A R I T H 
tain number of tens’, hundreds, thoufands, &c. multiply 
by the number of tens, hundreds, thoufands, &c. and then 
add or fubtraCt for what the given multiplier is Ihort of, 
or exceeds, the number of tens, hundreds, thoufands, &c. 
Ex. i. Multiply 2762 by 4002. 
Firft 2762 X4000=110480001 
And 2762 X 2 — 55 2 4 j 
ProduCt 11053524 
Ex. 2. Multiply 87645 by 99 
,o ; g s, %°} s “ bma 
Produft of 99 = 8676855 
To fquare a number is to multiply it by itfelf, and to 
cube a number is to multiply the fquare of the faid num¬ 
ber by the number itfelf. Thus, 4X4=16 the fquare of 
4; and 16X4=64 the cube of 4. 
Multiplication may be proved by making the multipli¬ 
cand the multiplier, for then, if the product is the fame 
as before, the work is right. There is alfo a method of 
pi'oof by divifion; for the product being divided by either 
of the faCtors will evidently give the other. 
Compound Multiplication, teacheth to find the 
amount of any given number of different denominations, 
by repeating it any propofed number of times. 
Rule. Write the multiplier under the leaft denomination 
of the multiplicand. Multiply the number of the lowed 
denomination by the multiplier, and find how many units 
of the next higher denomination are contained in the pro¬ 
duct, as in Compound Addition. Write down the excefs, 
and carry the units thus found to the next fuperior deno¬ 
mination, with which proceed as before. Proceed in the 
fame manner with all the other denominations to the high- 
eft, and this produCt with the feveral remainders will be the 
amount required. 
1 . s. d. Cwt. qr. lb. 
Ex. 1. 7 9 7s Ex. 2. 12 2 8 
__7_ _5_ 
5 2 7 4 § 62 3 I* 
If the multiplier be a compofite number, multiply fiic- 
ceffively by its component parts, the fame as in Simple 
Multiplication. If the multiplier cannot be produced by 
the multiplication of fimple numbers, take the nearett 
number to it either greater or lefs, and multiply by its 
parts as before. Then multiply the multiplicand by the 
difference between this number and the multiplier, and 
add or fubtraft the product from that before found, ac¬ 
cording as it may be required. 
1 . 
s. 
d. 
35 
17 
9 
by-67 
8 
2S7 
2 
O 
= 8 times 
8 
2296 
l6 
O 
= 64 times 
107 
13 
3 
= 3 times 
2404 
9 
3 
= 67 times. 
The method of proving the operations is the fame as in 
Simple Multiplication. 
DIVISION 
Is a compendious method of fubtraCtion, and teaches to 
find how often one number, called the divifor, is contained 
in another, called the dividend-, and the number fousrht is 
called the quotient. The fign or character of divilfon is 
denoted thus -=. 
Rule. Set down the dividend, and the divifor on the 
left hand of it within a curved line, alfo make another 
curved line on the right hand for the quotient. Enquire 
how' often the firft figure of the divifor is contained in the 
firft figure of the dividend, or in the two firft figures when 
that of the divifor is greater, and place the anfwer in the 
Vol. II. No. 64. 
M E T I C. ,6 9 
quotient. Multiply the whole divifor by the quotient fi¬ 
gure, and fet the produCt orderly under the dividend to¬ 
wards the left hand and fubtraCt it therefrom. But note, 
if this firft produCt be greater than that part of the divi¬ 
dend, a lefs figure muff: be placed in the quotient; and, if 
the remainder be greater than the divifor, a greater figure 
muff: be placed in the quotient. Bring down the next fi¬ 
gure of the dividend, annexing it to the remainder; then 
this number is called the dividual. Seek how often the 
divifor can be had in the dividual, and proceed as before, 
till all the figures are brought down, one by one ; and note, 
for every figure fo brought down, a correfponding figure 
muft be placed in the quotient, except when the dividual 
is lefs than the divifor, and then place a cypher in the 
quotient. If there be a remainder after fuch divifion is 
finifiied, annex it to the quotient with the divifor under it 
a fmall line being drawn between. 
Proof. Multiply the divifor and quotient together, 
and to the produCt add the remainder (if any); that fum 
will be equal to the dividend, if the work be right. 
Ex. Divide 462146141 by 17. 
Dividend. 
Divifor 17 ) 462146141 ( 27185067 quotient. 
34 . 17 
122 
190295471 
is 9 
27185067 
31 
1 7 
462146141 Proof 
144 
136 
86 
!i_ 
114 
102 
(21 
11 9 
2 or ^ rem. 
When the divifor ends with cyphers, cut them off, and 
cut off as many places from the right hand of the divi¬ 
dend ; and perform the divifion by the remaining figures: 
and, when that operation is finifiied, annex the figures cut 
off from the dividend to the remainder. 
Ex. 504J000 ) 416S9042I513 ( 82716 quotient, 
403 2 ' '' • 
1369 
1008 
3610 
3 3*8 
824 
5 0tL 
3202 
3 ° 2 4 
178513 remainder. 
Proof 41689043513 
When the divifor is 12, or lefs than 12, divifion may be 
performed expedition!!}', by multiplying and fubtracting 
mentally, and writing down the quotient below the divi¬ 
dend. But, when the divifor is a compofite number, it is 
much eafier to divide continually by thole numbers than 
by the whole divifor at once; that is, divide the dividend 
by one of thofe numbers, and that quotient by the other, 
and fo proceed. If there be any remainder after fuch di- 
vifions, multiply the laft remainder by the preceding divi¬ 
for, and to the product add the remainder belonging to the 
fame divifor; then multiply the fum by the next^prece¬ 
ding divifor, and to the produCt add its correfponding re¬ 
mainder; and fo proceed through all the divifors and re¬ 
mainders, and the laft fum wilf be the true remainder, as 
if the divifion had been performed all at once. 
X x. 
Ex. 
