ARITHMETIC. 
The following examples will furnish the 
learner with practice. 
1. 21 ells of Holland, at 7s. 8id. per ell. 
Ans. £S ..1.. 10|. 
2. 35 firkins of butter, at 15 s 3\d. per 
firkin. Ans. £26.. 15 ..2J. 
3. 75ft. of nutmegs, at 7s. 2\ d per ft. 
Ans. £27 .. 2 .. 2f 
■l. 37 yards of tabby, at 9s. 7 d. per yard. 
Ans. £17.. 14.. 7. 
5. 97 cwt. of cheese, at 11. 5s. 3d. per 
'cwt. Ans. .£122 .. 9 .. 3. 
6. 43 dozen of candles, at 6s. 4 d. per doz. 
Am. £ 13 .. 12 .. 4. 
7. 127 ft of bohea tea, at 12s. 3d. per ft. 
Ans. £77 .. 15 .. 9. 
8. 135 gallons of rum, at 7s. ad. per gal- 
lon - Ans. £50 .. 1 ...3. 
9. 74 ells of diaper, at Is. Aid. per ell. 
Ans. £5 .. 1 .. 9. 
The use of multiplication is to compute 
the amount of any number of equal articles, 
either in respect of measure, weight, value, 
or any other consideration. The multipli- 
cand expresses how much is to be reckoned 
for each article, and the multiplier expresses 
how many times that is to be reckoned. As 
the multiplier points out the number of 
articles to be added, it is always an abstract 
number, and has no reference to any value 
or measure whatever. It is therefore quite 
improper to attempt the multiplication of 
shillings by shillings, or to consider the mul- 
tiplier as expressive of any denomination. 
The most common instances in which the 
practice of this operation is required, are to 
find the amount of any number of parcels, 
to find the value of any number of articles, 
to find the weight or measure of a number 
of articles, &c. This computation for chang- 
ing any sum of money, weight, or measure, 
into a different kind, is called Reduction. 
When the quantity given is expressed in 
different denominations, we reduce the 
highest to the next lower, and add thereto 
the given number of that denomination; and 
proceed in like manner till we have reduced 
it to the lowest denomination. 
Ex. Reduce 58?. 4s. 2 \d. into farthings. 
58 .. 4 .. 2i 
20 
1164 = shillings in =£58 .. 4. 
12 
13970 ~ pence in £53 .. 4 .. 2. 
4 
DIVISION. 
In division two numbers are given, and it 
is required to find how .often the former 
contains the latter. Thus it may be asked 
how often 21 contains 7, and the answer is 
exactly 3 times. The former given num- 
ber (21) is called the dividend ; the latter 
(7) the divisor ; and the number required 
(3) the quotient. It frequently happens 
that the division cannot be completed ex- 
actly without fractions. Thus it may be 
asked, how often 8 is contained in 19 ? the 
answer is twice, and the remainder of 3. 
This operation consists in subtracting the 
division from the dividend, and again from 
the remainder, as often as it can be done, 
and reckoning the number of subtractions. 
As this operation, performed at large, would 
be very tedious, when the quotient is a high 
number, it is proper to shorten it by every 
convenient method ; and, for this purpose, 
we may multiply the divisor by any num- 
ber whose product is not greater than the 
dividend, and so subtract it twice or thrice, 
or oftener, at the same time. The best 
way is to multiply it by the greatest number, 
that does not raise the product too high, 
and that number is also the quotient. For 
example, to divide 45 by 7, we inquire what 
is the greatest multiplier for 7, that does 
not give a product above 45 ; and we shall 
find that it is 6 ; and 6 times 7 is 42, which, 
subtracted from 45, leaves a remainder of 3. 
Therefore 7 may be subtracted 6 times 
from 45 ; or, which is the same thing, 45 
divided by 7, gives a quotient of 6, and a 
rtmainder of 3. If the divisor do not ex- 
ceed 12, we readily find the highest multi- 
plier that can be used from the multiplica- 
tion table. If it exceed 12, we may try 
any multiplier that we think will answer. If 
the product be greater than the dividend, 
the multiplier is too great; and if the re- 
mainder, after the product is subtracted 
from the dividend, be greater than the divi- 
sor, the multiplier is too small. In either of 
these cases, we must try another. But the 
attentive learner, after some practice, will 
generally hit on the right multiplier at first. 
If the divisor be contained oftener than ten 
times in the dividend, the operation requires 
as many steps as there are figures in the 
quotient. For instance, if the quotient be 
greater than 100, but less than 1000, it re- 
quires 3 steps. 
Ans. 55882 farthings in £53 4 .. 2|, 
