ARITHMETIC. 
In speaking of the contractions and va- 
riety in division, we have already seen, that 
when the divisor does not exceed 12, the 
whole computation may be performed with- 
out setting down any figure except the quo- 
tient. 
Example. 
Divide 689543271 by 37. 
37X2= 74 37)689543271(18636304 
3 = 111 37 
4 = 148 q, q 
When the divisor is a composite number, 
we may divide successively by the compo- 
nent parts : thus if 678450 is to be divided 
by 75, we may either perform the operation 
by long division, or divide by 5, 5, and 3, 
because 5 X 5 X 3 = 75. 
When there are cyphers annexed to the 
divisor, cut them oif, and cut off also an 
equal number of figures from the dividend; 
annex these figures to the remainder. 
171 
148 
Example. 
Divide 54234564 by 602400 
6024,00) 542345,64 (90;$|£& 
54216 
As multiplication supplies the place of 
frequent additions, and division of frequent 
subtraction, they are only repetitions and 
contractions of the simple rules, and when 
. . . 18564 
To divide by 10, 100, 1000, &c. Cut off compared together, their tendency is ex- 
as many figures on the right hand of the di- actly opposite. As numbers inci eased by 
vidend as there are cyphers in the divisor, addition are diminished and brought back 
The figures winch remain on the left hand to their orginal quantity by subtraction, in 
compose the quotient, and those cut off the same manner numbers compounded by 
multiplication are reduced by division to 
the parts from which they are compound- 
ed. The multiplier shows how many addi- 
tions are necessary to produce the number, 
and the quotient shows how many subtrac- 
tions are necessary to exhaust it. Hence 
it follows, that the product divided by the 
multiplicand will give the multiplier; and 
compose the remainder. 
Example. 
Divide 594256 by 1000. 
1,000) 594,356 
Ans. 594$&. 
When the divisor consists of several fi- because either factor may be assumed for 
gures, we may try them separately, by en- the multiplicand, therefore the product di- 
quiring how often the first figure of the divi- vided by either factor gives the other. It 
sor is contained in the first figure of the di- also follows, that the dividend is equal to 
vidend, and the considering whether the se- the product of the divisor and quotient mul- 
cond and following figures of the divisor be tiplied together, and of course these opera- 
contained as often in the corresponding ones tions mutually prove each other, 
of the dividend, with the remainder, if any, To prove Multiplication. Divide the pro- 
prefixed. If not, we must begin again, and duct by either factor : if the operation be 
make trial of a lower number. right, the quotient is the other factor, and 
We may form a table of the products of there is no remainder, 
the divisor multiplied by the nine digits, in To prove Division. Multiply the divisor 
order to discover more readily how often and quotient together ; to the product add 
it is contained in each part of the dividend, the remainder, if any ; and if the operation 
This is always useful when the dividend is be right it makes up the dividend. — We 
very long, or when it is required to divide proceed to 
frequently by the same divisor. 
COMPOUND DIVISION, 
For the operation of which the rule is ; 
when the dividend only consists of different 
denominations, divide the higher denomina- 
tion, and reduce the remainder to the next 
A a 2 
