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22-x.
1
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^^^
A
B^ National Library Bibliotheque narionaie
■ T of Canada du Canada
CANADIAN
ARITHMETIC
IN DECIMAL CURRENCY
WITH METRICAL TABLES
FOR THE USE OF SCHOOLS
BY
J. H. RICHARDSON
APPROvatJ BIT THE COUNCIL OF PUBLIC INSTRUCTION
IN OCT. 1870
i
QUEBEC
PhinTed and published dy a. GoTi & C
1871
;,5^^Bffi(f*K;j
sm^^^
r »>'<i!efeF*''4'-:>j!&» '.'--
a A 103
85
Entered according to Act of Parliament of Canada,
in the year 1871, by Augustin Cote, at the office of
the Minister of Agriculture.
\
•iiwii^^^^m^mm^m.m
PREFACE.
f Canada,
e office of
The object of the following treatise may be expressed in one
• ZT\~^J''''^\ The author has aimed to make the work
practically useful : with this view, the rules are expressed
clearly and concisely, illustrated by many examples which are
carefully explained, and followed by numerous exercises, which
will afford the pupil that practice by which alone expertness
and accuracy in the managemonl of; numbers can be obtained
and by which the rules can be impresst-d on (ho memory of the
pupils. It was thought bett to leave the explanation of most
of the rules to the teacher with the blackboard; and as im
pressions made on the mind by seeing, are more important and
as ing than those made by any of the other senses, the
instructor or educator should make a constant use of this
acuity in communicating bis instruction*. It is, however.
thought that the rules are so clear, and the explanations of the
proS'empIo^d ' ^ ^ ' ''"^'^ '^*" ^'''^^ comprehend the
Of the exercises, some are proposed in purely abstract terms,
be ng mtended merely to afford practice to the learner in the
rules; and many 01 the exercises will be found to furnish im-
portant facts in geography, history, &c., both interesting and
instructive. The exercises are graduated so as to form a pro-
gressive course of instruction adapted to the different classes in
aschoo ; and miscellaneous questions are scattered through
the work, which are^recommended to be used as exercises when
taking a review of the rules already mastered
P J, A^Ik '"'' ^""^^"^ .°^ "°"^y' ^^'«hts and measures, with
exeroises thereon, are inserted at the end of the work' and
!^hn„r-fK'^^''°™,'"^",'^^'*.'° introduce the system into 'their
l^:Z:^S^o7^.'' ''''''''' ''^ iard throughout
nf ?hrh^ii?'''"^'f ?.'" /"™u^' arithmetic are Inserted at the end
of the book; and the teacher is recommended to begin at as
stul'whToh wi?lT'''r' 'r'''"''' }i}' P"P"« *" th'« '"^P«rtnt
SS'.oTi ? T r ^% '^°""'^.^ """'^ ^"^°'^"^ "I'^ans of cultivating
the intellectual faculties of his scholars and improving their
reasoning powers. *»"Fiuviug lueir
cnJJ'H f™^|f '"s ^re all new ; and no exertions have been
spared by the author to ensure the strictest ap.c„r..,ny [p ZJZ
part of the work, "^ n.^.cr^
J. H. RICHARDSON
•?
iBt June, 1870.
To Mr. JOSEPH RICHARDSON,
School Teacher, St. Dunstan.
Dear Sir,
I have found in your work a larger amount of
information on the fundamental rules of Arithmetic, suited to
the wants of schools, both as regards a text book adapted to
the capacities of children, and as an efficient means of lessening
the labour of the teacher, than in any other work on the same
subject.
I commend your Arithmetic most heartily to the notice of
teachers and others, interested in the education of children and
youth, and I wish your excellent work a widely extended
circulation.
With best wishes,
I am, dear Sir,
Yours truly,
/• . F. E. JUNEAU,
Inspector of Schools .
I
•J
1870.
amount of
, suited to
adapted to
f lesseniug
1 the same
» notice of
lildren and
extended
of Schools.
KICHARDSON'S
CAMDIAN ARITHMETIC
NOTATION AND NUMERATION.
Arithmetic is the science which explains the properties, and
shows the uses of numbers.
Numbers are expressions or characters that represent u.i. or
more things.
Notation is the art of expressing numbers by characters.
Numeration is the art of reading numbers expressed by
characters.
Ten characters, called figures, are used for the expression of
numbers.
The figures used In writing nv.mbers are : I, 2, 3, 4, 5, G, 7
8, 9, 0, called, respectively, one. two, three, four,' fl've' six'
seven, eight, nine, and zero, cipher, or naught.
(5 NOTATION AND NUMERATION.
Numbers higher than nine are expressed by two or more of
these figures together, thus .
Ten
Eleven
Twelv'j
Ttiirleen
Fourteen
Fifteen
Twenty
Twenty-three
One hundred and ten
One hundred and seventy
Two hundred and nine
Two hundred and twenty-six
is written
10.
11.
\-2.
13.
14.
15.
20.
231
110.
no.
209.
226.
When a number consists of several Hgures, the first figure on
the right hand is called the units' figure, the second figure from
the right hand the tens' figure, the third figure from the right
hand the hundreds' figure, the fourth figure from the right hand
the thousands' liguf*?, 4q. iT/ T
The cipher or zero alone is of no value ; but when used with
other figures, it changes their value. Thus, the figure 6 alone
denotes 6 ; but by annexing one cipher, il becomes 60 ; by an-
nexing two ciphers, it becomes 600, Ac The figures 65 denote
sixty-five ; but by inserting a cipher between, the value is
changed to 605.
To facilitate the reading of numbers expressed by several
figures, they are divided into periods of three figures each,
beginning at the right hand. The first period of three figures
on the right hand is called units, the second period thousands,
the third period millions, the fourth period, billions, the fiah
period trillions, and so on, according to the following :—
3
.2
.S o
3 ^
era
3
en
•a
t. o r:3
c g e
WHO"
a
o
g
'5
10.
II.
V2.
13.
14.
15.
20.
23.
110.
170.
209.
226.
NOTATION AND NUMERATION.
NUMKRATFON TAni,E.
11
a
.2
c o
3 =
£ O
3 33
in
C
o
3
c
■a
&• 'E
1^
-3
cri D
3 3
S 3
c
o
■3 —
I/>
C
o
rr en
«-H .2
o ^
3
O
O
en
■S -i
CO
e 3
s §
O 33
- . -^ 3
O C t. o
3 — S 3
D .~ .3 (D
■a
a
? go
5 "3
■s §
, to
^ 3
2 «■
tn j3 -a
3 t, o
O XJ
— 3
3
3 "3
a
•r r- en ♦J
353-=
-3 Q^ C
21,20,19,18,17,16,15,14,13,12,11,10,9, 8, 7,6, 5, 4,3, 2, I,
m
a
o
3
'3
O
en
C
o
73
(0
o
^
en
n
I
c
o
en
3
3
o
H
3
The periods after quintillions are called sextillions, septillions.
octillions Ac but It IS seldom necessary in actual practice to
express numbers exceeding millions.
of the'^^^eriUds"""'^"'^^ '' '^ necessary to remember the names
Thus in reading h<. .expression 472,536,000,704,006, by
liv ding the number mto periods of three figures each we find
that there are live periods, the tiflh jieriod from the right hand
being four hundred and seventy-two trillions, the fourth five
liPd nl-r^ ""'"'^-^^^^ ^"'"g "° millions, the
E E.Tr\ " T''T'''\ i*y '^•1''"^^^' '" ^he second period we
ha^e seven hundred and four thousand, and in the first period
SIX. I he whoe ,...mher is therefore read, four hundred and
seventy-two trillions, five hundred and ihirty-six billions seven
hundred and four thousaud and six.
„PH5L"I'f^M°'^ ^'r" ^^o^^^y "•''"ch numbers are divided into
periods of three figures each, is that which is employed by the
8
NOTATION AND NUMERATION.
French and ItalmriH. It is strongly ncoinmcnded for its sim-
plicity, nriil it htts hof^n mloptcH in sonic EnKlish works. Fn
most Enf,'lish works however, tlio periods arc made to consist
of six tlgnrcs each ; and as they have the same names as thoio
in thetahic given ahove, ^thonsands however heing hmiled to
three places), tlie niles given above will he aiiplicable in this
method, if the periods are made to consist of six figures each,
instead of three, and the second period be called millions, the
third billions, Ac, as in the following lalde. The answers to
the exercises are given according to both methods.
OLD NCMERATION TABLE.
IV. Trillions.
III. Billions.
II. Millions.
I. Units.
S Hundreds of thousands of trillions.
w TciiH of thousands of trillions.
j3 Thousands of trillions.
^^ Hundreds of trillions.
p Tons of trillions.
w Trillions.
' S Hundreds of thousands of billions.
^ Tons of thousands of billions.
S Thousands of billions.
tn Hundreds of billions.
*■ Tena of billions.
^Billions.
« Hundreds of thousands of nii'Iicn:.
M Tens of thousands of million?,
p Thousands of iLillions.
,<a Hundreds of millions.
»Tens of Millions.
,~*Millions.
< Hundreds of thousandi.
" Tens of thousands.
-'''Thousands.
-"Hundreds.
,'«Ten8.
>- Units.
2. 1
3. !
4. i
5. 5
6. '
7. i
8. 5
cd Tor its sim-
h works. In
lade to consist,
1(1 mes as thoio
ing limit«(l to
licnblt) in this
IlK'iros tJQch,
I inillions, the
ho answers to
i.
of trillions.
Uiona.
of billions,
lions.
)f million:
Uicn?.
NOTATION AND NUMERATION. 9
EXEHCISE 1.
Write down in words or name tho following numbers •—
1. 27 ; G3 ; 208 ; 305 ; 750 ; 932 ; 7605.
2. 5900 ; 10100 ; 25002 ; 200090 ; 402000
3. 0300200 ; 27000042 ; 600007000 ; 123456789
4. 5OI23()()()S0 ; 702300000007
5. 2600970400000 ; 900460000070004
0. 70'. 00006030002000; 500702300001
7. 6009004003002005 ; 2002002020
8. 2714683529123456742.
To write numbors in figures :—
/?uie.— Beginning ni the loft hand side, place each significant
llgure in its corresponding period, and fill up any vacant places
that may occur in any period with ciphers.
ExAMi'LP— \yrite in figures the number thirty-seven millions'
seven thousand and nine. * t-ujuuuons
f)nT'/'^,.'-'T '""''"'' '^',""°' "'" ^''''°"'l s-^ven thousand, and the
third thirty-seven millions, therefore wo write two cii)hers in
iumS S7009 ^^"^ '" ^^' '"'""'^ ^^ "^^''^ ^' °'^"^'" ^^^
EXKRCISE 2.
Write down tho following expressions in figures :—
1. Seventy four.
2. Two hundred.
3. Seven hundred and nine.
4. Two thousand and sixtv-seven.
5. Four thousand and two'.
6. One thousand eight hundred and sixty-nine
7. Throe thousand and six.
8. Nine thousand and sixty.
9. Five thousand seven hundred ana two
0. Fifteen thousand two hundred and thirty.
11. Ihirty-nino thousand and seventy-four
2. Six hundred and four thousand and nine
eHt ""'''"^"^ *^'^"^y thousand nine hundred and
14. Two hundred and four millions seven hundred and
sixly-hve thousan.l seven hundred and ninety-two
15. Ninety-seven billions six millions and thirty-four. '
in. , wo ftuiiGiiH and scvcnty-uiao
*^" andVour"'^'*''^ ^'"'""^ '"'""'^ ™"'''"^ '"°"'' *ho»8a"d
10
NOTATION AND NUMERATION.
M
18. Sixteen billions sixteen millions sixteen thousand and
sixteen.
on ^wenty-four trillions seven millions and ninety-six.
^0. Ihree hundred and sixty-live trillions two hundred
and forty-seven billions six hundred and thirty-nine
millions live hundred and seventy-three thousand six
hundred and ninety-four.
In Roman notation seven letters are used which with their
values are :
I.-
V.-
X.
L.
■ One.
Five.
Ten.
— Fiftv.
C-
D.
M.
One hundred.
Five hundred.
One thousand.
Other numbers are expressed by combinations of these letters.
When a letter is repeated its value is repeated, but no letter
should be repeated more then three times.
When a letter of a lower value is written after one of a
higher, Uieir values are added, and their sum is the value of
the whole.
When a letter of a lower value is written before one of a
iughor, their values are subtracted, and the dilference is the
value of the whole : thus.
400.
.^00.
600.
700.
800.
900.
1000.
2000.
3000.
3500.
MDCGCLXX.- 1870.
■ — ■ . I
A dash placed ov^r a number consisting of one or more
letters, multiplies its value by 1000.
Thus GLX.=160, but GLX.=1 60000.
Exercise 3.
Express the following numbers in fi^rures :
IV, XIV, XX. VIII, XVI, XLV, LXXXf, CCCXVIt
DqXLVni,^GCG, CDVII, DLIV, GMXII, MGXX, WMDCCG,'
MD, XL, LXXX, XM, XLMMGXXVII, MM, VlT, MXVIf,
VMMXLII, MDCGGLXVIII.
I.N.
sen thousand and
nd ninety-six.
ns two hundred
d and thirty-nine
rce thousand six
vhich with their
- One hundred.
- Five hundred.
- One tiiousand.
IS of these letters.
ted, but no letter
after one of a
m is the value of
before one of a
diiference is the
— 400.
— ."iOO.
— 600.
— 700.
— 800.
— 900.
— 1000.
— 2000.
— 3000.
— 3500.
ID —
GCLXX.- 1870.
of one or more
S[. CCCXVII,
XX, MMDGCG.
, VlT, MXVIf,
SIMPLE ADDITION.
Exercise 4.
u
Write tho following numbers in Roman Numerals •
n2t' f •^'' ^^- '04, 692, 573. 896, 365, 144 5270 9650 7408
9005 2560, 10724. 49650, 50070, 78964 42763 81796 802764*
453000, 792800, 1702500, 3742508. ' ' '^^'
SIMPLE ADDITION.
Simple Addition teaches how to add toffpfhpr i-am «,. ™«»„
quantities of the same denomination so'af'S'mS LTnt
The quantities to be added are called the addends thn
?heTr sii^"'' '' '^""' '' '''' ^''^"<^« ^^k«" together ?s called
«,h^?f >^"»+i^"^^^^^".*^'-"^"^s that the quantities between
which It stands are to be 3d together thiiQ 9 j. 7 »i;„r- o
and 7 added together are L '''^^^^^^' thus 2 + 7 that is 2
The sign = denotes that the quantities between which it
f ?s"equ:rtor ' as 3 + 2 + 4 = 9 that is the sum Sf it and
ADDITION TABLE.
2 and
1 are 3
2—4
3 — 5
4 - 6
6 — 7
6-8
7 ~ 9
8 — 10
9-11
10 — 12
U — 13
12 — 14
3 and
1 are 4
2—6
3—6
4 and
1 are 6
2—6
3 — 7
6 and
1 are 6
2 - 7
6 and
1 are 9
2 — 10
3 — 8 3 — 11
9 and
1 are 10
12 and
1 are 13
4 — 7 4 — 8 4- 9 4 — 12
6 — 81 6 — 9j 5 — 10
6 — 9l 6 — 10 6 — 11
7 — 10
8 — 11
9 — 12
10 — 13
r - 11
8 — 12
9 — 13
7 — 12
5 — 13
6—14
7 - 16
8 — 13 8 — 16
9 — 14
11 — 14JI1 — 15
12 — 16 12 — 16
10 — 14|lO — 15
11 — 16
2 - 11 2 _ 14
3 — 12 3 — 16
4 — 13 4 — 16
6 — 14 6 — 17
« — 16 6 — 18
7 — 16 7 — 19
8 — 17
9 — 18
9 — 17
10 — 18J10 — 19
11 — 191:1 — 20
12 — 17JI2 — 20 12 — 21
8 — 20
9 — 21
10 — 22
11 — 23
12 - 24
12
SIMPLE ADDITION.
I '
Pupils should be continued at the above addition table and
similar exercises until able to add with facility ; for without
practice in some such exercises the operation will be found to
be tedious and difflcult.
Rule. 1. Place the quantities to be added below one another
so that units will ^tand under units, tens under tens, hundreds
under hundreds, dec. 2. Then commencing at the right hand
side, add together from the bottom the figures \n the units
colnmn ; if the sum does not exceed nine set down the figure ;
3. But if the sum exceeds nine set down the right hand figure,
and carry the remaining figure or figures, which is the number
of tens in the number, to the next column ; because ten in any
column is equivalent only to one in the column immediately to
the left of it. 4. Proceed in the same manner with each coluam
to the last, the sum of which set down in full.
6.-
EXAMPLE.
724
40
151
742
Add together 724, 40, 151, and 742.
First we arrange the quantities so that units
are under units, tens under tens. Ac. Then
adding together the figures in the first column
— ; — we set down 7 their sum under the units co-
1657 sum lumn, the sum of the second column is 15, we
th'-refore set down 5, the right hand figure and
carry 1 to the next column, the sum of which
with I added to it is 16, which is set down in full.
Proof. 1. Bogin at the top and add the several columns
downwards, which should give the same result as by the rule,
or,
2. Add together all the quantities except that in the top line,
then to their sum add the quantity in the top line ; and if the
resL.!t is the same as that obtained by the rule the work may be
considered correct.
EX£RCISES.
1.
3.
3.
4.
6.
7324
2706
64736
928764
5316742
8orr
312
17;!4
236
7654321
2430
8964
83965
rsfi.sft
8978
3607
2106
27
626436
27836
10.—
I
i 14. Add t(
; 15. Add 1
t906vds. : 7;
] 16. Find
ff 87568 + c
;s 17. Find
72564902 +
• 18. Find t
^ 2463 + 3£
19. Find t
,786 + 2794 ■
^ 20. Add t
line thousai
and fin,y-sev(
isixty-eight.
21. Add 1
leventy-four
lUndred and
iixty-five ; fc
>ev6n thousa
SIMPLE ADDITION.
13
lition tfible and
ty ; for without
ivill be found to
ow one another
tens, hundreds
the right hand
es \n the units
iwn the figure ;
jht hand figure,
1 is the number
ause ten in any
immediately to
th each column
IS so that units
ms. Ac. Then
he first column
ir the units co-
lumn is 15, we
land ligure and
sum of which
i.
sveral columns
as by the rule,
in the top line,
le ; and if the
e work niay be
6.
6316742
7654321
897S
27806
6. — pounds. 7.— tons.
9264 746
1835 i)67
7409 843
7863 662
6298 479
6314 843
6701 247
8.— yards. 9,— bueheli.
729 3906
463 9678
397 2847
866 3964
279 1868
768 2547
496 9870
10. — inches.
9274
3768
9ft68
2374
4680
7531
9246
8218
4667
5108
3742
6938
2714
2583
9673
6678
6013
6724
1896
11. — days.
829
766
358
902
631
790
642
812
643
678
109
367
429
681
432
667
198
268
937
12.
-miles.
872
409
876
693
870
365
742
964
678
369
472
896
759
804
968
247
964
678
964
13,— feet.
9864
6957
8972
4669
8729
4596
9872
4658
2907
6784
6972
6578
9834
6786
9672
6584
9327
4686
9307
1869 lbs. ; 9724 lbs.
; 6002 yds. ; 28 yds. ;
; 14. Add together 7642 lbs. ; 9763 lbs ■
, 15. Add together 2479 yds. ; 248 vds'
Doe yds. : 7592 yds ^
< l^vJ'"*^ *''^ S""i of 90068 -I- 742 4- 96742 4- S7qfiq J_ 07/
H- 87568 + 93275 -I- 87563. "^^ -^ >'0'4>i + 87963 + 974
17. Find thp sum of 2796824 + 87073064 -I- onTnARno _i_
72564902 + 78569204 + 3041 63874 + 987653792 + 749 sS "*"
18. Find the sum of 9248 + 6702954 1^48 X TS^Ja?,? oA^,/ n
#f 2463 4-3964872 + 1 8978 + 924641 + 365 + ^'^^^ + ^^"^^
19. l<md the sum of 9874 4- 69481 i? -l is/. _l tn-r-i , «« .
'86 + 2794 + 18965 + 742917 + 97849^8 "^ ''''' + '' +
. lU. Add together two thousand four hundred anrt <i,^vJ'r, ■
^me thousand eight hundred and sixtyS, ;7our thouSnd
^Jn'f^r"^ together forty-six thousand nine hundred anrl
peven thousand two hundred an. ^ »ijirty-niae. ' ^'
14
SIMPLE SUBTRACTIO^f.
i I
ill
22 Arid together eight thousand eight hundred and eightv-
eigh ; nine thousand and ninety-nine ; seven thousand seven
hundred and seven ; six thousand six hundred and sixty • five
hundred and ninety-eight; nine thousand nine hundred and
ninety-nine ; seventy-six.
r,ino h^'^H '98^^'?'^''. s'^'y thousand and sixty ; nine thousand
nine hundred and ninety ; eighty-seven tiiousand seven hundred
and ninety-four ; fifty-two ; tiiree hundred and seventy-nine •
seven hundred and four thousand seven hundred and four '
ninety ; seventy-seven thousand seven hundred and seventv-
seven ; six hundred and forty-eigat. =cvcniy
24. The populations of the countries of North America are
Russian America sixty thousand, Danish America ten thous-
?t" -f' A a. America three millions five hundred thousand ■
united htates thirty-one millions five hundred thousand'
Mexico seven millions five hundred thousand ; Central America
two millions five hundred thousand ; and the West India
wtle poinXiSi;' J""' ""^ '""'"-^^ ^'^""^^"^ ' ^^^^ ^« ^l-
*n!^A ^ Zf"^" '■'^'^6'ves for goods sold on monday $72 ; on
Sh ""Lf^^' .°" woJ"esday $113; on thursday |68 ; on
in thJ week ^ ^" Saturday $8C ; what amount did he receive
rr^rL^ 'S'l?'^'' "'''^ 9f6 bushels of turnips the first three
^Is n«,° '\l ^ff'i, 'I" ^"'*"^'' ^^'^ ««'^°»d three months ;
748 busho 3 the third three months ; and .S97 busiiels the last
thnje months ; how many bushels did he sell in the year ■'
^„; f;8«n':'3inan travelled 180 miles by steamboat on mon-
lay 114 miles by railroad on tuesday ; and 27 miles on
horseback on Wednesday ; how many miles did ho travel in
hand si
from th(
any figi
add ten
.to the I
one to tl
we inert
Js the sa
Proof
jbers, an
I consider!
? 2. Sul;
onumbers
correct.
? EXAMPI
i 9386
4241
f
5 1 45 ren
9386 pr(
find the r(
; Proof,
?iven nur
■he given
I By the
Irom 9386
diflference be- ^nce to h
SIMPLE SUBTRACTION.
Simple SuBTRAcxroN teaches how to find the
Iween two quantities of the same denomination.
The sign — called minus, when written between two num-
bers, signines that the number which follows the sign, is to be
subtracted from the number before it.
Thus 17 — 9 read seventeen minus nine, signifies that 9 is to
ce subtracted from 17.
Rule. I. Write the less number below the greater with units
under units, tens under tens, Ac. 2. Beginning at the right
ExAMPLf
'1 73049
f 26586
|46463~
I
i 73049
rer
pre
nd 6 remt
he whole
k£
t hundred and eighty-
seven thousand seven
ndred and sixty ; live
id nine hundred and
sixty ; nine thousand
ousand seven hundred
3d and seventy-nine ;
1 hundred and four ;
undred and seventy-
if North America are,
America ten thous-
e hundred thousaad ;
hundred thousand ;
nd ; Central America
md the West India
lusand ; what is the
on monday $72 ; on
thursday $68 ; on
mount did he receive
■nips the first three
Jcond three months :
«97 bushels the last
>ell in the year ?
i steamboat on mon-
; and 27 miles on
iles did ho travjl in
SIMPLE 8CBTRACTI0N. ^5
from thf n' '"k'"""?'' '' '^"'^'''•'' ^'^'^^ "^"'^'•^ '" ^he lower line
from he one above ,t. and set down the remainder. 3 But if
Bny figure in the lower line is greater than the one above .t
add ton to he upger flgur^e, subtract as before and carry one
-to the next figure in the lower line. 4. Because by carrying
.me to the lower figure, we increase the lower line I muc^^
w mcroased the upper by adding ten. and thus the difFerence
is the same as if neither had been increased.
"^^Za ifX' X T^\X^!'T l^he given num.
^considered correct ; or ' ^ ' *^" ^""^^ "^^^ ^«
\ 2. Subtract the remainder from the ereafftr nf \\.^ „•
\ Example. 1. From 9386 take 4241,
I 9386
4241
,^I45j^emainder. The numbers being arranged according to
I 9386 proof; 'Um% ^H ' ''"" V?'^ ^ '^^^^-i'
i ^ ^ "".'" ^ nnd '1 remanis, 2 from 3 ant\ \
iiind the remainder to be 5145.
I.
N.
i the difference be
tion.
}he g,ven numbers, which proves thfcoJre^tneL'oHlfa^orr'
tence to be e.Sairth^' lXTeUTS;rSe"2o'rrtt.^"''^-
E.XA.MPLK 2. Find the difference between 73049 and 26586
^1 73049
1^- Here we say 6 from 9 and 3 remains then
Signifies that 9 is to .P^^remaind.r 4^^^ a^! K t^e'Tppe^ ffgirreTnfs?^^
T73049_proof ^ '^ ^^,« — ^s a 1 , ^ ^
■nd 6 remains, carr'y""" "''mX^ \ 1 f ""''.'' '' ^^-^ "
he whole remaindei^ is t^Tifbre f6463 ™'° ' ''"' ^ '"^"^^'^^ •
between two num-
vs the sign, is to be
3 greater with units
ming at the right.
1^
BIMPLE SUBTRACTION.
l.-^miles.
361845
121432
5. — pounds.
1357960
8G9478
15.— 3126428 — 246804
16.— 156938245 — 75060458
ExERGiSKs. 1 30. By h,
n . , „ yje extent r
i.— inches. 3..-tons. 4.— yards, ^urope 380
68791805 9287694 7920685 i 31. Afar
12310213 3124132 2310213 ^ one perse
— — . . lis ho loft "t
1 32. Whal
O.-^dolJars. 7.— hours. 8.— feet. tWie being m
7598764 3100450 60750012 i^^. The :
957829 801976 30170468 ^"'ope, is
„ „, _^ . npghest mot
[34. Theh
(tf LakeOnt
if the forme
J 35. North
17.— 87136924— 30271 #?»'h Amei
18.— 1401.^06— 71352 f'^l'' of eac
19.- 7325184— 820094 *'y 28 mile
20.— 24150685— 4629507 I 36. The d
Wiles, ami I
21. From seven millions eight thousand, lake two hundredt |e^j^Qol°^
and forty-seven thousand nine hundred and seventeen.
22. Take twenty-seven millions and five, from thirty-foui
millions. ,
23. Take seven hundred and ninety-four pounds, from four I
hundred thousand pounds.
24. Find the difference between 7 days and five thousand I ^^^'ltiplica
days. repeated as n
25. What is the difference between eight millions eight% which it i
thousand eight hundred ; and forty thousand and seven. tThe numb(
26. A person paid 3740 dollars for a house, and spent 2\ipkcand.
dollars in repairs, after which he sold it for 4500 dollars, wha iThp n„rr,K.
was his profit ? iltn L
27. What is the difference between the length of the riveiT ^^'^^"^
Amazon, in South America, the largest river in the world P^^ result (
9.— 7063485 — 6724185
10.— 7999816— 870908
11.— 15280054 — 8629071
12.-64259,360 — 4759643
13.— 5000000— 846921
14.— 7305030 — 25010S6
which is about 4700 miles long ; and the river St. Lawrencf
which with the lakes is about 2140 miles long ?
28. America was discovered in the year 1492 ; Canada ir
1535 ; the city of Quebec founded in 1608 ; Canada taken b
Great Britain in 1629 • city of Montreal founded 1642 ; Quebei
taken from the French in 1759 ; Canada ceded to Great Britair^
jn 1763 ; and invaded by the Americans In 1812. How manv
years elapsed between each (if the above mentioned events, aiii
the confederation of the British North Americnn Provinces
1867?
The multip
bduct.
29. What number added to 7968,
millions three thousand and nine ?
will amount to thrt'l
Jn simple rr
only one d(
A composil
us 72 is a c
tors, 6 and
p.«The siiin x
!twet>n two
ijether. Th
■ seven is eq
I
SIMPLE MULTIPLICATION.
IT
4. — yards.
7920685
2310213
1.
8.— feet.
60750012
30170468
26428
38245
M924
i)1500
25184.
50685
— 246804
— 75060458
— 30271
— 71352
— 820094
— 4629507
take two hundred
seventeen.
3, from thirty-foui
J 30. By how many square miles does America exceed Europe
f.u-op?380000o"r''''' '" ''^'""''' "'"'" ^"'"^ 15500000, and of
J 31. A farmer has 960 bushels of potatoes, lio sells 230 bushels
ilsXS?"'^"'' '^^ ''"'^'''^' *° another, how many bushels
'f32 What is the difference between the value of two farms
*^oV''::''S r'"' ^^^'^ '^o''^'-^- ^^^ the otl...r 796O doHars ?
I 33. Ihe height of Mont Blanc, the highest -mountam in
LU-ope, is 15732 feet; how much higher is Chimborazo, the
ghest mountain in America, its height being 21424 feet ?
^T oiln , '^ 'ooi ^ake Superior above the sea is 600 feet and
rf Lake Ontario 232 feet, ho^y many feet higher above the sea
1| the former than the latter ?
35, North America in its widest part is 3500 miles across, and
u h America 3200 miles, what is the difference between the
idth of each and the isthmus of Panama which is in o.-o part
ily 28 miles across ? ' '
36. The distance of the sun from the earth is 95000000 of
Wi es, an-1 the distance of the moon from the earth is 237000
-lies, how many miles further is the sun from the earth than
' pounds, from foui
and five thousand
ght millions eight'
d and seven.
ise, and spent 2lt]
4500 dollars, wha
length of the rive;
iver in the world
river St. Lawrenc*
g?
p 1492 ; Canada ii
; Canada taken b^
ided 1642 ; Quebc(
eii to Great Britair-
1812. How manvj
ntioned events, aiii
irican Provinces id
amount to throl
SIMPLE MULTIPLICATION.
Multiplication teaches how to find the value of a number
peated as many times as there are units in another number
y which it IS multiplied.
|The number repeated in multiplication is called the mulH-
iThe number which shows how many times the multiplicand
|to be repeated is called the muUiplier.
phe result obtained by multiplication is called the product.
^J^^^P>''P''cand and the multiplier are called factors of the
lln simple multiplication the multiplicand is always a quantity
lonly one denomination. • J 4 ''"'■"•y
[a composite number is the product of two or more factors
.tnJ V^ ^ composite number because it is the product of the
2tors, 6 and 12, 8 and 9, ^ .r 9, 2, and 4.
fc,;'^"^'"'"''^*^^ ''Sn of ffiulliplication, when written
! Pthpn T*? """I'^e'-s- S'&n''"'es that they are to be multiplied
l'letiis'4ua. to r05' = ^''' ^"' is read lifteen multijliad
I
i !
II!
18
MULTIPLICATION TABLE.
Twice
1
are
2
2
—
4
3
—
6
4
—
8
6
—
10
—
12
r
—
14
8
—
16
9—18
10 — 20
11 — 22
12 — 24
3 timea
I are 3
2—6
3 —
4 — 12
6 — 15
6 — 18
7 — 21
8 — 24
9 — 27
10 — 30
II — 33
12 — 36
4 times
1 are 4
2—8
3 — 12
4 — 16
6 — 20
6 — 24
7 — 28
8 — 32
9 — 36
10 — 40
6 times
1 are 6
2 — 10
3 — 16
4 — 20
5 — 25
6 — 30
7 — 35
8 — 40
9 — 45
10 — 60
6 times 7 times
11 — 4411 — 55
12 — 4812 — 60
1 are 6
2 — 12
3 — 18
4 — 24
6 — 30
6 — 36
7 — 42
8 — 48
9 — 54
10 — 60
11 — 66
12 — 72
1
2
3
4
6
6
7
8
9
10
11
12
11. Whentl
f' tie I.— I.
iplicand,
ight han
jKanulUplier
lOduct, belo
— 28|iuP(j or figu
fie next, a
! to one in
|x AMPLE 1.-
~ ^mmultipll
_ 5 J 7 mnltipli
— 63p2 procjuqt
— 7oi carry 6';'
_|y6; 7 tiff
— T'l-efore set d
21!
— 3:
— 84ll
8 times
1 are 8
2—16
3 —
4 —
9 times
1 are 9
5—40
48
66
« —
7 —
8—64
9—72
10 —
11 —
12 — 96
2
3
4
5
6
7
8
9
10
11
12
18
27
36
45
54
63
72
81
90
99
108
10 times
1 are 10
- 20
30
40
60
60
70
80
90
100
11
timet
1
are
11
2
—
22
3
—
33
4
—
44
5
—
66
6
—
66
7
—
77
8
—
88
11 — 110
12 — 120
9
10
n
12
— 99
— lie
— 121
— 132
12
I
2
3
4
5
6
7
8
9
10
11
L2
times
are
.T-mi|es.
76945
2
24|. — pounds.
' 793624
3fi 6
— 6i
—7634 >
— 6319>
72».— 5607 >
-7328 >
__ y'wien the mi
t^s are higl
~ %ie II.— Mu
- ^-Sp'y the pi
— 13S ^^^ '■'^''^*
P factor, &c.
.E.
SIMPLE MULTIPLICATION.
19
times
1 are
2 —
3 —
4 —
7 —
7 times
1 are
12
12
18
24
30
36
42
48
54
60
66
72
if. When the multiplier does not exceed 12.
'■,^le I.— I. Placo the multiplier under the units ngure of the
'^'■-^iplicand, and draw a line below it. 2. Then beginning at
3 — 21
4 —
7 — 49|
8 — 66
14l|j^ight hand side, multipl-yeach figure in the multiplicand by
pjuultiplier ; set down t!»e unit or right hand figure of each
bduct, below the figure multiplied and carry the remaining
28i||ro or figures which is the number of tens in the product
"lie next, as in addition, ten in any column being equjva-
! to one in the column immediately to the left.
|xAMPLE 1.— Multiply 7896 by 7.
'6 multiplicand.
7 moltiplier. Place 7 th« multiplier under 6 the right
10
11 — 7-
12 — 84
w hand figure of the muUiplioand, then 7
<2 produd. times 6 are 42, set down 2 and carry 4 ;
7 times 9 are 63 and 4 are 67, set down 7
70 carry 6 ; 7 times 8 are 56' ahd 6 are 62, set down 2 and
T6; 7 times 7 are 49 and 6 are 55 which i8 the last and i»
■efore set down in full, the whole product therefore is ^5272,
times
are 11
12 times
are
Exercise 1.
22
2
33
3
44
4
55
5
66
6
77
7
88
8
99
9
11!'
10
121
11
132
12
.— mi|es.
76945
2
-pounds.
?93624
6
2.— yards.
73648
3
6. — dollars.
134856
7
3.— pounds.
962847
4
7. — m inutes.
473582
8
4.— iji^Qjie?,
83169A.
5
8. — cents.
694273
9
I.— 7634 X 2
I.— 6319 X 3
.—5607 X 4
!.— 7328 X 5
13.— 79608 X 6
14.-J250ti3 X 7
15.— 16914 X 8
16.— 32592 X 9
17.-32649 X 10
18.— 78295 X 11
19.-32071 5^ 12
20.— 68742 X 7
_ 9^en the multiplier is a composite number, neither of whose
"8 are higher than 12.
1 M^\ II-— Multiply tho multiplicand by one of the factors, and
'"^piy the product thus obtained by the second factor, if
xM *•*« three factors, multiply the second product by tha
I factor, 4c.
141
20
SIMPLE MULTIPLICATION.
ExAMPi,E 2.— Multiply 7384 by 54.
Example
TJ,. f . , . • M 740
,.J I?- , ^. °^^^^ multiplier 54 beina 9 nnrf fi I 23000
we multiply the given numfcer by 9 one 5f the f«.' I
gives the whole product 398736. ftS
©020000
nZblr. **' """'P''"" *' ^'8''«'- ^h«n '2 and not a composite I Example
'* 3674
thft"''f ■",!• "^'"'^ the multiplier under the multiplicand so ^f^'!
that umts wll be under units, ters under tens, Ac. 2 Multh) y i^^
by each figure of the multiplier in succession, etting down th
products, so that the right hand figure in each will bLnTer he
figure m the multiplier which produces it. 3. Then ^dd tL
several^ products together and the sum will be''th" ^eTuiied^
the^3u"^tt\t'yi:aTthifoL'y the multiplicand and if
is correct ^^ *^ *''** obtamed by the rule the work
I
Example 3. Multiply 864 by 43.
2592
3456
37152 product.
When
ciphers.
the
firs^t'%uTe oTl'if 'y ^I ? '^"^ ''^ <^'^^ the
iirsi ngure ol the product under that fiffnrp
KeTf rJ-ifr ^ '^ ' «°/ ''' d'ownlhte
iigure 01 thd product under that figure thpn
oS&H'^l^r tl'ese partial prodS we
obtam the whole product 37152.
multiplier or the multiplicand or both end in
!.
2.
3.
4.
5.
6.
7.
8.
9.
10.
II.
12.
13.
14.
15.
16.
17.
7:
2f
r
92
78
7
35. What
36 What
37. Multip
lundred and
Zh";,„»'"° "■''"'""'"' """« ""» '*■■«- "the »daf loyei^ht,.
„. _ j„_ fliuiiip
•housand tw
ve hundred
Mii
)pf.
^r54 being 9 and C,
by 9 one of the fac-
other factor whicli
16.
8IMPLB MULTIPLTOATION.
'^ Example 4.— Multiply 740 by 23000,
SI
740
23000
222
{48
17020000
■"•r
Here we multiply 74 by 23 and to the product
annex 4 ciphers which gives the whole product.
Id not a composite < Example 5.— Multiply 3674 by 2008.
he naultiplicand so
ns, Ac. 2. Multiply
1, setting down the
h will bounder the
3. Then add the
II be the required
ultiplioand and if
the rule the work
and set down the
under that figure,
set down the first
' that figure, then
ial products we
52.
1 or both end in
leaving out the
5rs at the end of
Set down the first figure of the first partial
product under 8, and the first figure of th« second
partial product under 2, then adding together
these partial products we obtain the reouired
product 7377392.
ExEItCICE 2.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
7428 X
9205 X
7856
365
3456
287
3625
2794
6325
9637
73456
26004
3648
4905 .,
92876 X
78632 X
7013 X
X
X
X
X
X
X
X
X
X
X
X
X
63.
96.
36.
84.
56.
108.
365.
872.
704.
453.
500.
796.
406.
3672.
7005.
2405.
2064.
18. 53284
19. 392605
20. 746058
21. 7096804
22. 8193620
23. 3480006
24. 245600
25. 81243
26. 716018
27. 3576804
28. 4289654
29. 936087
30. 386790 „
31. 8927648 X 750638.
32. 2715906 x 3724.
33. 5816927 X 30876.
34. 8603059 x 63489.
X
X
X
X
X
X
X
X
X
X
X
X
X
7100.
3060.
70306.
73040.
24106.
30018.
7600.
834.
9006.
204.
7056,
8604.
36500.
35. VVhat is the product of 27648 and 7962 ?
36 What IS the product of 906874 and 27685 ?
bundreTS LTfn"*^ three millions sixty eight thousand nine
Ky eight ^ ' ^y^^^^" thousand two hundred and
I 38. Multiply forty miliious three hundred and sixtv five
22
BIMPJLC DIVISION.
39. Multiply 2G78 feet by Sand the product will be theheiKlAn»«;n«^
of mount Chiinbortizo. :wniainen
40. How many yurds are thf-ro in 763 piocos of cloth, on-'*' *''° ^""s'
piece containing 27 yards '( tir the tin
41. How many letters are there in a book, containing '' a^j ept do
pages, each page containing on an average oO'J words, and ^a J " .
word 7 letters '(• tS'" ' 'Viaor
42. There are 525960 minutes in a year, how muny are thdimher di
in 40 years ? iividond
4:}. A clock strikes 156 times in a day, how miny times do^,- „ .'
\i strike in a year ? wmg doi
44. If one barrel of Hour cost 7 dollars, how many doll:iiiP''e33 to
would 1387 barrels cost? minder se
43. How many panes of glass are thorn in a house in whi
there are 7 rooms ; each room containing 3 windows ; and eii
window 8 panes ?
SIMPLE DIVISION.
Division is the method of finding, how often one giv
number is contained in another.
In division the number to be divided is called the divider,
The number by which we divide is called the divisor.
'hoop. I
ich add
IS obtaii
■rect.
t)XAMPLE
f 1 54807
; 7829f
'54807 1
The remainder is any number which may remain, after tJ
division) when tbo divisor is not contained an exact numli
of times in the dividend.
The dombor whioh shows how many times the divisor
contained in the dividend is called the quotient.
5 over,
[in which
|ce and 6
'inch we w
"When the dividend expresses a quantity of one denominati *
the process is called simple division.
When the divisor does not exceed 12 the process is call' ?
short division ; when Ibe divisor exceeds 12 it is called l<y"
division. -t.
The sign -i- called 'he fsini.' u.f division, Wuum placed betwo- *'
two numbers, signif ihe number that precedes the sip*
IS to be divided By the number after it. J
SHORT DIVISION. |
nubi.— i. Piaco the divisor to the k-ft ol the dividend si
paraling them with a line. 2. Find how oaen the divisor
1.
2.
3.
4. 12
5
6.
7.
8.
9. I
10. II
11. I
12.
: i i»ii,.i« ii a i iiiiP
oduot will be IheheiKllntalned in the fln,t figure of the dividend, or. if not contained
13 piocps of cloth, oar'" ^'^^ "'"sl, how often it is contained in the number expressed
book containing v!! ,""; H"^""^?' "!! ^^ '^' '"^^ '^'•^'^ ««"••«« i" the dividend.
tge 5(i(] wordrand .« T ''\ ^°^" ^he figure denoting tho number of times. 3. If
^ • i visor is not contained an exact number of times in the
ar, how many are tho^mber divided, prefix the remainder to the next figure of the
'. ho,v PKiny times do^Litl' "''''f'"'' l^' """^«'- ^^"^ obtained as the first,
y lilting down the next figure of the quotient, and continue the
ars, now many doUilP'^ess to tho last figure of tho dividend, when if there is a re-
. *'°*'*"* s«t it down with the divisor written below
irn »n a house »n whit^* uoiuw.
S 3 windows ; and eai]
how often one giv
is called the dividen
tiled the divisor.
y times the divisor
quolietU.
may remain, after tjj
ined an exact numU
L^!?''^ 1*^!?^ *^^ product of the quotient and the divisor to
Lchadd the remainder if there is any; and if thoDrnduc?
W (Obtained 13 the same as the diWdend, the wZ ?s
Example 1. Divide 54807 by 7.
f 1 54807
7829f quotient.
7
First we set down 7, the divisor, to
the idftof the dividend; then as 7 is
■ 54807 nrnnf "?» contained in the first figure of the
:_ P™^'^' dividend, we divide it into 54, the
s^ number expressed by the first two fl-
A "invop th^.,tu " 8"'?s> m this it is contained 7 times
in Th- V"'?" ^^^ remainder prefixed to the next figure makes
in which 7 IS contained 8 times and 2 over, then 7 into 20
Ice and 6 over, and 7 into 67 nine times and 4 over. undeJ
^aich we write the divisor
ty of one iJenominati *
2 the process is call
ds 12 it is called la
, w.-tM placed belwi
that prece'des the sii:
r.
oft of the dividend s|
V often the divisor
■19
.a
Exercise 1.
1.
2.
3.
375064 -f-
736281 -I.
9406307-1
4. 123456789 4-
5 6342587 -:.
6. 1392684 i
7. 2222222 -i-
8. 7219634 .i.
9. 6312725 -L 10
10. iiiiiiiii ^ ii
11. 5300026 J- 12
12. 748742 4- 3'
2.
3.
4.
5.
6.
7.
8.
9.
13. 1425896^ 5.
14. 638247 -f 7.
15. 2468013 JL 9
16. 1357924 4-11.
17. 64289768— 4
18. 3725872^-12'
19. 13926741^ 8
20. 7326974 -I
21. 9.'lS72fiS-L
22. 7134267 4-
23. 7248956 -i.
24. 6372485 1.
6.
7.
9.
-j.
I
t4
SIMPLE tlVlSiOtf,
■ "Wlwi the divisor ip a composite number, none of wfioc
faclcrsisliigher than 12.
Rult II.— 1. Divide the dividend by one factor of the divis(
and divide the quotient by the other factor. 2. To find 11
correct remaitider, multiply the last remainder by the Drst div
sor and add the first remainder to the product.
ExAMfLE 2, Divide 83794 by 54.
6 1 83794
$|13965"-4 first rem. First, we rfiVide by the factor 6 an
obtain the quotient 13965, then %
divide the quotient by 9 and obtal
the quotient 1551, with a remainll
6, this remainder is then multiplif
by 6, the first divisor, and 4 the fin
... , ,„ , remainder, is added to the prodi
which makes 40 the true remainder, under which we write
.1551 — 6 second rem
I551f^ quotient
the divisor
739684
421963
5324061
93^2685
537^62
6. 3625738
7. 7248964
8. 9326147
1.
2.
3.
4.
5.
18.
27.
54.
99,
121.
81.
144.
42.
ExEhCISE 2,
9.
10.
11.
12.
13.
14.
15,
16.
12345678
74100632
3271496
53196482
42953684
31274635
53926845
143690782
77.
63.
108,
132,
49-
•110,
84,
144,
LONG DIVISION.
Bute III-— 1 , Place the divisor to the left of the dividend, ad
leave a space to the right of the dividend for the quotient.
Place in the quotient the figure which expresses the number
times th&t the divisor is contained in the least number of figur
to the left of the dividend. 3. Multiply the divisor by the figi
in the quotient, write the product under the number divid
and subtract, 4; To the remainder annex the hext figure
the dividend, place in the quotient the figure which express ^
the number of times that the divisor is contamed in the niii t
ber, and continue the process till the last figure of the divide; \
is brought dowa, when if there is a remainder, place it aft I
the quotient and «rrite the divisor below.
u
mber, none of who$*i
le factor of the divis^
factor. 2. To find tl
inderby the first div
iu«t.
ide by the factor 6 m
Jtient 13965, then \i
)tient hy 9 and obta^
551, with a remaind
ier is then multiplif
divisor, and 4 the fin
added to the prodi
r which we write
2345678
4100632
3271496
3196482
2953684
1274635
3926845
3690782
7L
63.
108.
132,
49.
•110.
84.
-r 144,
[ of the dividend, ar 1
lor the quotient. |
•resses the number |
jast number of figm I
divisor by the figi 'l
the number divid |
X the taext figure 'i
ure which express |
ntained in the niii 4
gure of the divider |
inder, place it afi I
SIMPLE DIVISION. 26
If when a figure has been brought down, the number to be
divided is less than the divisor, place a cipher in the quotient,
bring down the next figure in the dividend, and divide as
before.
Phoof. Multiply the quotient by the divisor, and to the pro-
duct add the remainder ; if the result is equal to the dividend
the work is correct.
Example 3. Divide 12345 by 49.
49| 12345 I 25!^^ quotient.
98 49 First we place 49, the di-
visor to the left of 1 2345 the
2305 dividi'nd, and write 2 in the
'004 quotient, 49 being contained
twice in 123, then write 98,
12345 proof the product under the num-
ber divided, and subtract.
—• To the remainder 25, annex
46 remainder. 4, the next figure in the di-
vidend ; then 49 is con-
tamed 5 times in 254, leaving a remainder 9, to which we annex
5, the ne.xt figure in the dividend, place 1 in the quotient, and
subtract, the remainder being 46. The quotient therefore is
251 f|.
liule IV. If the divisor ends in ciphers, leave them out, and
cut off as many figures from the right of the dividend as there
are ciphers in the divisor. Then proceed with the remaining
figures according to Rule III, and to the remainder annex the
figures cut off from the dividend, which will give the true re-
mainder.
By proceeding according to the above rule the operation is
shortened
Example 4. Divide 7423654 by 2900.
29,00|74236,54|2559ff^A quotient.
58
254
245
95
49
162
145
173
145
286
261
2554 remainder.
Here the two ciphers in the
divisor, and the two figures at
the end of the dividend being
cut off, we nrnceed. according
to Hule III, the remainder is
found to be 25 to which 54 is
annexed, dve-.thus obtain the
true remamder 255|.
26
i!
i
TABLES or MONEY, WEIGHTS AN» MEAsmiE,'
I
1.
2.
3.
i.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
7235
95126
425396
729643
352864
153928
325912
415236 ■
596432 •
702536 •
430025 -
300000 -
896528 -
235964 -
4986327
8296153
1738254
9326485
2196427
ExEHcis.-; 3.
39724685 -i-
74289642 4-
333333333 ~
923746859 -
2468013579-^
1357924680
931642734 .
IMlimil-r
30.
31.
32.
33.
34.
296.
2745.
4268.
736.
5396.
742.
248.
7463.
20.
21.
22.
23.
24
25
26
27,
28. 213964582 i5237fi"
29. 9173245863 V- 7 ; J"
"" 3926857962 -r 8392
7429638 ?4!)-r 3256
240006347 -T- 46823*
714000086 -f-JJSS'
--. 3000000000 ^ 426
35. 7070707070 r ''•
36. 531724956-;-
37. 2222^445 4-
38. 7139628745 -r
5364.
792.
685.
256.
19.
?n" ?,lu^^ 95000000 hy 704029
41 lT5f '' "?^ forty-seventh part of 726349 ?
^^^e^^o^M^&r^^:^^ ^^-- " ^oys. how .any
4A n- „ f '^^^t>y iho. product of |2 and 4
™i?i i!o:,f,St"'p,?l\r ■"''« ."■2 days, how „a„y
rago lo each square niile » ' Pwsons are there on an ave-
w|,4eXT„:rk",^,0^'„,ri? "■ • ^»y. ^ow ">a„y d.ya
48 n!^!^° seventy eight billions b, 869
^^^48. U,.,de ninety Tour trillions by Lven ,„i„i„„s,„, ,,„,„.^
TABLES OF.MONEY, WEIGHTS AND MEASDHES.
mnrted""!?"" *°'""" ""''""' '"» cen'» make one dollar
".oiraupuis, una live cent ten rnnt t,.,„T p ""' ^^'o^i 1 ifa.
cent pieces which are silver ' ^"^'"'^ ^'^^ '^^n' ^''d fifty
iiia«.S'miifi¥^»A-r»*m'^it>ii^^ "
fJ MfiASURfis.
724685 -1
- 296
2S9642 -f
■ 2745
)33333 -f
4268.
^46859 ^
736.
13579 -^
5396.
24680 -r-
742
42734 -r
248.
lllll-j-
7463.
64582 -r
52376.
45863 -r
715.
17962 -T-
8392.
38?45-r
3256.
)6347 -7-
46823.
)0086 -r-
74053.
)0000 r
426.
7070 r
5364.
4956 -•
792.
4445 -~
685.
8745 -r-
256.
9?
hoys, how many
days, how many
•e miles, and the
there on an ave-
how many days
ions and seventy
MEASURES.
lake one dollar,
'Jiich is made of
'"(^ wei-h 1 \b.
'e cent and fifty
^ TABLES aP MONJET, WBIOflTS J^V MEASURES. 27
' OLD CANADIAN CURRENCY.
2 farthings _ t k ip
4 farthings or 2 halfpence ~ ^*'""^''
12 pence .. ^ = P^^liy- ^'i^-ked d.
20 shillings or 24open;;:::::::z;:;:=l^;i;;3^^ :: i
UNITED STATES CURRENCY.
10 mills = 1 cent, marked ct.
10 cents = 1 dime, " d
10 dimes = 1 dollar, " $
10 dollars = t eagle, " E.
i AVOIRDUPOIS WEIGHT.
I 16 oliS Z 1 pound "^'''''^^ ''^•
I 25 pourids = 1 quarter, J l^'
I 4 quarters = i hundred weight " T^t
20 hundred weight = 1 ton. ' ,. J^''
This weight is used in weighing meat, groceries, grain, 4c.
TROY WEIGHT.
20 uennvweiffhi, ^ 1 ''^""y^^ight, marked dwt.
^u pennyweights = 1 ounce, « „,
12 ounces = i pound, « jb'
quo?s.' ^"'^^' '' ""''^ ''' ^^•^^^'^^ ^°'d, silver, jewels and 11-
APOTHECARIES' WEIGHT.
20 grains = 1 scruple, marked scr.
3 scruples = 1 dram, « dr
8 drams = I ounce, " oz'
12 ounces = 1 pound, » 15
LONG MEASURE.
12 lines _ 4 j„„.
12 inches ~ I !■" ,' marked in.
3 i^et Z °°*i " ft.
5i vards ~ . ^^^'^' " vd
40 perches = rod pole or perch, " ^ev.
8 ftirlongs Z 1"'/°"^' " fur.
P miles - i'''°' " m.
BO geographical miles or) ~ ^"^' " '^a.
69^ British miles / = * degree,
28
4
TABLES OP MONKY, WEIGHTS AND MEASURES.
2J inches
4 nails
quarters
quarters
quarters
quarters
CLOTH MEASUBE.
1 nail,
• quarter,
1 Flemish ell,
1 yard,
I English ell,
t French ell,
marked
SQUARE OR LAND MEASURE.
na.
qr.
Fl. e.
yd.
Eng. e.
F. 8.
''9 s?uar'efe"ef' f J square foot, n^arked
<j squttre leei = [ square yard
30i square yards = i square perch
40 square perches = 1 rood '
4 roods = , acre,'
Square «,re is used7„'i"S ™'«',r,^,
sq. ft.
sq. yd.
sq. per.
r.
a.
sq. m.
CUBIC OR SOLID MEASURE.
1728 cubic inches, _ , v. „
27 cubic feet, = } ^"^'« 'oot.
40 cubic feet of rough timber, or 1 " '"^'^ ^'■'^•
50 cubic feet of hewn timber [ = ' '°n-
128 cubic feet of firewood ^ - 1 cord
DRY MEASURE.
2 junts — I quart,
4 quarts = 1 gallon.
j gallons = 1 peck,
36 bushels = 1 chaldron.
marked
qt.
gal.
Dk.
bush,
ch.
marked
TKio ^r. "onoio _ , cnaidron, " ch
This measure is used in measuring grain, fruit, Ac.
LIQUID MEASURE.
= I pint,
^ I quart,
= 1 gallon,
rfcs^^^^^''°-=i£5^ad,
5 pipes = I II]'
TIME MEASURE.
4 gills
2 pints
4 quarts
31^ gallons
pt.
qt.
gal.
bar.
hhdd.
pipe,
tuu.
60 seconds
60 minutes
24 hours
7 days
= I minute,
= 1 hour.
= I ilay,
= I week,
marked
min.
h.
day.
wk.
6
21
MMMM«tM«,*«&l«««4k'>«ii«Ml«»<v«>>iif>>«rii
MEASURES.
rked
na.
qr.
Fl. e.
yd.
Eng. e.
F. e.
JRE.
marked
ces.
IE.
S(J. fit.
sq. yd.
sq. per.
r.
a.
sq. m.
cubic foot,
cubic yard.
ton.
cord.
1 qt.
gal.
pk.
bush.
ch.
uit, dc.
larked pt.
" qt.
gal.
bar.
hhdd.
pipe,
tun.
rked
min.
h.
day.
wk.
REDUCTION.
29
11 calendar months, or 1
^13 lunar months, or |= , year.
TSMZnVweirrno^^^^^ « 'eap year,
each month " ''"^'' ^^°'^' ^^^ ""mber of days in
Thirty days hath September
April, ,Iunp, and November '
P ebruary has twenty-eight 'alone.
And all the rest have thirty-one
Except m leap vear, when '
tebruary's days are twenty-nine.
CIRCULAR MEASURE.
30 degrees -l^T" u s
12 s.g.:s or 360 degrees = The^circumference of a circle.
MISCELLANEOUS TABLE.
12 articles = j (j^^en
20 articles
24 sheets of paper
20 quires
14 lbs.
196 lbs.
200 lbs.
4 inches.
6 feet
21 shillings
= 1 score.
= 1 quire.
= 1 ream.
= 1 stone '
= 1 b.irrel flour.
= 1 barrel pork.
= Vfathonr'* '" measuring horses-
=^ 1 guinea.
REDUCTION.
Jrizzziit:i Xua^y^orthrs" '^T'l °K^-^ -
d.irerent denomination. witCXing its rrue''"'' ^"' '' '
.eSjeKt?-? '^ - ^duS^-S.i;^J^-'^'- '^ « ^-
deS^ira^,^^S^^:^- ^w. to a higher
30
REDUCTION.
REDUCTION OF DECIMAL CURRENCY.
Dollars are rpdiicod tn r.or,» i
m = 7400 centsSo = 5!i ^00 Lmr""^ '^" ^'''f''^'^- Thus
llnis 47274 cents --. I472 74 andM^ '" '''''' '" "'" '^'"ount
•^p-^^-it, anu 90J865 cents = $9038.65.
EXKRCISE I,
2: HoTSn^e"nta";:tir ^" seven doHars ?
5. Reduce .f /g^"/! tTce m? '" *'''•'' '
6. Reduce $42965.37 to centa
7. Reduce $942.75 to cents
peI°e)7o Secimll curS°° =™""y (P0-><l8, shillings .„d
""Hlpl, ,„e fa«hi„;/ oil's 17 '""" '° ""'^ ^ '■ -'"'"
7or(
_ ""'=> auu cents.
'"""^■7frr/"^''^'J'«.lo,la.„„ace„.,.
'''^ ' X 4 = <1!ICQ
far 31 X 5~ 12- ^f?,,
• ■''•-- 12|i- cents.
*J9o'!92'|Ti;;r~
*irst we multiply £47 hv i «n.^ ux •
•4 shillings by 2SLdob'ain;"'t""''''' ''^" ""'"P'^
^y A and Obtain .2|, cents !ho i^":,: ff "^. ^L^^^^^n^s
'he dollars and cents contained in ^47 4 f '' *^'"''^^'
a 7i
f cents ai
f cents 0'
number
4 JE19: 13
1. Ho
$74.56 ?
2. Ho
1742.90
3. In
there ?
4 Rec
5. Rer
6. In^
there ?
7. Ho\
15264.48
8. Hoi
$279.65 '(
'ttmitmn^^^X,,-
CURRENCY.
ing two ciphers. Thus
tiff a (Jot or a short line
from the right hand
expresses the rminber
'6 cents in tho amount
cents = $9038.65
REDtTCTION.
31
dollars ?
-four dollars ?
ars ?
4?
3nlg.
sents.
3ents.
'unds, shillings and
uce them to dollars •
™ to cents ; 3. Then
ice and farthings by
ie products together
nd cents.
Is. = 20 cents, and
s and cents.
88, then multiply
'tiply 31 farthings
ddi is $190,9211
%
I
i
Exercise 2.
1 RelcTxi/l'r'irt'^ Tu' ''' ^l"''' in £18 : 9 : 6 ?
X- «e('uce A17 . 14 : IJ to dollars and cents.
3. Reduce £75 : 18 : 10 to dollars and cents
l>. nuiuce i,^4J ]>) . 6i to dollars and conts.
>. How many do ars and cents are there in £764 • 8 • 7* ?
». Keauce A'/b 18 . 5 to dollars and cents
0. Reduce £182 : 16 : 4 J to dollars and cents
1. Reduce £826 : 9 : II to dollars and corns
12. Reduce £248 : 4 : ^ to dollars and cents
7o reduce dollars and c^ls to pounds, shillings and pence
U.h"?.;'' ^-'"^^ the dollars by 4 to reduce them to pounds,
and inhere is a remainder reduce it to cents, and to them add
he given cents, divide the number of cents thus obtainedby 20
to reduce them to shillings, then divide the remaining cents by
f A and reduce the farthings which will thus be obtained to
pence.
$7? '"'i'j-.o ^!?r ^''-''^ '' P"""*^^' ^'''"'"^^ ^^^ P°nce.
2 67i = 1n- ^V^"T'^«'*- First we divide 78. the
li - 18 farthings or d4f the quotient is £19. thwi
cents are 267J cents, this divided by 2*o' JTs'sSaf and^'!
cents over, which divided by ,4, Jl8 farthings or S/tS
number of^pounds, shillings aL"\ence in m'A^ittJoll
ExEnciSE 3.
f74.5?7 ""^"^ '''''"^'' '^"""«« "^"d pence are there in
$742.9oT ""^""^ P"""*^'' '^'"'"^^ «"^ P«"ce are there in
there\" ^^^'^'^^ ^""^ '"^"^ P"™^^. shillings and pence are
5 Reduce |758'2?'tn7rr"'^'.^''''''"^^^"J P^nce.
6 In ssq^toQo i: *° °^'^ Canadian currency.
there ? * ^'^^ ^°^ "^"^ P"""^^' «l'illings and pence are
15264^47? ""'"^ P"""*^'' '^'"'"^« '^"d pence are there in
$279,6??' '"''"^ P"""*^'' ^'"'""^^ «nd pence are there in
32
REDUCTION.
"*i.j/i to old Canadian currency
REDUCTION DESCENDING
To reduce a ,uanlii,j m a lower denominalion.
nulron l'^n^.twe';r' ^'^^" ''^-^^^-^ '^ '^'e
ti^e higher; ancnrparoTthoo "",?'"' ^'''"'^ '^'^"e^ one of
lower deno,«inat on add u to T h'° '' ™'"^^^ ^« ^''^'^^
each product in succession ^nil thr ' '^^^^^'^ ^^"« ^'^'^
required denon^ination '^"'"''^ '^ ''^'"^'^ '« the
them to sq poPchS: aid'a^^'^^,-
them fn- P''"^"' '^^30} which deduces
the^^numSr^sSr. '''? ^^ ""'^ "^S
is 237160 '^"^^ y^'"''" *" ^9 acres
196 roods.
40
''840 sq. perches
235200
1960
237160 sq. yards.
Example 4.--Reduce 23 cwt, 2 qrs 17 lb. n .
cwt. qrs lbs «, ^ ' ^•' '^ °^- ^o ounces.
23: 2: J7: ,3
2|
94 quarters.
25
2307 pounds,
16
I42T5
2367
37885 ounces.
r^ducp'^?h^"'!'P'y ^^^ ^""dreds by 4 to
reduce then> to quarters, and add 9 ♦»!„
number of quarters in the anLfX. ^?
t.
2.
3.
4.
5.
6.
7.
8.
;ncy.
rrency,
iG.
mnnaiion.
omination by the
hich makes one of
reduced be of the
Proceed thus with
' is reduced to the
ds.
in an acre, we
ores by 4 which
hen multiply 196
40 which reduces
a lastly multiply
; which reduces
nus we Hnd that
ards in 49 acres
3 oz. to ounces.
ndreds by 4 to
and add 2 the
7uanlity; next
>y 25 to reduce
17 the number
y; and lastly
the number of
13 the ounces
^es 37885 the
REDUCTION. 33
REDUCTION ASCENDING.
To reduce a quanlily to a higher denomination.
Rule. — I. Divide the given quantity by the number of the
given denomination which it takes to make one of the next
higher. Set down the remainder if there is any after the quo-
tient ; 2. divide the quotient by the number of that denomina-
tion contained in one of the next higher, and so on, until the
required denomination is reached ; and set down each remain-
der in order after the last quotient.
Example 5. — Reduce 28964 gills to gallons.
4 I 28064 gills.
&c.
First we divide the given
number of gills by 4 to reduce
them to pints, then divide the
pints by 2 to reduce them to
quarts, and divide the quarts
by 4 to reduce them to gallons,
we thus find that in 28964
gills there are 905 gals. 1 pt.
Example 6. — Reduce 73907 farthings to pounds, shillings,
2 I 7241 pints.
4 I 3620 qts. I pt.
905 gals., qts. ' pt.
4 I 73907 farthings
12 I 18476 d. 3 far,
2.0 I 153.9 8. 8d.
£76 : 19s. : 8|d.
ExERcrsE 4.
Reduction of old Canadian currency.
1. Reduce £17 : 19 : 4 to pence.
2.
3.
4.
5.
6.
7.
8,
£128 : 14 : 7^ to farthings.
£742: 18 : 9i to farthings.
£1084 : 11 : 2i to farthings.
7968 shillings to pounds.
374285 pence to pounds.
72485 farthings to shillings.
73900714 farthings to pounds,
RBDUOTION.
Exercise 5.
Avoirdupois Weight.
'uce 235 tons to quarters.
— ^ 6 cwt 2 qrs. to rounds.
■547 cwt. 3 qrs 21 he i^, ..
213 cwt 23 iL 1 ; ^^ ^ ounces.
Starters to tons. "''^•
70604 pounds to hundreds, 4c
?g^IJ °""^es to quarters. '•
/Wi&86 ounces to tons, do.
Exercise 6.
Troy Weight.
'40a grams 10 pounds, ounces Ac.
Exercise 7.
Apolhecaiies Weight.
2 ^°^^^^to...,ples.
3542^6^7 s?ruplX"uV; ^" '^ ^-'•-•
7312648 graFn^to?o^d^r„r^*<^•
73J2648 grafnrto Torr' """««« *<=
e'tiiiis 10 pounds, ounces 4c.
Exercise 8.
LONG MEASUflB.
49 feet 7 inches to lines
-43 perches 5 yards to Sches
-7 mi es 4 fur "ii n^^ *
-P57 lea. 2 m 7 it o^ P''"^^^-
inch's ^"'- ^^P^''-^ yds. 2 a. 7 in. to
-2700005 yards to miief '
■9263 lines to yard''
■73D9876 inches to .^agues.
Exercise 9;
CLOTH MEASURE
2 " ,•' >^ius to nails.
i- Reduce
2. .
3. .
4. .__
5. .___
6.
7. . . .
8.
8.
9.
10.
11,
12.
)uno6s.
ins.
c.
grains.
5.
6.
REDUCTIOM. 35
1)274 nails to English ells.
408 yards to Eng. oils.
3'i'2 French ells to Eng. ells.
EXKRCISE 10.
SQUAHE OR LAND MEASURE.
1. Reduce 36 sq. perches to square feet.
2. 32 acres 3 r. 25 per. 17 yds. 5 ft. 121 in. to 8ii.
inches.
3. 93264 scjunre feet to rood^s.
4. 7500086 sq. inches to acr. .
ExERCISfi 11.
LIQUID MEASURE.
1. Reduce 27 gallons to pints.
2. 29 hhdds. 17 gals. 3 qts. 1 pt, 3 gills to gills.
3. 796425 gills to barrels.
4. 27435 pints to jiipes.
EXERCISK 12.
TIME MEASURE
1. Reduce 17 weeks 3 days to hours.
2- 24 weeks 6 d,2l h. 34 min. 46 sec. to seconds.
3. ■ 742913 seconds to days.
4. 42000134 seconds to weeks.
EXKHCISE 13.
=ls- 2 ft. 7 in. to
1.
2.
3.
4.
5.
6.
7.
In $7204.27 how many cents are there ?
Reduce 764285 cents to dollars and cents.
How many dollars and cents are there in £724 : 19 : 6|.
Reduce $3965.79 to pounds, shillings and pence.
How many farthings are there in £3: i : 16 : 7J ?
Reduce 796427 farthings to poundfe.
Reduce 7 tons 14 cwt. 3 qrs. 22 lbs. 13 oz. 11 drs. to
drams.
8. Reduce 1111111111 drams to tons, hundreds, 4c.
9. How many grains are there in 11 oz. 14 dwls. 13 grs of
gold ? *
10. Reduce 37096 grains of silver to pounds, ounces, Ac.
n. In 7 lbs. 9 oz. 7 drs. 2 Rcr. hnw m.iny scruples are there?
12. Reduce 73962 scruples to pounds, ounces, 4c.
13. Reduce 7 leagues, 2 m. 32 per. to feet.
14. Reduce 12345678901 lines to leagues.
Hi
m
36
15
COMPOUNjj ADDITION.
16
17
18,
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29
30,
31.
32.
■ \uL7''' ' '"''' '' '-"--^ '-^^ ™«ny minutes are
Reduco 123045607 seconds to wo*^ks, davs *c
How ma^l 'o^^S^K^e'.'irrtKTn^ 'il^lSr ^'^^^ '
low many yard.s are there in 80 french e Is ?
Kce ttjll'r). °"^ '° "^'"'«h oils ' "" '
te. uce .$.37.25 to five cent pieces.
jn 1/ stiillinffs how many two pencps are (horov
Heduce 36 sixpences to fonrpences *'•'"• ^^
Tc^Y JtETf"£r ^ ^ '^- -^h are there in
COMPOUND ADDITION.
/?u/e. Set down the quantities l5 be added so th«f fha
cm.^^""bl'i5^o'z';Tc^r2';rs^Tl J^^^'^''^^ '^ -^ 2"
and 139 cwt. 3 qrsl 14 IblllL "*''•' *^« '^^t- ' q--- 21 lbs. ;
cwt. qrs. lbs. oz.
First we divide 42, the number
or ounces in the first column by
10 set down the remainder 10 oz
under the first column, and carry
Li* second column with 2 lbs
added is 78 lbs., this we divide by
^^, and set down the remainder 3
87
243
94
128
139
3
2
1
3
24
17
?l
14
3
15
11
13
10 Ans.
)s. and (
If the no!
fives 3 ci
indor the
pimple ad
10 oz.
KXAMPI
md .$942
$ (
7204.8
10503.0
7248.9
942.6
1 $25959.5
I
1 $ c
73M
928.. 3
4275.9
897.3
2956.5
3724.4
5963.7
I
I 4. Find
f $3247.86 i
5. Find
2J yds. 2
39 m. 5 pi
6. Reqt
$7294.63 ;
7. Add
JE2348 : U
£79 : 16
8. Find
$94.07; i
and $2976
9. Add
4 oz. 9 drs
oz. 15 drs.
9 t. 6 cwt
and 16 t. i
COMPOUND ADDITION.
37
in 40 Hcros, 2 r, 9.8
iclies ?
•es.
Is are there f
i I gals. 3qts. Ipt.?
m'lny minutes are
lays, 4c.
nt pieces are there?
71 fifty cent pieces?
yards ?
1 ells ?
re there ?
: 10 : 5?
. each are there in
but of more than
IN.
so that the num-
lination. 2. Add
) the right, and
er denomination,
umn added, and
)coed thus with
e addition,
lbs. .3 oz. ; 243
(Vt. Iqr. 21 lbs.;
42, the number
irsl column by
5mainder 10 oz.
Jran, and carry
linn 'PU^ _.,_.
••••■'. xfic sUlIi
mn with 2 lbs.
is we divide by
lie remainder 3
t)9. and carry 3 qrs, the quotient, to the next column, the sum
If the next column with 3 addod is 12 qrs., which divided by 4
kivcs 3 cwt. without a romaimlor, wo thoroforo place a cipher
bndcr that column and carry 3 to the next which is added as in
limple addition. The whole sum therefore is 694 cwt. 3 lbs.
10 oz.
Example 2.— Add together $7204.85
ind $942.68.
$10563.07; $7248.90;
$ cts.
7204.85
10503.07
7248.90
942.68
[$25959.50 Ans.
In addinR dollars and cents proceed as In
simple addition cutting off the two right
hand figures which will be cents and the
remaining llguros dollars.
1 1 $ cts.
J 73 .15
928,. 33
4275.94
897.38
2956.59
3724.48
5963.72
ExEHCtSES.
1. £ 8. d.
243 : 17 : 9
84 : 15 : 7f
976 : 9 : lOi
1348 : 14 : 111
3. cwt. qrs. lbs. or.
749
248
9456
18 :
13 : 10^
8
: 10^
94
78
135
79
86
243
97
2
3
I
3
2
1
23 4
14
19 8
14 3
11
7 5
8 14
; $5326.47 ;
7 fur. 21 p.
2 ft. 9 in. :
4. Find the sum of $963.17 ; $485.93 ; $978 85
$3247.86 ; $984.76 ; $596.34 ; and $4275.98.
5. Find the sum of 34 miles, 7 fur. 38 par. 4 yds
n yds. 2 ft. ; 27 m. 13 p. 2f yds. 1 ft. 7 in. ; 21 per
39 m. 5 per. 11 in. ; and 2 m 3 l\ir. 4i yds. 9 in.
6. Required the amount of $7248.05 ; $324.96 ; $365 30 •
$7294.63 ; $8726.48 ; $679.84 ; $5986.77 ; $89.56 ; and $7694.37*.
7. Add together X734 : 15 : 7 ; £896 : 19 : 8J; £98 : 7 • 6 •
£2348 : 14 : 9J ; £3974 : 18 : 6| ; ^■'Aj : 18 : 7 ; £768 : 9 : 7 '
I £79 : 16 : 8|; and £9872 : 4 : It.
f 8. Find the sum of $794.63 ; $9874.56^ ; $78.90} ; $863.95 •
$9407; $7942.18}; $1734.86; $3257.98; $704.37 ; $53.91
and $2976.54.
9. Add together 7 tons. 16 cwt. 21 lbs. ; 39 t 3 qrs. H lbs
4 oz. 9 drs : 13 cwt. 2 qr«. 1 4 oz. ; 14 t. 9 cwt. ! rr !4 Ihg 13
oz. 15 drs. ; 18 t. 7 cwt. 3 qrs, ll drs. ; 3 qrs. 7 "lbs.'4 oz' 9 drs ■
9 t. 6 cwt. 2 qrs. 24 lbs. 6 oz. 13 drs. ; 15 cwt. 3 qrs. 17 lbs" '
and 16 1. 9 cwt. 2 qrs, 10 oz. i • ,
38
1:1
COMPOUND ADDITION.
sec t ,^'>Sether 37 weeks fi ,
84 yds ? J "^f^'- 17 yds. 2 qrs an, l^'^^ ' "°^ «924.68:
, '9- Add together 2«^ . «• » o^- 10 dwts.
Ihs. ; 459 cwt 2 ore .s ik"^*- ^ ^''«- 24 Jbs ■ «7 , .
736 cwt. 2 qrs 19 .^ . i«?- ^ ibs. ; 175^cwf •? ^^ ' ^^^ «wt.
qrs. 4 Ji)s. ^ -^ '^^- ' 367 cwt. J gV. J4 f,f '.3 T^s. 14 lbs. ;
9n A .J "J • '^ ics. . and 42 cwt 1
2^- Add l„„lh„ 7, . ' ^™'">' 'Id K596 87 *'■"*■
tON,
sec. ; and 36 wks 6 ,]'
grs. ''°'^' I
B176159 ; 19245.08 ;
^4b.93; and $924 68
29 yds 1 ,p. 3 ^ ^ •
^•2qrs.3„Js.;and
-and £578 .16. 4^^:
$736 14; $968.13*'
and $96.83. *'
'"' ' -52 gals. 3 qts
' &■ ; and 38 gals.'
3 grs ; 28 ,bs. 18
.• 13 lbs. 7oz. n
*«• 9 02. 10 dwts
'•^T'-s. 14 lbs • ■
• •■ and 42 cwt 3
yds. •• 37 m. 3 f
P- 2f yds. ; and'
^fJ ''• '7n. •
; 127 a. 3 r. 27
£5; $4253.08-
^8296.87. '
i^ yds 2 ft. 1 1
8 in. 3 i. ; J32
COM?aUl?P SCBTJaAOXION.
39
HJ\"'nlK^A ' '^i'^- ^^^-^^ ™- 2^ s. ; 92 d. 20 h, 47 m. 38 s.;
!l85 d. 2 h. 39 m. 8 s. ; and 47 d. 9 h. 28 m. 47 s.
25 Add together 61 gals. 1 qt. 1 pt. 3 gills; 24 gals. 3 qts. 2
Ig. ; 48 gals. 2 qts. 1 pt. 3 g. ; 96 gals. 2 qt. 1 pt. 2:g. ; 37 gals.
|2 g. ; and 59 gals. 2 qts. 1 pt. 3 g. "^ ^ e > 8
26. Add together 7 tons 14 cwt. 2 qrs. 23 lbs. ; 19 t. 18 cwt.
qr. 24 lbs ; 48 t 11 c. 1 qr. U lbs.; 82 t. 17 c. 9 lbs. ; and
13 t. 16 c. 2 qrs. 22 lbs.
COMPOUND SUBTRACTION.
Compound 8i-btraction teaches how to find the differenoe
between two quantities of the same kind but of more than one
denomination.
Rule 1. Place the less quantity below the greater so that the
numbers in each column will be of the same denomination. 2.
Then beginning at the right hand subtract each number in the
lower line from the one above it, but if any number in the lower
line is greater than the one above it, add to the number in the
upper line the number of units of that denomination contained
in one of the next higher; then subtract, set down the remain-
der below, and carry one to the next higher denomination in
the lower line ; and proceed thus with all the columns to the
last.
. ^««°X- '^° *^? difference add the quantity in the lower line,
and If the sum is equal to the quaMity in the upper line, the
work IS correct. '
r.r^^'fal ^o/™."* ^^ "^^^^^ ^ daJS'^UJiours 37 min. take 18
w. d d. h. 20 mm.
wks. d.
27 6
18 3
fa. min.
11 37
6 20
17
Bc. ; 234 d. 23 1 -11
27 6 11 37 Proof.
In this example as e^ich number in
the lower line is le?s than the number
of the same denomination in the
upper lino, it is only necessary to iind
the difference in each column as in
simple subtraction, which shows the
whole difference to be 9 weeks 3 days
5 hours 17 min.
40
COMPOUND SUBTHACTION.
15 Ans.
02.^weVdd'i-f5^'";f ^'^^^"' than 6
. from 22 leavp« \^,t- ^' ^^^^ 7
"Wch lake„"S^8 ,e„,3 tl"- ^ oarry I ,?9* Jes To'
^' $ cts.
7962.54
1326.78
fixERCJSES.
3.
cwt. grs. lbs.
128 2 17
96 3 22
5" pfnTff l^l"-23 take $12345 67
^^^e^i^^'Z^-^^^ ^ ''ons 13 ewe. 2 ,rs. ,9 I.s
r. J pS:T7fdr;S^;JiP- " ^^«- ^ « ^ m. ta^e 7, a 2
15. Find the di/rereToe between r8Th'""«°'^ ^^^ '"^ ^«ft
^ 16° A V ' Sf • ^°/- ' ^'•«- 2^8 g's^'- ' ''■ ' d''^- 2 scr. 14
the cargo ril2lf5'92 wSrirthTr^l ^''?«'^«-^0' ^he value of
7. From 96 yds. 2 ft Tin 7 r "^^ "? ""^ ^^^ vessel ?
•« From 117Lons fake '9yt!!nT7V^'!r^-'^■^,!f^, «-•«'•
--.-. . r.„r. ^^^ 20 lbs. 9oz.
18.
7 drs,
19.
20.
From 963 acres takfl 7/. n o ««
653
1.
2.
3.
4.
5.
6.
7.
8.
9.
to.
II.
12.
13.
14.
'4
PI ON.
» 16cwt. 2qrs. 18 lbs.
being greater than 6
^'ol^J« number in the
ch makes 22, then 7
es 15 which we set
'arry I to 9 makes 10
quarters being more
I'ne which mak(^s 6
to 8 makes 9 which
rence therefore is 7
*• qrs. lbs.
^ 2 17
> 3 22
' cwt. 2 qrs. 19 lbs.
'ks. 3 d. 47 min 32
' qrs. 3 nb.
paid on account
^ qts. 1 pt. 2 gills,
•om 684 m. 3 fur.
1 in. take 71 a. 2
•S.I 7 lbs. of iron,
las he left ?
• 4 drs. 2 scr. 14
70, the value of
vessel ?
's. 2 ft. 6 in. 8 1
•s- 20 lbs. 9 oz.
fls. 6 ft. 128 in
?als. 3 qts. Ipt.
COMPOUND MULTIPLICATION.
41
21. Innd Iho dilfprence between the Julian year of 365 days
' hours, and the true year of 365 days 5 h. 48 m. 50 sec.
22. The latitude of the city of Quebec is 46<> 48' 30" north
md that of Montreal 45° 31' north, required the diflerence? '
COMPOUND MULTIPLICATION.
Compound Multiplication teaches how to multiply a quantity
[of more tlian one denomination.
When the multiplier does not exceed 12.
Hule.—l. Find the product of the first number on the right
I hand, and the multiplier, divide this by the number of that de-
nomination which makes one of the next higher, set down the
remainder and add the quotient to the product of the multiplier
and the number of the next higher denomination ; and proceed
thus with each denomination to the last.
Example 1.— Multiply 72 cwt. 2 qrs. 15 lbs. by 9.
cwt. qrs. lbs.
72 2
.15
9
653
10 Ans.
First we multiply 15 lbs. by 9,
then divide 135 lbs., the product, by
25, the number of lbs. in a quarter,
set down 10 lbs., the remainder, and
carry 5 qrs. to the next product ;
then 9 times 2 are 18 and 5 added
are 23 qrs., which we divide by 4 set down 3 the remainder and
carry 5; 72 multiplied by 9 =648 and 5 added makes 653. The
whole product is therefore 653 cwt. 3 qrs. 10 lbs.
Exercise 1.
1. 16 cwt 3 qrs. 17 lbs. 5 oz. x 2.
2. £29i : 17 : 9| x 3.
3. $79048.39 X 4.
4. 27 miles 3 fur. 27 per. 2J yds. x 5
5. 56 gnls. 3 qts. I pt. x 6.
6. 39 acres 2 r. 18 per. 9 yds x 7.
7. f829568.09 x 8.
8. 19 tons 14 cwt. 2 qrs. 23 lbs. X 9.
9. £794 : 18 : 7J X 10.
to. f. 369085.63 x 11.
11. 23 weeks 6 days 9 h. 27 sec. x 12,
12. 243 cwt. I qr, !7 !hs. !3 r.?.. x 7.
13. 7 lbs. 6 oz. 2 scr. 19 grs. X N. "
14. $96428075.69 x 8.
15. 39 acres 2 r. 25 per. 23 yds. 8 ft. x 12,
4^
III '
iJ
If I
COMPOCND MTTLTIPLlCAnoN.
7 3B f/^'o^ 'I"- 2 nis. X 9.
19. $897?65V5fJlP'-3gilisx5.
20. 4 cwt. 2 qrs. 7 oz 7 drs x 6
exc^r;^!^'^ '^ « --P^-'^ number neither of whose iactoJ
the one required. ^" ^^^ '^^^ product will be I
I Here the factors are 8 anrl 7
J3Ans.
Example 3.-Mmtip]y ^63: 5: 2|hy 252.
63
442 16
2656 19
d.
f
6
«nH ft example the factors are 7 r
and 6 we therefore multiniv .if •' °'
quantity by onp nf f^ r ?^ ^^® S^'^'en I
product by^nother^ft' ^f ^°?.^^ ^' ^he I
product by 6 wE I'ivlfii.^ '"'^"'^
amount. ^'^^^ *^e required
15941 17 9 Ans.
I $739278.56 x 14
2. £896: 14- 7iy'
3. $394065. 97 ^16
4. 74 cwt. 3 qr. 14 lbs. It oz y l«
• ^fi"r\2r.35per.27yds X20
l?„^lt3.'Trs.2Sls.X2T-^''
U. £
12. 8
13. 4
14. $
15. 4'
16. 2
17. 3
18. $
19. 6
20. 2
21. 7'
22. $'
23. 9
24. 7
25. 41
26. 8
27. r
28. $
29. 2;
30. 11
When
Inumber.
Rule.—
Multip
Inumber (
[multiplie
I required
When
Multip
last prod
duct add
number (
mullipliei
EXAMPl
cwt. qrs.
6 2
15.
6.
7.
8.
10.
?2^b«V„?Td--'°""•'^ '*:»'■"• 26 sec. V 9.
7 lea.2 m"'6 fur'^i^ "''"• /" f'"- ^ '^4. " "'
$296874?!68 X 27 P""- ^ ^^'- ^ 25.
65
3
263
46
2
n
309
2
OAHON.
COMPOUND MULTIPLICATION.
43
3.
5.
either of whose factorsi
' o«e factor, multiply
he second product by I
e last product will be
bs. by 56.
rs are 8 and 7, we
Mhe quantity by one ,
8, and multiply thej
other factor.
13 lbs. 6 oz. 5 drs.^x 30.
gills. X 32.
X 36.
63.
X 72.
X 75.
147.
he factors are 7 el
multiply the given!
^.^ ^^ctors as 7, the!
o,. and the second
gives the required i
It. £396: 14: 9i X 28.
12. 8 tons. 16 cwt. 2 qrs.
13. 48 gals. 3 qts 1 pt. 3
14. $7496876.48 x 33.
15. 42 wks. 3 days 17 h. 14 min. 28 sec.
16. 24 yds. 2 ft. 11 in. 7 lines x 45.
17. 37 acres 3 r. 29 per. 22 J yds. x 48.
18. $785965. 38 x 56.
19. 6 lbs. 3 oz. 6 drs. 2 scr. 13 grs. X
20. 24 cwt. 1 qr. 24 lbs. 7 oz. 12 drs.
21. 74 miles 6 fur. 37 per. 4 yds. 2 ft.
22. $9687428. 79 x 120.
23. 94 gals. 3 qts. 1 pt. 2 gills X 128.
24. 7 bush. 3 pks. 1 gal. 3 qts. i pt. x
25. 49 wks. 2 days 19 h. 12 sec. x 560.
26. 8 yds. 2 qrs. 3 nls. x 220.
27. 17 acres 2 r. 29 per. 28 sq. yds. 8 sq. ft. x 98.
28. $5976.84 X 147.
29. 23 bush. 2 pks. 2 qts. I pt. x 1000.
30. 19 cwt. 2 qrs. 18 lbs. 13 oz. 14 drs. x 504.
When the multiplicand exceeds 12 and is not a composite
number.
Bule. — When the multiplier does not exceed 100.
Multiply the multiplicand by 10, and the product by the
number of tens, to this add the amount of the multiplicand
multiplied by ihe number of units, and the sura will be the
required product.
When the multiplier exceeds 100 and is less then 1000.
Multiply the multiplicand by !0, the product by 10, and tb$
last product by the number of hundreds ; and to the last pro-
duct add the amount, of the first product multiplied by the
number of lens, and the amount of the given multiplicand
mulliplied by the number of units.
Example 4. — Multiply 6 cwt, 2 qrs. 9 lbs., by 47.
cwt. qrs. lbs.
6
9
10
X 7
65
15
4
V 99
263
46
2
n
10
!3
Here the multiplier 47 not being a compo-
site number, we multiply by 10, the product
by 4, and to this product add 46 cwt. 13 lbs.
the ])roduct of the given multiplicand and 7,
which gives the whob product ^09 cwt.
2 qrs. 23 lbs.
309 2 23 Ans.
u
-MuJiinli, -_ . ^
««;t. qrs. iJbs. ^ '^'•
^28x5
10
^ 20 Answer.
„ - ^^ Answer.
26 iS 6^^ ^ 3
10
266 iTTi X 4
10
2667 Tr'T X 3
10
^!!i'i_£»;^ Answer.
COMPOUND MULTIPLICATION,
4ft
73 acres 2 r. 26 per. 18 ydi. X 147.
$7964.78 X 237.
4J lbs. 9oz. 17 (hvts. 19 grs. X 253.
7 tons. 14 cwt. 1 qr. 10 lbs. X 246.
9 weeks 6 (1. 18 h 42 inin. x 298.
£84 : 6 : 9i X 2756.
34 gals. 3 qts. I pt. 3 gills, x 759.
7 bush. 3 pks. 1 gal. 2 qts. X 365.
3 per. 4 yds. 2 ft. 7 in. 11 lines x 1700.
3 qrs. 23 lbs 14 oz. 12 drs. X 476.
$895.08 x649.
4 acres 2 r. 29 per 26 yds. X 583.
5 days 18 h. 36 min. 19 sec. X 897.
3 lur. 21 per 4 vds. 2 ft. X 958.
£24 : 1 1 : 7i X 3428.
27 yds. 2 qrs. 3 nls. X 249.
36 lbs. Uoz. 17 dwts. 3 grs. X 352.
25. $649.73 x 716.
26. 14 cwt. 2 qrs. 13 lbs. X 641.
9 gals. 3 qts. 1 pt. 2 gills. X 742.
13 bush. 2 pks. 1 qt. 1 pt. X 256.
7 weeks 4 d. 22 h. 13 sec. x 493.
3 qrs. 24 lbs. 14 oz. 6 drs. X 658.
Knd the amount of
14 lbs. of sugar
8.
9.
llO.
111.
12.
13.
14.
115,
16.
17.
18.
19.
20.
21.
22.
23.
24.
27.
28.
29.
30.
at
5 lbs.
4 lbs.
7 lbs.
3 lbs.
of coliee
of tea
of rice
of raisins
iFind the amount of
7 yds. of cloth
8 yds. of flannel
12J yds. of cotlL
3 pairs of gloves
11 yds. of linen
11 cents per lb.
35 "
78 " "
9 " "
12J " "
at $2.70 cts. per yard
« 65 " "
" 16 " "
" 95 " per pair.
" 26 " per yard,
$ ctd
$7.41*
I
Find the amo int of
5 geographies at 75 cts. each.
7 grammars " 24 " "
6 arithmetics " 42J " "
4 Histories of Canada " 90 " "
3 algebras " $1.09 " *'
$31.81
ft 4.85
■I
m
^'"^ 'h« amount of
^i' yds. of cotton
o^MPotrvD Division.
^^*%20cts,pe.,«,,.
19 .< P'^'^yard.
___ Iji76.,
TJ'en divide h^v '^'"■'°'' '« 'he left of ,^
^°^-est denominl? "^^ ''''' '^"otient and ' '"^'^ ''^"^ o J
Phoop mT "' "^ ""'ii there is 1' ^'"''"^ '^us to the
P^oduTtVe^," 'Pjy the <Tuotient Z ZT"''''''''- ^
"127- V- i^ '''''^'•^•«^^s-i)y7 '°'- ^
Operation 27 -:. 7 «
^'e therefore set dow? ?.«"? ^ over
f the remainder to m,. , '^"'^ '"^dMce
the number of „„«l"^'''e''s then 24
quarters in the^J^SnV""^ ^ the
''" ■7- 7 = 3 „, ^"otient make 9fi
When the divisor fc ^ '^^t. 3 grs Iq iL ^^'na'nder.
^«^'ors exceedr/r '^ ^ ^^^Po^ite numbe 'nei ''•
^«^''— ResoJve,, . "'''^«'- of whose
^«'^tors as in UnleT T'7 '"'° "'''<^^^- Divide H
until aJJ the fan, ' ^'^''^'^ '^e resyJt bv ^^ ""« "'"the
'" '^^^tors are used. ^^ ^""'her, and so on
2
3
27
8
"^Ans.
7
S proof.
\v.
|144
When th
quotient tc
■JsroN.
;S' per yafri.
' per pair.
' per yard.
BXA,MI'LE
J W.
144
COMPOUND DIVISION.
'2— Divide 144 weoks 6 days U hours by 72.
47
d.
6
?.4
2
li.
14
Here the factors being 8
and 12, we divide the given
quaniity by one of the fac-
- — — tors as G, and the result by
2 11 40Ans 12 the other factor.
2 20
5roiv.
iivide
quantity con
""^the dividend. ■>%
^^j«« by it, set dowii
'"^'^'^^ it to the nel
""^ier Of the sa,ne|
jh^ nuniber thus oh-f
'i proceed thus to the
3niainder. 1
^^;;ivisor, and If the I
^^"'^K IS correct *
by 7.
■=: '^ = 3 and 6 ova"
,^°wn3andred.rc;
'0 quarters then 24
"^''ters, and 2 the
^"ot.ent make 26
fe'^ Which we set
'"amder 5 whiS
^5»U remainder.
'^'■"^6'' of whose
'''e by one of the
•'^e'-- and so on
1,
2,
3
4,
5,
6.
7,
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
23."
24.
25.
26.
27.
28.
29.
30.
-r 4.
-f 6.
~ 10.
Exercise 1.
$7396874.53. -i- 2.
£963 : 7 : 4. -i- 3.
7 tons 12 cwt. i qr. 17 lbs. 8 03.
68 gals. 3 qts. 1 pt. 3 gills -J- 5
91 acres 2 r. 29 per. 26 yds. "8 ft
793 yds. 2 qrs. 3 nis -^ 7
13 lea. 2 m. 7 fur. 37 per. -i- 8
$946874.25. -f- 9.
734 cwt. 2 qrs. 14 lbs. 13 oz. 8 drs
36 per. 4 yds. 2 ft. 9 in. -i. 11
734 gals. 2 qts. I pt. 2 gills -i- 12
468 bush. 3 pks. 1 gal. 1 pt. '-^ 14
£9648 : 17 : 8| -^ 18.
4263 yds. 3 qrs. 2 nls. -f- 63.
927 acres 2 r. 19 per. 28 yds. 7 ft
234 lbs. 7 oz. 4 drs. 2 scr. 16 grs
42()cwt. 3 qrs. 12 lbs. -i- 108 '
426 lbs. I9dwts. 17 grs! - 180
$76498705.36 -^ 154
365 wks. 5 days 17 h. 56 min. 48 sec.
9-26 gals. 3 qts. I pt. 3 gills. -^ 147
£1097 : 3 : 4J 4- 243
963 bush. 2 pks. 1 gal. 1 pt. -^ 198
9364 cwt. 2 qrs. 19 lbs. 1 oz. 10 "drs. -^ 363.
793 miles / fur. 36 per. 5 yds. 2 a — 648
749 eng. ells. 3 qrs. 2 nls. -^ 294 "
$9400037.04 -^ 648.
279 acres 3 r. 8 per. 7 yds. -^ 8 1
463 wks. 6 d. 23 h. 41 min. 36 sec. -^ 512
734 qrs. 18 lbs. 15 oz. 14 drs. -^ 594
-r 56.
•f 96.
-f 144.
When the divisor exceeds 12 and is not a composite number.
^«/e.-Divide each denomination as in rule 1, and write the
quotient to the right of tlie dividend.
48
B-Samplk.-
623 "^
OOMPOL'M, DIVISION.
l>'vide 635 tons. 4 cwt -i n u
I.
17
0.
2
3 Ans.
12
20
244
I7S
66
4
?67
267
Operation, 8!i x 7 ~ fi9ci ^ „ i
t'lis boing roducp.Mn T . ' '""^ 635-622 ■- \i
remaining. thi?«" ^""laine-i txvico and 1
». 3'J6 wks. 5 fl* 17 h t;7 .
''•■7Sfc'eV3n8'P^-^o^'"«-2746
15. 3786 tons 19 cw? T" " ^'^^^ 2 a 52 in ^ Qfi,
'6- If 137 lbs" 0? sTgar' 1% V^',.' ' «^' « d-- - 3^65
«7. If f7lS7%4 h "''' "''^ «- i^H
19 if.fJ^^-costiSo-f '^^'''^«'- ''aSligst oontaininj
'"• ^' a person spends SOni «« • """"«i
3 V^- by 89.
= 623. and 635-622 — li
''n""ds and 4 cwt a"d<i
^onla.ned tw.co and 1
g'\K^'V°"'ttined exact,
s tiierefore 7 Ions. 2 cw;
39.
3- -r 69.
■-f-74.
drs. J.3I3.
■i- 'J27.
'46.
52 in. -^
oz- 8 drf..
'hat will
i964.
-f-365.
one poun
ong 93 persons wl;.
''acljgst containingj
r, how much would
how much will thaj
quantities of morel
T many timts. J
dend to the iowesll
'Simple division.
COMPOUND DIVISION. 4^
KxAMPLK 4.— Divide 14 vds 2 ft i,, 1 1 1
H Yd'. 2 ft In I i ' ''""" ''y 3 y<i8. 1 ft.
3 yds" I ft • " ''"es=645-nines.
57()0
, , iW? Memnindor. thfre'ara Lsf r '"°" T ""'' "'«'
and 1440 in the divisor ThlTmZttaJcT '"^ho dividend,
the quotient 4 ■^^^, ^'"^ ^^" ^^ ^^'*0 we obtain
EXEHGISE 3.
I. Divide 248 gals. 2 qts. 1 gill by 34 sals I ninf
for is""* ■""">' "•■"■«■" '■■'*«"'» m<><>lmLT>,ltlgM
rence of llik wh.iol Mng ,? fti*""^'^ " ""''i"' ">« ciroumfe-
JmlVZ.>,7"\rir """ ""'''■ ''^ <"»> distribmed,
ou? ofs 7bs"'?"'' "'""■ "'°°"»' ™* * -• » -Iwls., may b, made
J^"°":Tr "'■ °''"''°«' « "■ '"■ P^-- ">,. may be bought
made'i°uT„ra'."nrort„"'?''""» ' ">^'- ' "- -y >«
cbL^„';;.s°i.r7r,br7r';.°i;e'?iS;"'^- ' -■ "•^«'"»
^ is. "?: 7:^ orsj;?f„t.i!",?irr """ -f =' ^ '« '
bought for $220 *'^-^^' ^°w much may be
.ro'y!whKa°s'i?s°we';gb'.f "'^ "^ "• "' ^«-- '^^per ounce
. ,;'4io?,S itVn'", ?„"Si*' °"' "' ™''° ™' °f
r.ok„„"7eaT,V;rot'urr" '"^^ '" ""l"!"* 'miles,
J%?r """>■ '""•'" <"■"■»"■ " i3.78Tir y^Smay be bough.
an'd" 3S?'=i,rte"°"'J' % ■"*,?" ■"'■"'"•'■y l» "...W. IV
e«nmples, which may will, i™„nSv'"h.*-'? i*"" l»"»wl'ni
every such operation /e,ni','^l CrStiXa'r SXK
00
'iXAMM.K 5..
7
8.
18
15
19
Multiply n . ,x . ,, ^^^, ^^
JCl? 14
: 9
oi=|orniiiii
OJ
Example 6.— Divide jC.}?
Wo fi.sl mnliiply by /, (h.,
„■ "nn, "'" product of /i
jn
37
19
I 150
133
14 : OJ hy4i
8.
14
16
d.
0}
4
3 I ^7: 18 ; OAns.
1
17
20
356
19
166
15V
and to 1^6 tlu pnu cTadST,?''''^'™'^^'""
t'ie result is 19 Ju w,." ^^ ^''f "'""erntor
vi'lend and 4 wo ?Lf l; ^ • ^^ "'« -^i'
9
14
12
Tu
171
1.
£28
19
2.
£ i
1!
3.
£ 4
2
4.
JE 7 •
16
8f X
6| X
6 X
7i X
Exercise 4.
'7f.
n.
5.
£ 64
17
6.
£847 :
12
7.
£408 :
8.
£ 7 :
3
7^ + ei.
H -7- 47*.
m -f 43 a
n -f 2i|
1
N,
'•«! n)l,|li,,|y by /, Ih.,
'""'"T, 11,,.,, /•„,, J^ jj,
'''I'iiU'o vvf niuliiniy
: fMli« nmlliplic,„i,i
" ('ivide tJm prorluft
"■'' Rives llio resiill
■ ^ji> I'lis addtHJ to
I'lo product of 4
•■ '•4 -"Oiftlio product!
iiuniher in the di-
aler 01' tJie Irflclion
d -i the niiinerntor
I wo divido £150 •
\-- ^ : O4 tJiedi-'
)btain £7 ; 18 |)
SIMPLE PROPORTION.
MISCELLANEOUS QUESTIONS.
I. WeJuco $73%8 42 to cf'fits.
ftl
2. H"Juc„ 81000703 cont8 to dollars.
^'..'1-indS^^^^^ ^mu,,
4 '''•om$IOO(J.i7tal(o$;i74 82
^ Multiply soifj 28 i,y 305
«• i)ividn $42()«., 8 Lctwe.,; II persons
7. Divido $37240.07 by 821
«• Hnduce 17 tons 19 owl. Ur 14 ih, t. ,
H-;Jucc7i6,>3284 dra.ns Avoirdupois, to tons, hundreds
>!• Fn.m27Icwt 1 ar 14 Ih 1 '^'- '^ ^''«- ' ««'■• '8grs.
19 lbs. 15 0.. I4%V8 '^' ^ "^^^ '3 drams, take 3 qrs.
12. Multiply £763 : 19 .. 4^ ^y 12
13. Multiply 32 yds. 2 qr. 3 nls. by 276
.D.vue764n,^ .Uur, 26 per. 3 yd.s.' by 9
5.D.v.de9n5e.vt..cr.24 1bs..4ds.by74"
6 Rod.,,,, ,,,74 grains Troy to lbs. '
I'. Heduco £742 IQ • « <„ 1 ,,
18 o J ■ • ° 1° flollars and cents
'} + 6J.
5} -i- 47J.
10} -r 43 »
■'1 + 51 j
SIMPLE PROPORT/ON.
52
SIMPLE PROPORTION.
m i
The first of the terms in a ratio is called the antecedent, and
the second the consequent.
The first and fourtlz terms of a proportion are called the
extremes; and the second and third the means, thus, in the
jtroportion '
As 20: 15 :: 60 to 45,
20 and 45 are the extremes, and 15 and 60 liie means
In any proportion the product of the extremes is equal to the
product of the means.
Thus in the proportion, as 12 : 9 : : 36 : 57. The product of 12
and 27 the extremes, is equal to the product of 9 and 36 tho
..IVr*^ ^!l' ''°"'"' P™P«''t^""'^l "multiply the second and third
terms together, and divide the product by the first term.
ExAM.-m.-Find a fourth proportional to 7, 21, and 9.
21 X 9 = 189
189 -^ 7 = 27 Ans.
Exercise 1.
Find the fourth proportional to
1
2
3.'
4.
5.
6.
9,
8,
6,
10,
27,
3, and 15.
24, and 13.
15, and 4.
15, and 6.
135, and 3.
32, and 16.
7.
8.
9.
10.
11.
12.
14,
36,
92,
29,
75.
12,
19, and 28.
47, and 54.
68, and 23.
lie, and 14.
18, and 25.
90, and 48
fh«MtT Write the three given quantities in succession, so
hauhe term which is of the same kind as the required answ
h tH v: ''*'' ''"" '• ''''' «"^^- •«'- ^- ^-"r
than the third term ; set down the greater of the other two
hTll'V. ''''"^ P"'' ' ^"* '^ '^' ^"^^^'' '^ '° fc« less than
the thud erm, set down the smaller of the other two terms in
he second place. 3. Then multiply the second and third terms
together and divide by the first. 4. When the first or second
term IS a quanlily of more than one denomination, reduce both
to tiio lowest denomination contained in either.
the antecedent, and
rtion are called the
means, thus, in the
lie means.
emes is equal to the
'. The product of 12
Lict of 9 and36tho
le second and third
!ie first term.
', 21, and 9.
19, and 28.
47, and 54.
68, and 23.
IK', and 14.
18, and 25.
90, and 48.
in succsssion, so
3 required answer
is to be greater
)f the other two
is to be less than
ler two terms in
1 and third terms
e (irst or second
ion, reduce botli
SIMPLE PROPORTION. 53
PBOor^ Multiply the answer by the first term, and if the pro-
duct us he same as the product of the second and third terms
the woric may be considered correct.
E..AM..Z.K.-I. If 3 lbs. of sugar cost 33 cents what will 5 lbs
cost at the same rate ?
ll)s. lbs.
As. 3:5:
cts.
33
3 I 165
Here as the answer is to be in cents
vve write 33 cents in the third niace
hen as 5 lbs. will cost more than 3
lbs. we write 5 lbs. in the second
r.<L , ^.^^^ ' '^''-'n dividing 165 the nm
^^''"^'' ?'»ctol the second and third terms"
by 3 wo obtain the answer 55 cents
wiu'27 cwt.'3-^;s. costT' ' ''• ' ""• °^'^"°- -«^ ^"0 wha;
cwt. qr. lbs. cwt. qrs. $
As. 28 1 9 : 21 s . . A^n
4 4 "^ • • ^^^ In this example
the first and se-
cond terms are re-
duced to lbs. tho
lowest denomina-
tion contained in
either. Tlien di-
viding .<$ 9352,50,
tiie product of tho
second and third
terms, by 2834
the pounds in the
first term we ob-
tain $330 the first
nn, . part of the answer,
•01 Ans. then reducing the
remainder to cts.
we obtain the se-
cond part which
is 1 cent the whole
answer therefore
is $330.0 land 166
remainder,
ICG remainder.
U3
25
87
25
574
226
435
174
2«34
2175
430
65250
8700
2834
1 935250 1
8502
8505
8502
3000
2834
54
SIMPLE PROPORTION.
Examples. If 17 ]h<i u ,^■. .*•.
n^^Hy be bought for i^taUhe sau/: rate f ' '"^"'^"^ P°"°^«
. ,^ * lbs. oz.
A3. 14 ; 24 : : 17 4
16
106
17
276
24
U04
552
14|66il|l6(^3oz.2drs.
29 lbs. 9 oz. 2 drs. Ans.
102
98
42
2
16
32
28
ou!.^:r.-s-/xieT'°
4 rem ,
EXKRCISE 2.
same rate ^ °''°^^^ ^"^^ ^^^^ what will 86 lbs. cost at !he
3: wl^I ^l?]^,rT^ -"-t Will 93 acres cost '
bought for $6.50? ' °^"^^' cost, if 13 bushels can M
d4s i^n'^CeirrS.: K :;:;:^^?^ '" ^^ •^"^«- <" '-w .any
cost $m "'"'' ^^'""^ "^^y ^« ^'^"ght for $374. 16, if 28 gallons
rateof?;-.;;i1^5';i!::^^;'';Klv'T^''" ^^"^y^- ^^ the
H d ist.f
4, Iiow many pounds
SIMPLE PROPORTION.
65
s. Ans.
the third term to
Ls in example 2.
rould be obtained
s. 4 02. by 24 as in
lUon and dividing
SG lbs. cost at the
93 acres cost ?
' bushels can '.i
•ys, in liovvmany
■16, if 28 gallons
lbs. of sue j; if
'29 (lay.«, pJ the
the sami ™^t'e?' °^''°''' '°'' ^^''^•'^ ^^^' ^'^' ^^ y''«- ^o^t at
9. Ifl76cwt. 3 qrs. II lbs. of flour be bought for £ 1 94 • 2 ■ s
how much may bo bought for £304 • 9 • ^7^"'''°'^ -^'y* ■ ^ ■ ^'
in Sh^I^ ™K-"l ^''^ '^'" ^^ required to do a piere of work
" M '^.T' ^^'"^^ ^ * "™^n <=an do in 48 days ?
foH4Sroil^SlLname^rr.'''^'^-'«' ^'^'^^ ""^^ '^ P^'^
14' wValTs"th?v«ln;S'1c;'°"V 74 pounds of cheese cost?
per cord? ''""^^ of firewood at £l : 2: 3
HsVuonslf t^slerte^ "^"^ ^'"^ "'^"^ ™"«^ ^« P^^^ ^o''
wouldYhl't^e'fSjfm'ontlf? '^ ''''''' ^"°-' ^-- --^
y: "-^ ^U's ni^'co^-^^ ^^ ^ ^'''^^' °^ '^'"^h^ ^h^t w«"iJ 13
'tf. ]:• a steamship sails 3700 miles in 13 davs, how manv
''" q' t'^Yl'^ "'^* ^^ °" «" average per day ? ' "^
3 qr's. fost'auhelme rate"^' ^''' ''^^ "^^ ^^'^ ^^ -t.
be'boJghtfoi'J"! l[ r' °' '°^* ^'-'^ '^"^ "^^"y s^i'°"« -ay
muchl^tKS"?rarum.°" '° ^^^^™^^ *'-^« P- -^«^- ^ow
cwt'3Trs^Kl'ar&^r°/^T^'^°^^ ea.h weighing ,3
for lyds'Vj':tnlV. -r" '''' *''''' '°^ "^"^'^ ^"«' ^« P^'^
,•« ?hk ^i^ ^u!^] ^^^^ ^'^^^ ^^""o^'S a shadow of 6 ft. 2 in what
.IS the height of a steeple which throws a shadow of Tmt 4
25. If 56 men can reap a field of wheat in 13 days how manv
men would i take to reap the same field in 1 1 da/s v ^ ^"^
26. A bankrupt owes 18472.94, but the value of his efTerts i«
TL'ltcS' '' "'' '' '''''' ''^ '''' ^°'^-' -'-' is !h?;|ue
27. If a regiment of soldiers consisting of 954 men occnnvin<T
a besieged town has provisions sufficient to last them 13 wE
moved?' ^''' '^' P'^^'^'""^ ^'''' "'^'^ «'■ the soldieJs 7revt
28. How many days would a person take to travel a certain
3 Snr4r,^iV";f..^_ i-S- ^If^y. in.e can travel thrjame
ui ...H in .,, ,!aj= walking i 1 hours eacli dav ?
fnn u , . P ,"^^ P!'*'^'^'""^ ^""•^'ent to last a crew of 27 men
!s incre:S^to'3T.a"''' "'" ^^"'^ P^-^- '-^ ^^ ^1- -"
5b'
SIMPLE PROPORTION.
m
m.
2 'ats'^ll'^.rZir" '" ™ »°-"-^'* ™""' •"' ".= mte or
how oiany'r," Culj'.hrfl'";- * l"'- '"■" <■»«« i" 4 day,
35. A b«nKp7owes S7wLm? i"""?,."" ' '"^ ' r. 9 pe'?
M^glf ri^loTf '1 -' »™-- "-'«"• "- --y tarrals „,ay be
c'Lu^o'er" '""''° """ "f " lbs. 3 oz. of coirae if 3 lbs. 7
A'V^Vl!\'J:l'^- ' '"■ ' "'• " ■='»"- ««'. ■" '"e rate of
wiS |„t ffo%lr„.-'3?a^Lrr/v.^'e?r " ^^' ^ '* • «.
40. How much cloth nt «■? 97 „ *''P«rf
72 yards at $2.53 per yarj 9 ^^'^^ P"*" y^'"**' ^o«ld I'e equal to
$7 9G Jr fnTbs •/' '^"^'- ' ^^«- 20 lbs. of sugar at the rate of
Cor'WSl'r''' "^"^ ^' ^'■'' P- 3 g-l- 1 qt. may be bought
ta^ii.f,I c.Ti7%ts'falZ'^ hogshead of sugar con-
a T-8. 17 lbs. cost $139 ? ■■ '>«§^S"«^d containing 15 cwt.
sam^'rate v'^- °' ^'^^^ ^"^^ ^'^'^O what will 93 lbs. cost at the
4G If 17 bushels of wheat coc^t «iq 7^; u
may be bought for $237 ^ * •'^' '^^^ ™a"y bushels
p|"472g& AtiriS ^"^ ^^'■''' -^^' --t be
^ SO. What cost 79 cwfo^knr^^^^^^^
97 lbs. ? °' """'^ »^ Ihe rate of £1 : 2 : 3 per
wha't woulSte li/Teng^r^l'/fhe'raTo ' f^'"'^ '' ' ''■ ' '"•
137 feet high ? ^ ^'"^ shadow thrown by a steeple
ceiSpergalfonV'^"'"- ^ '^''- «^" "^^'^sses at the rate of 36
N.
acii chost contain in<»
llie wliole at G3 cents
lb. of sugar, if 3 cwf.
weight cost $78. IG
lie ? '
lounttoat the rate of I
fa fence in 4 days,
3 acres 1 r. 9 per ? '
s are worth $4557.69
wes '! '
nany barrels may be
z. of coffee if 3 J bs. 7
^ cost, at llie rate of
' per. is £59 : 14 • 6
"f
I, would be equal to |
s is f 15, how many
134.25 ? ^
sugar at the rate of
qt. may be bought
ahead of sugar con-
containing 15cwt.
3 lbs. cost at the
ow many bushels
'3, what must be
3 lbs. cost ?
t per pound ?
Leofjei : 2. -3 per
idow of 8 ft. 9 in.
•awn by a steeple
at the rate of 36
SIMPLE PROPORTION,
67
53. How many miles can a person walk in 37 days at the rate
iof 40 miles 4 fur. in 3 days ?
54. If a steamship sails 2450 miles in 9 days 6 hours, how
[many miles would that be on an average per day ?
55. If 7 cwt. 3 qrs. 15 lbs. of sugar cost $96, how much would
that be per cwt ?
56. If $26 is charged for the carriage of 49 cwt., a distance of
180 miles, what would be the charge for the carriage of 76 cwt.
3 qrs. the same distance ?
57. Bought a hogshead of sugar weighing 14 cwt. 2 qrs. for
i$l28, how much would that be for each 12J lbs. contained in
ithe hogshead ?
58. How much will 24 yds. 3 cirs. 2 nls. of calico cost, at the
rate of 27^ cents for 3 yds. I qr. 2 nls. ?
59. How many days would it take a person to walk from
Quebec to Montreal, the distance being 1.80 miles, trasfelling at
the rate of 63 miles 2 fur. in 4 days ?
60. If 390 acres 3 r. 20 per. of land cost $964, what will 78
acres 2 r. cost at the same rate ?
61. What is the value of 24 oz. 17 dwts. 13 grs. of silver, at
$1. 35 per ounce ?
62. What cost 178 cwt. 2 qrs, 14 lbs. of flour at $4.17 per cwt?
63. If 173 lbs. 8 oz. of coffee cost $49.35, at what rate per lb.
must it be sold, to make a profit of $8.17 on the whole?
64. At the rate of $36. 18 for 9 cwt. 2 qrs. of flour, what must
be paid foi 75 cwt. 1 qr. ?
65. If a ditch 3 acres 2 r. 18 per. in length is dug by 14 men
in 5 days, how many days would the same number of men
take to dig a ditch 7 acres 1 r. 14 per. in length ?
66. If 26 acres 1 r of land cost $156. what will 74 acres 2 r.
20 per. cost at the same rate ?
67. If 67 cwt. 2 qrs. 14 lbs. of flour cost $210, how much
must be paid for 26 cwt. 3 qrs. 9 lbs. ?
68. If 37 cwt. 1 qr. of sugar cost $333, what will 49 cwt.
2 qrs. 12 lbs. cost at the same rate ?
69. What will the assessment on 74 acres of land amount to,
if the assessment on 724 acres is $17.24 ?
70. How many men can finish a piece of work in 78 days,
which 204 men can do in 123 days ?
71. If 47 men finish a piece of work in 63 days, in how many
days would 86 men finish the same piece of work ?
72. How many cwt. of flour at $4 per cwt., should be given
in exchange for 29 f.wt, ?. qrs. of sugar nl $9.5n per cwt. ?
73. If a person travelling II hours per day finish a journey
in 23 days, in how many days '\ill he travel the same distance
walking 9 hours per day ?
74. From 37 yds 2 qrs. 3 nls. take 9 yds. 3 qrs. 1 nl. and find
the value of the remaiinler at $7,50 per 2 yds 1 qr.
58
ii;
COMPOUND p^OPOMlON.
75 Xfth ""^-ixuN.
COMPOUND PROPORTION.
divide both SnmT '^^."sequent, by anv n. ^l ^^^'^'ng an
ExA«p,E -.1/ th °"^'"^^ numbers '"^ '''' '''^^'^
w^'at mustbe "aid /-or h'^^^ '''' ^0 cwt isr. „,-,
l^^OO : ,2000-* mge'oflb ol't'^^^jj^- ,««'-
480 ".^e carriage of 80 i ! *^®°
— — . P^ace 80 cwt in th« « r- '^'^
960000 «nd 60 owTX^he^J^'^M^oe
48000 «s. the carriage for sSn'^' "P^
^- second place ''"O °i,ies in the
u . 00 5760000 th„ .. i" rf'viding
^t will be fnnn 1 ^^ *^°swer
example ;fj=^;;"f;«s Possiole, as'^^iir Kf ^^ «^««el]ing all
reduced. ^— ^-ame as that g.lot%trw;i^%^ffif^|
HON.
groods each weighiPff J
TIOJV.
of the ratio of twn I
't and consequent of
antecedents Ind con-'
equired answer
3d by dividing an
number that wiii
J^ using the results
^"''«s cost $4.80,
■<:00 miies.
w;rite 14.80 in the
Then as the car-
.of 80 cwt. we
in the first place
^ the second, and
e for 200 miles
re than for 180
^„y«0 miles in
''•'O nj,ies in the
inen dividinj?
product of tht
'fi the third term
am the answer
' cancelling all
fi t'le following
with the terms
COMPOUND PROPORTION.
59
by 5
example,
First we cancel 60 a consequent, and
write 3 m place of the antoce I 'nt 180
in which CO is contained exactly 3
limes, then we set down 2 in plar;e of
80 and 5 in place of 200, 40 being con-
«A ni. A„. «n"'^'i';^^>'^'l' ^^^''^"^ '" "'e antecedent
M 00 AnsSO and 5 times in the consequent 200,
and riivirKn^ h„ r multiplying $4.80 the third term
and dividing by G, we obtain $4.00, as in the lirst
ExEHCISES.
1. If 15 men in 12 days mow 60 acres of grass how manv
acres can be mowed by 24 men in 15 davs ? ' ^
4. II $134 pay 17 men for 8 days" work, how much will ha
requirod to i)ay 13 men for 6 days work ? ^
57 mnnln^s VJ'^' '" ^.'"'^H ?"^ ^^ feet in length is built by
b/ men in 18 days, working 8 hours daily, what leneth of wall
leet high can be built by 94 men in 15 'days woSg 10 Ss
msTr'ooll^y^l'lilir °" ^'^«« ^- '' '-y^ 'f the gain on
27^davs%EnS Vl'^ ™'" ^"!. P''^^'^'""^ «""'"«'^nt *« '^st
davs wil) H^ia^ ^^ '^""■''' Pf ^«y to -^ac'' man, how many
to^gOOmpn^r^r'''''""' '**«'''■ ^^^ i« increased
Ounces peTday 5 '"'^""'^ '° ^^"^^ ™^" ^'^'"«- ''^^^^^d to 12
8. If 15 men in 8 days earn $130, how manv dollars will qq
men earn at the same work in 26 days » ' ^^
dng bvlSSf if ?/'!' '"7' '^ ''^* ^'^^l^' «"^ '^ f^^t wide, be
•ench 740 ^P? nni ?^^^r'' J'^'"' '"^"^^ "^'^^' ^'^ ^^ take to dig a
in rr '°?^' '? ^•^'^^ ^^'^P a^'^ ^ feet wide in 25 davs ?
10 If a person travels 207 miles in 8 days walking 11 houV-^
hTurtp'^rX?""' """"'" '^''^^'^ i7da;TJilkinT9
wi'; ^'^ the value of 60 yards of cloth IJ yd. wide is $112
Ti Jard w!de ' ''' '"'"' °' "'* ^"''^^ of theMme Sd of cloth
12. Ifthe carriage of29 cwt. 210 miles cost $4 how mnnv
cwt. m.glit be carried 190 miles for $13 ? * ' ^"^
gain".f37 in'e ifZtf ? '" ' '"°"^''' '^'^^ "'^"^ ^«"^'"« ^°"^d
14. If 24 men do a piece of work in 32 days working 10
w
OMATEST COMMON MEAgunB.
men „iiu ..ke .„ Sa'p 5strda' iT'^y^", ^ "'■"• '»»' ™"y
ho :. qi-?„ S* f:n -^S ? ^'^^ ""«■■'' »
2^ y u"*- '° ''""''« each day r ^^ ^''^''^'^^ P'^^gh 29
quarters wide'cost tiiJ^h!.' ^'^^^ /^^^^ containing 29 yds S
in 17- dayfwTC&rnS IVt''"' "" ' "" «"*
be required to digiiren^h 10,^1 rJ'''o«- many mea would
days working lO^hou™ a„h ja'y%* '""« """ ' "■«»' »'"» '" M
hhdd,, each weig1,i„g"',rcw.Tq|:.''for"5^„X^",'' '''■"'^' "'»
GREATEST COMMON MEASURE
exX°Sutle;™^°;i=S -t,?'' 'J"","-'" "-* i'
are measures of 36 ^ '"""""loi-- Tlius 3, 4, 9, 12, and 36
byVh°re°.°or„?S;rm'aTbe ^xTK™^"? '^ '"^ "™W
a remainder. ^ ^^ exactly diviaed without leaving
thJJl^igrerntSTy^r numbers is
without leaving a remainder ""^^ ^^ ^^^^^'^ divided
isthp"r^;pVV-4''''''°'"™°" measures oi 20 „pw .q but 9n
t1" ; °I.^ ^'^ ^uaiinon measure ' ~ ' ^"' ^^
To «„d the greatest common measure of two numbers.
r'
ASUilB.
1 17 men do tho same
' in 10 days, how many i
■travels 190 miles in 8
Bl 340 miles wallcing 7
i-iO in 5 months, how
14 months?
in 4 days, how many J
■s ? •'I
by 27 men in 4 davs>
rs ? ■' *
I in 8 days working 9
36 horses plough 29
oontaining 29 yds, 3
be paid for IC pieces
Jntaining 34 yards, 5
ork is $60, what will
work ?
!res of land, in how
long and 4 feet wide
many men would
rid 3 feet wide in 20
ch weighing 17cwt
for tlie carriage of 8
liles ?
LKASr COMMON MIILTIPLU.
LSURE.
that will divide it
3- 4, 9, 12, and 36
ers is any number
ed without leaving
more numbers is
<e exactly divided
20 and \0, but 20
ro numbers.
Awfe -Divide the greater number by the less ; if there is a
•emamder divide the less by it, and proceed thus dividin-^ the
astd.visor by the last remainde until nothing romains.°Th.
ExAMPLE.-Pind the greatest common measure of 355 and
775
^55
77oJ 2
710
65
First we divide 775 the great-
er number by 355 the loss,
this leaves a remainder 65, bv
which wo divide 355 the le«»
n"i?ber, the next remainder
IS 30 by which wo divide 65
t^e'ast divisor. Thon dividing
•jO the last divisor by 5 we
lind that 5 is the greatest
common measure it being con-
EXEHCISES.
Find the greatest common measure of the following numbers.
I 355 I 5
325
10J65I2
60
5 1 30
30
|6
gained exactly 6 times in 30.
1. 315 and 725.
2. 93 and 123.
3. 724 and 1248.
4. 968 md 8724.
6. 1325 and 6495.
6. 81 and 738.
7. 1254 and 964.
8. 5696 and 1334
9. 1023 and 1581.'
10. 6785 and 2345
11. 118 and 576
12. 348 and 3144.
LEAST COMMON MULTIPLE.
A common multiple of two or more numbers is anv n,.mK
Ithat can be div ded bv Mr^h nf fi,» „:,„ 's any numbtr
leaving a remainder ^ " """'^"''' ^'^^Out
I The least common mulUple rf two or morfi r.i,mK„ • ...
lowest number that can be divided breach o7th«^.^^'^ 'K^^""
without leaving a remainder. ^ ® ^'^^" numbers
LmheS' '^" ''^' '°'°'"°'^ ™"'^'P'« °f ^^° or more given
r,n!!K !""'■ ®^* *^'"^" *^' ^'''" °'''"*'^''^ '"^ a line and cancel
I any that are exactly contained in any of the others. J. Find .
02
LSAsr COMJfO.V MVLTlFLt.
'T: I
L last l,ne. 4. Then multmly logolher all the numbnrs in
h, .,«t l„.e and all the <ii,i,„n,, and the product win bTlh
least common multiple. ^^ win oe ine |
the multiple founci ^farno^^%y1t^testTotibr ""'^^ '
Ex^MPLB.~Find the least common multiple of
«^ «. 4, 18, t2, 20, and 15. First we set down
the numbers in a line,
then on inspection
we lind that 6 and 4
are exactly contain-
ed in 12, they are
therefore cancelled,
and seeing that no
other number will j
measure as many of
bers as 2 we therefore take 2 n<. Hiuicnn iJ^^ remaining num-
quolients and the undivided numhorf^ ^'rf''"^ ^°^" ""'
set down the quotiSits S ur^?vTir ^''^t ^ ^^ '^'^'^or and
line, we then cJncel 2 and 5 wh^h n ^ ""'"^^'"^ ^" the next
and niulliplyu^g together t J 'm^ contained in 4 and 10,
IheL.C. M.3G0 remaining numbers wo obtain
To find the L. G. M. otherwise.
Rulell-l. Set down thogiven numbers and cancel any thai
are exactly contained in any of the others. 2. Divide he re
mairnng numbers by any number that will exactly divide on
:Lr;:^i:i;r;;;r.r\;:^^'r"°^'*'"-
dividing any of the undilir^m,:?: fyt: ^^^^0^
3' proceed tburwi/r rT' ^"' "'" ^nai.idod numbers.
3. Proceed thus With each h„e until no number greater than
X 2 X 2 X 3 X 2 = 300 Ans.
Find tl
1. 3, 5, 7
2. 2,4,6,
3. 17,9,;
4. 16, 2, ^
5. 9, 16. t
6- 18, 4, 1
7. 9, 2, 8,
8. 6, 3, 5 I
A fractic
equal pari
fraction ex
'ininator,
A vuiga
I of whirh is
The uen(
I number of
, I'he num
the numbci
VULOAR JPEACTIONS.
99>
ne last hne 4. Then multiply together all the divisors and
! 12 20,15 ""^'"^ ^''^ ^''"^' c^niraon "nultiple of 6, 8. 4, 18,
li|J6)_ 8(4) 18 12 20 15
81
8
6 (4) (4)
15 X 8 X 3 = 3f50 Ans.
Tn this example we use
the same numJbersas in the
first. First wo cancel the
numbers 6 and 4 each of
which is exactly contained
the uncancplled numbers «<» Hivi^nn'" '1' "^®" "^'."^ '^ ""^ °^
highest factor c(x^i?mon7o?5thrr*°'* see.ng thai 3 is the
and 12, we divide thfl.n hv \ ^ '^'!'^'"' '*"'^ ^^^ numbers 18
4, we alsrdrSr20 by 5 ft be "n. fhllfT '^r '^"'^'^°'« « ^^^
the divisor and 20 nn^ 1» . ^ he highest factor common to
div ided nuXr in th^nexU^nT N '?' ^"°"*^".' '^"^ « »^« "'^-
are each contained in s nn J • ^ o""^ ^^ '=^"'=«' * and 4 which
2, the hVhestTtor commit"! ^ *^ '^'^'^°'*' ^^ divide 6 by
qUent. Then the Dpo^rf^n^ h"'* ^ """^ ^^' down 3 the
uadiviaednum"beV1SsUe[!c. m:S! " '^"^ ' '''" ''''
Find the L. C. M. of
, 1- 3, 5, 7 and 9.
2. 2, 4, 6, 8 and 10.
3. 17,9,27, 18 and 11.
^. 16, 2, 4, 8. 5 and 9.
fi' ?L '6. 5, 3, 27 and 28.
6. 18, 4, 17, 13 and 6.
J „9' 2, 8, 7, 5 and 4.
»• 6, 3, 5 and 24.
KXERCISES.
9. 12, 24, 48 and 80.
0. 18, 36, 14, 19 and 6.
11. 36, 92, 7, 4, 8 and 9.
2. 2, 3, 4, 9, 7, 5 and 8.
J-28,44 96. 38, 17,42and58.
4. 9,11, 17, 19, 21. 23 and 25.
15. 7 2, 9, 15, 18, 37 and 46.
16. 18,27,94, 108, 62, 13 and 15.
VULGAR FRACTIONS.
I equafTarts" Into Th^ch ^nn'^''''^ '"•^'•"'^^^"^^ «"« ««• "^^e of the
WllS^^^S',^::^^^^^^' °""^b^^ or terms, one
64
III
w
VULGAR FRACTIONS.
taken. " «'|uui parts, and that seven of those parts are
SoDe??mnrnni"'^' ?fvulgar fractions, viz :
A7"op:XSnTnt ''™P'«-,««?H.ounrt and complex.
thanit,5enomina?or. a.7'."V^'"''' '''' """"^'■^'«'- '« '«8S
ie^^^'^'^^'^'-^^i^?"' "" —tor is not
annexed?as"27M8fj"75f o*"* whole number with a fraction
intoSVunuTsdiS^^^^^ '^ the equal parts
parts iSS'^whJcVSh" ^JiP'''^sses one or more of the equal
nute?aS;or'Sdenorna7n^'°^ '''I* t'^^^'*'" ^'"'«'- '" •'«
» lu us uenominator, or in both, f 9 ■•■ 2 §
thefr»clion,s„o°S„*ed "^ Uie same number the value of
REDUCTION OF VULGAR FRACTIONS
To reduce a fraction to its lowest terms
fraction >;:?hl''' ''''. ""'"''''''' ^"^ ^''« denominator of the
traction by their greatest common measure
nnmL!iZ^'T '''" """'™'°'' '^"'^ ''^^ denominator by any
ihnT tV . ' exactly measure both; divide the quoUemI
thus obtained in the same way ; and continue the process unt
no^number g.ater than unity can be found that ^ZlZfe
T^^^'tT!"^"^'''^ ?« to "s lowest terms.
t f «f f ? Ans By rule 1 we divide 216 the numerator and
^88 the denominator by 72 their greatest com
terms. '"''"• * '" ''"^ iowesl
I 6 I ^ n An^-^By ™le 2 we divide 216 the numera-
tor and 288 the denominator by 12, and
12
h
IS that a quantity is
n of thoso parts aro
iz :
nd and complex.
3 numerator is loss
le numerator is not
ibor with a fraction
of the equal parts
more of the equal
id, as i of J, ^ of
iction either in its
11111
a fraction be both
inber the value of
nominator of the
VULGAR FRACTIONS.
EXERCISK 1.
Reduce the following fractions to thoir lowest terms.
65
I.
-iV
5.
2.
-ilf-
6.
3.
~m-
7.
4.
4H^
f.
-nn-
..7 1
9.
10.
11.
12.
To reduce an i.nprop - . :otion 1. a whole or mixed number.
I '"'^--D'V'dethenumvu-.opby .i.e denominator and there-
I suit will be the whole or r., oi number required,
ExAMi'LK 1. Reduce |^ to a mixed number
G3 ^ 20 = 3 ^ Ans.
Example 2. Reduce i]^ to a mixed number
146G .^ II = 132 .^ Ans.
ExEiu;isi: 2.
Reduce the following fractions to whole or mixed numbers.
1.
2.
3.
4.
5.
6.
7.
8.
-nn-
-mi-
9. -a^iOyia.
10. -iifpi-
11. -ZJ^lAll.
12. -fiiflwfl.
To reduce a mixed number to an improper fraction
ft«/e. IVlultiply the whole number by the denominator of the
fraction, and to the result add the numerator, below which
write the given denominator.
Example I Reduce 0/, to an improper faction.
9 X 1 1 = 99 and 99 f 6 = 105 .-, \o^^ Ans
Example 2. Reduce 19| to an improper fraction
19 X 8 = 152, and 152 + 4 = i5G .-. x^a ^ns.
Exercise 3.
Reduce the following mixed numbers to improper fractions.
1. 9-f}..
2. ll-,\¥.-
<» '
.1,
4.
5. Ul^3^
6. 274-.}f-
7, 93-f|-
8, 204Vy»,
Vr
9, 609
10, .365-*!l«'4.
11, 28
12, 96
8f -
-n-
To reduce a compound fraction to a simple one.
m
$''%
11
VULGAR FRACTIONS.
If there are a denominator I
" ,"''7 J f * "'■ S '" »™pl. rmcuon. '
Pir« *''*X9 =T80"=-4r Ans.
u . EXEHCISK 4.
Beduce to Simple fractions.
1. f 01' f off off
•^•|of|offofi-of|.
4. f off of _^ oH.
6- i of I of 2 Dili of 5.
M 01 i off of I of i.
8- ^V of -ft- of 41 0,2
-f?-ofl-^^of2|| ,,.
-.VoffoflofV.oj'i:
|onof3-^, o?6. '"'
f of I off off O/ J.
(fa
*avfng1"olS„"J^,^„^^^^ to equivalent fractions
2- Divide the commoL dlno • «^ J '°°'"°" denominator
denominators, and ZuuZZ ,' *'' '''^' '' ^^« »'-"
given numerator., and th^re stlt'f '^ ''« «^^^ «^"-
luirea numerator^ beioww IT ' '' '^' '^^* °^ ^'^^ ^^■•
'or. The other numeltls ^i^ L?'^ !'^ ^'^°''"«" '^^""^i^a-
common denominator " '^"'^'^'''"t ^^i^tions having a
3.?;T5";a'^^^^^^^ multiple of the denominators
3!?t^ = ^4^3'2^5l = ?;?H-nrstnumerator.
X ^- 126 i/ie fourth numerator.
fether for a new numej
«' denominator.
■he compound fraoticul
jple fraction.
5~ Ans.
8 the numerators bv
■nen we muJtiply 4 ji
lalor 180, which male'
i to its Jowest t( rn,s iff
fraction be a mixaj
proper fraction.
VULGAR FRACTIONS.
67
off of I of i.
A-of-^f ot2 x&.
I-A-of2|J c/a,
of3-^, o?6. ^"•'
>f§offo/J.
equivaient fractions)
of the denominators I
mmon denominator
e first of the given I
tty the first of the I
the first of the re-
common denomina-
the same way.
fractions having a ^
the denominators
'St numerator.
:t:on(i numerator,
ird numerator.
LiitJi numerator,
JThen writing 315 the common denominator below each of
lese we have the required fractions |f g, j^f , xas^ and |f|.
ExERcist: 5.
I Reduce the following fractions to equivalent fractions havinK
common denominator. '5 imviug
J. i a 4
3) 4) t-
'■• ?> ?) ., .
2- h !, h I -^-
3. -i^ -if , ii-, ih
•5: 1' f'2 ti ^' " ' '
7.
l>nV,if, +f,-if.
8.
-iV> -iV, -iV, -^A"
y.
•tf;-tl-if, -JI-, if
iO.
-A,-3V,-^uS i^
ii.
-eU-, -.V, i^^, -V, -h
12.
n,-ih f#,-if,-it
To reduce a comjplex fi-action to a simple one.
fl«fc.-Multiply together the outside numbers or extremes
for a new numerator, and the middle numbers or means for a
ficw denominator.
fmpro%Tfrrtionr"'' """^'^^'^ ^'^^ "^"^^ '^'' ^« ^^^"-'l ^°
Example. Reduce _A^to a simple fraction.
jA^ _ A _ 3 X 2 6
2* f II >r~5 ~ ~55
Ans.
f 11 X 5
Exercise 6.
Heduce the following complex fractions to equivalent simple
I ones.
1.
2.
3.
4. -^
f
7
9
'J
T
'i
2J
6.
7.
8.
ii.
_»
9, ^
10.
11.
12.
^1
6
7
:^-
7i
To reduce a fiaclion from one denomination to another.
68
VULGAa PltACTlONS.
~5 oz. ~ -^ _±_ 1 '
• ^ X 16 = xo = lo" lbs.
de„„=S„'!;K-«™ '*« f™- ""noes .„ ,b, „, „,„, ,_
f Of I of 4 =: 2A -. o „p ,
9/, J ^" ~ o Of a day.
lij<_GO_ _ 2880 _
5 ~5 576 minutes.
Exercise 7.
Reduce -,V of a n i, ute o t^.f,?" f '^ ^''^rter.
Reduce -.iL of a nf. V "^'^ fraction of a dnv
1 0. Keduce f^„°ofY« luf 'r''" A*" "^' '™«"'«" o^" a .il]
quantity. ^--^^ '^^'^nfty to the fraction of anothergivH
eon.at:^tt;r ^?rSn,;? ^- -west denominatio,,'
f ction Of the other as Z^Z^'TTn'' "'"^" '^ '^ ^« "'«
denominator. "nio.ato,, and the othor q.iantiiy ,,
4d'ni''-,- =3420min.-|,.
Hero wp '^ '"• = 6^^35 min. | HU = .^^- Ans.
3420 for nnmerS 'and 21'f ""^'■'■« '« '"inute., nnd !hu- oh, ■
10 ns lowest terms is ^^13'"'^ ''' ''^^"°'»i"a>o;^'Siolr;.du ^
1.
2.
3.
4.
5.
I Here we
llain the (
I Example
IpliS.
and (
' fl^re we
hd divide
I'hich gives
Find the
. I of a cw
. f of a bu
,f of?of
■f of A of
, f of fr Oi
^fofaof2
Ihtle.—Ri
deiioininaloi
[and below
[ONS.
J from a lower to a higL
or, if from a higher J
"■alor, as in reduciionf
'"Jefractionofapuuj
1_
— 20' Jl^s.
'0 lbs. we multiply ti
day to (he fraction of]
a day.
576 minntes.
fa pound.
I quarter.
n of a d,iy.
ion of a perch.
>f an hour,
ition of a line,
fraction of an acre .
JJ to the fraction 4
on of a gill.
ictionofa ton.
on of another giveni
'West denominatioiii
y which is to Jbe i|J
' otiier quantity a<\
fsl5min.,is2days
.¥3 Ans.
^and thusobUniii
ar, whic/i reducMl
ADDITION OB' TRACTIONS. 69
Exercise 8.
What fraction is 3 ars. 2 lbs. of 2 cwl. I qr. 1 i lbs. ?
Reduce 7s lOJd to the fraction of £3 : 7 : 6. ?
What fraction of 17 dollars is 28 cents?
What fraction of 2 weeks is 3 hours 17 unn. ?
What fraction is 3 yards of 17 yds. 2 qrs. 3 nls. ?
Reduce 2 qts. 1 pi. to the fraction of 7 gals. 1 qt. 3 gills.
Reduce 7 fur. 30 per. to the fraction of 2 miles, 1 fur. 17
rches.
8. What fraction is 2 oz. 17 dwts. of 9 oz. 3 dwts. 11 grs. ?
9. Reduce 7 Inches to the fraction of 4 yds. 2 ft. 3 in. 8 lines.
0. Reduce 1 cwt 8 oz. to the fraction oi' 7 cwt. 1 qr.
"0 express the value of a fraction in the denominations con-
ined in the integer.
!/;«/(? —Consider the numerator as so many of the given de-
[mination, and divide by the denominator.
(Example 1. — Find the value of ^ of a cwt.
4 cwt. -7- .'j = 3 qrs. 5 lbs.
Here we divide the numerator considered as 4 cwt. by 5 and
ilain the quotient 3 qrs. 5 lbs. the value of ^ of a cwt.
Example 2. — What is the value of & of 2 chaldrons 1 bush.
fpks.
2 ch. 1 bush. 3 pks. X 3 = 6 ch. 5 b. 1 pk.
and 6 ch. 5 b. 1 pk. -f- 7 z= 31b. 2* pks.
Here we multiply 2 ch. 1 bush. 3 pks. by 3 the numerator
nd divide the product 6 ch. 5 b. 1 pk. by 7 the denominator
■hich gives the resul*. 31 bush. 2^ pks. the required value.
Exercise 9.
Find the value of
I of a cwt.
f of a bushel.
f off of an acre.
fof a-ofaJE
f of (\ of I of a mile.
-\^- '"■^ 1^0 of a yd long niea
iof|of2^ofalbApoth
8. f.of| of a v'jhaldron.
9. f off of 7 bushels 3 pks.
10. 2f of If off of 17 gals 3 gills.
11. -i^i- of 7| of 7 miles 6 fur. 32 per.
12. -^, of ^ of 2f of 4 acres 2r. 17 per.
1 3. ^ of f of f of 3 cwt. 2 qrs. 22 lbs.
14. I of i of -^ of 1 7 hours 29 m 53 s.
ADDITION OF FRACTIONS.
liiile. — Reduce the given fniclions to others having a common
Idonoininalor, add the numerators together for a new numerator,
land below th'-'ir sum write the common denominator.
70
ADDITION OF FRACTIONS.
1 '"''^^ilUNS.
ormixcVSb^^.'" '''"P''°P«'- f'-a'^lion reduce it to a ; ■
, ; /'''•""'^'■iWr j, f, 8, and J
p. 84 TTJ- -— Sg^jf Alls I
Example 2 Ari.j < ,
' 1722 = Mi
and 4 + 17 I •>
f^ind the vaJae of ^''""'' ^'^•
^- ^ + f + f + f
f-f + ^-^f + f + A
'■ I + -h + ,^ + ,«;; .,
'■ A + 23,;. + j5..
+
-♦• sS.
IONS.
reduce it to a wJ
xed mimbors. add I
"J« niunhers.
'compound or coiiipj
t- H + Jr
- 3 A Alls,
>thers having a c„.
^' ('J. 70 and 72 li
"'» 8'' the connni
viiich rerlaced to
id 3XX.
■ + ^^'A
m
hU Ans.
fractional parts aJ
3ie numbers.
14.
jir..
IK).
17.
18.
19.
20.
fiUBTRACTlON OF FRACTtONS.
zoff + 5 + 8,23 or ,v
1 + i + 1
L ^ -^
fofg- +
3* 64
71
^^hi
+
2
r
2*
6.
+ 1
1(
^
21
.. of 77
SUBTRACTION OF FRACTIONS.
//H/e.— Reduce tha fractions to others having n nnmm r, ^
N"ulor. Subtract the numerator of e subU-alS™i"nf f^;
the nnnuend, and set down tljo differPiirn vvi h^h„ ^ *^^*'
3nominator written below it. If there are who ,n ,^1?°'"'?°"
dilierence as in sim,,le snblraction' in t e subTracIfnn^^f
iiAe.i numbers the new numerator of Hip « Lnoi 1 • ^"°" °^
han tliat of the nnnuend rbtract i f ' ' n o^ ^^ ^' ^''''■^'''
&inator, to the difference add the numerator of I'^T"" '^'T
(nd carry one to the whole .mmi.L oHhe t^trahend "''""'"^'
Example 1.— From ji- take -,a-.
l«AMi'i.E 2 -From 1 7A take 9-Li ^"
17-^
9 i_i =
/7//4— 9>sf = 711J An..
Having recluced fhe fractl^rs to fc Imt ni a' .n^
lenommator we find that 187 the numeritor n ? ^^^mT""]
tgieator than 90 that of the mir u.^TTc JL'e foiV" bt?]"*;''?
bm W\ the crmmon denomiuianr add % to Ho .m ^^ "
|id carry I lo <J the whole numl er' w ich subtrao e f^n'"?-^
|u.s 7. to Which the iractional r;mai;;derSa;mS mSng
„. , ,, , E.\EncjSE II.
Fmd the Value of
1.
2.
3.
4.
5
6.
7.
8.
if - P.
i +
if
?
H
i
a + ?
2t-^
29^ -17^
12;Vi-96ff
+Aof^-2iy
O
10.
II.
18ff-(2| + 8 A)
12. 41 of ^^^
^ of 1«^
17J
li^ai
Mi
If i
i
V2
nule.-
SUBTRACTICV OF PAACTtOm.
MrjLTIPLlrAHON OK FfiA.,a()N8.
If any of the qtiantitias are mixe.i numbers r. 1 1
them 10 improper Iractionr o tr ' ™"'' "'""^^'"^ '•''^
J^theres.tis.Hmpropern-actio„re.>c:-:r::;::;:;
'he results in lliei. place ""' measures Jjolh, and '
Example 1. —Multiply | by f
Example 2.-Mui 'ply tTJLrSMxf ^^d -,V
numerator we^muiUp ly ^o^eiher 2rS''';o""^'J ^*^^ ">"!
numerator 475, and 9 ana 1 2 « IL • *"^u'^ ^h'^'' &'vesJ
then reducing iio imiZ ■ ' l.^r ^ F^«^' ^'^^ denominator l(J
4j^. ^ P' ''''^^'^" i'«4 we obtain the answ^
„. . Exercise 12.
Find the value of
i X f X
-/^ X -A
5^
"3
II
1
2
8,
4
6.
6.
7.
8.
9.
10.
11
12. (| + ^)x(A^:^
t3. (I - f) X (f - f )
X i
,x f X f
-iV X -/^- X f
2f X 4« X
^f X 4 X 5-S_
X 8
i X -g
-A-
1 1
13 X
2 r
X -^
X 1
-A
X i
X I
;4- & X f X -/g- X W
15. 61 X 2f X 5f
16. f X 4 X 8i X ^
6
I7.(2i+4f)x(7|~2?)x.
18- i* X H X I!
19- I X I X -S- X !!
20. (3i + f+|)^%^_J
■ACliOMB.
' mixed numbers redui
npound fractions reduJ
numor.if.ors together I
s< •oramwdenominaij
t?uc>? it to a mixed nuf
vidin,g a numerator!
neasuros bolli, and
Ans.
!i and -./-
= 4,^8- Ans.
to improper fractioia
fiator and 7 in the ihiij
nd 19 which gives tJ
is the denominator 101
we obtain the answj
'< i X Vr X 1^
X 2f X 5f
X 4 X 8^ X !
6
+ 4?)x(7|-29)x
xHxI!
i
I X f X !!
3f ,
+ *+!) x(8i-d
DECIMAL FRACTIONS.
DIVISION OF FliAGTIONS.
73
Iiule.~R.Anco mixed numbers to improp'cr fractions and
co,npound fractions to si.npie ones Invert the terms of the
divisor and proceed as in multiplication.
Example I —Divide f^ by -t-
p. J .. , Exercise 13.
Fmd the value of
1.
2.
3
4.
6.
6.
7.
8.
^- -4-2^
-I- . a.
1 I -=- 13"
6* -^ f off
9. (12| + i)--(9f-f)
10. (7| X f) 4- j^
12 iloff ^-ja.-ofii
13.
4|
-9f
14.
U
-^-(t+?)
15.
n
-^2f -^
1
16.
H
--23
17.
(2i + 7f-
#)-
-3f
18.
(tx
i)Mi>
:f)-
^23 of
2
_3
fof4^
19
4f
4"
20.
8.\
-5X^
.fi
t
X 3i
X 2f
DECIMAL FRACTIONS.
In decimals the denominator is omitted nnH n rint nall„^ ^u
decimal point is placed to the left o^f^'nuZerato ''"'' *''
Thus -,a IS written • 3, -z±^ is written ■ 74.
When the number of Ijgures in the numerator is less th«n
of Ii6.,res m ,t oqual ,„ ,ho number of cipherTin ule'Smi-
^Thus ■ 0056 X 10 = • 056 ; 0056 X 100 =.- ■ 56 ; • 0056 x 1000
74
DECIMAL FRACTIONS.
one
To cJivido a decinifll h^, m
plnc.!«, ,10. """" • "1 100 Iwo places ; by (ooo l|,rc
I0«0 = :1Slt '" = '"'' ■ '»*' - 100 = . 2854 ; 28-5, ^
value. ' • ■ '^00 = /„., .za^^ .^^^^ ^^^^^ ^^^ ^^^^^ ^^^ ^^^^
repeating or circuIaSgrorna^ called a
„ The /onU„u'arrpetu2';ri V'V ' '"'P^^'^'' ^'^ P«"od.
figures, isexprossed by wr"w?hfn'^^ «'' several
dot over the first figure aTdannth. P''""^ o^^e and placing a
figure is to be repef t"eci h\"'pS/; d7ot If ^ ' °^ '^ ^"^ '-
-Peat.g period i.eS^.^, tTsl '4^: X^ fte^^^
"lai point • thus • 4 • '?9/i o„«
A mixed repoatL or cfrcuE.''r''''?^ ^^^'■"''^'«-
deoiSr' P™'- ■"- •MVa.iei are ™i.e, „„„„,„„„,
in fTeSiLtS'Sl-ri^-.r*?' -"»■' "-»' it is
dred and seven » v nno vi •?,'.' '^ therefore read, four him
".- „„, fori?"s'e';trteL'';,,s°3Si::; """" '» -""'■»""
Exercise J
Express the following decimal fractions in words
• '' ' ' -00072 , 9. 71042.560
2.
3.
4.
•0C4
•207
■652
34-506.
30964
• 000063.
92,000507.
• 00000000724
671-408263.
drid^7"i;^en^>•!S' er^;;;^' ?h"'"° *^-««-' -ven hun-
are required to make ud tL ,. ff"""''' T """^ ^''^^^ 'hree ci,,he?s
he given number andThede Si nofn^ih^^" '''' ' "^"'"^^ ^^
fore written - 0009723. "^^™ai Pomt, the decimal is there-
Exercise **
1. lorty-six thousandths.
3.
4.
5.
6.
t'eciiiial point one
ices; by 1000 thro."
= • 2854 ; 28-54 ^
do nol change its
h all have the same
ised and in which
peated, is called a
repeater or period,
isisting of several
ce and placing a
last; or if but one
it.
is written • 345'6
'ne in which the
ire after the deci-
decimals.
i ono which has
eating period and
lixed circulating
e Ilnd that it is
read, four hun-
7 is read forty-
m words.
71042-560
J2,000507.
00000000724
•7I-408263.
nd seven hun-
at three ciphers
'.he 4 figures of
iimal is there-
DECIMAL FRACTIONS.
78
2 Nine hundn-d and eighty ten thousandths
ADDITION OK DECIMAL FRACTIONS
Jl'ZmZ'y ^': ""'"^'"-^ '« ^^ -^^'J^d so that the decimal
Seatitio:.''"^"^ ""^^^ '-'' °^'-- -^^ P-— in
cnnals repeat then, to as many places as may ho Judged neces,
and■8^'6T•~^^^ ''''''''' ''■'''^' 9-3684, -70134, 19-748,
1 • 368^^ the^Tnr °°"''""' ^^^ "^^^ ^"^1 ^""''1^ numbers
• 70l34 uS ?6 .'olm' '" ^'"^P'*^ '^'^•^'^'°" ^« obtain the
10 • 748484 '^•
8-63
76-94519
*^ind the value of ^"'"'''^ ^•
>- 2-43 + 7-9638 + -72+1. 9654 + 23-845.
3.
4.
5.
6.
7.
r49T: + ■''' + ''• ^^^9^ + -«3+ 1-74 + .982 +
94-026 + . 87+. 085 + 6-954 + I0-869 + .7406
•928 + 34 -71695 + -718 + 9- 7015.
96-74 + -9863 + -712+ 19-042 + 365-98 + 4-307 •
•7"^'>805+l2-93+.98i+. 34 + 91-642.
205 + -736 + 7- 964085 +-36 + 41 -68.
8 712-84 + -96 + -73014 + 25-63 + . 98 + 94 608,
7fi
DECIMAL FRACTIONS.
SUBTRACTION OF DECIMAf. FMACTIONS
fr^^ointti':^^^^^^^^^ .n.,er,p,acing the -lo.
traction "^" ^'■"^^' an<« proceoij as in srimplo sub,
^24^ ^'''°'" 24-64 take 9-7901.
, ?:Z!^1L aMZriCfir '^' ''^P^'^^"'^' decimal
l4-848ii uaction ^-''-^--enco as in simple suh.
Exercise 4.
Find the value of
1. 4-231
19-48
1-372
2.
3.
4.
5.
4-9542
23'-- 7 36
— 2-964.
— •68742.
— -90834.
-- -2C875.
— 79'489.
6.
7.
8.
9.
10.
14 5603 —
II 68014 —
2-863 _
7245 —
4-35964
9 49,"
•732.
1-93478.
•976387.
2-178.
inark oifin t o''K'odu cTaTnlL'"?""' f T'"'''' ""'"^-•«. "•
n both factors. When therTaronnf""' '""' '^'^''econtaine •
the product as are con a'ned ^-^h^.h ?"f ^ ^'^'='"^'^' P^^^^s '
flciency by prefixing dphe"s ^ ^'''^"'■»' "" »P ^''^ .
Example I. Multiply 24 S by -23.
nrnd^Pf H ^kP'*"'''" of decimals in tho
produc . there being 2 figures to therisrfit
i;[u;^S^«'^"^'"*'--'-torLit'
Example. 2. Multiply • 27 Ly • 3.
nin^no'-"^ example there being 2 decimal
^ e p?oducTf 'T^r^^i''^ in ti othe aTd
Exercise 5.
_ -OST Ans.
F
*he v.'ilue of
'*9 X
■48.
-57.
-638.
67,
4. 9-49 y
5- 8-63 X 5-34
«. 28 76 X 6-48
FACTIONS,
aler.placirig the do.
as in iriuiplo sill).
repealing decimni
18 in simple suh-
7t
DECIMAL FRACTIONS.
DiVISfON OF DECIMAL FUACTIONS.
liule. 1 -irtho divisor does not contH.n as many decin.al
places as ho d.v. end. ann.x as many ciphers as will n.ako the
number of dr-cmal placos oqual. !„ the same way if th(3 divi-
(loud do..s not contain as many decimal places as tho divisor
(iiinex as many ciphers as will make them equal 2 Then
divide as in division of whole numbers and the quotient will bo
a whole numb..,- 3. Ifw „ all the ligures in the dividend
have been uPed there is a remainder, annex ciphers and continue
he dmsion until nothing remains, or until the quotient has
been continued as far as may be judged necessary.
Example I. Divide 3^4-5 bv 6-25
G25)32450(51'92 Ans. ^
Hero there are two decimal places
in the divisor and but one in the divi-
dend we therefore annex a cipher,
then dividing as in .vhole numbers
and placing tho decimal point in the
quotient after the \n.i figure in the
\t'a dividend has been used we annex
' -^" ciphers and obtain the quotient 51-'J2.
■0.
3125
l200~
625
57;>0
5G25
KAMPLE 2. Divide 2-428 by
Gu.
2428 (4-04G
2400
2800~
2400
4000
3600
400.
Find the value of
1. 0163 .i
2. 37 a J.
•"!. 87-4284 J.
4. 75-903 -L
5. 3-9184 1.
G. 1460-31 J.
7. 96-4 i.
8. 68-64 4-
In this example we annex two ciphers
to the divisor, then dividing as in whole
numbers we obtain the answer 4-046
Exercise 6.
•49.
3-84.
•24.
13-54.
3-16.
1267.
•7{j4.
0. 269-4
10. 174-2
11. 907-14
li 3-78 iU2
13. 2035-46
!4. !:' 7C-'i
15. 17-4296
16. 104.3u:)
•75.
7-5.
•9123.
t-06.
8-68,
o UoH.
7-90.
•79.
^t ^'
I'
78
DECIMAL FRACTIONS.
BEDUCTION OF DECIMALS
then prefixing a, .oint'o I mmS^^ t'"/" ^"-»^'^'« ^ li"'es,
Example 2. «o,luce Wto a decimal "'' '' ^'*'' '^"s^'''''
75) 100
75
•013
250
225
25
ann.'xing anothf-r cii.h!. "^..I'"'"*' then
once, we tl.erefbro ^i^^^^ r.nu'' ^^- 'i^^i^ori:'^::;^^
c.pher to 25 which btZi^O ^t 'is ^T'''' '''^ «»"«""
leaving a remainder 25 which be in^h ' 'contained 3 Um.s
remainder it is evid.nrthat the Vi '', "' '^" P'^^vious
-i|; ho continuaiiy repeal, ^^/^^o!K ZX^^I^^
., . . EXEIICISE 7.
iieduce the following vu„ariractions to decimals.
o" f \ ^' ^^ I S). Ha I r^
q ?| o- Bis- 10. -224^ 14
•^' -ffi I 7. A- I 1 . V I J*-
4- ^
A
8. A
10. -alfa
11. .^,
12. -^
A
H
16.
«^SX^i'S;f dSiS\;j';^-;^.i-Iont vulgor iVaction.
many ciphers annexed is there «n!""r" ' ^"^ ^ ""'' ^'^h as
thus -83 = _jia_ " "S there are hg„res in the decimal.
rp- , DECIMAL FHACTI0N8
Thus. •4 = A
•28 = g|
•4.1<5 r:r 4.6 3 _
U H 11
Jt,„r"" " "'«''''^«'-'°'<'i"'"ocimaT,„~i,!;;-a"iS v„,«.
X8.
sininatir, annexing
«' fJeoiiii.il p|„ces
"t Ic Iho fiuoiient.
"Jivicleiiditlifcomcs
'iit'8 leaving a ,.(,,
'wn 7 in ui(. quo-
^i^ goes 5 times,
VI' •/,) III,' answer
lexing a cipher tlie
wiiicii (lie divi.^or
''ore place a cipher
J'lx a point, then
.I'.'o dividend be-
ivisor is contained
'nl, and annex u
ontained 3 times
«s the previous
in the quotient
thereCore placed
iimals.
13. ^.
H
DECIMAL FRACTIONS.
79
15. ^^z
ilgar fraction,
ti a unit with as
in the decimal.
Jivalent vulgar
s many 9's as
— t a^
3 3 3'
livalenf vulga
/fi//e.— Subtract the llmio part of tho mixed repeating docimal
from the whole, and write the remainder as numerator ; and
for denominator write as many O's as there are figures in the
period, with as many ciphers annexed as there are figures in
the Unite part.
Example. Reduce -32648 lo its equivalent vulgar fraction.
3-264« — 32 = 32616 the numerator; then lor denominator
wo write three 9's with two ciphers annexed, there being three
ligures in the repealing part of the decimal and two in the
Unite part. The denominator is therefore 99'JOO,
Therefore -32648 = ^ff^g = |5f. Ans.
EXEIICISE 8.
Express the following decimals as vulgar fractions.
1. -6
6. -3
11.
16-348
16. -1243
2. -74
7. -64
12.
9-63
17. -31425
3. 021
8. -923
13.
•541
18. -647
4. -432
9. -123426
14.
-362
19. 6-436
5. 6-009
10. -7642
15.
-5423
20. 2l-243i
To reduce a given quantity to the decimal of another given
quantity.
Bute.— Divide the number in the lowest denomination m the
given quantity by the number which makes one of the next
higher, annex the quotient to the quantity in the next higher
denomination, and divide by the number of that denomination
which makes one of the next higher, and proceed thus until
the required denomination is reached, the last quotient will be
the required decimal.
Reduce 15:, bf!. to the decimal of a pound.
li'irst we divide 3 farthings by 4,
9-75 which reduces it to -75 of a penny,
prelixing 9 pence to this and dividinc
by 12 we obtain -8125 the decimal
■790625 Ans. of a shilling, then prefixing 15 shill-
ings to this we obtain -790625 the
Example 1
4)3
12 ,
20 J1TST25'
decimal of a pound.
80 ' ^ •
Di'CIMAL FKACTIONS.
3r 18 per
l"a~Tr
138 per
240 per
23
^iO - 23 -f- 40 = 575 Ans.
1 Red ExEHGiSE 9.
2: Reduo'e' hTd^yi''^ ll^^^ iJ^^fl"^^^ ^fa cwt.
3. Reduce 5 fur 3 npn ,° ff '° '^^ decimal of a vear
^- deduce 1 foot 6 f!\lTe7.T"'f ""'^ '"'''
5- Reduce 1 6s 1 1 4d to thP I^°"V^' °^ « yard.
6. Reduce I pint fgui^^l h?«T' "''^ P°""^-
7. Reduce 16 dwts 2 gr tj th« h'""^' P^^ ^^^^^n-
8- Reduce 35 min. 30 sec tr. fh. J^'"'-'"^' «f « 'b.
9- Reduce 4 cwt 1 qr 20 lbs i '>, '^^'"a' of a day.
0. Reduce 2 qrs 3 n s to h! 1 ^'^ ^^°'™al of a ton
he product to the „„„ |„„„, j.'^f „"'';"'' "■» <l«i™«l part of
'"WBt, and the numbers to lh„T„rnrT°°' °"'' ™ "" '» ">«
ke the required value ^ ""^ """ *«'™l Points will
''■"S5"'°^''»™'"-fl3l5„rad.y.
24 . Pirst we multiply • I s n «h„ •
deamalby24th^LmK
iSe^ti'b'i^^rthe "'^ ''«"'' «^^^^^^^^^^^
multinlv nnf? M ^'''^" decimal
right 'of'th.'t.ii'll""'".^^'' to the
3-15G0 hours
______60_
~9^360rmin.
-— — ^
"H^ROOiT
DECIMAL FRACTIONS.
81
EXERGJSE 10.
Find the value of
1.
2.
3.
4.
5.
6.
7.
•43 1 5 oi" a cwt.
•0274 of a day.
•63248 of a furlong
3.528 of a lb Troy.
•73125 of a £.
•175 of a rood.
•0348 of a bushel.
2-875 of a yard.
9. '613 of an acre.
10. 4-5063 of lb avoir dupoids.
11. •OSes of a gallon.
•749 of a mile.
•268 of a cwt.
•9163 of a sq yard.
•775 of a gallon.
•39525 of a ton.
12
13
14
15
16,
PROPORTION OF FRACTIONS
12?;S* ^^^ '^' ^""^ '''' ^^ ^^"*^ ^^^^ '""^' be paid for
to tn ?4op,'laS •• ''•'' '' ^'^^ ''' --^ '-- reduced
As f yd : V yds: : f -^O th«. ^^x^ ^ X i =. ...^ cents.
Exercises.
win lo'lrSolt ? '"" "' ""''' '" ' ^ '^^^ •" ^-- --y ^ays
1 t ydTf* ""'" ^ ^ ^'^^ '^''°''' '°'^ ^' the rate of $4.70 for
co!t Sr' '"'''■ """^ ^' P"''^^*^^^^ ^^-^ ^^3.20, if ^ cwt
^^4. ^If 3 a cwt of flour cost $9.30 what must be paid for 7 f
7 1 yds ? * ^ "t'^ ''"^t ""*- t''« ''ate of $28 f for
if?i^3''gdsrsrS"^^'""'^"'- ""^^^ ^°«^^' f- ^'7.42
37V;dsaVtSl^L^^^:rit"f '^'^•^'' ^-^^^ --* ^^ P-d for
08^c;,??''',°!"I'y pounds of coffee may be boueht fnr <r 1.124 if
th 'Ue'r^te r' "''"''' ''''^'' ^^'^l^^'" 3-28 «wt cost at
82
PRACTICE. i
»115oP'3^™l''?»''' '■''■■ '»-"e='-35 acre... .1,0 rate .[I
'^^^ .Sf Ji'la'; '"= ™'- »^ »»•* '"^ Of .sa, ,r .he value "
MISCELLANEOtii QUESTIONS
t Rir.s''f',?.r,r;„,r--o»f73,a„<; la^,,.
a com,„o„ *;;;„■ 'llor' '* '° »I"'"l™t rra«i„„sh.vi„.
10- Jieduce 4278m Z iZhl , " '" '"^'^es. .
.. lo Multiply $73.5^14 '>o to ill "'"? P'^'^^ of decimals.
diVHletheresuliby 13 "' *" "'^ J^^^^^^f add $48.05 arid
'«, MuUiP'y the resuuif+4'f9l"f4tJ^-2^^y ^-23017.
piaces of decimals by -24 ~ '^^38 carried to four
W. IZn!! ofVSf ^ 1 'J + ^> «^^^9« 13.
+2^f ^^H + $-'40.63f +J792 I8i * ^^•'^* + =^^^-^6-32^
2^: J'- ^e^^'S'??2?^^^^^^^ and|9e2.37,.
^- ^^'"'^ '^' ''^^^ °f $9264£3f - $748.61^ x 9.
p ^. practTce.
t^ractice teaches how to finri (h,. . 1
goods at a given rale iV?he"l\trU,-„'l"^" f'"^" ^"'^"'''y of
All aliquot pari is a nimnti^.r ■ 1 ^''^I^ot pints. '
numhp..^r.: ':'.'*' *^ .'I"'i"tity which is p.nniaJnriH -„
Tims 9 m?""? '" "^ ^'^■^" quantity. -n-mf^rj ^n exact
sli,uotpar?o1'-rdXr'^"°^P^'''"^^^^*'.-nd 10 cents is an
60
25
20
16i
10
8i
5
4
H
acres at H,o rate oi'|
oftea, ifthe valueofi
noNs.
734 and I96.S,
uts.
6iJ-. £11 ; 14: 8i
43.18. "
«6, 8, 14, 12,
nt fractiuns having
!S,
lbs.
?5 X 76 ?
Lces of decimals
add $48.J5 and
!fe 2-49346.
7-29 by 4-23017.
carried to four
il3.
f + $1246.32^
Mnd$962.37f ?
f — 1856.37,4,.
X 9.
en quantity of
iris.
nod an exact
f* cents is an
PRACTICE.
TABLE OF ALIQUOT PARTS.
83
Of a dollar.
cents.
60 =
33J =
25 =
20 =
16i =
Ui =
10 =
8i =
6i =
6 =
4 =
n =
u =
5
)
?
i
i
Of a ton.
10
cwt =
^
6
t< —
1
i
4
It __
^^
" =
X
2
'^ —
1
1
^"
2U
Of a cwt of
112 lbs.
Of a cwt of
100 lbs.
qrs. lbs.
qrs. lbs.
2 or 50 = I
1 or 25 = »
20 lbs = A
3
OfjE 1.
Ofaqr. of
28 lbs.
2 or 66 =
1 or 28 =
14 lbs
7 lbs
4 lbs
3i lbs
= i
14
7
4
3i
2
1
lbs = ^
I
X
7
I
9
h
■A
lOs
68 8d
58
3s 4d
2s 6d
2s
IsSd
Is 3d
l8
I
1
8
1
= i
= A
■A
Of a shilling.
6d
4d
3d
2d
Ud
Id
= A
When the given quantity consists of one denomination
Example 1. Find the value of 28 lbs of tea at 50 cents per lb.
50 = J_28 It is evident that the value of 28 lbs at $1
m Ans. P^'-'b would be $28, therefore the value of
or $14. "^"'^^ """'^ ^^ ^^'f that sum
Example 2.-Find the value of 246 yards at $1.80 per yard
50 cts. = i
25 " =i
246 at $1.80.
123 value at 50 cts.
61.50 value a i 25 cts.
12.30 value at 5 cts.
f 442.80 Ans.
Here we add together
$246 the value of 246
yds. at $1,$ 1 23 the value
of246yds. at 50 cts. per
yd., $61.50 the value of
246 yds. at 25 cts. per
84
flr
I i
PRACTICE.
yl., and $12.30 the valup nf o/.r „ i , r
obtain tI.o amount or 246 y°s^\V*f- ?^ ^ ,^^«- P'^'' Vi- ; and thus
or taken together $1.80 per yd ' '"''•' ^^ ^'^^ ^nd 5 cts. :
2^4^ at $4.85
4
25 cts. z= i
10 cts. = I
4936
617
308.50
,0?^? we multiply
1234 by 4 and obtain
the vahie at $4, then
nnd Mio value oft 234
IJjs.i. 85 cts. fay taking
aliquot parts thus 50
cts = J of $1,25 cts.
- f °r rl^ ^'^•' 10 OtS.
the results add $1.211- the va'nBnF J r -; i o*^ 50 cts., and to
g'ves the value Jf 1 2I4 J';i.I^;r$°4 I5 v z\ 'gsel.f "'^ ^^^^^
cwr«- ^-«^^i--d the val or Z t^ al'.a : 2 : 4 per
value at $4.
value at 50 cts
vnm value at 25 cts.
U3.40 value at 10 cts.
___i_^£[£value of J of a Ifa
$5986.1 IjAns
2s. =r 1
10
4d.=^
246
3
738 yalueof246cwt.at£3.
4 2 - of . II ll
$ 766 14 Ans.
Find the value of
1- 746 lbs. at $0.87*.
2. 475 lbs. at $0.75."'
3. 1234 lbs. at $1.46
t' iT'^'^^s. at$1.57*
o. 286 vds. at $2 78
6. 954 yds. at $4.56.'
/. 354 cwt. at $24 50
8. 2468 at $314 18
9- 7694* at $87 26'
10. 4281 at $96.54. '
11. 42502 at $220.15.
12. 796^ at $76.94
J 3. 1357, J, at $156. 13.
14. 7S4,5„- at .$96.35.
Exercise I.
16. 5324 at Us. 6d.
17. 948 a( £3: 7- 9
18. 3576f^at£7; 9': 0*
19. 2459gat£9: 3-8
20. 1208f at £2:9' 4"
21. 3274 at $1.35. ' "
22. 498 ,a at 2s. II Jd.
'"^ 4956| at $234,56.
864f at£l3 : I6 •
'274 ft- at $1.28.
3724 al, $1.17
3469,^-at$1.12i
224 at £3 : 5 ;
235 at £2 ; 7 • 9'
2485|j at $19.45.
23
24
25.
26.
27.
28.
29.
30.
4f.
PRACTICE.
85
s- per yd. ; and thus
, 25 cts. and 5 cts. :
It $4.85 per Ux
lere we multiplv
4 ijy 4 and obtain
value at $4, then
'no value of 1234
<'ii85cts. by taking
not parts thus 50
= I off I, 25 cts.
of 50 cts., 10 cts
of 50 cts., and to
^^at^|4.85 which
■• at .£3: 2:4 per
When the given quantity consists of more than one dononii-
nation.
Example 1 . What is the value of 240 cwt. 2 ors 15 lbs 19 ny
at $7.40 per cwt ? i'- • ^-^i^^. i/ oz.
$ cts.
2 qrs. = i 7.40
240
\2i lbs. = i
2ilbs.=i
8 oz. = I
4 oz. = J
29600
1480
177600 value of 240 cwt.
3 70
925
185
37
18
2 qrs.
12* lbs
2i
8
4
lbs
oz.
oz.
$1780.86 Ans.
In this example we
multiply $7.40 the
value of 1 cwt. by
240 and obtain $1776
the value of 240 cwt.
Thentaking parts for
the renlainder and
adding we obtain
$1780.86 the value of
240 cwt. 2 qrs. 15
lbs. 12 oz. at $7.40
per cwt.
Example 2, What is the value of 12 tons. iO cwt 2 ars
14 lbs. of hay at $14.10 per ton. allowing 112 lbs to the cwt ? "
$ cts.
10 cwt. = J 14.10 '''-' S':'
12 "^' ■'■'
2 qrs,
14 lbs.
2^0
169.20 value of 12 tons.
7.05 — 10 cent.
352 — 2 qrs.
I 88 — 14 lbs.
$176.69 Ans.
s. 6d.
per
: 7: 9.
£7 •• 9 : 6*.
9:3:8.
2:9:4
35.
• Hid.
!34,56.
^ : 16: 4f.
1.28.
Fi
7.
1
1.12^.
2
5: G.
3
7: 0.
4
19.45.
5
6
Example 3. What will 3 qrs. 12J lbs. of sugar cost at £2 :
value of 2 qrs.
— 1 qr.
— 12i lbs.
£2 8 6| Ans.
15:6
2 qrs. =
1 qr. =
I2J lbs. -
£
s.
d.
2
(5
6
1
7
9
13
lOi
6
Uf
EXERCISB 2.
Find the value of
17 cwt. 2 qrs. 14 lbs. at $24.56 per cwt.
38 cwt. 3 qrs. 12^ lbs. at $220.16 per cwt.
31 tons. 12 cwt. 1 qr. 20 lbs. at $14.21 per ton.
3 Ts. !7 Ihs \i 07. nt "S^O ?.f. ".t>-^ .--— r'
374 miles 2 fur. 21 per.^at $48.05 per inile.
34 wks. 4 days at $9.48 per week.
7. 4 chaldrons 21 bush 3 pks. at $3.50 per chaldron
86
\h t
8.
3.
10.
11.
12.
PRACTICE.
'7 Jbs. 8 oz 5 if "a ^ u^ '^^ ^^-26 per gal
15
16.
n.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27
28
]r f* S^als. 3 qis. I pt. atje J■
14 miles 7 ffi. 3 fpe/afsfl ^,' •" «* P?*- ^^t
258 cwt. 3 n..« 9i*^K„ .7^t-^^Per mile.
'^Wt- 2 qrs. 23 lbs.
'o ppr acre.
3 :GJ per gallon.
1 / : 8 per week.
243 lbs.-14 Til' j^3\'t'|o^4 ^'s^.Per <^wt.
136 days 7 hours at I'fc,?!^"^ ?'''* '^•
74 cwt 18 lbs at Ssf \'^^^ ''"' ^^y-
28 fur. 35 ner 93 „ , '^^ P^'' ^wt.
1 '7 cwt iribs'i,^^tl'.'/^ •■ ^ •• ^ P^'' ^"''long.
76 gals. 1 qt I 14 at s or' '^'-
3 qrs. 24 lbs 8 oz at I fi .aP^' ^^"o"-
9 weeks 2 days at S7 S ni P^^'=^*• o'"l'2 lbs.
'■ 27 d^Ts ,4 b7urs'ariP2r ^'/'-
>". 90 acre«) 9 r i« *'-*4 per day.
M. 4°S V,.'," f ;■;■ ■' H«8 per acre.
Gross • h ^^^^ ^^^ ^^^^
weight ofThe^caserbag: r&nn"US?^L^«^^^^^r with the
^ TSnet'wSSs°;Varrl""^' '"^^^ ^- --te i„ goods
'r.t'-^{}Z^^^^^^ ''' -eand^Xhave
tare 6 lbs. per owf. Im ?lSs'V^r?wl '' '' ^^^- ^ 'J'^-^Aour,
cwt. qrs. lbs.
Gross
Tare
46
2
43
1
Tret
Net weight"42~
2
_3^
2
1
__4
21
_6
15
T ,u 42 cwt. 1 qr ,1 lbs'''' *^ "^^ weight
weighUstr/^^rfifr d in ^he fol/owin. «,....„„ ... . .
ounces. -'''^^ "^ Possible without"reducUo^"S
H
CO]
Find th(
C. 4
26 owl
7 ches
7 hhdt
tare
13 ban
9ib
120 c\\
per
hhdd
11 I]
19 bag
tare
124 c\v
20 pi
2 ■ barr
14 U
7 hiiddi
19 1fc
9 casks
cask
17 cwt.
per c
42 bags
per b
14. 14 hogs;
40 1b!
15. 96 cwt.
3 lbs.
COMMIS
Per cent
Thus if a
to be 5, 7, 01
on each $100
Gommissic
mission raer
accounts, Ac.
Insurance
a certain sun
pay to the c
iiicicJiaiidise,
the property
Brokerage
elating bills,
9.
10.
11.
12.
13.
wt.
■Uon,
c.
3Wt.
5Wt.
•long.
12 lbs.
ether with the
"re packed.
1 which goods
in goods,
and tret have
J qrs. of flour,
vt 2 qrs at 6
be 2 cwt.
ed from the
cwt. 2 qrs.
lis at 3 lbs.
' <'bs. which
net weight
eduction to
COMMISSION, INSURANCE, AND BROKERAGE.
Exercises.
Find the net weight of
87
1. 26 cwt. 2 qrs. 12 lbs., tare 15 lbs. per cwt.
2. 7 chests tea each weighing 194 lbs., tare 16 lbs. per chest.
J. i iJhddB. of sugar the gross weight being 93 cwt. 2 ors .
tare 3 qrs. 12 lbs. per hhdd. * '^ ** '
4. 13 barrels rice each weighing 2 cwt. 1 qr. 9 lbs., tare 1 qr.
9 lbs. per barrel, ^
5. 120 cwt. 2 qrs. 12 lbs. flour, tare 8 lbs. per cwt., trot 3 lbs
per cwt.
G. 4 hhdds each weighing 13 cwt. 1 qr. 14 lbs., tare 2 qrs.
1 1 lbs per hhdd. ^
7. 19 bags Indian meal each weighing ! cwt. 3 qrs. 9 lbs.,
tare 4 lbs per bag.
8. 124 cwt. 2 qrs. gross, tare 9 lbs. per cwt., tret 4 lbs.
20 per cwt.
9. 2 • barrels sugar each 1 cwt. 3 qrs. 14 lbs. gross, tare
14 lbs. per cwt.
10. 7 hhdds tobacco each 3 cwt. I qr. 2 lbs. gross, tare 2 qrg.
19 lbs. per hhdd. ^
11.9 casks butter each weighing 2 qrs. 15 lbs., tare 14 Ibe. per
cask, tret 3J lbs. per cwt.
12. 17 cwt. 24 lbs. of flour, tare 11 lbs. per cwt., tret 4 lbs
per cwt.
13. 42 bags rice each 1 cwt. 3 qrs. 23 lbs. gross, tare 8 lbs.
per bag.
14. 14 hogsheads of sugar each 11 cwt. 2 qrs. 7 lbs. gross, ta^e
40 lbs. per hhdd., tret 2J lbs. per cwt.
15. 96 cwt. 1 qr. 17 lbs. of flour, tare 12 lbs. per cwt., tret
3 lbs. per cwt.
COMMISSION. INSURANCE, AND BROKERAGE,
Per cent or percentage means a certain rate per 100.
Thus if a merchant sells a quantity of goods, his gain is said
to be 5, 7, or 8 per cent, according as his prolit is $5. $7, or $8
on each ifilOO worth of goods sold. *• > ^ > -*"
Commission is the percentage charged by an agent or com-
mission merchant for buying or selling goods, collecting
accounts, A-c, for another.
Insurance is a contract by which a company on being paid
a certain sum or percentage called the premium, engages to
pay to the owners of certain property such as houses, shina
liiercliandise, ikc, a certain sum, in case of the destruction'of
the property by fire or other accident.
Brokerage is the percentage charged by a broker for iieffo-
ciating bills, buying or selling stocks, Ac.
88
■If
tl
eo«m,.,o«, ,«,™^«<,,,_ ^^^ 3,,,,^„^
1.
2.
3.
4.
^■-P-TalV^^^^^^^^^ or brokerage on a
the Iro^uXZ''^^^^^^^^^ 'y "- ^i van rate „er cent, divi.e
insurance or /rokerage' ""'"'^ ^'" '^ "'« ^^"''"iBsion,
Example l.^What is the commission on $248 n. 7i
EXA«P..2-Wha! '.h" ''' = ^''-''- Ans.
2i per cent?' "''^ '' ^^^ P^'^'^'um of insurance on $4560 at
and $61651 go = ?6L65. Ans.
■C'XERCISF^
pf ;i lit crSstn on SI/' 1.P- -nt ?
Required the oorSllZZfomVL':! ''''' '
6. To wU does hTcomm" °" ^'^724.6lif ^^,S ',e„, .
per cent ? ''°'' ^^« commission on $7428.4oVmount at 12i
per cent? *^« ^'"o'^erage on $7964.80 amount at 7J
is: ma! rthr^^iiu^'n' $K - ^^«^«0 ^
6. Find the hroker^Z mV!tnf. '' '* P^"" ^'^^ ?
cent? ^"^^ the brokerage amount on $10oS at 7^
,20.- ^tl pretuTTrnsu^nr'^"^^ °1! ^''^'^^ 2 Per cent ?
oa . _ . '^ "Je insurance nn «7/,b „. «,
per
'ROKERAQE.
or brokerage on a
•ate per cent, divide
e the commissioii,
5^48 at 7^ per cent ?
ins.
irance cm $4560 at
ns.
40 at 2i per cent!
ns.
)er cent ?
percent?
H per cent,
er cent.
I per cent?
amount at 12^
H per cent,
the amount of
nt to the amount
;ent?
!enl ?
\ per cent.
r cent.
amount at 7J
1984.60 ?
per cent ?
I-
ism?
10000 at 7 J per
Oat 2 per cent?
J at the rate of
ent?
> must be paid
STOCK.
89
w'rti.^5f9rri|'?efc'"ntr"°^ "'^'''^ '^''^ - merchandise
vaL'rtt.2"72^?oT;^t%rtr^ " ^^"- and furniture
o^^:^Ii^:±7^^l^:^^^'^0, What premiu.
w o'rth S58.5Vat (1^;/? "^"""^^ °" ^ ^^^^^ ^^ ^«-
cent." ^'^"''■^'^^''«P''«'""^'"o''in8uranceonfl0074at 2x por
29" To wlLf l^r.l'^K""! *' -^^ commission on $20742 ?
cent ? ' brolcerage on $2248 amount at 4J per
$I248olo at 2I pt'ce'ir"'" '' '"^"'"'^"'^^ °" ?«°<i« ^orth
STOCK
sell for bss than the originaTcS "'"""' '^'''" '^^^
thJnSoO U*il'aVovrp";"'r a[at'r? '^ '^ '' f' '' ^^ --«
§100 it is below ,ror'a a dScou'nf^^rif T'im^^^ ^'^^
at a premium of 9 per cent its vaTe'isllOO A9 - Sq t"?
a d.scount of 9 per cent its value is I 00 _ ftilil ^ "^^' '^^^
..RoTttSjlill^Jea?^^^^^^^^^^
Example 1.— What is the value of 'S79f» ^tnM, ,. o
discount? *'^" stock at 8 per cent
, ^ f 720 X 92 = $66240.
and $66240 -J- 100 = $662.40 Ans
sinrr.'pVTmTut'oro^^eJcS" °' *''" ='-' -"o" '« »
^ $250 X$ 106 = 26500.
and $26:100 -;- sinn — atocc; nn . .
given s™.""" '""°''°' -'■ "'»«'■ ""y "» purchased for a
va,uf„r,ri;"J„r """"' °' '"^ «'™° '""■ '"^ '«» ^^ "'
'msmm
90
INTERBST.
1.
2.
and 1200000 -^ %t\^n^^^ X 100 = 200000.
"W00^$,,2U,ovaluoof$I00atl2,crce„t = $r785 7U
wnat IS the value of $2400 qtnr^t „4
percent. '^"" ^'^^''^ «' a premium of 9
When stock is Sellinrr nf „
^ „,value Of $5740 Kk 1 ''"' °'°' """"' P"- "l"" i» th.
*• ^fcSkt '' ""• "'" ""o™ P" -hal ,s .he val„e .r
5. What amount of stnrt mo„ »,«
7. When stock Is sellinVat fpL, „ V 5f n"' ''''»™ Paf ?
;■ "f;&f ""^ « ' f- -"' *eS U .hat U the valoe
„ ^p«l *ek"? " "" "'"' ■>*" P-r What is the value of
•2. What is the vaiue of ,4650 stock at n per cen, disceun. ,
WTEREST.
re|;S'..i c'etS.J'a.etrSnf"' ""^ -^ °'"-ey, and is
SIMPLE INTEREST.
simTSnttr' " ^'^^''^'^^ «" ^''^ Pnncipal only it is .ailed
^w'"l;'u1,rpryr,-/„S^^^^^^ for one or more years
product by loS^^'and fhTre's'it^^, rrelr.^*^"'- '^'^^'^'the
year. Thfl ipipmo* r._ ^ "^""'i wui be the mtfirpct r^- ^_..
multiplying t£'io;e;est1SonrveTrh' J^' ^'"^^^^ ^V
for which the interest is required ^ ^' ""'"^''' °^ y^^rs
INTEREST.
91
iircliasefj for ^2000
nt i
'cr cent = $1785.71}
t a prerouim of 9
3f7} per cent what
m par what is tlie
hat is the value of
i for $980, when
cent above par '
' 1 1 per cent, how
what is the value
r; cent discount ?
mo when it is
It is the value of
cent discount ?
f money, and is
I ; and the sum
ent interest the
= $105.
nly it is Called
iiore years,
int, divide the
erest for one-
is found hy
mber of years
E.\ AMPLE 1.
1 5 jici' cent.
-What is^lhe interest on $248.70 for I year at
$248 70 X 5 -1104.'} 50
nnd $[-2'i.i:,u-f I00r=$l2,4;i5 Ans
^ E.\AMPi.E 2. \Vh;il is th(3 1, lerobt on $280
|KT cent |ier unruun ?
S-2«() X G* =$1820.
Then ;i«l8vO -r 100 = $18 20 Inten'st for I vear
I" ' years at 6J
And $18.20 X 3 z= $;)4.(iO Intei
Exercise 1.
Find llic interi'si on
1.
2.
3.
4.
5.
'st for 3 years.
55356 for 1 year at 7 per cf>nt.
$2540 for I year at 5 per cent.
$yG4 for 2 years nt b^ per cent.
$3248.50 for 3 yeart< at 4^ per cent.
$7384. 6') fur 2 years at iter cent.
a. $948.30 for I jear at 5f per cent.
7. $-<450 lor 2i years at 9 jier cent.
8. $1248 for 4 years * Ci pi r cent.
9. $842 for 2| years at 7JL per cent.
10. *2I46.J0 for 1 1 years at 10 per cent,
11. $11248 Air I year at 6 per cent. *
12. $789 for I year at 6f per cent. "
13. $214.00 for 1 year at 7i per cent
14. $928 for 2 J years at G per cent.
15. $398.40 for 3 years at 5^ per cent.
16. $3460 fcr 1 year at 4J^ per cent.
17. $864.90 for 2 years at 9 per cent.
18. $1654 for 1 year at 33 per cent.
19. $792 for 1 year at 7 J j)er cent.
20. $1245.50 for 2 J years at 6 per cent.
yeJr°s and aionU.r'' °" "" ^'''^'' '"" '^'''" ^^^ '™^ ''°"'''*' °f
Iiule—¥iud I he interest for the given number of years by
rule 1 ; and for the months by aliquot parts as in practice
liXAMPLE 3.— iMnd the interest on $560 for 2 years and 5
months, at (i per cent per annum.
$560 X 6 = $3360.
anrl $3300 -r 100 = $33.60 Interest for I year
4 months =
month
$33.60 Interest for 1 year
2
67.20
11.20
2.80
2 years.
4 months.
1 month.
$81.20 Ans
'■""^^"^^^mmm
IMAGE EVALUATION
TEST TARGET (MT-S)
k
//
^^%^I%
< <;^
:/.
(A
V]
<^
/a
7
'c^l
^
■W J>>
e-P' -"^
%
%'
1.0
i.l
118
U, 1^
IIIIIM
^ 1^ 12.0
IL25 III 1.4
Hiotographic
Sciences
Corporation
18
1.6
23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 873-4503
S
V
<F
<1?
1^
r
n
\ VI
92
INTEREST.
*ind the interesl. on *
3. $958.60 for 2 vears 2 ,^ '''.k ^ ^ ''«'' '''^^^■
4. $1340 for 3 yS mor?f"h "/. V ''''' '='^"^-
5. $9r,4 50 for 2 v^ars 8 n/n ^''^ '* ^'^^ '"'^^■
(Buno t« -. J; .'^'^ '^ months at 4f per cent
7,
8
9,
10.
11
$862.40 for Oi^onhsatV-'^P"^
$1248.50 for I v3 7 ? f'^'' ^^"'
$063.72 for 1 LmLTfi''' '' ^ P^'' «'^"^-
$054.90 for 2 veari^i n,^ f.* P*"* ''^"*-
,„ $358.60 for 3 yea s S Z"![" ^^ ^ P'"" ^«nt.
2. $1234 for 2 years ? m^n^^! S' ^* P^' ^ent.
3. $964.20 for TmLiSTr/' ^* P'"' <=«"*•
14. $2468 for 1 year 2 mn^.V^ ''"'' ^^"t-
15. $258.20 for 2 yea^s^r""' "l ^* P^'" ^«"'-
"r/ years 11 months at 8 per cent.
To find the interest on a eiZIT
fiule.-Find the interest oTiV""' ''' '"^ """^^^^ "^ days,
f- 1 year. TRen as 365 daysl to Z" ""' ^* ^'^ ^'^«° ^'^
Js the interest for 1 year to til . ^""" ""'"^'^'' ^^ days, so
Example 4 Find thp ^ '"'""''' '^^^^'''^d.
cent per annum '"'^'''''' «" $6^0 for 98
centWe$5T2S"?hen' ''''''''' °" ^«^0 i^or
. days days
As 365 : 98 ;
days at 8 per
1 year at 8 per
.!'i;!"ii''-"iiAn».
Example 5. Find th'^YS^ ' f"'-''*f'i Ans.
«' 6 pe.- oenl which i,%V S„ '"'"'''»' <"> *M0 J rye„
. days days
As 365 : 79 .•
130
W.49M Ans.
PinH 11 • E.XERCISE 3,
*:'"d thointore.';ton
: $964 fo^^f L'^y« «' 5 P- cent.
3. $248V60 f liSZ^S'^r'-
4. $796.40 for n rin vc^ . ^}, ^^ ^^'^ ^ent.
5. $496,20 for 56 da ? ! S P"'' ^'^"t.
6. $928 for "79 dav?«, r ^ ""' '^'^"^
7. $324 50 inr4-^l ^ P"' ^6"^-
«. $2345fo 92l;vs"u4l'P'''^'°"^-
udys t.t 4^ per cent.
COMPOUND INTEREST.
93
■ cent.
c;eiit.
3r cenf..
' cent,
ler cent,
cent.
t.
'r cent.
t.
r cent.
3r cent,
cent.
cent.
3r cent.
'y number of days.
1, at the given rate
number of days, so
ired.
98 days at 8 per
>" 1 year at 8 per
20th May to the
20th May to 7th
'1 f 500 for 1 year
9. $500 Tor 198 days at 5J per cent.
10. SG24.40 for 204 days at 6J per cent.
1 1. $920 from June 3 to Doc. 20 at 6 per cent.
12. $428.00 from Aug. 21 to January 4 at 7 i)er oont.
13. $1234.50 from May 27 to October 2! at 5^ per cent. •
14. $805 from January 14 lo July 27 at 6J per cent.
15. $1024 from March 28 to June 4 at 7 per cent.
COMPOUND INTKREST,
When the interest is added to the principal at the end of a
year or any period, and llie interest is calculated on the amount
for the ensuing year or period it is called compound interest.
To find the compound Interest on a given sum for a given
time at a given rate per cent.
Rule I. —Find the interest for the first year at the given rate
per cent, add this to the principal and take the amount as prin-
cipal for the second year. 2. Find the interest for the second
year add it to the last principal and take the amount as prin,
cipal for the third year. 3. Proceed thus until the interest has
been found for the required number of years. If the given
principal be subtracted from the amount for the given time the
remainder will be the compound interest,
E.\AMPLE. — Find the compound interest on $500 for 3 years at
5 per cent per annum.
Interest on $500 for I year at 5 per cent $25.
Amount at the end of first year $525.
Interest on $525 at 5 per cent $26.25.
Amount at the end of second year $551.25.
Interest on $551.25 at 5 per cent $27.5625.
Amount at the end of thiij year $578.8125.
The amount $578. 8 125— $500 ^he original principal = $78..
8125 the compound interest on $500 for 3 years at 5 per cent.
E.XERCISES.
Find the compound interest and the amount of
1. $740,60 for 3 years at 5 per cent.
2. $1240 for 2 years at ^ per cent
3. $690.40 for 2 years at ^ per cent.
4. $684 for 3 years at 6 per cent.
5. $920 for 2 years at 4 percent.
6. $2960 for 2 years at 6J per cent.
7. %9.?.1 for fi year? at 7 ppr cpnt.
8. $1000 for 5 years at 6J per cent,
9. $600 for 2 years at 5 |)or cent,
/
94
DISCOUNT.
;° So fcl >'"'■*«' 6 per cent.
fixAAfPjE _.4, ^''^"'"^ '^^'■"^- ^'-"'^tracted from
«780-^13.65j'i'7C6^ 6 clays at 5 per Snt is s,' T-'^ ""
•P'uoji the present worlh. ^l3.6o and
Pi„^ .1 Exercise 1.
J A lot'"'"''"' ^"'•l'^ of
2- A not: orSo £ ? r;!" S^"^-' ^^ ^^ P- oe„t "
3. A note of $024.40 d.t 4 '" u^"'"^*' ^t 8 W Tn,'
'^' °^^^^y ^«e y2 days hence .f q' ^' ^'''' "^"^^
J "cjx{..e at y per cent
5.
6
7.
DISCOUNT.
95
JnlJ/at"6pV;'c!!r '""" J"- 10 at 6. nonlhs, discounted
Jnne2Vi";iS^' '""" April 6 at 4 months, discounted
'P«>--tora -teof Ji-^A jote^of ,,.^^0 ,^^^^^^ p,,,,,,^ , at 9 months, dis-
coiL^j'iLirfprcer^'^ "^^^ 7 at 10 months, dis-
cent'pP^annJm?' ''''"""* °" ^^'^'-^^ ^°^ ^^ ^^^i^^ ^^ '0 per
cent'peTannifmt''^°°""^ °" ^'^'-^^ ''- ^ months at 8 per
per anJI^m ? ^' ^^' ''''""""^ °" ^^^^ ''°' ^^^ ^^^^ ^^ ^ ?«'' ^^"t
•"nl has been doducN
f ays ;,re added to
on the 7lh of j,„v
M.
a note has to run
'" I'le sum for thi^-
iterest as discount'
'•willbethepn.em
fa note of $460 due
ays is found by ttio
n subtracted from
of a note of $78o
"■'- •> per cent''
3m JVfay 9, we finrj
'A he time from
J.he interest on
nt is $13.65 and
opr cent,
per cent.
^ per cent,
•ercerit.
3 percent
t!r cent,
cent
iofhif ,^f- h • ™''' ^'Tf" ^''°^^ '■«'' "^"^ calculation of discount
nn rfi IrSl'^'l " ^T'""^^^ ""^'^ '" ^^tual practice, yet it does
not give the true discount, for the true discount is the intprost
on the present worth for the time it has to run at the Kiven
ra e per cent. It s therefore evident that the discount foundZ
too small '^''^'' ^'^^ ^""^ consequently the present worth
To tind the true present worth of a note.
nule.~As $100 together with the interest on flOOatthe
given rate and for the given time is to the amount of the note
so is $100 to the true present worth. The discount is found by
subtracting the present worth from the amount of the note
daysS arvfpt'cenU '''' ^"""' '"''''' '' ^''' ''"^ ''
As $100 4- $1.44 = $101.44 : $540 : : $100 : $532 - 3343 An'*
7Ul7vVIf 7?'' ^°^'^^."' I'u^" ^"'^ ^^-^^ ^^'^ '"forest on $100 for
73 days at 7i per cent. Then proceeding as in simple nronor-
tion we obtain $532-3343 the true present worth ad tJie
l^roni this It IS evident that the process is correct for the
present worth with the interest added, for the given t? rt he
given rate amounts to the exact sum of the St ^ ' i^o bv
t';i^dist^u;!r^""^ ^^^^^ '^ ''■'' - »' -"^^ -- ^^^
Exercise 2.
Find the true present worth of
1. A note of $945 due 3 months hence at 6 per cent
2. A bill of $1000 due 4 months hence at 9 per cent
m
■ t
06
3.
4.
5.
* DISCO UNl'.
EOUAT/ON OF PAYMFNTS
payments. '"°'« '« detunn.nerj is called B;;uaUon t
Of months „. ,„,::„, ,,: raVwhTcMftr"' "^ "^ "™'"
"e paynienl of the whole. - ° ""= "'''""»<' "mo to
Example -Ifn nn„n„
3 monUi<; <K/.nn ■ P^'^^on owes a riobt of <ii!i9nn
-A-;''/.jn-rpa-eSiE=^^^
too J ^ = '«oo
tnn ^ '' = 2000
JOO X 7 = 1400
The d- ~ ?^
1 jf Exercises.
ihLlH^ '^ ^''^ equated time fn i! Payment of the whole^
Sf !»' «f fix months. $370 Ll'^er ' -F'/'"'"* ^''^^^^ rf'- '"
^{16 cad 01 Hi months ? ' "" ^"" "^ ^ '"-^"Ihs and |600 at
CO at 9 per cent
"t «'J por cent,
icn at 7 per cent.
SNTS.
money which is to be
h'ch ihe tin^^^o for (JJ
s called IStiuation of I
3stions in equation of
e IS that which is
^ment by the number
Jcomes due; 2 divide
^y the sum of the
the equated time for
ipO payable $600 in
under in 7 months
I the whole ?
BARtfitt
9?
ducts by $1200 the
ent 4 i months the
tiy adding together
ile at any rate per
"Id to correspond
iiounls due for the
'1 2 months, $300
equated time for
$500 in 3 months
e remainder in 8
3nt of the whole ■■'
at of $490 due «i
Uhsand $600 at
in I! mdnths ? 'no"iiis, U.,0 in 9 months, and $6200
i4ahictn'n::;;,thrar,d'S f!^^'''! ^^ p--»^- ^-^o
equated fime for the payn.ent'of the whole y'""""'' ^'^' '^ '"«
l".yablo'$82"in '7° mTJhs" $40^1^8' mr.^"^"' f '^--^^ -»««
months ? ' ^^^^ '" ^ months, and $450 in 10
BARTEH.
.sSd''';,™b;b:',l;''''"«° "feood, by i,v„ parties at price,
oik» goods «,„! ,fr , ' '>■ "«' iM^i'y orihs
g and $27.00 -^ 42 = $0.61,28 A„s
ought'rto^L^v?fb?oTo^bTr^^« "'^ ''^ ^' 60 °«"ts per lb.
and $24.00 - 60 = 40 lbs Xns.
ExEiteisKs.
^«;-yards^?ctt:ltttle?tl^n ^"'''^ - -changed for
, 2. IIow many pounds of cofU at S" T^ ^'^ ^^"^ '^
to receive in e/diange for 2^0 J.^J/f «<^"/^^'^''- Pound, ought I
3. A grocer has 72 Um nf .0, , ^"^ ^^ ^ents per lb ?
*«S«K«5«**
ni
9g
VRont AND LOSS.
gallon ? ^ tiogsliearj of molasses at 31 conts per
6. A grocer owes $248 of which hn nnvc coin
8. How many bushels of wheat at « I 91 r,„„ i u ,
KL%'" ^^^^'^"^« '- ^3i;sL^;;fyLPtT^rJ6^'Strp;?
vafued arSTy' o'tTSe^Zncr'"! ^^ ^'^ ^'^^'^ '^^ ' ^orso
many shee,, should he receive ? ^ ^'^ ""^ ^^•''" ""'^ ^°^^'
II
1,1 ! 4'
PROFIT AND LOSS.
tJS^a-ll^^-i?e^-^^--ity of goode whe„
y?We.-Multiply the difference between the hnvi,,. ,
and IJ cents x !« = 36.^the^v^lo"s.'"'' ^^"^ ^"^'''''-
Exercise I.
PilOFIT ANI> LOSS
PilOFIT AND LOSS. gg
it at if 2o",'oHS''tl,^'.' '"' °"""^i"'"fe' ^J« '»^«. f-'- $105 and soli
^. 1 Jjoughl )0,) l|,s. (,l cliopso ;it l(i cents ue' 11. and sold it -.f
' ' '■?" s I'f'r II... what di.l I lose on thn wl n^« • '"^ '°"' '^ ^^
.,,, , - ■,, — ■"■^^- '" > '"i-^u ill ID cents lie' II.
llj oeri s per II... what di.l I lose on the whole '^
0^1/ 1 buy 2i;} y,ls or cloth at $:iAO j.er vrd and sell
b3 8o per yard, what is my gain o.i the wholo ?
it ut
selling'price";,|'gi;j; ■ '"" ^''^ ^""' ^^''^^■' ^"« P^-e cost and
' nnf":^^' ^'" ^'''"" '°'' '' '.' '^'' ^''°'« fe''^'" O-- loss, SO is
^lOU to the gain or loss per cent
A, «I72,S : SJ90 .• : ,|00 : lo <„ „,„ g„i„ p„ ,3„,
As j;792 .• »I50 : .- sioo : ,8 jj ,he loss per cent.
HXKKGISE 2.
y..f-i,';i,at'ts1h''„7^';i?e,l?/'' ■ '''" '"^ '°'^ «' *"^ P«^
.b.^:''aus le'lt^r' c™ ""'=' '^^ "• '^ '""" "■»'■ '' -°'» >»-
.y ■^.ir.X'cS.JrtiloVfrc.Sr''' " '»^ *'»»» «■'- w-
flW.-As SIOO is to $100 will, the gain per com, „r dimi-
iirioc ' '"'' '""' """" "° " ""' '"■-" ""^ '° ">" »=I"»S
100
PROFIT AND T.088.
As $100 .•$114 : .<n ,. .^ "., „
AS ii.lOO:$y.{j: 6560: $520.80 Ans.
rnr I. ' ;;'7 -■;;™i.y or n„,„. r,.r r.m .ha. must , .„„ „
"a i/nf 4 p™'!,'; "will;??,! >i,°',::s^"f *■]? """ -'" "«>™
'• "Dui/ It 200 hiitil oic r.r I "^'^''ne for them ?
t"o wl.o„fa, ats"o'/f .0° ,: \-;,?/^f ;,.^^ P- i^usiu-, anJ sold
«. Bought a qnaiitity if firewood fnr ^1 '"•'™'.''^ ^'"' '^ '''
Kim 9 per cent, what must 1 sell it Sf '" ""'"''' ' ^■'^'' '°
Boinng^^il'^aJelir."'^" "^^ ^^- o^oss per cent and the
/?«/e.-As $100 with the (?ain per cenf nn r • • u
^0^8 per cent is to $100 so is Z Ji '^""'"'shed by the
E.A„P,H 7._Sold a aualti ! r ' ^'^'^^ ^° "'« "rst cost.
"T «';.^i ^"^ the m'stS "^ °' ^^^^ ^^'^ ^'75 gaining 8 per
A« $108 : $,00:: $175: $162,031? l,,e first cost
Example 8 —If i «pii .q „u J^ °^'-
'T^ ."o';.«^"-'^' '^«t OS y^"^ '"' ^'' *^-«^y losing 4 per
Ab $Q6 : $100:: $70 :$72.91| the first cost.
1 rri Exercise 4.
, 2. Sold a quanti V of flour for sU^n -'"'^ "''^^ ''•"'' g'^Hon ?
<m.saetion wh,,t whs tile dm co;t v '^"'"'"°" '"l"''" '^^"'«n the
oeni. w^lt^'li;:S ^^^^' ^^ ^' ^^« ^'-hy losing 5 per
What wa« tirfirsi\ostV'"' °" ^ ^^^''^^ ^vhich I .„id for $190.
barrel at wfmt rain
• PABTNEnaillP.
101
:.. What was lIiM (irst cost of .30 cwt. of sugar sold for $350
till' gam on tlio wlmlc l.oiiig 13 por oi>nf'
(! Sold 3',0 l))s. of butUT for «G,J losing at the rate of 8 per
cnni what was the tlrst 0081? « lui^ ui o |.ei
7. If 1 gain 15 jmr cent on a farm which I sold for $3120
wlidt was the first cost? •p^'nu
.S. Sold l'20 yds. Of cloth for $311 gaining 7 p.r cent on the
IniiiSiiction, what was the first cost i*
percent and the
PARTNERSHIP.
Partnership or Fellowship is the method hy which the profits
or losses ol a firm or ccmpuny are divided among the rospecUve
Partnership consists of two kinds, Simple and Compound.
SIMPLE PARTNERSHIP.
In Simple partnership, the stocks or sums contributed by the
several partners, all continue in trade for the s.ime time.
/?u/e.— As the whole Slock is to each partners share of the
stock, so is the whole gain or loss to each partner's share of the
gain or loss.
Inthe same way the effects of a bankrupt may be divided
among h.s creditors: As the sum of all tf/claims is to each
sTare o^dSn-r '' "" "^'"' °'''' ''''''' '' ""''' '''^''''''
ExAMPLK I.— Throe persons enter into partnership, A. nuts
into the busm.^ss $750, B. $840, and G.$9S0; they gain $800.
what IS each partner's share? j b-'" *o"v^,
The whfile stock being $2570, therefore
As $'2570 : $750 : : $800 : $W3.46.7^ A's profit
' '"" : $'261. 'l7^i^|B-s profit.
• ^O^^f?j/"s profit.
$800.00 ^VVhole profit.
Tlie correctness of the operation is evident for thn gain of
each partner added together is found to be exactly ,$800 the
whole gain.
«!7rn,"o'^ '^■r"'^?!;"'^"-''' ^'^'''"^ '" business owes; $500 to >\,
$760 10 B, and $1520 to C, iho value of his effects is $1250
what should each creditor receive '' * -^ ",
As $2570 : $S40 : : $800 ,
As $2570 : $980 : : .$800
r
102
nAUTNEILSinp.
'''Oir profits a,.Ku,m to §,S25vvlm^i " '"" "'"^' "'" '' >""'•
»r Wheat al m.li ,,er b, h" "„„*,V' "in I,'""'?'' " «' """'I' '
PW barrel ; wl,„t sl,a,e slio, i,??.„.r, '"'':'"'' ""'""'U is.so
S1600 ,„ A. S^IS^^'J-J 'I ' « » «;!."« e.lV.c., i, ,6800, „w,.,
shouhl fad, n.ccivc ? ' '^ "" '° '"'""' S'TOO to t). wlml sbaro
SSE?'r°'^''^«S'.V-B'a°!,';r'',:,' ??""■ "'■ »""■"
£,JVa,r:f;iJ^o,it;:[-;;i5r«c..o,,it,,,. „r „ ba„.
^ i;.sl,;r?U;;'^'; trir-r"?^'" •» A. S4T00
Si A 'a sfiaro.
3^, '*'s simio.
Total eiTi-cts.
'.puts in ;!!l2H0uii,j
giiiii ()r.«<)r»'2 ?
'• A puis iiiio tliM
III'' end of a jciic
|i'.rtricr's sharo }'
"cnpitnl of If: 1 2000
y, C $.'i'250, and D
this siKJuld cai'li
ue of the cargo is
I'lt) Ijalarice to (; ,
t'K' loss does caih
>iitrijjul"s towards
re), B 960 bushels
>lso( Hour at 45.80
1 again of $2000 >
00 towards whielj
sliare of the gain
'i the liouse I'ti-
for fg.lOO, what
A's share being
is $G80n, owes
to D, what share
SOOO, of which
laneo to C, the
isiirance ; what
'"'S of a bank-
aim of the Mist
"I of the third
to A, S',700
f Ills oU'ecty is
pital of J7oOO
bnlanci\ wh.-ii
PARTNKKHIHp. jq.j
guS^ng V;S? ^''"'" "'^" ''^^«'- «' ^'- °"'i '■'•« year tho
COMPOUND PARTNKRSrilP
.{i^^rls^a.-S^;.=^
/?We.-MMlli,,iy the stock of e„oh partner by the time l,e
c ntmuos u. business Thon as the su.n of the product h!
C^$I300 for 10 months, what is the shore of each iH gain ol
SI240+ 9 = $11100.
$ 980 + 7 = $ 68C0.
$1300+ 10 = $13000.
As$3IO'?0:$|||f.O
As $31020:$ 6800
As $31020 .$13000
$31020.
f 920 : $330.98G/i A's share
$020 : $203.4558 B's share
$920 ■ $385.5577 C's share."
$920.00 whole gain.
ExuncisES.
the share of each in a gain of SfJ-iOO v ' ^' ''** '^
whatSeTsSid'o^lSvif 'f V!;f-^"'"''^ ^''.^^^ '" ^™^«'
'or 9 months andB "/foo for ! I monlh;?''^ contributed .4000
>>fmmfm^'im
fl^SS'M-
104
i :.f
INVOLUTIOxN.
each in a gain o/lsoS ^'^ ^ ™'"''^'' ^^"^ '« ^'^« '^^''^ of
$3800 into Iho b„4l> s li' " T"T^T '^'^'^ ^ ^''« '^'•'^"ghl
they find Ihat h y taVe ^'e'' "^^^^^^^
should each recciveV ^ ^ '^^' ^'^^^ ^^'^^^ ^^ "»is
I!
It
INVOLUTION.
of 4, 4c. ' "' ^ ' "* ^ ^ X 4 X 4 or 256 IS the fourth power
l3eLteVr5"°5t'?2^^"^^ ^ ^ 4 = 16 ; 5 is a rod of 125
secI'rpo^ero?r,uare'o; tht7"' 'I '''''i '' '« '^'^"^^ ''-
timesaslactoritisSedthefhir. ''"^''■'' "^^"^ *^'^^n three
four times as factor'^ is el Pd thi ^e'^fr' ''"'^^ ' ^^en taken
5a.es as factor iri^ValS'^tl^r^^^^^^ "'^^^ '^^-
afS:nS^itra^i;r;;:",i,f,i,^e7- V ^^*'' «»-- -i-^en
on^ the root ha^fi^S l^iSr S^Io-^Stn^
3^ -'rx'a^x F= tr th?ch"irrh"'\i:°^i"' ^''^ '^-^ ■« --t*-
written 3^ • 3 x 3 x 3 v i -s, ^"^'^^ J'^''"^^ PO^^r of 3 and is
is written 3^ "^ "" ^ "^ ^ "^ -- «' 's the fourth power of 3 and
Jh^e method of finding the power of a numhcr is called Invo-
To find any required power of a given uun.her.
iui,c.~tmd the continual uroducl of iim «■;„„
•1 of §3000, lowiids
Tor 16 months, aii'ic
oC the proiiits should
A contributes $ I Sou
$2600 for i I months,
lid each srslain ?
a capital of $2700
inths, B $700 for I ['
what is the shar.) of
tal of $4500, Ihreo
vith B who broiighl
ommenced business
vhat share of this
taiued by the con-
4 X4 x4or64is
s the fourth power
I>eing continually
^ is arool of 125
or it is called the
^'hen taken three
ube; when taken
ver; when taken
c.
II figure written
i it indicates how
oduce the given
'f 3 and is written
wer of 3 and is
power of 3 and
'v is called Invo-
cr.
given number,
'>y the index.
EVOLUTION.
les
When the given number is a vulgar fraction find the required
power of the numerator and of the denominator. '"'''^'^""^^'^
When the given number is a mixed number reduce it to an
szl:tzss:"' '"" "'"'"^ ""»'" °' '"« »""■-'-
Example i. Wliat is the fourth power of fi ?
6x6= ,36 the second power
36 X 6= 216 the third power
216 X 6= 1296 the lom-th power.
Example 2.— What is the third power of 3-». ?
^ = V then
-10 X -1:^^ = A on the ?econd power
and ^^ X -UJ = J^^fl = 37,-S- Ans.
ma^"hp;TnH! "P/ration of finding the 4th power of a number
iZ^Sth n^^fi "'r'^ ^^' ''".'^'"^ ^''^^ ^'i"^''^ "*' il^ square ; to lind
ube tSTmn'h V"™^'^'- ""!' ^^'^ P'-od'-ct of us squa.e and
cube '■ n flni f' S ' '"'''''"' "1^ """•'^^'^ "nd the square (.fits
it fourth nn^'^^V-P^'^l'"'^^""'"^'^'' '^'^e the product of
square ol its fourth power. ^^ r «
Find the value of
Exercises.
The pquare of 21.
The cube of 15.
16^
183
The fourth power of 9.
The fifth power of 4.
The sixth power of 8.
8. 17<
9. us
10. 11«
1.
2.
3.
4.
5.
6.
7.
U. The second power of 27.
12. Tlie .«qiiare of 78.
13. The third power of 13.
14. The cube of 19.
15. The sixth power off.
16. The fourth power of 24-,
17. (3f)3 ^
•18. (|1)5
19. The cube of 239.
20. The fourth power of ?.
EVOLUTION.
num'be?or" '' '^' ™''^°^ "'" "'''"^''"^ «">• '''' °'' « g'^en
mu1f?nHld°hv'ifilr™''^"^ °'' ""^^l"^ ^ """^''^<- ^^hich being
rivin^nuLi'''''^ " ^'^''" ""'"^^■'" °f ^""«^' ^i" Induce I
n J*^ 'I'^^'^u^^'^ ''°"^ '^ ^ ^'i" "f^ure wrillen a'ove the sian a/
prejixed to Ih. number of which the root is re<,uired ^ ^'
;,l'- I;
106
fivoLtriroN.
wii
EXTRACTION OP THE SQUARE aoOT.
To extract 'he sernnH «..
^"^e-,. Poi„t oft '"'" "''^ °'^ ^'^^" --h-
%-s eaC. cirene;:/rtrit ;"^ ^^^^^^« °^ ^-
highest square contained in the flJ ^"'''- ^^ ^'"'^ '''«
'« the quotient. 3. Subtra t the ! '"""'' ""' '^^^^^ '^« '•°o'
q"otientfro.nthefirstpe oVt theT" '/ ''' "^"''^ '" "-
Penod, and double the pa t of h T'?'"" '""^^ "'« "«^t
Of the next divisor 4 P^d hn ''°°' '''"'^''^y ^«""d for part
fisor is contained in th" divl7"' """ ^^'« P-' of'ti.
t^us Obtained to the part orttfo°?''"°^ ''' ^''' «^"-
the part of the diviL alreadv t h ^'^^ ""^ '"^ "'^° ^°
d-isor by the ,ast «,..« XJI il tht ' -^'^^ ™"'"P^>^ ^'-
P'-o^uct, and subtract it S the . T°'r '' ^^' '^^^^ the
"«>^t period to the ren^aiuderfo a n^'i'"' ' '"' ^""^^ "^^
^-^^ P--t of tl,e root found fo ' rt T.^"'^"'' '■ ^^^'^
P'-oceed as before until a! , ^''^ "'^^ ^'^'^O'' and
^-n. inhereisarl il;';^'::':^^ '"" '"'^ ^^"^"^
figure of the decimal. "" ^^° "^'Phers to find each
Wact the square root ofavui,ar fraction.
n-e;ator;::;';LlX;:l-;;;e numerator for a new
^'enominator if both be coL 1 '^•^"«""nator for a new
f-ction to a decimal a .d 7' Td Tl' '"' ''""' '"'^^^ ^^e
<"■ Whole numbers. ^ '^ "' '" ^''^ extraction of roots
To^/^nd the square root ofami.ved number.
who;;;ur:^;::::nX-- ^ecima., annex u to the
re root of 16, that is a
vill produce 16; 3/,^
at is a number whos ■
H^rootofig, ihatisa
RE ROOT.
given number,
nto periods of two
gure. 2. Find the
"i and place its root
'f the figure in the
ler annex the next
eady found for part
36 this part of the
ig the Jast figure
^otient and also to
Then multiply the
ient, set down the
^ ." and annex the
^•-^nd. 6. Double
next divisor and
ve been brought
Jhers to find each
)n,
rator for a new
linator for a new
'f not reduce the
Paction of roots
annex it to the
iVoLul'iof^.
Example I. "What is the square root of 54756 ?
lot
547561234 Ans.
4
43
4641
147
1^9
1856"
1856
Hero by placing a point over the
second llgure from liie right, and
over each altprnnto figure towards
tii9 lell wfc divide Uie given nimibei-
into three periods. The highest
square in the tirst peri( d is 4, the
square root of which 2 we place in
the quotient, then subtractinL-- 4 from 5 and to I the remainder
annex 47 the next period w'liicli makes the new dividend 147.
To find the second figure of the roi t we double the first and set
it down to the left of the new dividend, and finding that 4 is
contained 3 times in 14 we set down 3 in the quotient and
annex 3 to the part of the divisor already found which gives
the complete divisor 43; this being rnnltipliod aiid 129 the
product subtracted from 147 we have a remainder 18 which
with the next period annexed is 185G the iie.^t dividend. Then
we double 23 the part of tho root found and obtain 46 part of
the next divisor; finding that this is contained 4 times in 185
yve place 4 in the quotient and annex 4 to the part of the
divisor found, this gives the conqilete divisor 464 which is
contained exactly 4 times in the dividend.
The correctness of the operation is proved by multiplying 234
the square root by itself, the product being exactly 54756 the
given number.
Example 2. What is the square root of 6/g ?
6-,^ = 6.4375
6.437512.537 Ac.
Here we reduced -^g to a decimal
and annex it to the whole number 6.
Then finding that the highest square
contained in 6 is 4 we place 2 its square
root in the quotient and set down the
decimal point after it. Then bringing
down the next jierind we continue I he
process as in the first example, and
finding that after all the periods are
brought down there is a remainder
of 366 we anne^ two ciphers, and thus by annexing twocipiiers
to each successive remainder the operation may be cuntinued
until the required liumber of decimal places is obtained.
36600
35/j69
"TT31
''^'^mmmm,
los
I'inrl the s.juare root of
liVoLt'TloN.
EXEIICISE I.
I
2.
a.
4.
5.
6.
7.
8.
9.
10.
II.
12.
1 1 5(3.
G6G.
1 132-2.
30 ■57296 1
432.
Gf
39-25.
I72fi.
123456789.
•289.
3|-'8r"^^^'
30-25.
562.
78-5.
145491844
784.
3675068.
2490084.
8206 36.
T„„„ ?"'""'"" """« CUBE ROOT
fo Bxtract the crihe root „r 1 , , "^ """* ""mbers.
"" " "■« cul'e root of 78402752 ?
SVOLtTTION
109
J X 4 = 16 X 300 = 4800
4X2= 8x 30= 240
Complete divisor~5044
422 = 1764x300 = 529200
f2 X 8 = 336 X 30 ^ Wm
^ C4
78402752 | 428 Ans.
04
il402~drvid€ttd.
10088
4314752 dividend.
Complete divisor 539344 43l4'^5t
■e remainder we haveT4402 for .3'^-^^'"* ^'""'^ "^
divisor multipl, 16 which is the siTon^'h'"'^' . l^ «°^ *»
already found, by 300, this gives Sothin Pf''""^*'^«''o«t
divisor; although this is annfrpntivl'/^^ f'"^' P^*"* «f t'ja
dividend, yet on (rial it wilf K.L ?^'''"''* ^ ^''"^sjn ih.
lake 2 and annex it to the nart nf (h^l ?" F^""^' ^^ therefore
ad^ng together 4800 the part of thpS ^'^^^y^^^nd; the.
which is the product oT i^%%rsM^^^^^ ^'^""^^ = 240
inst figure in the nuotient and ^0 ?n^ f/ *''^ quotient, 2, the
or the last figure p a°"d ?n thp m,.;- ^T^^^"" ^'''^ ^' the square
divisor 5044^histultfpl^efb7rgKl0"08S'S;" S!^^ 1°™pS
from the dividend leaves 4314, wh ch witI??^I^ "*"' '"^'"^cted
nexed becomes 43I4752,-a new dividend Th«n f^« Pf"^"" *"'
divisor we add together 'i9q9nn A!! " ^"*^" *« ^"'1 the li'ext
300 ; 10088. the pCS of 421^^8 TuUinuL'^K T'"P''«d bj
.6 square of 8, the last figure nlacedrte '^ ^-^ ^^^ •" *nd 6*;
Exercise 2.
Find the cube root of
1. 39304.
2. 14886936
3. 175616.
■'i. 80621568.
5. 14455457856.
9. 5735-339
6
1879080904.
1234)67
636056.
ni
11. 1777q.Voi
2. 48-627125.
3. 12895-213625.
14. 1092'727
15. 40001 T%ff_
16. 54872. "^
Iljl'
r II
(*
EtOLUl^ro*.
EXTRACTION OF ROOTS IN GENERAL,
Kule, Willi exampte. ,
Example 1. Pfnd the cuU rool of 78402752.
4800
244
S044
248
529200
10144
539344
78402752 ) 428 Ana
H402
10088
4314752
4314752
4
41
8
4
120
2
122
2
124
,:„■,.,:, 2
1260'
8
126S
we place 4 the root of 64 the hSst ilZ '" ^\^ ^''^ ««'"'""
first period, in the second 16 the nrnHn.. r''?"**'"^'^ *" ^''^
Uself, and in the third under tl^fJnpr/^,^ multiplied by
which subtracted from the firsfDerfori^P- "''^ ^^ ^^^ """^^ o'' ^
which the nejit period is annexed ihiit*''^' ? remainder 14 to
14402 Then 4 the part of the root atSi""?^ '^'^''^^"d
the lirst column making it 8 th.s Lu tS 1°""^ > ^^^^^ to
IS added to the second Llumn maSni^ K ^/ i '' ^^ ^^^'^J^
added to the first column TaS"f 19 '"'^•^r'*'"'' ^ '^
annexed to the lirst column maS 120 Z f"'''''''' [' ^''^'''
the second making H 4800 this is annni m ^ ^^'^ ^'P^^rs to
in the dividend, but on t, ikl 3 is foS?o"hI,^"",!'^ ^ ^'""^«
fore setdown 2 in the ouotiLt and IrfH o ♦ ?? ^'^^' *« t'^ere-
which makes it 122. tl^fs muU p ied by'2 s 2°44"whf h' S"!^'"
the second column makes it ^OU ihL ■ ,!■• ^"'^^ «c!ded to
10088 the product set down in the^h^rdlr'^'"'^^^^ ^^ 2 and
from the dividend leaving a remalider 43?1 ^ V '^^^'^^'"^i
next nerind jc! pr-ro-c'] -• •!,.■*"*' ^ to which 7^') *h^
.he quotient to the «,n c„i"ft1,fo„"LS S^l'Xly
EVOLUTION.
Ill
GENERA^.
'2752 ) 428 An»,
2
8
1752
i752
I liJ
•tfs of three figure!?
in the first column
contained in the
4 multiplied bv
54 the cube of 4
a remainder 14 to
^ea the dividend
'«nd is added to
y 4 is 32 which
nd anoiher 4 is
B Cipher is then
' two ciphers to
ontained 3 tiniog
'ohigh wethere-
■he first column
. which added to
|j]ied by 2 end
1 and subtracted
which 7.=19 if,^
14752. foiind
igiire placed iir
t 124, multiply
ii\eti?S2*^^d'fdd'2^rttii;.v'^^~^ -'"- -'^-''
I2C, one cipher is l£ ad led fnt?/«fl'?'T" ^'"^^^ ""^^^^ "
and two c phers to tSe'l ond maETt'SoT'lll^'l'?'^
contained 8 times in thn Hivm„„^ ^. . ^*^200, this bo nff
tient add 8 to tlVl^lXmTtmlw tff.H '" "^V^"'^
and add 0144 the nrodnnt « .'h '^ ?^ ' .^^ ^^® S"™ by 8,
it 539344 ; this is then mnlf ni ^\'^°o°"^ ^'''""'" which makes
s.t down below ?hed,virnd'^''t.S ^^'^^^^ theprodSc?
We thus find the whole root to b?428 '' '' '"'''"^ ^''"**'"«'*-
Example 2. Find the fifth root of 847288609443.
2 4 8 ifi 847288609443 (243 Ans,
2 » on iV oi
6
2
8
2
100
4
loT
4
ioT
4
4
He"
4
mo
3
1203.
4
8
12
12
24
16
4000
416
8
24
32
48
80000
17664
"97664
19392
4416 117056
432 21184
4848 138240000
448 1738827
5296 139978827
464
576000
3609
579609.
16
64
800000
390656
1190656
468224
16588800000
419936481
17008736481
5272886.
4762624
51026209443.
51026209443
In this example the fifth root i- 'n-j-,-- i^
Pnnciple on which the rule S the ex?r«.^^/"J'i^°*'"" "'"the
depends. "«= i u»e jor ijie extracUon of the cube root
112
KVOLUTION.
divide ir^!f;:,;'-,^'-nnum^ the fifth column and
4theproductorthe(irstcomin n^ o*^- '" ^^^ ""-st column
product of the second colSmnZH 9 '^ '..'"/'"^ «'^^°"fJ- « tf".:
of the third column and 2 rihe ?on,^h ^"^ ^t^' '^' ^''« P'-^'J"^
the /ourlh column and 2 the i^.Jp ' /.""'^ ^^ ^'''^ P^'Ju^t of
first period, subtract am) tn..'" '''® quotient under th,
wh^ch give; 5.7SKift'il-r'-'er add the next %^\^:^
ti^ri^^^^^^^^^ '0 t,at employed in
Jt^'> column, two to he second Uri f^l"^ .°"^ ^'P''^'' ^^>
to the fourth, the number in fhonLf ^"^ *^« ""''d. and f^ur
second 4000, in the third VnnS i/ •'"''V""" ^'^^n is '00. in tl"
next figure is found to be 4 whinT'' '" ".'^ ^°"''^h 800000 t£
°^f iply 104, the sum by 4 ani ai'dThf ''' '^' "^« "^«^ '^°'"'"n
column, multiply 4416 the sSm h! /^ ^^'^l"^' to the second
the third column, mul iplv 976^4 L/"^^^^.'^^ P''od"ct to
the fourth column, mulLiv 1 1 oL^I 1"",^ add the product to
the product below the dSnd«SH ^ ' 'u^ ^°^" ^^62624,
the remainder. To find thp thf^H r^ """^^ ''^^ "^xt period to
process and find that momu^^^^^^
?9"e^cts --r/?S'in z Sit ;;^ss
bT^h- e°x'tSS„i^ r ~ ''"' ^° "" ''""
the LtraSrth°e^t?S^t'^tw^" "^•^'i.*^^ -'« "-^ ^"^
pends any root may be extracted I^''«°«d.ng examples de-
the'^^pScrd^Sg^S^T we^^re'xtrt T ™^^ ^'^^^ -
and the secon'dTooT of^h^e re uft"'theT^'?[ '''' ^'ven nLb
second root of the. given nimbeV Sf ^'^^"^^''oot by finding the
and the second root of lEe second rltr'^K^^^' °^ ^^^^ '"^sult,
ng the fifth root of the given Sum hepi h ^. '"^^ '""'^^ ^y find!
the result; the twelfth root hv«-?'^ ^"'^ "'^ second root of
given number, the seconSrooW^tt"^ the third root of the
root of the second result and fhno ^"^ ''^^"''' »"d the second
m every case in whfch the index ofS' ^'^ ^'^ '"^y P™«eed
composite number. ^ ^' '^^ '"°ot to be extracted is a
1 I?- J X, Exercise 3.
«• i'lnd the fnurfh rn-^* -^m
2 Find fhp fi«T ? . ' '9'V^dy0625.
3 PvtlM»f"^'"°°^ o*^ 6436343.
3. Extract the sixth root of 5289852801024.
B fifth column and
•ce 2 wliich is thn
1 tho first column,
llie second, 8 tli,'
'"rd, Hi the product
J'^ tho product or
fuotient under ilin
Id tJie next period
that pnii)loyed in
hng one cipher to
the third, and f(jur
then is 100, in tho
'urth 800000. The
> the first column,
uct to the second
W the product to
t<ld the product to
Etdown 4762624,
he next period to
through a similar
m in the fourth
■idend, the whole
by involving 243,
qual to the given
■he rule used for
>g examples de-
may either uso
second root of
the result ; the
' given number
't hy finding the
3t of the result,
ith root by find-
second root of
ird root of the
ind the second
3 may proceed
i extracted is a
4.
5.
6.
7.
8.
DUODECIMAL MULTIPLICATION. 113
Find tho seventh root of 3797498.13583241
Hoquirerl tho eighth root of 208«-2 7064576 "
KUract the ninth root of 1352G05460594688
Jmd the tenth root of II 25899906842024
nxtract the eleventh root of 116490258898219.
DUODECIMAL MULTIPLICATION
denomination r.r each tlnio thM 2 is cmL neV,'^ «? ''!? H"'
^ Example. Multiply 6 feet 3 inches 6 lines by 5 feet 9 inches
. First placing feet under feet
inches under inches and lines
under lines, we multiply each
term in the multiplicand, com-
mencing at 6 lines the lowest bv
6 ? ^f«' the highest denomination
36 6 10 111' 6"" Ans '" '"^ multiplier and obtain the
— ii^" partial product 31 ft. 5 in 6 1
and obtain the partial proanoTut.T^r.f'M ^l^^
fi"" tL";' aJilln'/,"^ t^'^'".^"^ partial product 1 in.'sT 7"'
ft.
6
5
sT
4
in.
3
9
5
8
4
1.
6
_9
6
7
8
J)4
DUODECIMAL MVLTU'LlCATlos.
[«"4iyMV ":E^4■'»^
8. Mult plv 10 ft 4 in V'. Y ''• ^ '"•
«■ Multiply 18 ft" « n' J ■ K^ ^ "• 6 in. 5 I.
i^y^nn.3m. II J. by28ft.4i„ gj
'• " J ~° "• « in. y J
^ To fl rf h Rules.
I Whoi • .V Exercise 2.
;." CUVt'a'reVoV/'^""'-^ ^ 9 in?
3- Find the area nr! f " "^"'*''« ^^^ose side is 7 ft m -^
't »?&°SgMVS°??r, "">- '«"«"- 's n ft. e i„.
in.
\T10S.
I.
7].
5 1.
4 1.
in. 9 1.
vhich tho opposite
figure whose sidps
P'es. Multiply the
g, thai is a parol-
but whose length
the breadth,
a parallelogram of
fies are not right
cular breadth
a plane figure of
licular height and
v'm six sides of
el. Multiply the
s 5 ft. 9 in ?
's7ft. 10 in.
' rt. n in.
f which is 7 ft.
1. in length and
8 ft.
J 111. and
'h is 1 1 ft. 6 in.
'S 24 ft. 7 in.
uiid
MISCELLANK()i;.S QirKSTIO.V.S. 115
.11. l!;ol,asiM,ln triaimi,. isJt
'■■Bill I II. .1 i., wl.al i5 i„ „„,, ,
< a :, :,:';;:;:;: i:;:r;;T rrwi,;;': " "'■■'^' ' "• « - "■ '«"«"■•
10 in. and perpendicular
8 in.
if)
MMd thn area of a .s.|,iare wlios.. side measures 7 ft « ,>■
^^^•1"7 •.''/:.!•■["":''!;■"' --tent .u^'":;^! I'Jl
17
is 21 ft _^
IS- What is thearoa'of' "a
111
ID.
whose length
II
3 in. and lici<,'iii 7 It. 4 in.
n, I ,. ^ rhombus whoso lonffth ia 9i n
and uorpondicular lieifrht <j 11. 10 ii'/ ^ *
1 ho b
"'''^'' 0' *i triangle measures 17 I'r =^ ir.
"""o' ma^K'';'," " |.V'" '"■ ~ "hill.."™ .4' ■
and its per-
in. long, II
MISCELLANEOUS QUESTIONS.
buli,et'raTsaffl,"iK;';;'r'"rV''^' «' ^'-^'^ P- ^^^hel. 48
.'.t 55 cents nor bu I el ■ ' '"'n'',' '''"'' ^" ^"^'^^'^ of potatc es
2 A ffrocPr bnm V'. ''''^' o'''""''' '"^ '"'^ceive for the whole'
a chest Snea Sinin'ri^ iVr:,?'';','^^"^ '' ^' ''^^ '^^'- «"'•
he pay for the whole" ° '"' ^^ ^'"^' ^"''^ "^ ' ^^'^at did
sl.arJsS'.^^i;::,Sv' ""'"' ^™°"^ 17 persons, what
ros'ilt''by"8' ^"''' "^ " ^ ' ^" ^°"^- '^"^ """^s and divide the
remahSSST?"^' '^ '"'"" '^■"™ ^^^«^-^0 ^o leave a
por annnm/' ''^' '"^'"^''"''^^ °" ^''' '^ ^^"^ ^ months at 7 per cent
<-'. IJiV.'lll' fh;i c !• - . .- .. ■
14 cvvt.
lUll ol
/ cwt
9. What is the
I'Pi- (!ent per aiinn
]rs., and II cwt. I rfr. 2i II)s
5 lbs., 19 cwt. 2 qrs. 13 lb
s. into 18 eqna! parts.
ompoiind interest on $5G0 for 24
m
years at 6
no
»HHCKU<ANK..IJ« QIIK8TION8.
3y
10. Find tlio valuo oC it nv j con i,
11. Hoduco 17,' r/i?.°' L ■ "" ""'• '^^■"''■'"I'ois.
M'Is. Jqls.tog,l]saM,lmuiiij,,yUi.m.ulu,
fr 0'. _ I
13.
14.
''""^""^■«"^-^''(?X8,-|-(,^, XVi,-^^,
Hl'dlK;,. ii .)
I » 'I
." «.u:; *VS'?,';V;«,1' f7;;-;;«i --.^.i, .„„ „,.,.«, „„„,„
17- A, and H iwih... '■ i ' ' '"'"' I"''" 'immm? '
«f «« for 5 mo th '1 / '' JS -.■'•'^'Vl'' A. pnl. inlo tho husi,.,..
I 'J- He( uco •<» .«9 .7;L LvT s'-
must e sell it p.r'poui,Ks ' s ? ^^^f ".'f ^'o" ".1 ^^ ^'''^' ^'^
on? cwi' :„,, X,,l l';JJl^^, «f Bugar c« „J what „,;„ ;
he^rece,vo for the wbol" ? " "' ^^ '^'"'^^ P^''' ^^^sfad, what did
'^^^S^^^^^^^TIT^^' of the floor or a roon. .,
f3?40(> •')■!!, /'hvX '™'"'"*^f'^'^ business with a nni.,! r
Wou0.whatist/.esh"reof,a,l ^''^ "''^"- '^''""'^ «"'ouni ,o
69 da,. i^I'Sr'''' •''"'''-- ^^^--.^^ .'ays ^
cost at the sa,n;',;!L"i "''"- "''' ^ '■■^^«. what wdl 432 barrels
34. Reduce $296,5010 old Canadian currency
0/. Avoir Inpois,
Ulllllijijy i|„. ,.(,.,,,11 1^
I'lys, workiiiff !) !,
'"' "■XjK'OlO.I lo .J„i!„
"I <i''<:iiiiHl lructioi,>.
oUUu^ iiitf'rostwoiiM
' 1111111101/
""^''it()tli(.husiri,.*s
's. wliat is t|i(. Shan".
MrSCELtANEOUS QUESTIONS.
117
' «</iiivaient viil'
71 r
2 r. 7 per.
3 whal is the value
'ntspnrlb.,2Slbs
'■r lo., at wiiat nuo
"11 tlio wfinio !»
ell it at $19.50 p.r
-t $42 what will 5
tsporlb,, mustbQ
Its ])('r U) V
'olfl I at 65 cents
biisJic'l, what (lid
loor or a room 21
'til a oapK.ii ,,|'
B S8500, and (J
rofits amount lo
3i seconds and
liis.
will 432 barrels
:y-
;I5. ir32 horsps oat 70 biishHs of oats in 7 .iav« how tiiHnv
h.-hHs w,l 2S horsos ...t in -i dnys ,M U>. s.,,'" nil!;" ' "'""^
If.. W hat wid b.. ih- .inicuiit ,d',5'(.()() ut (h.. ond of 3 vara
ill -jM'i; cnnt : .>r annum, •■nniponnd ini..r...vi / ^ ™
.17. Fiml liio i<Mst conini.in mullipjo or2, .'), 7 « 9 IR '>«
.^0, jlrdnr,. i!)'.2r,-.S.^, gills to hn>r,bo.ids.
■'.U. Divric ;| nr.S2'i7(;,S.l() by 2.i
, jl Ht^'l'iio ^2iH : I!) : n_ i,, dolLirs and conts.
U What IS tho anio.int ol $;'r(J I'.ir .j y^ars and 4 months
at '.J per cent per annum, simple interest ? !
valnorUt'^3oT8';;l^l'''''''°'''*X''' ■' " ^"'''^ ^""^ ''"'•"iti'ro
\mnori ,u .>j.j.iH ni a |HN'niinm of 2^ | t cent/
'li. Find the sipiiii-e root of ,V,'<i
4^. Heduce £!)2fi : 1 1 : in|to dollar, and cents.
^il'olB^'l' ri'i'r^'S'r "[ ''^T ••"•'«'« i^' «724S owes A
;i!|.rVcerve"v'''^ ''''''''"' ''''"-•"'' l'"^ '""•'■'■is should
47. If I buy 74 yards of cloth for |!234 aid sell it (it «1 M , on
jani, what do I pain on the whole ? ^' ^^'^^ f '"^
58. Hedure 7 miles 3 fur. 2.^ per. 4 yds to feet
p.i'/Vor''3?wt'iTil.s ,I11> •"' '"^"^''' "'^' ^'0^' what must .e
|niii lor »,) Lwi lo Ijjs. Ill the sann' r-ate /
M ■ II"'!""'' l'«^' /." § *" '''f"'^'i''-"t '1''^' -a: fractions ?
... HHuce 0^3, ii-i, i^i,. to their lowc: frms /
.;■ r^ "''^' •'' *'"• commission on 948 .'if) ai :A n-r cent ?
53. From f of ^. of ,*728(i.7() take $13,>i '• ', * ' "* ^
ya'rd?^^'"" '' ^'" '"'"" °'' "^'^ i"'''^^ '" ololh at $3.70 per
■i:). Reduce 3947208 square inches to rood-
S() A farmer sold 26 bushels of o;its ui 60 -
3' bushels at ,58J cents per bushel, and 3-
cuts per bushel, what did he receive for the v
■•^7 Jt a person ow.-s another $250 pavab.
* Ltd poyable m 8 months, and ,*475 navablo n m .i '
i-juired the ec,uat..d time W the',;I „|"?t1f h \dml""'"^ '
•)8. It a man travels 140 miles in 5 davs wlkinff in i,n,
;j'J. Find the compound inlerost on .?r)70 for U
cent per annum. ■
Ac.
<;enls per bushel,
bushels at 635
•olc ? *
in 6 months,
(i-r^ari: .1,? '"'""''' ""''' *'(^-oO, what mu.
ij-2 vards at IIh> s.'imhi ivi(,> ■»
\ ears at 7 per
Ijp Jiaid for
62. J I 9
o*. ii ., men -lig a trench 00 feet long, 12 feet -vido nnri r
foot deep ,n o days working 10 hour, eaclf day- ; il. how" Zny
m
I
118
days will |5 men d
MISCELLANEOUS QUESTIONS.
feet d
01
63. W
'p working l/j
a tiMiicii SO feot I
Ci. I<
liai.
nnu
m IS t.'ie cosL of
per diiv
ong. 10 feet wide
aii.j a
bv i
I'oni '2.1 I, 'ike i}
and divide ti
to 111
;'*'< f''iairsat,«l.30eacl
e n
le
product hv e
"lainder add i
I ?
«^:w;:i"i;;,T!;:™°'»"^i'^«
multiply til
e Ml 111
and 18 ft. 4
07. Wh;,t
in.
i /or 111
2 ft. 3
is th
111. wide, ami
wide at 3 cents i)or
"Ji'in,!^-a room ?G ft. g in. I
price
sipiare foot V
ii.'ii
68- What is the into
''• ■-' in Uiickat
I^HeceoltimhorSiit.Gin 1
12
months at
■'•'•SL on $76.'[) Cr ihi
cents per solid f
'OMo
'eol.
ee years and Jb
iu uns at /per cent pr annum
each at the end ol
70. How
be given in
a year, the whole
and r *iocn ' , ""■ i"i
manyhush,.isofoatsatoj,
exclmnge,br37lh..of,:a
'.fc'ain being ;j;8;3o;
larc of
oj ('en
71. What is the cVb
'^. Jieduce £734 : 1
root of 13824'
73. :/
'5 : 'J to doll,
ts per bushel, sIk
at '".^ceiitsper ])ou
!Oll!l,
nd :■
be sold to
iirs and cents.
su,'arcosl,,*9..-,o per . vV .f , !'
.oo-ain !•) ,..„„'.' -y''- 'It What
rain 12
rate per lb. must
71 H^KiVrT'^'; "r^"«-''oio.
^75. What amouni'Ust oTv7;'''''"f '^^'^''"^^ ^'"^'^^i
acres 3 roods at -5 1 7.20 per ac - '"' ''^"' "^ ^ ^^^n
UILS.
Of 79
did he sell .-' 'J^./icis to C, how many bushek
Operation.~i 4. 1 -^ 7 ti o
l-.^or-,., of\i;!:tvro/<^' buTS '^'^ 'I^'^-^i^y «old toG i,s
bushels, therefore As 5 f . ,r 'J"a>itity sold to C is 3
^^to A^ and B.:'th^;4-bif^/;-"r'^'^'- q^-n^i^v
the quantity sold. ' ^"' + '^^ bush. = 86» bushefs
in 'olia^sandC ;;iKu°'ir'; '" : ' ^^^^ which B can do
^ , OperaUon -A. d' as i.^of o wf \ ^'"'^ '''^" ^'^- I'" ee d^ v
iSS;^^^^Sirr'^-'-?^
to 3^1 ^ay:,\i:;LSs.r:;n;^ '" ' "^'^ -'''''^-^r:;^.;in t£
J „7.^7, '*'"-' ^- s'art to walk at the s nnp r r
I^ai.e Ucaupurt, a di.tance of 12 mi "V'!"" ^'';"" ^''^"'^'"'^ ■'^"''
" '' ^^' ^™v-''s Irom Quebec
iTIONS.
'=' 'Ofeet wicio, an.J8
• •'50 each ?
'J «^ iiiultiply the M„„
room ?G ft. 8 in. |,„,,,
loot y ^
iihor 2 5 n in i
""'■" |)er soh(i IV.or/'
ihiee years and lour
'P- A. put into ilip
what is ihosharoof
eing $H30 '!
3 iwr bushel, shouM
'■^ cents per pound/
nts.
rate per Jb. must it
dociinal IVactions.
air of a farm of 79
Miscellaneous OuestioNs,
y and a variety nf
- are no set rules
Ihe number, then
to A., I to \i, an,j
ow many bushols
tily sohl to G is
sold to G. is 3(i
ols, tlie quaniiiv
''• = m tiUSh.•l^;
Which B. can do
'"" Uuee do it?
^' 1^,, and G. 1,
/, + i = \-n.
VOr.C so IS I diiy
\>m Quebec and
s 'rom Quebec
119
10 Lake Beauport at the rate of 3 miles per hour, and B from
Like Beauport to Quebec at the rate of 4 miles per hour when
and where will th y nie-t? ' "
^ Opmilion.—TbeY apiiroach each other at the rate of 3 4- a —
/ iiules per hour, therefore they will meet in 1-2 -i- 7=: !'s7ni,r7
Tlieu as A travels 1^ hours at the rale of 3 miles per hour t ev
wi 1 meet I ^ x 3 =: 5a miles from Quebec, and as B travels 4
mi.es per hour 1^x4 = 6'; miles from Lake Beauport
5. A and B start to walk round a circular island 30 mile^ in
circumference from opposite sides, at the same time and in (hn
s.une direction, A ti'aveliing at the rate of 5 miles per hour and
Bat the rate 4 miles per hour how many milel wi A hl^^
to walk be;, i-e he will overtake B ? ^ ^
Opmitim —In evei-y 5 miles walked by A he gains I mile nn
II Thei-eforeas I mile : 5 : : lo miles half of thfcircun?erenc2
10 niiles the distance ti-a veiled by A. '"'muence
G A B, and G working together can Unish a piece ofwot^k
12 days, w uch A alone can (inish in 36 days, and B alone in
'0 days, in what time can G do it working alone ?
Operahon.^A, B, and G together can do tJie work in 12
'lays, therefore in 1 day they can do /, of the whole, A working
u^one can do t,ie work in 3(i days, therefore in I da' he can 3!
, , of the w.Tk, B working alone can dn the work in 40 dav^
Uiorefore in I day he can do 1, of the whole Therefore A « n!l
fl tog,.ther can do .V + A- = .^o of the work in 1 diy B
A, B and G can do
day
A'oi'k in
., , , ,, ofthewoi'k in I day, therefore in one
G can do i _ ^ = -^ therefore he can do the whole
. ./;\^ = 32/, days.
7. If 5 men or six boys can do a piece of work in 45 davs •
m what tim- can I man and I boy working together do it" '
Uperahon.-ln 45 days I man will do^ and 1 boy i of the work
th^'refore in 45 days I man and I boy will do x . I - ax
01 the work, hence as |i of the work, is to 1 the whoirwoii so
IS 4., days to 122,^, days, the time in which 1 man and I bov
cin do it. ''
8. If 8 bushels of wheat cost as much as 10 bushels of barlev
iind as much as 15 liushels of oats ; and if the price of I bushS
of wheat, I bushel of barley, and I of oats is . 52 «0. whal is m
value per bushel of the wh.-at, the liarley, and th" oais''
Operalion.— nm prices of one bushel of wheat, one ofbarlnv
and one 01 oats a.-e as x, 1, and ,1 hence by reducing these
Iraetioris to equivalent ones having a common denominator and
using the numerators we lind that the iirices are 15 19
"tiid 8, then •' '
-! .-m
120
tiio barley per jjii she
MISCELLANEOUS QUESTION,.
As I
•?'? «0 : 9(J
Ct'UlS
oats
^+ '2 + 8 or 35 : 8
r
9. WJ
r IJiisIiL'i
.■xf)
liatuuml-erisUiatofwi
'i cents the price or i|„
10- What is th
value ?
e value ol
'''^'' ^ + 1 + i is 230 ?
ii house of
Ans. 293i?
!'• Divide Si 000 bi
which ?840 is *
*j40 more thau B
12. A,_„. .„
12 feet above th
twei
■r> A, 13, a,i,J c
Ans
and B $200 more than C
Ans
so that A
4 •/■
ofilc
$1900.
may h,
ilV(!
post ,sj Of its len.lh iu ([
s share c^|pS0,B;sSl6i0,G
13. What
W'at
numb
what if
I'O mud, i in th
s$l3S0,
sum will equal 9«
14- If A can d
I or
it.'^ Iim-rh ? Ans. 28i
« water, a: id
's that to which if°i2 be
, feet,
a Med, twice ihr
f <iay.. a;:/s",„^v],s.f^?f ;!S ;? « -«y^. wi.ic,, B'Vr„ ,ii
together do it ?
15. Il'A, B, andC
ays ; in wJiat time ca
can do in
n the three work
Ans. |2a
Ul'f
tmio vx' j^' ., — K- : ^"',r*> ana li a ono r, qx i_ •' .
lo. A can build a wall
con do iu " "
days,
which
I
1 7. A and B
together
»"" take^to do the wor
days.
A
ns. I3.L
and G can ;;;- ■;:'TgT,uS"'^^,^^" '^ ^"-^^S
in what ume can A, B, and G togSr re^' ■"'y '" '' ^^«"^«
nnn:'r.-J.^."l^P"'-^J'aseal
$2000 of th^ cost, what
19- A person bought
louse A
are the sums paid b,v A
Ans. lOiQ hours
The horse cost 3
Ans. A $003:221. B^
and B ?
half as much
cost of each ?
a cairiage, horse
'""OS as much as the h"
101.291
'"1(1 harness for I
3 1
30r
-o-asthe'ho^eanjrS^-lH'-^-i'^e
Ans. 530 ha
'arness ; wiiat w
'as the
20. A person owr Mg^'r^fb';,??' ''°T' «'««
r\rtn „,!,.,*:_..,__ . » 1 '> "' a ijuildmo- en ,1 <> „,.,
$1000, what is ti
carri
■ wuo, wnai IS tUe value of dm ii„i i- *
2! Divide $250 amon/A^B; ?;.'•
three tunes as much as BlindV; in'..
ngsoldf ofhissh
age,
are for
22. A alone ca
nuich
alone can do in 16 d
a do
Ans. $.-,000.
so that A will ha
as A and B togeth
Ans. A$|/i,i;B$4s,C
ve
ei'.
piece of work in I''
. - $64.
'ays, which B
clays, A leav. it , '^Vont innl^'^,"'^'^ ^ "'-^^^ ^Vo''ic lo^etlTc
aaer by G, and they tSiT " I ll.^'^''^ and is .ioinSif
would G alone d
It
yHnish it together i„ 3 da
2d
ys, m wh.'ii (^
Ans. 12 days
r 3
ajs
ime
c«nt.s the j)rico of ihv
MWOELLANEOUS QUESTIONS.
24. The sum of the squares ofTwn'nt ^t ^'''''' ^ ^i^ acres,
the square of the lirst th„in Y ""'"bers is 61 and if from
WillbU WhalVrthe'nuLKsr' " taken the remain^
2o. Half the trees In an orSrJ .m , '^°'- ^ «nd 5.
pear trees, a sixth plum trees „nH^^ ''^^ "'''°'' '^ ^°"'*''»
Cherry trees. How m^any tS^rthere^l.^^rhe'rl^'^"' ""^
. 26. If 3 men or 4 women rnn ^« „ • -^"S- ^00 trees.
■n w.a. .i„e wU, one =aS"„:^?r ££ i°e^.S
pncoof3gallonsoril,ese iSnc I orShTi"^ 8in, and the
"stt'nSX Sn'e^l™ and Gin ,0s. 4d.
Of a church at the distance nf 9 ,^T' V ^ 'awards the building
from the second, anf3Tmi?i^™'^\£°"?.t;e first, ^ rnS
that their share shall brrorinrn^^i.^ '^'''^- ''"d they agree
distances from the church iSw ^^.P''"'^"''^'^"^' to their
contribute ? ^- ^^°^ ™"ch must they severally
29. A merch'lnt-sdls 'soVJr'J'!' 'l '' ^* ^^'^ ^^^ ■- * : 5*
the stockings at 60 cents and thf^f'"^' ''"^ g^^^^s for |ho
Required the number of each ^ ''''°' ^' ^^ ''^"ts per pair.'
30. If A co^,ld^?aKJ'?;'iav^"''^p«'•''°^^^
What time would botl/ together'eap if/'' it^liVI '.'^^' ''^
S^y'L^'S^t£sS^iA'^^^"^^-----^i5"
many were there in each? ^"® """'^«'" ^^ men; how
33. D... ,.„ in. .„„ nart-lnXi/f oVo'e?dd„;^?»,,
Of
equal 36.
!ft; l?l^,"'.lf* '« "^^ elder of his
Ans. 80 aiid iCO
jo
P«"y.and„on,.e.,™;„dr;:;||L---«^^^^
mmmm^
122
MtiTillC SYSTEM.
3(3. Three snirlipra a n „ i y^ ,• . , ^"S' 15 hours.
following „i,„2"^;3 th?;;a"s^?' ^;:;l%"^ SS'r'P '","''
ofto„ as A lat.s 6, tak,,s 7; how man? vtiM ,Ldfl,av„r" "
15 years te worlh'«,i8oio rwl'r \v.s Ji'sTi guS ^^ral'?" "''
the prices at wljich A tmd n cni-i •*';'^'^;^3- itcquire.l
chants liaving gai el at I .o,nf , ' ' '^^°'' °'^''« ^'"'^^e mer-
■■b fcamui ai uio same rate per cent '(
direction. A t.vtve iSr ,lv ''/r '•"'•^' '""' '" ^'^^ ^^"'^
days turns and loos Tikr^ ""'«« P"r day, and after 9
those 9 duvs he tC Imni nfo- '"' ^''^ ^ ''^^ travelled during
overtakes 'b 2^ iay ' S Te"u,no^r"'f '"^' ^'^^ J°"''"'^^^
-luired to lindthe ite 2';,;;;^ uZuUXS^Sy '' ''
of U,e latter ...^r Sor? ij ' 1 " Tf''- ^'^'^^^ '"^^ ^^'^ P''ice
mixture at ^Lo^^pei^alloiiV ' ''"' ^"' gained l.y selling the
Ans. lji2.32S.
MKTllIC TAIiLli OP MONEY
16 c",.s?:a„ad "„°S,;5 ="""'' " "■'"'■ »'■'«" i» worth abo,u
also two Sous, seldom a Decime centimes called
fr|i:Tr,s°„r5 s.s:"r,;;ii', »,.?"""-■ -"»^ «-- ^■■i'-*
es, it being fournl
the youiij,'er.
i'^iO ; and $57G0.
^ould do a jdoce of
Hi, 3 women, and i
Ans. 15 Jiours.
TO carti-idges in the
B takes 3 ; and as
11 each liave 'i
B, 1 98 ; C, 308.
is ca|)ital by a liftl,
, and at tlie end of
gin&l cajiital?
.lis. §10590.21-2.
!iiin «'J8G.40 to B ;
(iG.3G^. Required'
of tlio three mer-
B for $1342.60.
and in the same
1" day, and after 'J
i travelled during
Jiiig his journey,
irst set out. It is
■ travelled '(•
miles per day.
per gallon, to be
lal was the price
3<i by selling the
Ans. ^2.32f.
KiHTS, AND
1 is worth about
Centime, 2 Cen-
centimes called
illed also half-a-
3, called also a
METRIC SYSTEM.
FRENCH OR METRIC TABLE OF LENGTH.
123
J^he unit .s called a m5tre and is rather more than 39 English
thJ';;etr"iT TToo! ?Soo"t^T(?ot'"'n,'""'^"'^^-^
of length so obtained are denoted hvfhS^ ' "f '^/^ measures
the Greek Language) XcasSfllio''°S\^'^^ '■™°»
1000; Myria, 10 oW- nmH^P f .i^fv,^ 10 ; Hecto, 100; Kilo,
decametre means Tm£httlare Z'^ -f ^re ; so thai
1000 metres, myria.netre 10 000 "''^'■''' '^'•om^tro
mel'e^f ?r[oo™Too7and''the"Sl^ ''' '''7?" ^^ ^-'''^"^ ^he
are denoted by theTllowinll^f"^?' ^''^ngth so obtained
language) pre'fixed to tTe lorT mL'o '' nL' '''V''' ^^^'»
the metre is divided by 10 cJnti bi inn m Vr ^?"^^''"^ "^^^
that decimetre, means liat a m^itr/ il^^,' ^''i'v^^ ^^^^ ' «»
mMre, by 100; millimetre bvionn-n'^'^l.'^''' ^^ '^ ^ ««""-
following table of lengT' ^ ^^ "^'''■*^'^°''« we have the
10 Millimetres make'' 1 Centimetre
10 Centimetres _ 1 Decimetre.
Decimetres 1 Metre, the unit
Metres i Decametre.
Decametres i Hectometi'e.
10 Hectometres 1 Kilometrp nnn Wr,„ i
10 Kilometres _ I MSSe^*^' ^"^- ^''^'-^^ nearly.
^ne above are abreviated thus- IVfiiiim <-„ .•
Decam., Hectom., Kilom., Myriam " ' ^'"'""•' ^*^'^''°"
FRENCH OR METRI^ABLE OF WEIGHT
The unit of weight is called a Gramme which ~ t^iv .• u
grains nearly. "'<tuime, wnich = 15J English
make 1 Centigramme.
1 Decigramme.
1 Gramme, the unit.
I Decagramme.
- I Hectogrammes.
HM ~'7'~" — *'""o 1 Kilogramme
Ihe above are abbreviated thus- Milli.T Conti^ n/ ■ n
Deca., Hectog., Kilog ' "'"'fe'' ^^-nlig-, Decig , Gr.,
^"""' I SirZr-"mnl ''''■ ^voirdupois nearly.
M line, oi J on = 1 ootUalog. = 20 English cwts. nearly
'''''^^f,™^^P^:niE APPLICATION OP
WKIGHT'/iJ^H^^lIi^.lil.Sli^.S^™ ^^"
10 Milligrammes
10 Centigrammf^s
10 Decigrammes
10 Grammes
10 Decagrammes
10 Hectogrammes
11
124
u y>
i
iij '
METRIC SYSTEM.
metres? ^ "linamelres are there in G4209750 milJi-
7" Re'duco o^rf'""^? '° milligrammes.
graLfes'"'' ' ''"'''■ ' ^™-"--' ' ^^cigs, 3 milligs. to milli-
gramm'ST "^'"^ '^^'^g^^n.mes are there in 2409048 miUi-
6 hectoms 5 decams 4 metres 3 dPHm« 7^ '^T""' ' '"''"'";
grammes 9 centigs 8 SS gsTSA'^^^ ^
mill.gs ; and 32 kilogs 4 hectors 7 H°°'^ grammes 6 dodgs 7
milligs. ^ nociogs 7 decags 3 decigs 8 cenligs 4
1^- {■>■? 38 francs 4d 8c take 21 fr 6d 3c
4 hectoms 3 decams SZ^tresT, e.,n.f/' '^ ""^'''^"^^ ^ kiloms
H. From 39 kilogs 7 dec .1 4 ^^n t ?"" '"^^ ^ '"i^'ims.
IS' n'"'l° ?S '"""^ ^0 8« by 6. by 2
2?: Sivit lK™r,?/„t'i'r/'' '■ "y »• by 45.
by 4, by G9. " ''^'^'°^' ^ grammes 9 decigs 2 centigs
^ 2l- wSStle^'^rfo^/i™^^^^^^^^^ ?'• P- ^"°^™-o.
6c per kilogramme, 1-y practice v^' ^ ''''^^''' ^^ ^ f''ancs 5d
5d 4c ? '''^ "'"i' ^° l)urchased for 34 francs
5d!thaV mus7S'T«idtt uii'^^/"'' ' "^7™^ «°«t 2! francs
for IJ myriams ? ' ''' ''^'^"^'''^ °' 274 kilogs 8 hectogs
J docims, 5 ccnlims,
•i8 contimelros ?
in 04209750 milJi-
3 milligs. to milli-
in 2409G48 milli-
1 9c ; 6d 7c ; 87 A-
'' decams 4 deciras
enliins 1 millim •
ntiins 8 milJims ;
ammes 4 dccigs 5
fitigs 9 milligs ; 5
ammes 6 denigs 7
iecigs 8 ceiitigs 4
ams 3 kiloms 9
nyriams 2 kiloms
MS 7 millims.
kilogs 4 lieclogs
's.
34.
ns 3 metres by 8
ammes 8 centigs
9, by 45.
dpcigs 2 cenligs
5r kilogramme?
>, at 4 li'ancs 5d
8 deoimes 9c,
ogs 5 decags if
d ?
purcliased for
for 34 francs
cost 2 1 francs
ilogs 8 liectogs
MENTAL ARITHMETIC.
125
^S n J moil dig a drain 9 decams long, and 4 dccim^ rl..Pn
l.er cenrr' " "'" '"^'-'''^''^ °" '^^'^'^ ''^^'^s at 6. at 7, at 9
pnr^co.d '/"' '' "'' '■"'''''^^' °" 9^"^ '"'•''^"^s 8d at 5, at G, at 8
31. Find the interest on G93 francs 4d at U per cent
1 1 !:'": ''^\"l'''-««ton 1248 francs at 81 percent
at 4i;:;^tUVe"arZ;;r' '"''^"^^' '^^ 7600francsfor 3 years
irj!^sli;i';^^r^T/:^!-^;"^--^-'^the amount of 4500
MENIAL ARITHMETIC.
Exercise I.
1 . Flow many are 70 + 30 4- 24 ''
2. How many are 80 + 36 + 40 + 21 '
^. Ilow many are 31 + 3G + 72 + 9 + 14 ?
;i. How m,.ny are 73 + 16 + 28 + 15 + 1 1 +. 18 '
5
6.
7.
8.
9.
to,
II.
12.
13.
14.
How many are 84 - 13, 104 - I7,l34 -06 V
How many are 96 _ 7, 756 - 382 964 - 728 ?
How many are 237 — 68 — 54 ?
How many are 754 — 231 — 120 — ''7 ?
Fmd the i,roduct oCig x G, 17 x 8, 2^9 x 9.
iMiid the jirodiict of 92 x 3, 274 x 3 G23 x 5
I'.nd the product of 327 x 10, 24G x' II,' 754 X 12
Hmd the |)rodiict of 18 x G x 8 x 10 x 12
D.v,do928by4,627by. ll,852by 12
1 ^ n'^'-f ?ro' !'^ ' ^ ' ' ''"^ ^y 23, 429 by 39.
5. ivi, e 468 by 26, 666 by 74, 696 by 87
G. Divide 6300 by 36 and the product by 25
17. How many are 42 + 56 — 28 -i- 5 •/
18. How many are 132 + 48 72 '-i- <) v
19. How many are 942 — 324 — o' -f 97 ?
20. Huw many are 349 + 357 — 86 -^ 31 ?
EXEUCISE 2.
To multiply by 20, 30, 40, 50, 60, 70, 80, or 90
r ^o?T^""'' ** '"'P^^' ^° "-^^ nHillipiicand and multiply by 2
or 20 : 3 for ,3 ; 4 for 40 ; , for 50 ; 6 for GO ; 7 for 7i f 8 or
80 ; and 9 lur 90.
To multij.Iy by 200, 300, 400, 500, 600, 700, 800 or 900.
126
MENTAL ARITHMETrO.
II
t
8. Multi )Jv 96 hv sn •' k^ Inn = ^^ ^""0.
rp. ,. . , , Exercise 3.
1- Divide IJOOOby 10 CmS P'?»S'^"""'l"Sor.
1 Wh Exercise 4.
$2.76 andjVsV^ ^""^ «' ^'••^^' $2.40, $3.20, $4.80, $5 60-
3.' Mul?ip|? %'i .'if,7,- ^^,f--n 174.82 and $36.40 ?
+ m7''' '^ "" ^-^'"^ «f ^ «f ^72.90 X 2 + $73.60 -$42.30
ixru 4- ■ , Exercise 5.
What IS the value of
1. 18 lbs. ofsiinfar at in r^Pnt'^ nor Ih nt 1 1
2. IG lbs. of beer at 12^ cents r er lb 'nt 1 1 *"'"/" ^"^ '^- ''
s wi.uib per ID., at 1 1 cents per lb. ?
■ "i"L''P'y J^y 2 for
f 600 ; 7 for 700 ;
MENTAL ARITHMETIC.
127
p, 2000, 3000 4c,
idend as many
and divide the
e divisor.
. $4.80, $5.60-
I $.36.40 ?
by 12.
10?
?
t by 36.
X 2 + f 64 —
3.60 —$42.30
Us per ]b. ?
ts per lb. ?
""•'""""""""•''""'M^ryarU.atlJoe^lspor
3. 25
yard ?
0. 49 yard, l,„c„ „i 3„ coirts por yard /
8. 28 yards cloth at $3.50 per vani nt «A nn
9. 9 cows at $27.50 each, at iJo each ?^ ^^° ^'' ^"'"^ ^
0. 347 slates al 20 cents each ?
2 9?Ah ""?'', "°"'" '^^ •«5.25 per barrel ?
12. 234 bushels potatoes at ih cents pi/bushel ?
, ^ . EXEBCISE 6.
1 irfiihc r ExEncisE 7.
the same rSj.;'^"^^'- ^°«' ^4 cents, what will 10 lbs. cost at
theU?rK' ''''''''' '''' *^-28. what will 6 yards cost at
cent's f^ 2I0S''' P*^'' ''' '' ^°^«"' ^ggs at the rate of 41
samt rite^? ^^'^ '' ''^ '''' ^38.40, what will 10 lbs. cost at the
be bought for $10 ? ^* ^^' ^'^^ many bushels may
purchased'for $6"?'"'' '''' *'-'^' ^°^ °^«"y dozen may be
purcha''sejfr$l 2^0""'' ''''^°""'^" '' '' '^^-^^ Vev 3 lbs. may be
value/'' °''''""^"«''''* house is $1350, what is its whole
bu'shelT''' "''' '' ^"^'^<^'« °^ «ats at the rate of $,.80 per
at Ihe samVr'ate?'"^'*'' '"'' ^ ''^''■^'' ^^at will 8 lbs. cost
i
128
MENTAL AUITIIMETIC.
\'l What, must l)o pai.l i;.r G yiirds of sillc. if tho vnluo nf «
pi'Jco coiitaiuint; 30 yards is .^ij ? ' ^'"° °' "^
Exercise 8.
Tnko aliquot pai Is as in practice.
KxA^PLK.-Fiml ihe value of 280 nrticlos at 25 ceuls each • 25
coiils=i of a dollar audi of 280 = $70 Aps. """'» ^'"'" - •'^
Find tho vaiut! of
I. mi lb? al 25 cents per lb., at 20 cents per lb.
.f $J^/' «• ''S*'-'^*^ l"-'- yard, at $1 per- yard.
.}. ^/|,)J (U.i at 50 cents pe- dozen
0. 40| yds at ^l.oO per yard, at $1. 25 per yard.
S o,,u ih" ^\ L'''!^'^ P*"" P°""''' "i' 8 cents per lb.
8. . Oi lbs. at ^1 20 per lb., at ,^1.25 per lb.'
I f ^ yds. atiji2.40 per yard, at «2.50 per yard,
ir'i V""^^-'' It '2J cents per oz., at 20 cents per oz
2" iol'.u!^'"; ^im^"-""'^ ^'' '^«^'^"' <»' 75 cents Jer doz.
1^. JOi cwt. at 1^10. 9o per cwt., at $10.50 per cwt.
E.\ERCISE 9.
"■ Knl fl"^ ^"'"'"ission on $300 at 5J per cent, at 6 per cent
^. iMnd he comunssion on ,?450 at 5 per cent. '
J. 1' ind the commission on $800 at 6 per cent
4. iMiid the commission on 1^1250 at 6 per cent
«. Howmuchis8percontof$950, orsiOOO?
7. ovv much IS 12 per cent of $2150, of $1500'
H. Jiow much 1,^ 1 1 per cent of $1800, of .$2000 ?'
10 W ,"!t !' 1/" {"•"'^'^'•'^So on $980 at 5 ,,er cent ?
I ■ W ; k H .^'"f •^''«^° «n «''^^»0 at 8 per cent ?
• ■ W ^ n" t''''"''"''-° «" =^*^'''^ It « P'-^ cent?
V W ; 1" ^'■"'^■'^'■i^^'c 0" «960 at 1 1 per cent ?
CO tal^ii;^,;!^^'^';;-^,;;;;---- on $1120 at 5 per
at 8*: ^"ul^'J ;S^;i;- °'''— '- «« $8^0 at 7 per cent,
at 'rfpo^S; Vt 7 I'J" 'Sn'tT ' '"'"'"'^"^^ °" ^ ''~^« ^^ '^ P^- °^n'.
17. Find the commission on $2170 at .3 per cent, at 4 per cent
n liru '""^^^ "^ ' '-^ PC c™t of $ I dGO'' P
ce.,?." ' " "''^■^''o'^cmge on $7500 at II per cent, al 10 per
c«nlM?pi;'cenT. '"'"'"'"^- "' ^"^"'■^"«<^ ^^ ?-^600 at 2^ per
if tlio value of a
25 ooiils each ; 25
WENITAL ARirnMRTIC. 129
,_,. ^ , , KxKnciSE 10.
What IS tho interest on
3;iS£^^ J J;:^^-;i-ann,.,n?
4. $ia',0 for '] v<.,rre „. B ' "' '"''■ '"'"I'm ?
8 $ '(i or3 ^ a's ''5\'rr!* Porannn,„ ?
a. $10.-0 for 2 SsaJo'SrrTf'''"'" ''''''*''"■
l2.$l050ibr4i;eJSsU!;:sf:=;-
Find the interest on
9. J ,800 jbr 4 months at LT cen fZ ZZ'
?■ S-nn r"' ' '"'^"^''S at per cent per an Z"
12. $920 lor 6 months at 8 per cent per annum
T,. , ., . Exercise 12.
Find the interest on
3. $1000 ",r 2 Years and ^Tnn X^''^'' """"^ P^'' ""'i^'m.
4. $2500 for 3 year ad 3 mon n I ^'' "'''' ^'^ """"'"•
5. $1600 for 2 years and 9 mon hs Tt I f '""! P^'" """"'"•
6. $3600 for 5 years and 2 men . n \ ' ^ •""" P"'' '"^"""ra-
7. $4800 for 4 Jears and I inon h nf^ ''''' '""' P'^' «"""'^-
8. $2460 for 2 Jears a 3 mo" s at s''"" """' ^''' •'^"""'"•
9. $2740 for 3 years and 4 iZ t ,s ,fi ? ^ ''"^ P"" """""'•
to. $5000 for 2 years an 8 n on s n r '''' "'"' P"'' """"'"•
11. $4600 for 3 Jears an 6 n on Is a 8 f.!r ?'".' ^'' ''^""""'•
12. $6200 for 4 years and 2 monS a^t^ ? ^ ^ j^ ---•
EXEIICISE 13.
irewood honght for
7 Z'!^,f r!!!';?;!'" °" ^ ^"«"tity of
$3 17 and sold for .^i
ufl ?
2. What is my loss
for $2975 ?
on a house bought for $3460, and
sold
180
ANSWERS TO THE EXERCISES.
b
If ■
I
lb., wha7?,',he "o'fr" °°" *"*•"> """ '■ ""i " IS '='">■» l»r
cw^a„'J'S!a':.7,SVr^;v'.r'- »'-''«■' '-""at »^'P»
ANSWERS TO THE EXERCISES.
NOTATION ANMLMERATION.
Exercise 1.
^ndIST-\]Z'lunt^^^^^^^^^ '^0 hundred
fiily; nine Sred and h ^ ' ""^^"''^"^ ' '"^«° ^""dred and
dred and five tJi.rty-two ; seven thousand six hun-
twlntHlve'Z:LVd"si^hS = f'" ^5°"^°"^ one hundred;
thousand anS £ h^dS an^J wl>ThouSd'""'^^^
twcnSl^e^e^Soi^Tnd'rfv^'l ^'— t^^'undred ;
seven thousand Z hnrli^iJ'^^f = 'I^ ^"*^''«'^ ™"»io»s
hundred and SftJ <,Tfhn?, ,^ ^"'^ twenty-three millions four
ought at f 9.20 per
its bought for $39,
cost 70 cents por
lid at 18 cents i)er
PI 20 and sold at
lo?
Its por gallon and
)n the whole ?
01. r which I pup.
r barrel ?
nought at $21 per
J them at $4.45
ib. and sold at
5ES.
IN.
; two hundred
n hundred and
ousand six hun-
id one hundred ;
; two hundred
lousand.
two hundred ;
indred millions
ee millions four
.nd eighty-nine,
d thousand and
three hundred
hundred and
undred trillions
d and four,
ns six billions
billions seven
id and one.
three millions
s two thousand
ANHWRRs to the EXERf1fHK.S.
131
^iv inMui?. ' ""."1"",'''" ''""'"'•t'd and fonrtoon rjiiadrillion^
•SIX hundvd and .MKlity-liin'o tnliions llvo Ini.idn-d and tu iiv-
nine In hons o„H hundred and twenly-tl.r ^ . II Irs ur
hundred and lilty-six ll.ousnnd^ven hundred and fo.^ly-iwo.
COMMON NOTATION.
4 Five thousand and twelve millions tlir-sn hundred thousand
Sliliiolill'JjHrilevr"" """'"••"* """ '-"--"^ ^"- '-":^"'
0. Two billicms six hundred thousand nine huiidrefl /inrl
s«^venty millions four luiiidred thousand ; nine "nm ' h lioni
aml^l'iu- ""' """ '''''' ^'""^""•' '"'"'"- -v-'" 'y 'l.ouiand
G Seventy thousand four hundred billions six thoiisnini nnrl
fli.rty millions two Ihousaiul ; live hundn.l u I ' tvon
. bix thousand and nine billions I'.iir Ihousand ami three
u;orur;'r;rr.;r;'' "^^ • ^^° '"-"-"'^ -^ ^^^^^i^^
l7rZ^ «"« hundred ami twenty-lhren million four hunS
and lifly-six thousand seven hundred and forty-two. ""'^^'^
KXEUCISK 2.
1. 74.
2. 200.
3. 709.
4. 2007.
5. 4002.
6. 1809.
7. 3006.
8,
9000.
I,"i
9.
5702.
10
10.
I.V2;i0.
17
11.
.11)074.
IS
12.
00i009.
l<l
13
14.
7020908.
2U4705792.
20
97000000034.
2000000079.
40004000 'i004.
1 00 1 CO 1 00 10.
24000007000090.
365247039073094.
E\EnniSE 3.
im, \mm'''' '''''' ""«'' ^'■^■'^7- 'ooiboo.'VoooViio?;
E.NERCISE 4.
LXXIV, XLVII, XGt, LXXXIII, CIV, DGXGII DLXXIII,
DCCCXGVf , CCGLXV, CXLIV. VCCLXX, TX^DCL, VlTCDVIII.'
IXV, MMDLX, XDGCXXIV, XllXDGL, LLXx!
LXXVMMMCMLXIV, "XLMMDGGLXIir, LXXXMDCCXCVI,
DG GCMMDGG LXIV, Cl)!.MMM, DGGXGMMDGGC, MDCGMMd'
MMMDCGXLMMDLXVIII.
132
ANSWEttS TO THE EXERCISES.
SIMPLE ADDITION.
1. 21457.
2. 14087.
3. 150452.
4. 1535072.
5. 13007874.
6. 43684 pounds.
7. 4677 tons.
8. 3997 yards.
0> 34681 bushels.
10.
11.
12.
13.
14.
15.
16.
17.
18.
104275 inches.
10819 days
13449 miles.
135743 feet.
28998 lbs.
17255 lbs.
544895.
1697762131.
12668043.
19. 17519901.
20. 25300
21. 112980.
22. 43027.
23. 941494.
24. 48970000,
25. $519.
26. 3718 bushels.
27. 321 miles.
1.240413 miles.
2. 56484652inche3.
3. 6163562 tons.
4. 5610472 yards.
5. 488482 pounds.
6. 6640935 dollars.
7. 2298474 hours
8. 30579544 feet.
9. 1239300.
10. 7128908.
11.6650983.
12. 59499717.
13. 4153079.
SIMPLE SUBTRACTION.
14. 4803944
15. 2879624.
16. 81877787.
17.87106653.
18. 1330154.
19. 6504490.
20. 19521178
21.6760083.
22. 6999995.
23. 399206 pds.
24. 4993 days.
25. 7968793.
26. 554 dollars.
27. 2560 miles.
28. / 375,332,259,238,225,
29.i9ffir'^^^--
30. 1 1700000 sq. miles.
Jl. 554 bushels.
32. 3978 dollars.
33. 5692 feet.
34. 368 feet.
35. 3472; 3 172 miles.
36. 94763000 miles
1. 153890 miles.
2. 220944 yards.
3. 3851388 pounds.
4. 4158475 inches.
5 4761744 pounds.
6. 943992 dollars.
7. 3788656 minutes
1. 467964.
2. 883680.
SIMPLE MULTIPLICATION.
Exercise 1.
4. 30660.
8. 6248457 cents
9. 15'>68.
10. 18957
11. 22428.
12. 36640.
13. 477648.
14 175021.
Exercise 2.
( 5. 193536.
6. 30996.
7. 1323125.
8. 2436368.
15.
16.
17.
18.
19.
20.
135312.
293328.
326490.
861245.
384852.
481194.
9. 4452800.
11.36728000.
12. 20699184.
13. 1481
14. 180;
15. 6505
16. 1891
17. lUl
18. 3783
19. 1201
20. 5245:
21. 5183i
22. 19751
23. 1044e
1. 1875
2. 2454
3. 2351
4. 2469
6. i057(
6. 1989/
7. 2777;
8. 802U
1. 41093
2. 15628
3. 98693
4. 94774
6. 4445 f>
6. 44762,
1. 267fft,
2. 26421^
3. 106.S45
4. I5200f
6. 6980H
6. 2368«%
7. 4404ff
8. o063f^.
9. 6413§|;
10. 4l325i-J
11. 15358gJj
12. 4285||.
13. 7230t#^
14. 864,9jf.'
15. 13661 Ai
16. 16965|1
mmmMmt.
17519901.
25300.
112980
43027.
541494
i8970000,
5519.
i7 18 bushels.
!21 miles.
lars.
lies.
J2,259,238,225,
)4,55 years.
Osq.
hels.
liars,
t.
miles.
72 miles.
) miles.
312.
328.
490.
245.
852.
194.
00.
Ml.
)00.
184.
:3. 1481088.
14. 18011160.
15. 650596380
16. 189109960.
17. 14474832.
18. 378316400.
19. 1201371300.
20. 52452353748
21. 518350564160
22. 197515403720.'
23. 104462820108
1. 187532.
2. 245427.
3. 23515761.
4. 246913574.
5- 1057097S.
6. 1989544.
7. 277777f.
8. 802l81f.
1- 41093-ff
2. 156283V
3. 98593^.
4. 94774||.
6. 4445 f4-.
6. 44762|f.
AN8VERS TO THE EXBRcrSEs.
1. 267ff,
2. 264'2Xf
3. 106.34ff.
4. I5200ff.
6- 6980H.
6. 2368g%.
7. 4404ff.
8. o063f^.
9. 6413f|,
, 10. 41325+1
11. 153585V.
I 12. 42851^.
13. 7230x|x.
14. 864M.^
15. 13661 AJl.
16. I5965f|l.
17
18,
19.
20.
21.
22.
23.
24.
25.
28.
27.
28-
29.
30.
31.
32.
1866560000.
5. 67756662
5. 6448458108
^ 729668016 '
'■ 30267798624.
•• 8054092548
• 14117835000
• 6701431839424
. 10114033944. '
. 179603438052
■ 546199612851.'
simple~dFvision
ExERcrsE 1
9. 631272A..
10. lOlOIOlOA
11. 44166844.
12. 2495802
13. 2851791.
14- 91l78f
15. 2742234.
16. 123447^.
Exercise 2
r. 50340Tf^.'
8. 222051 A.
9. 16033311.
10. 1176200M
11. 39291-,t6p
133
I 35. 220133376
I 36. 25106806690.
37. 530334468132
It- i?1^^344006640.
39. 21424 feet
40. 20601 yards.
41. I903S74 letters
42. 21038400 m r
43. 56940 timS
44. 9709 dollars.
^5. 168 panes.
I''. 16072442.
18. 310489A-.
19. 1 740842 &
20. I22II62I.
21. 1341038?.
22. 792696*.
23. 1208159?.
24. 708053|.
Exercise 3.
12. 403003 4A
13. 87660511'*
14. 284314^5
15. 641986*1''*
16. 997852;v;
3343,^,fly.
134205^V
27063im.
78l00fS|3.
1255096|||.
457378m||.
1830087|||.
3756623^ff.
148882ff*f.
i282'^Tf4m.
467928fJ|:
228l830j^..
36. 671369?||T
37. 324444^11.
38. 278891 fllei
40. 15454|-f.
41. 3 apples.'
42. 91 ff
43. I65f|.
44. 225 miles.
ii- 25||^{f '^««"«-
47. 89758,342#e^
48. I3428429?}||^5j.
I
}■
134
ANSWERS TO niE EXERCISES.
REDUCTION.
1. 700 cents.
2. 9400 cents.
3. 1900 cents.
4. 92424 ceiits,
1. $?3.90.
2. $70,82J
3. $803.7()§
4. $599. 29, V
1. £18: 12: 9^
2. £185 : 14: 6.
3. £246 : 18 : 3.
4. £436 : il : 2i
6. £189 : 11 : 0^
Exercise I.
5. 964258 cents.
6. 4296537 cents.
7. 94275 cents.
EXEftCISE 2.
?1025.93|.
«975.90g.
$3057.72-,V.
$1579.33|.
Exercise 3.
8. $704.28
9 $4950.64,
10. $286.05.
9.
10.
11.
$307.68J
$731,274
$3305.98
12. $992.96i
5-
19: 7- f.
lOA.
1. 4312pen6e.
2. 123583 farthings.
3. 713221 farthing.".
1. 18800 quarters. 4.
2. 45650 jioonds. 5.
3. 556739 ounces. 6.
1. 5760 dwts.
2. 99916 grains.
1. 3744 scruples.
2. 90057 grains.
f. 7140 lines.
2. 8094 inches.
3. 2437 perches.
4. 125070439 inches.
i. 1248 nails.
2. 315 nails.
3. 214 yds 1 qr 1 nl.
1510s: Hd.
£76979 ; J
6. £2339
7. £1316: 2
8. £69 : 18 :
h 9. £198 : 12
— f . ' 10. £435 : 14 ;
Exercise 4.
4. 1041178 far.
5. £39S : 8.
6. £1559: 10 : 5.
Exercise 5.
341172 ounces. 7.
12 tons 1 cwl. 8
700 cwt. 4 lbs.
Exercise 6
I 3. 7 oz
I 4. 1 lb,
Exercise 7.
3. 1368 lbs 11 oz6drs 1 scru.
4. 1269 lbs 6 oz 5 drs i scru 8 grs.j
Exercise 8.
5. 11347 fur 20 per 5 yds.
6. 1534 m 30 per.
7.21yds I ft 3 in 11 lines.
8. 38 lea 2n] 1 fur 1 1 per I fl 6in.j
Exercise 9.
4. 463 Eng ells 3 qrs 2 nls,
5. 374 Eng ells 2 qrs.
6. 410 Eng ells 2 qrs.
8 : 2,1.
51 qrs 7 lbs 4 oz.
21t[9cwtlllbslOoz.
15 dwts. 22 grs.
3 oz. 8 dwts. 17 grs,
ANSWERS TO THE EXEECI8E8.
135
7. 1510s: Ud.
i. £76979 : JS : 2.L
1 qrs 7 lbs 4 oz.
lU9cwtmbsl0oz.
dwts. 22 grs.
)z. 8 dwts. 17 grs,
')7. 6 drs 1 scru.
! 5 drs 1 scru 8 grs.
Exercise 10.
1. 9801 sq feet. •? «„ oo 4-* j , ^
2. m43&3 s, inches | t l[ ?, ^ '///sV^S?!'"-
liXERCISE II.
I 3. 790 bar 3 gals 1 qt 1 gll!.
' 4. 27 pipes 27 gals 1 qt Ipt.
Exercise 12.
I 3. 8 days 14 h 21 min 53 iec.
I 4. 69wks3d2h42minl4sec.
Exercise 13.
17. 1150 nails.
216 pints.
59039 gills.
1. 2928 hours.
2. 151 11286 seconds.
1. 720427 cents.
2. 17642.85.
3. $2899.9IJ.
4. £991 .•8: UJ^f
5. 379037 farthings.
6. £829: 12:2f.
7. 3967451 drams.
8. 2170 t. 2cwt. 3 qrs 2 lbs
12 oz. 7 drs.
9- 5629 grains.
0. 6 lbs. 5 oz 5 dwts 16 grs,
11. 2255 scruples.
12. 256 lbs. 9 oz. 6 drs.
121968 feet.
5412 lea 1 m 3 fur 32 per
^4 yds 1 ft 3 in 1 1.
255171871 sq inches.
,^J^ 'per 16 yds 4 ft
101 in.
13
14
15,
16.
19. 39644 gills.
20. 2287 gals 1 qt.
21. 277740 minutes.
22. 203 weeks 3 days 3 h 20
min 7 sec,
23. 290.
24. 710.
25. 36 English ells,
26. 120 yards.
56| Flemish ells.
74o.
102 two pences,
361 five pences,
54 four pence?,
32 packages.
27
28.
29.
30.
31.
32.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
II.
12.
13.
COMPOUND
$27833.89.
Jei3l08:19:2j
104 miles 3 fur 20 per 4*
yds 2 ft, f 2
$38409.96.
Jei0140:5; lU
$28375. 96J.
107 tons 2 qrs 24 lbs 6 oz
9 drs.
154 wks 2 d 23 h7mirx
12 soc.
12 1 acres lr8 per 24 J yds.
292 lbs 7 oz 4 grs
$38121.82.
ADDITION.
-14. 251 ydslqr2nl3.
15. £3619 : 1 : 4
16. $9388.82^.
17. 185 gals. 1 pint,
18. 91 lbs4oz 14 dwts 1 gr.
19. 3751 cwt3qrs4 lbs.
20. 339 miles 6 fur 38 per li
yds.
21. 409 acres 3 r 25 per
22. $42174.44.
23. 539 yds 1 ft 6 in 9 lines.
^1. 006 day3 15 h 40 min
25 sec.
^,^- ?28 gals I qt I pt 3 gills.
M. 172tonsl8cwt Iqrnibs.
136
ANSWERS TO THE EXERCISES.
COMPOUND SUBTRACTION.
1. $6635,76.
2. i;679 : 8 : 9J
5. 7 tons 6 cwt 3 qrs 5 lbs.
6. 4.iweeks6d5min36sec
o 1^*^^ 3qrs3n]s.
8. $18094.63.
9- £167:2: ll|
10. $8888.89
11. 56 gals 3 qts 1 giu.
1/. 437 miles 4 far 39
jds 1 ft
per 5
4. 120 tons 1 5 c^t 3 3
15. 6 lbs 9 oz 6 grs
16. $87654.78.
I». ilO tons 12 cwt 1 or 4 lbs
6 02 9 drs.
888 acres 10 per 12 mU
2 ft 16 in. '
4hhlds 10 gals Ipint.
11 min 10 sec.
1" 17" 30'ii
19.
20.
21.
22.
COMPOUND MULTIPLICATION.
Exercise 1.
o" «n<?,^* ^ ^""s 9 lbs 10 oz.
2. £884 : 13 : 5i-.
3. $318593.56.
4. 137 miles 2 fur J7per 1*
yds. '^ ^
5. 341 gals. 1 qt.
10. $4059941.93.
11. 286 weeks 6 d 12 h 5 min
24 sec. I
12.
13.
'J03'=w»3qrs241bsllo2.
82 lbs 7 oz 2 drs : sen,
y grs.
$771424605.52
1285 yds 3 qrs 2 nls.
09 tons 8 cwt 3 qrs 1 7 lbs.
--■ J373 gals 2 qts 3 gills
19. $35894634.16
20. 27 cwt 2 lbs 12 oz 10 drs.
14.
16.
17.
18.
Exercise
12
1. $10349899.84.
2. £13450: 19 : 8i.
3. $6305055.52.
4. 1348 cwt 14 lbs6oz.
5. 1 134 acres 1 r 37 per 25J
yds. *
6. 774 yds 1 qr 2 nls.
7. 613 weeks 5 d 18 h 57 min
32 sec.
8. 299 lbs 1 1 oz 4 drs
9. 198 lea 2 ra I fur 33 per
1 Yd.
10. $80156133.36.
U. £11108: 14:2.
13,
14.
15.
16.
17.
18.
19.
20.
21.
264 tons 19 cwt lib 13 OZ
6 drs.
1567 gallons.
$247390923.84
1531wks.20h40min.48s.
124 yds 1 ft 5 in 3 lines.
18^0 acres 3 r 27 per 2IJ
yds. *
$44014061.28.
398 lbs 3 oz 1 dr 1 scr 19
grs.
1763 cwt 2 qrs 12 lbs 14oz
5615 acres 38 per 3^ yds
$1162491454,80; ^
14.
15.
iCISES.
TION.
3res 26 per 4 ft 127 in
.onsl5cwt3qrs3 1b^
9 oz 6 grs.
54.78.
Js 2 ft 11 in 11 linn,
ons 12cwt 1 qr4 1bs
: 9 drs.
teres 10 per 12 v. Is
16 in.
ds 10 gals Ipint.
10 sec.
' 30'ii
noN.
!vf3qrs24Ibsllo2
7 oz 2 drs 2 scru
4605.52.
■res 3 r 29 per 13J
Is 3 qrs 2 nls.
3 8cwt3qrsI71bs
tls 2 qts 3 gills.
j34.16.
2 lbs 12 oz 10 drs.
5 19cwt 1 lb 13 02
Ions.
?23.84.
i-20h40inin.48s.
3 t ft 5 in 3 lines.
es 3 r 27per 21J
11.28.
oz 1 dr 1 scr 19
2ffrsl2lbsl4oz.
'3 38 per 3i yds.
i54.80!
ANSWERS TO THE EXERCISES.
23,
24.
25.
26.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
12152 gallons.
1173 bushels 2 pks 1 ga
2 qts 1 pt.
27603 weeks 2 d 9 h 52 min
1911 yds 1 qr.
27.
28.
29.
30.
. $58939941.06.
. .£23484 : 6 : 4*.
. $835454.70.
5984 cwt 1 qr 10 lbs 7 oz
9S2 lea 2 m 6 fur 22 per
n yds. ^
3261 yds 1 qr2nls.
1353 lbs 3 oz 6 drs 2 scr
10828 acres 3 r 29 per lU
yds.
$1887652.80.
10834 lbs 6 oz 1 dwl 7 grs
1898 tons 10 cwt 10 lbs.
2970 weeks 4 d 4 h 36 min
£232442: 15:3.
26541 gals 1 qt 1 gill.
2897 bush 1 gal 2 qts.
6610 per 2 yds 6 in 4 lines.
Exercise 3
137
1733 acres 1 r 15 per 17*
yds 1 ft. f *
$878595.48.
23578 bush I gal.
9923 cwt 9 lbs 1 oz.
17,
18.
19.
20.
21.
22.
23.
24
25.
26.
27.
28.
29.
30.
470 cwt 3 qrs 1 1 lbs 13 oz.
$580900.92:
2732 acres 1 r8per2f yds.
5 1 80 days 8 h 56 min 3 sec.
424 miles 5 fur 10 per 4
yds 2 ft. ^
£>^4264 : 10:6.
6894 yds 3 nls.
130l9 1bs9oz8dwts.
$465206.68,
9377 cwt 3 qrs lbs.
7373 gals 2 qts 1 pt.
34G8 bushels.
3797 wks 1 day 23 h
min 49 sec.
657 cwt 1 qr 8 lbs 2
12 drs.
40
oz
1.
2.
3.
4.
5.
6.
7.
$3698437.26^.
£321:2:51-.
1 ton 18 cwt 10 lbs 10 oz
13 gals 3 qts If gills.
15 acres 1 r 4 per 29 yds
6 ft 30 in.
113 yds. I qr 2|- nls.
1 lea 2 m I fur 39 per 3
yds 1 ft 3 in 9 lines. i
8. $105208.25.
9. 73 cwt 1 qr 21 lbs 7 oz
12 drs.
10. 3 per I yd 2 ft lO.in li line
11. 61 gals 1 pt 3 ,a; gill's^
33 bush 1 pk 1 gal 3 qts
I pt 2 gilis.
£530 : : i i J _ 5.
67 yds 2 qrs 2f nls.
13 acres 2 r 10 per 10 yds
6ftl43?Jin.
COMPOUND DIVISION.
Exercise 1.
1 scr. 18ji.
12,
13.
14.
15.
16. 2 lbs 5 oz 2 drs
qrs.
17. 3 cwt 3 qrs 20 lbs 4 oz.
18. 2 lbs 4 oz8dwts24Hgrs
'9. .$496744 84. " '
2 wks 3d 18 h 47 min
28i sec.
6 gals I qt lJ.i4 gills.
£4: 10:3^-1-' 120.
23. 4bush3pks3qtslA8gpt.
24. 25 cwt 3 qrs 4 lbs' 12 oz
14 drs.
1 mile 1 fur 32 perl MJ ft
2 Eng ells 2 qrs 3 nls.
$14506.23.
3 acres I r 32 per 2! yi?-.
20.
21.
22.
25.
26.
27.
28.
29.
30.
6 days 8 h 14" rain 57 si^
— 432 rem.
1 qr5 1bs 14 oz 12fff drs.
138
ANSWERS TO THE? EXERCISES.
1.
2.
3.
4
5.
6.
7.
8.
9.
10.
$56896.05.
^25 : 4 : Syy.
49 cwt 2 qrs 9 lbs 7 oz.
llgalsSqtsIptl^^gillg.
f.'n'les 3 fur 2 per 5 yds.
5 week^s 5 d 6 h 10 mi„
10 lbs 4 oz 1 scr 33? grs
1.
2.
3.
4.
5.
30 suits.
40 dozen.
5068-1^ times.
13 persons.
KXERCISE 2.
^'•%™'"l%3/ur36per2ycis
12. £34 : 3 : 8 U-
13. 3gal3 2qts%5f,gills.
14. 3 acres 3 r 26 per 4 Yds 3 ft
71 in.
15. 10 tons 7 cwt 2 qrs 9 oz
8 drs.
16. 11 cents.
17. $856.4298
18. Gift cents.
19. $2.64.
20. 21,43<Vcents.
EXEKCISE 3.
12. 37 ounces.
13. 8 boards.
14. 15840 steps.
15. ll^^cwt.
16. nm yds.
£268
£79:
£18:
£60:
: 2 : 5f - |.
7:1. ^
11:3.
13 10-1.
6. 13|| spoons.
7. 21^ lbs.
8. 5 stoves.
9. 29 parcels.
10. 976 ducats.
11. 67ff^cwt.
Exercise 4,
5. £10
6.
7.
8.
7 •■ 7i - H-
Jei7: 16:10*-rM
£9:8: Oi J i8s^^*
£0:6:7
1. 7396842 cents
2. $816007.03.
3. $7982.98.
4. 625.35.
5. $345392.20.
6. $390.56,8,.
7. $45.35Ma.
8. 35939 lbs.
9. 140 tons 2
4 drs.
MISCELLANEOUS QUESTIONS.
qrs 1 lb 14 oz
10
II.
12.
13.
14.
15.
16.
17.
18.
88 lbs 6 oz 4 drs 5 grs.
1= S^t I qr 19 lbs 9 oz
15 drs.
£9167 : 12 : 9.
9021 yds 3 qrs.
84 miles 7 fur 20 per 4 yds.
13 cwt 4 lbs 11 oz 74^ drs.
|2'9liVo^9'^-tsl8gr,.
Jei836:ll:3.
5.
39.
10.
SIMPLE PBOPORTION.
Exercise 1.
9. I 7. 38.
15
lOf.
8. 70f
9. 17.
10. 56.
11. 6.
12. 360.
!I8ES,
s 3 fur 36 per 2 yds
AV, in.
8 s^.
''^,^'sV'?f« gills.
3 r 26 per 4 yds 3 ft
3 7 cwt 2 qrs 9 oz.
nts.
ents.
2. 37 ounces.
3. 8 boards.
4. 15840 steps.
5- Hi^cwt.
6- i^m yds.
:10J-M.
;* - -If?
NS.
oz 4 drs 5 grs.
1 qr 19 lbs 9 02
2 : 9.
3 qrs.
7 fur 20 per 4 yds.
lbs 1 1 oz 74^ drs.
: 9 dwts 18 grs.
1:3.
10.
5fi.
11.
6.
12.
360.
ANSWERS TO THE EXERCISES. I39
I.
2.
3.
$21.50.
$3G. ^^
v.n-
EXEHCISK 2.
243 gals 2 qts 1 nt
0. 421.74 |i^. ^ ■
7. 693 miles 2 fur 10 ner
8. f 278.3;Hf
9. 277 cwr 1 qr 13 lbs lO oz
10. 91 men.
11. $283.92 A.
12. $988.!)3
13. $14.06.
14. £21 :2:9
15 $468,094.3
16. $58.33i '■
17. $50.37.
18. 284 8 miles.
19. $7 1. 38 A.
20. 180 gals 2 qts.
21. $383.76.
22. $892. 18A.
23. $1.02.
24. 196 feet 9 in."
25. 66 men.
26. $7032.545!,,-.
"• oL^I^^'^s 3 days, nearly.
oof days.
n weeks 3 A day^
$140,561 ' ^
£ti: 16:0^.
$216 39.
124.86.,^.
h\h tiays.
60 conty.
'47 bands.
37. $7.0JfV.
38. £25: 11 -. ^,
\ 39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52
£31 :3:6.
55 yds 2 (jrs 3 nis.
61 cwt 2 qrs 15 lbs.
$509.91-,2i^;V-
27 gals 1 pt I gill.
$116.73.
$1-25 55.
204 bushels.
$51. 58^^.
82^ cents.
1 9^ f cents.
28.
29.
30.
31.
32.
33.
34.
I 35.
36.
£90: 12 \i.
103 feet 5 in 10 lines.
- $6.30.
53. 499J miles.
54. 2643f miles.
55. $I2.15W.
56. $40.72.
57. $1.10.
58 $2.02^].
59. II days 9=// hours.
60. $193.60.
61. $33.58.
62. $744.92*8.
63. 33„V. cents.
64. 286.5^.
65. 10.^^, days.
66. $443,484.
67. $83.32.
$443.58.
$1.76.
321 men.
34 days.
70 cwt 2 qrs 155 lbs.
73. 28-1 days. ^
74. $92.9 If
75. $I4.94|.
68.
69.
70.
71.
72.
1. 120 acres.
2. $24.40
3. 4662 bushels.
4. $76.85.
5. 144 foet 3 -flinches.
COxMPOUND PHOPOirnON.
6. $.30.16,
7. 33 (lays.
8. $1098.50.
9. 85 men.
to. 339 miles
a
fur.
;l
140
ANSWERS TO THE EXERCTSES.
11. $l92.S8f.
12. 104 cwt I7A-
13. «IG40.3,'Ji
l^i. 50Af (lays.
15. IGjfi^ days.
i5- Ih'h ^ays.
17. $1004.
18. 10 men.
lbs.
!'•>. 72 acres 3 r 13.^ per.
20. 3p (Liys.
21. $il3.G!i.
22. $129.81.
23. 11,1. days.
24. 33 men.
25. $18.37.
1.
2.
GREAT EST COMMON MEASURE.
1.
2.
3.
5.
3.
4.
5.
4.
5.
7.
8.
2.
2.
10.
It.
5
2
4.
6.
9.
9.
93.
12.
12
6.
6.
LEAST COMMON MULTIPLE.
I"'
1. 315.
2. 120.
3. 10098.
4. 720.
5. 15120.
6. 795G.
7. 2520.
8. 120.
9. 240.
10. 4788.
11. 11592.
12. 2520.
"VULGAR FRACTIONS.
ExEnciSE 1.
13.692408G4.
14. 128707425.
15. 536130.
16. 10228140.
1. 1
2. f,.
4
5
6.
-4''4^H=^.
Jfifi.
»1 9-
7. ,^.
9. -,',.
10. f
11- ffff.
12. -.Ws^,.
E.XEIICISE 2.
1. 138f
2. 1.
3. 86.
4
5.
6.
105 ,¥3.
8. I0Jf^3.
9. 408'^^.
10. 6944X
11. 8610'^o,
12. 6734.
1- ^^^.
3. ^^^^±.
4.
5.
6.
EXERC
''mi"-.
ISE 3.
7- '^f?^. 10. ^oj)\D-,i
9. ^fj-^. 12. fy.a.
ExEncisE 4.
3. 9\V
4.
5.
6. ■
7- af^-
9. 238,.
10. ,\%%:
11- 14xV
12. « '
10.
II.
12.
1- A.
2. 22J
3. /,.
1.
2.
3.
4.
6.
7TT "
196.^,
1.
2.
■6^0.
1. 2 qrs 1
2. 1 peck
3. 2 roodf
ANSWERS TO THE EXKRrrsES.
Exercise 5,
141
2 .TO 40^ « J8
■ m, 00, m, m:
2 ilWt _216(^ ma ^)0 2268
2,'320, 2520, 2520; Zm, 'mF
^ 10020 IlOll 11088 11 15 J
12012, 12012, 1201;> 12012;
'''^■^^ jW5r> 5010 a5(!l 748()
4.
0.
71120, 7020; "7020, 70;X)7 "7020:
288 189 221 432 HUti
.»(, 504, 50i; "504, 5047
10.
11.
12.
g 48195 138«0 KW-'JO 15708 32725
■ 08905; 58905," 58905; ,580()5, 5,S905;
7 .2;Wi2i. 57120_ H922(J_ 2;>5.%0 2154S0
271320, 271320, 271320, "2713207 "271320"
g iT2S_ 3m_ 2m _832
561{i, oOUi, 5616; "Soia
9. J^Jl'L J*J"8« 1«89.>5 42H208 30J212
705132, 705132," 705-132,' "7051327 ikiSir
J01680_ jmn_ 12582!} 100440
343170, 343170, 34;n76, inSlTOT
_2717 J'04_ Ji688^ 5824 2816
915^ 9152, 9152, 915^ "9152;
5W76 18734 42891 32;>38 43848
53244, 53214, 53244, 532i:j; 53214:
Exercise 6.
1.
2.
3.
22i.
4.
5.
6.
1. Mf of a pound.
2- 4 iir of a quarter.
^- rs^TTTT of a (lay.
4. 1 96 j\ perches.
5- H of an hour.
Exercise 7.
6. 82^ lines.
10. 1-,^.
11- iH.
12. «^A.
1.
2. K
■Ns'
Exercise 8.
5-/0 T of an acre.
HI Eng ells.
11.4gil]s.
of a ton.
o -l■J■7-
3 3 .' s u u
ExEiicisH n.
!?• ^'^•
5^d.
1- 2qrs 12 lbs 8 02.
.2- I peck 1 gal 1 qt H pt.
o. ^ roods.
4.
.5,
G.
2.^ : 4|d - ^.
1 fur 16jB^ per.
1 ft Sin 7g^ lines.
142
AN8WEU8 TO THE EXERCISES.
7. 8oz 3dr8 12
8. 'J l)U8h«lH.
y. 1 bush 3 pkH
10. 34 gal8 1 qt 1
1- lm^
2. 2H.
3. 4.^%..
5. 1,1/^.
6. 23VA.
7. un-
4- I-xW/«.
1. If.
2. A.
3. 1^
4- 71M-
5. 38^f.
6. 79|J.
7.4.
1. 1*.
2. 1,^4.
3. -HI.
4- m-
6. 2Jf.
7. *i.
grs.
3,/^- qts
pt3/„- gills.
11. 10 miles I fur It-A per
12. 2 acres Ir 30fg^ per.
13. 3 qra 18 lbs.
I 14. 6 hours 59 min 66 sec.
rXEHOISE 10.
8.
9.
10.
11.
12.
13.
14.
II,
6.
7.
8.
8
9,
10
11.
12.
13.
14.
8.
9.
10.
11.
12.
13.
14.
mm-
46,W4
309,aVi^.
. 6H.
Exercise
, I. iff.
26./aS-.
EXEUGISE 12.
.6
4 B'
-A.
• mi
■ m.
E.\i:ncrsE 13.
17^.
7J.i
Hh
6,V.
15.
16.
17.
18.
19.
20.
9.
ir.
11.
12.
15.
16.
17.
18
19.
20.
17^.
mi
13 uVo^Va'l •
mm-
15. ^m-
16. ^.
18. Hm-
19- 2m.
20. 1,
1.
2.
3
4.
5.
DECIMAL FRACTIONS.
Exercise I,
Thirty-six, hundrerltlis.
Sixty-four, thousandths.
Two hundred and seven, thousandtli')
Six hundred and fltly-two, thousandths.
Sevonty-lwo, hundred lliousandths
6. Thirty-four, and live hundred and six, thousandths.
RorsEs.
nilea 1 fiir IJ-jS^ per.
3re8 Ir 30 fg^ per.
'8 18 lbs.
3ur8 59 mill 56 sec.
ANSWteRS TO THE EXEUCISES.
143
15
• mh
J()
17, V
17
• im-
18
'tAWift.
19
mk-
20
■AWAWu
9.
mih
10.
3.W6-
11.
i^h-
12.
mm-
15.
983^.V
IG.
m-
17.
^iUh
18
5M.
19.
-^A
20.
iHU'
15.
^m-
16.
u-
17.
2/6¥a.
IS.
Hm-
19.
nn-
20.
1.AV,.
5.
12' Six"ll,m,'r'l'l"' "'i'' '"■'■"ly-r""'-. Inuirli-eJ t,illi„„U,s
E.\EIICISE 2.
I.
2.
3.
4.
5.
1.
2.
3.
•016.
•OiJHO.
•000640.
•84000000700
•00000000350G.
30-9272.
IGI-13839.
II3-5.'i,)|
1.
2.
3.
4.
1.
2.
3.
460G51G.
1-267.
18-80I4G.
•40366.
4-6855.
•IIO'i.
■18468,
•477862.
6-3583.
1. 18-7.
2. 9-765625.
3. 364-285.
4. 5-G058345 +
5. 1.;'4.
6. 79-2-6.
1.
2.
•375.
■040875.
thousandths.
3. •183.
4. •2.
5. •69583.
•000408.
•000000 1 07G00.
•00001)96000.
•000000-20064,
•00702.
6.
7.
8.
9.
10.
E.XEHCISE 3.
5. 487.7719.
6. 1)6.6120199.
7. 284-954336.
8. 835-75511.
ExKncisE 4.
5.
6.
7.
155-307.
5-0G73.
10-94814.
E.XERCISE 5.
46-0842.
186-3648.
■4896.
•0-2548.
Exehcise 0.
7. 7'608524-t-
8. 97-5.
359-2.
8.
9.
10.
■92822>
•62G8858.
2'18076.
5.
6.
7.
8.
9.
10.
11
9.
lu.
11.
12.
12.
13.
14.
15.
16.
23-226.
994-34396 +
Exercise 7.
6. -009765625
7. -9.
8. •0-227.
9. 6 2617058.
10. 35'6883li.
•6426.
•3933.
•262G32.
3-02778.
3 -.56 7.
234-5.
2-2119032 +
2-1896482 -f
1 32- 10759.
I' I
144
11. -Tl
12. -5625.
ANHWfiRS TO THE JiXEllOtStH.
13. 1623076.
1. #.
2. U-
3- xHs-
6. i.
7. 8J.
H. -6 1 2244897959.
15. 134-226337448.
10 ■003O2305O76'2nG07.
ExKnf;i8K 8,
8. Ul
12. 9 ,?^:
j3- m.
EXKHCISK 9.
IS. fill.
16- iifiJi.
'7. iUH-
19. 6H.
20. 21^|f J.
1. -58,
»
2. •32979452054.
3. 034375.
4. -5.
5. -847918.
6. -21875.
7. -0703125.
8. -0246527.
9. -2225.
10. -6875.
11. -594948 +
12. -7808984375.
13. 031521739,
14. -0365.
15. -361445783.
Exercise 10.
1.
2.
3.
4.
5.
Iqr 18 lbs 2 02 6 4 drams.
39 minutes 27-36 soc
25 P''- 1 yd 1 ft 1 1 in 2-8992 lines.
3 lbs 6 oz 6 dwts 17-28 grs.
14s Ij d.
6. 7 sq perches.
7. 1-1136 quarts.
2 yds 3 qrs 2 nis.
2 roods 18 per 2 yds 3 a 112.32 in.
41bs. 8oz 1-6128 drs.
1-8176 gills.
12. 5lur39per3yds2ft2 64in.
13. I qr 1 lb 12 oz 12-8 drs
14. 8 sq ft 35-5248 sq inches.
15. 3-1 quarts.
8.
9.
10.
11.
16.
7cwt 3
yr:
ib
'S o OZ.
ctatti.
4i8079r)9.
26337448.
530507620007.
15- m-
>6- mi-
18. m-
19. 6^4.
20. 2I*|?J.
ANSWERS TO TIIK RXEllCISES.
145
14375.
1739.
783.
PROPORTION OF FRACTKJNS.
'• 'if Jays.
2. $16.3342.
4 $20.I9».
6- SlOgJ.
1. 2.
2. $118.67i.
7. 35-79018gaIIon8.
8. $1 17-5622807.
9. 48-I7C516 1b8.
10. $2 r)69896907.
H. $34,375.
12. $105-2350877.
MISCELLANEOUS.
3
4.
6.
6.
7.
mi
$387,701.
1008.
8. 12736 ounces.
9. 185748 inches.
10. 2 roods 29 f^q per 4 sq yds
3 so ft 1.34 sq in.
11. 2 1b8 7oz 1 dr 1 8cr4ers.
12. 143 19 ounces. j
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
138 Tf r.
11-432389937.
$167.83.
100-27754.
6-1187.
•704352.
$321.56^+,
6 fur 8 i^rPer.
$3784.75^5^.
$434.04^5.
$■■?<; ;5.75|J.
$2.124. 35 m|.
$4024.31iZj.
$76640.58-4fttf.
1.
2.
3.
4.
6.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
$652.75.
$356 25.
$1801.64.
$10059.62*.
$79r).08.
$4350.24.
$8673.
$775396.24.
$671422.07.
$41391 52^.
$937105.16|.
$61305.79i.
$211967.76 A.
$75625.11^. "
£1278 : 15.
PRACTICE.
Exercise 1.
j 16. £3061 : 6.
17. £3211 : 7.
18. £26744 : 16: 111
19. £22583 : 17 : li
20. £3129 : 2 : lOi*
21. $4419.90.
22. £73 : 3 : 8.
23. $1162661 79*.
24. £11945: 9
25. $1631.12.
26. $4357.08.
27. $3903.23,1-.
28. £7.'?3 • i'>
29. £561 : 1 :'3.
I 30. 48347.51J.
7
7*
tie
ANSWERS TO l^E EXERCISES.
1. $433-23*i.
2. $8558-72.
3. $449-355725.
4. I27-2681.
5. $17985-86^-
6. $327-73f.
7. $16-1 ui
8. $7710-4375.
9. $159-53f.
10. $126-51 A.
11. JE41 : 19:2J.
12. £470 : 16 : 6|.
13. £64: Jl : 10,
14. £32 : 19 : 2.
15. $1266-09|.
Exercise 2.
16 £858 : 18 : 3J.
17. $491-7234375.
18. £1136: 17: 1|
19. $678-1028125.
20. $1 87.40 ,V
21. $2858-89fa.
22. £71 :2:8i.
23. $1307- 1 7A.
24. $148-93+.
25. $9-82 .\.
26. $67-60.
27. $34-201
28. $1293-764,
29. $623-36^,
30. $2722-19^1.
is
1. 22 cwl 2 qrs 13 lbs.
2. 1246 pounds.
3. 87 cwt 1 qr 16 lbs.
4. 26 cwt.
5. 107 cwt 2 qrs 14 lbs.
6. 51 cwt 12 lbs.
7. 34 cwt 20 lbs.
8. 108 cwl 3 qrs 1 lb.
TARE AND TRET.
9
10
42 cwt 1 qr 2 lbs,
18 cwt 6 lbs.
11. 4 cwt 1 qr 18 lbs.
12. 14 cwt 2 qrs 23 lbs.
13. 79 cwt 3 qrs 5 lbs.
14. 152 cwt 1 qr231bs.
15. 82 cwt 1 qreibs.
1.
2.
3.
COMMISSION, INSURANCE,
$68.78
$58.58
$408-5544.
$28-0404.
$130-8853.
$928.55
5.
6.
7. $2221.33
8.
9.
10.
$215.32.
$1008.471.
$56.52.
11. $129-409.
12. $443-3756.
13. $597.36.
14. $36-102.
$521-5512.
$63.22.
$129.07k
$725.
$54.80.
$167.85.
15.
16.
17.
18.
19.
20.
BROKERAGE.
21. $15,895.
22. $176.93f.
23. $190.64 J.
24. $206-7731.
25. $910.
26. $1532131.
27. $235.06.
28. $2540.89*.
29. -$98 35.
30. $280-91f.
1. $2616.
2. S17.14 SSOA
3. $2466. *"'
4. $11457.60.
STOCK.
5. $830-5084.
6. .*,77.^2 ,",0
7. $4684.68-M.
8. $1092.
9. $8741.25.
10. $8602. 1 5-j^.
11. $6388.08
12. $4097.
smmmm.-
SES.
18:3J.
234375.
: 17 : 1|.
328125.
: 8}.
H-
i-
L
ANSWERS TO THE EXERCISES.
W
qr21b5.
lbs.
jr 18 lbs.
qrs 23 lbs.
qrs 5 lbs.
1 qr 23 lbs.
qr 6 lbs.
:erage.
. $15,892.
. $I76.93f.
$I90.64|.
1206-7731 .
, $9(0.
$1532131.
$235.06.
$2540.89J.
•$98 35.
$280-91J.
$8741.25.
?3o02.15-j£5..
$6388.08
$4097.
\.
2.
3.
4.
5.
6.
7.
$24.92.
$127.
$106.04.
$438-5475.
$886.15.
$54-52725.
$1901.25.
1. $140.25.
2. $196.80.
3. $103.84f.
4. $197-1329.
5. $135.03.
1. $25.13-X-.
2. $560968.
5. $59.1266.
4. $5-2475.
6. $4-3774.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
II.
12.
Amount.
$857-337.
$1380.151.
$767-5457.
$814.6549.
$995,072.
$3341. 56 j.
$1398.68.
$1370.0866.
$6t>:.50.
$944-3327.
$1045-0748,
$3029-9447.
1. !?=482.40i.
2. $908.04.
3. $6i5.v3.
4. $829.71.
5. $484-9622.
SIMPLE INTEREST.
8.
9.
10.
11.
12.
13.
14.
6.
7.
8.
9.
10.
EXEIICISE I,
$312.
$134.9831.
$375.63|.
$674.88.
$50.29|.
$46095.
$139.20.
Exercise 2.
$188.65.
$45-5155.
$138-3754.
$42-6313.
$142.44.
Exercise 3.
6. $27-306.
7. $18-9899.
8. $26.59if.
9. $13.90.
10. $21.8 lyig.
15. $65-736.
16. $142.72J.
17. $155-682.
18. $55.82i-.
19. $59.40.
20. $186.82J.
11. $55-3588.
12. $210-8083.
13. $37.49§.
14. $1475658.
15. $60-2466.
11.
12.
13.
14.
15.
$31.15ff.
$11-1788.
$27-345.
$28-7345.
$13.35|ff.
COMPOUND INTEREST.
DISCOUNT.
Exercise 1.
6. $977.4246.
7. $034.77.
8. $1557.40.
9. $851.52.
10. $445.60.
Interest.
$116-737.
$140-151.
$67-1457.
$130.6549.
$75,072.
$381.56i.
$466 68.
$370.0866.
$61.50.
$196.3327.
$155-0748.
$629.9447.
11. $2335 30.
12. $3387,01
13. $71-5284!
14. $13.2789.
15. $32.04.
U8
ANSWERS TO THE EXEROISEg.
1. $93I-03/i4.
2. f970'8737.
3.
4.
Exercise 2.
f 247.4 1.
fdl6'2962.
5. IGC9 C437,
EQUATION OF PAYMENTS,
!• 4-,^ months.
2. 6 1 months.
3. 8 ji moDihs.
4. 10^^ months.
5. 2^1 months.
6. 44 months.
7. Sjf^ months.
8. 8| moDihs.
1. 26 cents.
2. 460 pounds.
3. 128 pounds.
BARTER.
4. $9.4039.
5. 2 cwi 12}? lbs.
6. 27V»3 Hia.
' ' '-; (ients.
9. 22 sheep.
6.
PROFIT AND LOSS.
J. $53 57.
2. $144.
1- HH percent.
2. 114 per cent.
3- 4|^^ per cent.
1. $2332.60.
2. $1030.08.
3. $1393.20.
1. 32ffi cents.
2. $2245 45 A.
3. $1840. " '
3.
4.
Exercise 1.
$9.10.
$12.60.
EXEHCISE 2.
4. 4f « per cent.
5. 5| per cent.
G. 81 per cent.
Exercise 3.
4. $23-265.
5. $884.80.
6. $35.52.
Exercise 4.
4. $169-64f,
5. $309.73 B1-,
6. $70-6535^1"'
5. $12.77^.
6. $95.85.
7. 6i\ per cent.
8- 7| per cent.
7. $232.50,
8. $294.30.
7. $27I304A,
D'
2.
A'9 6
B's -
C's-
3.
A's
B's-
C's -
4.
A's g
B's -
ANSWERS TO THE EXERCISES.
SIMI'LE PARTNERSHrP.
149
1. A's sliare$392-l5,^8
B's !f;5G!)'84-}.5l'^.
2. A's share $2;i!)0-60 ^JUO-
B's $3 180-43 ,Wi!
C's $2078-95 /iiJ.B-
3. A's gain $1181 25''^"'
B's $975.
C's $1593-75.
D's $750.
4. A's loss $42i.
B's $340.
C's $935.
5. A's share $1622-081414,
B's $424-25mfe
C's $553 65^ft.
6. A's gain $2 1 95- |i|a
B's $3064-88^.
COMPOUND
A's 8hare$108.62|ff.
B's $182.1242^..
C's $122.24fg^.
D's • " ■ '
2.
•$187.1 V,^.
A's share $368.42 ,!^.
B's $394.73if.
C's $736.84,^.
A's gain $1486.453^^
B's $2601. 29 „\.
C's $23I2.25^f.
A's gain $121i.53ii
B'e $888.46,^3.
A's loss $126-66^.
B's $95.
C's $158-331
A's share $962-83(21-.
B's ^$1444-24^-
C's $ 1 504-42 ^(<,
D's $2888-49 ,a^l
A's loss $3142-22f
B's — r- $3647-224.
C'8 $3310-55|,
10. A's share $3300.
B's $2760.
C's $36d0.
A's share $2 155- 17.5* 9 .
B's $2894-08.J7.|.
C's $3448-27 M^'.
II
D's
$4002-46:0-/,
8 3
12. A's gain $606-66«?
B's $793-33^
PARTNERSHIP.
6. A's share $244. 02i4>!^.
B'e . $209.16,^.
C'8 $326.81-}^^.
6. A's Ices
$209. 90f^.
B's $279.87 ,Vff.
C's — $400.22-ff g.
7. A's
B's
C's
gain
$87.0911.
$93.J4i4.
$1 19.75ff.
S. A's sharp $1696 921^2
B's $1003.07V,V
1.
441.
2.
3375.
3.
256.
4.
5832.
u.
6561.
6.
1024.
7.
262144.
INVOLUTION.
8. 8.3521.
9. 537824.
10. 177I56I.
11. 729.
12 6084.
13. 2197.
14. 6859.
15.
16.
17.
18.
19.
20
6 V J •
i4' f S fi 4-.
13651919.
•a OX'
m
I.
ANaWEBS TO THE EXERCISES.
0.
6.
7.
8.
9.
10.
II.
12.
34.
2. 248.
3. 25'8069758.
4. 750-964712.
33'«81.
6031.
20.784.
2-47847879.
6-26498.
41-569219.
imiuioe.
•17.
1. 34.
2^.246.
3. 56.
4. 432.
5. 2436.
1. 375.
2. 23.
EVOLUTION.
Exercise 1.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Exercise 2.
6. 1234.
7. 497.933859.
8. 86.
9. 179.
10- *. ^, f
11. 26-1.
Exercise 3.
132. 5. 26.
12!. 6. 48.
s> 'n> ft"'
6 15142259.
•244948974.
1-62018517.
5-5.
23.7065391.
8-86002257.
12.062.
28
1917.04668.
1578.
90.6.
12. 3.65.
13. 23-45.
14. 10-3.
15. 34-2.
16. 38.
7. 32.
8. 19.
DUODECIMAL xMULTIPLIGATION.
Exercise 1.
1. 29 ft 8 in 3 lines.
2. 36 ft 2 in.
3. 38 ft 3 in 2 1.
4. 107ft II in 41.
5. 133 ft 6 in 8 1 6'"
6. 171 ft 5 in 11 14"'
I. 33 ft in 9 1.
2 61 ft 4 in 4 L
3. 142 ft in 1 1.
4. 22 ft 7 in 3 I.
5. 187 ft II in 3 I.
6. 28 ft in 8 1.
7. 85 ft 3 in 6 1.
8. 288 ft 10 in .1 I
9. 78 ft 2 in 8 1.
10. 75 ft 5 in 7 I 6'"
Exercise 2.
7. 68 ft 1 in 8 1 3'"
8. 96 ft 4 in 10 lines 9'" 1
9. 96 ft 9 in 5 1 4'i' ll""
10. 170 ft 3 in 5 1 7i"
11. 550 ft II in 013'!'
12. 7704 ft 6 in 5 1 7"" 3"i"
nil
11.
12.
13.
14.
15.
140 ft 8 in 8 1.
49 ft 1 in.
48 ft 5 in 9 1 41"
86 ft 3 in 7 1.
30 ft 6 in 4 1 4'"
16. 58 ft 9 in 4 1.
17. 155 ft 10 in.
:!5ft
U 111
2 1.
19. 100 ft 10 in 5 I 6'"
20. 1360 ft 5 in 8 1.
IBS.
1 -i '
259.
974.
517.
391.
257.
)68.
3.65.
23-45.
10-3.
34-2.
38.
ANSWERS TO THE EXBROISKS.
161
MISCELLANEOUS.
, 7. 32.
I 8. 19.
ON.
8 1 3'ii
10 lines 9'" Hi"'
5 1 4"" II""
5 I 7"'
n 013"!
n 5 1 7"" 3""
n 8 1.
9 1 4"'
7 1.
4 1 4"'
4 1.
in.
1 2 1.
in 5 1 6""
in 8 1.
1. $156.55.
2. $72.45
3. $548.48^.
4. $23.43^.
5. $1497 68.
6. $50,841.
7. $225.16.
8. 2cwt3qrs 196 lbs.
9. $88.09.
10. 8 lbs 2? oz.
11. 22152.
12. UHdays.
13. 1A\.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
•2,3-571428,-25, 75.
293.
$1000.
A's share $137. Olff.
B's $78.98H-.
2,V
30.
31.
32.
33.
34.
35.
36.
37.
38.
31 m?.
$789.42 ».
64.
73-,^- cents.
8J per cent.
$204 70.
120 pounds.
$60.48.
268 feet 5 in 4 1.
A's share $1261. 72|f.
B'o 5i734.56fA
C's $803.70^4.
624.
2267 days 23 h 12 min
24 sec.
69 yds ^ nails.
$2769.
£741 : 2 : 6.
218i bushels.
$24.00.08-
6040.
141.23ft.
hhdds 9 gals 3 qts
39. 24517
1 gill.
40. $807.66.Jf.
41. $995.92^.
42. $536,461
43. $88.38.
44. 23.
45. $3706. 37^
46. A's share $2202.35/AS7.
B's $3024.
C'6 $2021.04mg.
$27.96. ^^
39414 feet.
$257.55 ,fi6>.
47
48.
49.
50.
51.
52.
53.
54.
55.
66.
57.
58.
59.
60.
61.
62.
63.
61
65.
66.
67.
68.
69.
70.
71.
TO
73.
74.
75.
.375,-671428,-54,-5.
$54-5387i.
$2896 33.4.
$10167.60.
2 roods 20 sq per 20 sq
yds 6 sq feet 84 sq inches.
$61.41|.
8H .iionths.
22i? days.
$152.71.
$79.68^.
$196.15A-.
4idays.
$993.20.
742.
$14.66'^.
$7.7Ii.
$1780.10.
A's share $340.35-^.
B's $255.56fi8.
C's $234.07 AZj.
48|| bushels.
24.
lO^f cents.
•4, -875, -3, -8.
$685.85. ■'
152
ANSWERS TO THE EXERCISES.
ANSWERS TO EXERCISES ON METRIC SYSTEM.
9
10
11
12,
13.
14.
15.
16.
17.
1. 1795 centimes.
2. 17 francs 4 decimes 2 c.
3. 6907654 millimetres.
4. 7 decams 2 metres 4 decims
8 centims.
5. 6 myriams 4 kiloms 2 hec-
toms 9 metres 7 decims 4
centims.
6. 9000 milligrammes.
7. 94703 milligrammes.
8. 2 kilogs 4 hectogs 9 grams
6 decigs 4 centigs 8
milligs.
. 852 francs 5 centimes.
. 66 myriams 3 kiloms 9
hectoms 2 metres 8 de-
cims 7 centims 7 millims.
180 kilogs 4 hectogs d
decags 7 grammes 2
decigs 2 centigs 8 mil-
ligs
16 francs 8 d 5 c.
85 myriams 6 hectoms 6
decams 9 decims 3 mil-
lims.
20 kilogs 6 hectogs I gram
5 decigs 7 miUigs.
1735 fr 2 d 3 c ; 2726 fr
7 d 9 c ; 8428 fr 2 d 6 c.
18
20
149 myriams 6 kiloms 7
hectoms 4 dreams 4
metres.
2245 myriams 1 kllcm 1
hectom 6 decams.
58 kilogs 8 hectogs 3
decags 3 grammes 7 de-
cigs 6 centigs 5 milligs.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
418 kilogs 3 hectogs 7
decags 3 grammes 4
decigs 4 centigs.
138 francs 8 d 3 c.
416 francs 4 d 9 c.
19. 415 myriams 3 kiloms 5
hectoms.
138 myriams 4 kiloms 5
hectoms,
27 myriams 6 kiloms 9
hectoms.
199 kilogs 1 hectog 2 grams
2 decigs 3 centigs.
11 kilogs 5 hectogs 4
decags 2 grammes I
decig 5 centigs 8 mil-
ligs.
222 francs 3 d 2 c
440 francs 4 d.
225 francs 9 d 3 c.
194 francs 5 d.
2 deoags 4 grammes G
centigs 4 milligs.
15 francs 5 d 9 c.
245 frs 9 d.
2J days.
129 frs 2 d 4 c.
150 frs 7 d 8 c.
193 frs 8 d 6 c.
46 frs 6 d 4 c.
55 frs 9 d 6 c.
74 frs 6 d 2 c.
31 frs 2d.
102 frs 9 d 6 c.
1072 frsSdOc.
Amount 5248 frs 8 d.
Interest 748 frs 8 d.
THE END.
3ES.
IG SYSTEM.
9gs 3 hectogs 7
s 3 grammes 4
3 4 centigs.
3S 8 d 3 c.
3S 4 d 9 c.
•iams 3 kiloms 5
ns.
'iams 4 kiloms 5
ns.
ams 6 kiloms 9
IS.
s 1 hectog 2 grams
?s 3 centigs.
[3 5 hectogs 4
2 grammes I
> centigs 8 mil-
s3 d 2 c,
3 4d.
!9d3 c.
1 5d-
4 grammes G
4 milligs.
5d9c.
!4c.
1 8 c.
I6c.
4 c.
6 c.
2 c.
6 c.
d6c.
48 frs 8 d.
8 frs 8 d.
CONTENTS,
Dellnitlons
Numoration and Notation .'..'.....'!.'.'.'.!.*.*.'.'.'.*!!'.,'.'
Numeration table '.!".'.*..!."!.'!!,"!'
Old numeration table , .'.*.',**,'",'.','*".."!!!'.
Exercises on numeration and notation .".".'.'.'.'.»!!'„'.*.*!.',*,*"
Roman notation , , ^ * '
Simple addition ...,. .........!....!!'.['. ..,!7,..!
Simple subtraction ,.,, '.'",'//",'.'.'", ".'.'.','.,',
Simple multiplication '..".'.'V.'.V.'J!!',,.'.".'.*"."
Multiplication table .!.'!!.'!!!!!!!*.".*."!]!"'
To multiply by a number not greater than 12 !!.7.','.',i' .*.*'.'"
To multiply by a composite number and by a number
greater than 12
Simple division ,,,'!.'"..'.'.'".'.
Short division '..**.'.' '..*.'.V.'..'!!!!![ '.!!!!!!!'
To divide by a composite number...'. ,'.".!'..'!.'.','.'.",".','"'
Long division , , !!!!.!!!!!!!*
Tables of money, weights, and measures. .'.'.."*.'.".*!!!."'*.',**,'*
Reduction of decimal currency ,....'.'.".'
Reduction of money, weights arid measureB.*,*!.",*!!.','"" ""'
Compound addition , , ,. [['"
Compound subtraction !'.'.'. !'.!!!' '.
Compound multiplication '..'.'...., .,.„",.. ".'.'
Compound division ., , [ ','.','.'.'.'.'.'.
Miscellaneous questions ',.'!!!!'...'.'.'.'.'.'!.* *.'.'.'."" '
Simple proportion ,.,,'.'.'.'.'/./."*".'.*.'."', ''.'.'."".
Compound proportion ,. ..'..'.*.,'.'."',",'.',',"!.'.".""
Greatest common measure '. „"".','.'.'.','. ",'.',',',"
Least common multiple '..'..'.""'.'..
Vulgar fractions, deflnitions, 4c '."..'.*.','."!!',.',".".'.*.'
Reduction of vulgar fractions ....''.'.'.'.'.'.'..,,,',
To reduce a fraction lo its lowest terms .",.','.".„'. m.","!!!^^'
To reduce an improper fraction to a whole "or'mixed
number
To reduce a mixed number to an improper fraction.','".'.'.'.*
To reducft .a r.nmpound fraction to a siropio fraction
io reduce any number of fractions to equivalent fractions
havmg a common denominator
To reduce a complex fraction to a simple fraction.'.',',',',",",',','
Pag ft,
I
5
7
8
9
10
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14
17
18
19
20
22
22
24
24
26
30
33
36
39
41
46
51
51
58
60
61
63
64
65
65
65
65
66
67
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To reduce a fraction from one denominalion lo anollier
Addition effractions
Subtraction of fractions .'.'.'.'.'.".".'. '.
Multiplication of fractions...'.*.',*.'
Division of fractions .'.'",
Decimal fractions, definitions,"&c*,'.".'. ""
Numeration and notation of decimals ' '"'
Addition of decimals '
Subtraction of decimalB .'..*.'.*.*.*.*.**.*.'.*.', ' '
Multiplication of decimals '.'.*.'.
Division of decimals ....',*.'.'.! '
To reduce a vulgar fraction to'a'deci'mai'.*
To reduce a finite decimal to its equivalent vii'lga'r 'fractio'n
"^"gi/eXntr"..'"?:!.'!.!" "^ ""' "'«"°*"'
To find the value of a given *decim'ai .'..
Proportion effractions '
Miscellaneous questions ,*.'.*.'.*.*.* ' ' ""
Practice "' •"••••
Tare and Tret
Commission, Insurance, Brokera«*e'
Slock ^
Simple interest
Compound interest .'..*.*.*.*.'.
Discount
Bquation of payments '.'.',
Barter '
Profit and loss ,*.*!.'.*.'.*.*!!,
Simple partnership ..'. *.'
Compound partnership '„
Involution ,
Evolution..., .'.*'.!!!!!*..'
Extraction of square root*.".*,".".'.'!
Extraction of cube root ,*.'
Extraction of roots in gene'rai".
Duodecimal multiplication
Miscellaneous questions
Metric tables and exercises ...'.
Mental arithmetic
Answers to the exercises .'
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73
73
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77
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94
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97
98
101
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no
113
115
122
125
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82
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86
87
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94
96
97
98
101
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106
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no
113
115
122
125
13Q