•i 8.4 
, What is the value of of 
.a lb. troy ? 
3 
I 2 
4)36(902. the anfwer. 
A R I T H 
What is the value of \ of 
ol. 3'S. 74d„ 
Anfwer, 
1 . 
s. 
d. 
8 
3 
7 " 1 ' 
4 
1 1 2 
14 
6 ( 
4 
13 
6 
6. What is the proper quan¬ 
tity of jr of 7 cwt. 3qrs. 
8|ib, 
Cwt. qrs. lb. 
.84 
7 3 
P*L 
Anfwer, 3 
264 
4. What is the proper quan¬ 
tity of J -3 ot a ton ? 
11 
20 
16)22o( 13 cwt.. 
12 
4 
16)48(3 qrs.. 
Anfwer, 13.cwt. 3 qrs. 
Problem X. To reduce any given quantity to thefra.lili.on 
.of any nrcater denomination oj the fame kind. Reduce - the 
.quantity to its lowed denomination mentioned, annexing 
thereto the fraction (if any) ot that denomination foi a 
.■numerator; then reduce the integral part to tne fame de¬ 
nomination fora denominator, and, laflly, reduce the fac¬ 
tion to its loweft terms. This and the laft Problem prove 
each other. 
Ex. r. Reduce 12s. 8d. 2^—qrs. to tlv 
pound fierling. Titus, 12s. 8d. 2 J j-j- t ] IS 
a.numerator, and il. =; gfoqrs 
6l0ia ‘ 6l°X I I + ' 0 _. ”/j:v 7 1 tbefrne. 
lherefore,———=-7— - — f „—n 1, 
960 960XH lofo 
Ciou required ; the greateft common mealurc being 960. 
Ex. 2. Reduce i6s. 9 d, ?a q rs. to the fradtion ofa guinea. 
16s, 9 d. 24 _So 6 |_ 8 o 6 x_ 5 j 4 - 2_4032 
M E T I C, 
the given fraction is to its denominator, fo is the afligrted 
numerator to its denominator. 
Ex. Reduce 4 to a fraction of the fame value, whofe 
numerator fhall be 12. As 3:4:: 12 : 16, the new deno¬ 
minator; and if .the new fraction. 
P-Ro* it 1 .Em XIV. To reduce frabiions of different denomi¬ 
nators to thoje of equal value, having a common denominator. 
Multiply each numerator into all the other denominators, 
except its own, for a new numerator; then multiply all 
the denominators together for a common denominator. 
And when any of the propofed Quantities are .whole or 
mixed numbers, compound or complex fractions, reduce 
them firft to ample ones by .their proper rules. 
Ex. Reduce4, f,tj. f, and to a common denominator. 
fraction 
= 61 ciS-qn 
for a denominator. 
6720 
of a 
. for 
Thus 
guinea, 
Ex. 3 
Thus 
guinea 1008 1008X5 
the anfwer. 
. What part of Si. 3S. 7|d. is 4I 
al. 13s. 6d. 4488 
H- — -—-qrs 
81 . 3 s - 7854 
5040 
13S. 6d. 
yj the anfwer. 
f of 
Her ling. 
Ex. 2. 
Thus 
Reduce 
1 X r 2 X 
iyl. to the fraction of a penny. 
l^d. 
8 
Ex. 3. 
Thus 
Ex. 4. 
Thus 
640 3 2 
Reduce to the fraction of a farthing. 
1 X 2 °X 12X4 
1440 
1X12X4 2 
:-—— qrs. 
7 2 3 
Reduce 17 -| 80 grs 
17280 
: ib. the anf. 
24X1X12 5 
1 X 3 X 4 X 5 X 7 = 420 ^ 
2X4X5X7X2—560 1 
3 X 5 X 7 X 2 X 3=630 }■ 
4X7X2X3X42=672 
6X2X3X4X5=720 
(1 
new numerator for 
if 
- If 
2X 3X4X 5X7=840 the common denominator : winch 
put under ever) - one of the new numerators found above, 
and you haver a new fet of fradtions, viz. , 5 _ia, 0^0 * 
I4I", and all of the fame denomination, as appears 
from the operation itfclf; and all of the fame value with 
their refpedtive original fradtions, by Problem I. 
If the denominators have all one common meafure, di¬ 
vide them by it, then multiply both terms of each given 
fraction by the quotients of all the other denominators, 
which will produce as many new fradtions, in lower terms 
than the firft rule. 
Ex. Reduce -f, f, and to a common denominator. 
The quotients are 4, 3, and 7, the greateft common mea. 
fure being 3. 
Wf| 
5 _ 5 X 3 X 7 . 
12 12X3X7" 252 
Then < * = ± XJX± = LL± 
9 9 X 7 X 4 2 5 2 
8 8 X 4 X 3 96 
Problem XI. To reduce frations of one denomination to 
their equivalent of another denomination. When a certain 
number of the leaf! denomination are contained in, or 
.equal to, one of the greateft, multiply the numerator by 
t]ie laid number when the redudtion is from a greater to a 
Iqfs denomination, but tlpe denominator by the faid num¬ 
ber when from a lefs to a greater. When a certain num¬ 
ber of the leal! denomination is not equal to one of the 
greateft, reduce the given fraction for a numerator, and 
the integer the iVadtion is to be brought to for a denomi¬ 
nator, botti to one denomination. 
Ex. 1. Reduce £ of a penny to the fraction of a pound 
Til u s--- =—-1 • 
8X12X20 640 
_2i 21 X 4 X 3 252 
the new fradtions re¬ 
quired. 
troy, to the fradtion of a pound. 
864 
5X24X20X12 5 X 
Problem XII. To reduce a fraclion toits equivalent that 
[flail have any afgned denominator. As the denominator of 
V the oiven fradtion is to its numerator, fo is the afligned de¬ 
nomination to its numerator. 
Ex. Reduce £ to a fraction of the fame value, whofe 
denominator may be id- As 4:3:: 16 : 12, new nume¬ 
rator; therefore, is the fradtion required. 
Problem XIII. To reduce a fraElion to its equivalent 
that Jhq.ll have any ajjigned numerator. As the numerator of 
When the feveral denominators are all divifible by the 
fame number, divide them by their greateft common di- 
vifor, letting the quotients underneath ; then find the leaft 
number that all thefe quotients can meafure, and divide 
this number leverally by all thefe quotients, fetting the 
new quotients underneath. Then multiply both terms of 
each fradtion by its nevv quotient, and you will have the 
correfpondent fradtion required in its loweft terms. 
Ex.. Reduced^, =p ££, and £, to a common denominator. 
The firft quotients are 12, 8, 6, and 3 ; the greateft com¬ 
mon meafure being 3. Now the leaft number thefe quo¬ 
tients will meafure is 24, which being divided feverally by 
each of thefe firft quotients, the ndw quotients will be 2, 
3, 4, and 8. Multiply the terms of each given fradtion 
by its refpedtive nevv quotient, and they will be |4, 
A 4 , and 4 |, being reduced to a common denominator, and 
in lower terms than by any of the foregoing rules. 
Problem XV. Several fraBions being given, to find as 
many whole numbers in the fame proportion. Reduce the frac¬ 
tions to a common denominator, and the feveral numera¬ 
tors will be to each other as the given fradtions. 
Ex. Suppofe the given fradtions, |- and £; find two 
whole numbers in the fame proportion. Thefe reduced to 
a common denominator are -§- and Therefore the num¬ 
bers 5 and 6 are in proportion to each other, as -|-and £. 
That is, £ : f :: 5:6; for ^=^= 3 £. 
8 4 
ADDITION of VULGAR FRACTIONS. 
Reduce complex and compound fradtions to fingle ones 
(by Prob. VIE and VIII.) and fradtions of different deno¬ 
minators to a commopdenominator (by Prcb. XIV.) Add 
all the numerators together, and under their fiim write the 
common denominatorj then, if it be an improper fradtion, 
reduce 
