures on the left from the product of the negative part 
of the wiven number by the multiplier ;_ prefix this difference with 
a negative sign ever it before the affirmative part, and we have 
the product required. 
3 Examples. 
_ (1) 2) “i hy 
15632 2734 589367 
hatred ee uD ALS, 
40688 TIS72. —«..: 2925569 
The reason is obvious, for 9x 15632=9 x —1000049 x5632. 
’ Now here any one of these products may be made to contain 
only a single negative unit in the-first place of figures; by sub- 
tracting each of the negative digits from 10, as im the prepara- 
tory rule. , ge 2 ve 
_ Thus in the first example the product 40688= 160688" for 
160000 =— 100000 + 60060 = —40000. 
Again,-11872= 189872 ;: also 2925569 = 17125569. 
DIVISION, . : 
“ {f the negative part is divisible by the divisor, wyite the quo- 
tient below, and place the negative sign over it: But if not di- 
visible ‘by the divisor, increase it till it becomes divisible; then 
whatever number was added to the negative part, in order to 
make it divisible, we must add an equal number to the affimative 
part and divide hy the divisor, and set down the quotient after 
the negative part. 
Examples. 
PRS C2) pat? (3) 
‘487832 5);8540 767988 
- 21958 27708 12569 
The reason of this operation is obvious, since the number tov 
be divided consists of an affirmative and a negative part; there- 
fore by increasing each equally, viz. the negative by a negative, 
and the affirmative by an affirmative, thé difference is still the 
same. Thus in example.Second, the number to be divided is 
73540=—70000 +8540; then if to the first ofthese last num- 
bers. weadd —30000; and:to the second we add 30000, we shat 
have — 100000 and 38540, which are together equal to 78540. 
reset 3 bia XXXII, Com- 
