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1
2
3
4
5
6
\
tt
I i
AR
BROTH!
3-
V
PRIMARY
ARITHMETIC
BY THE
BROTHERS OF
. ,^HK CHRISTIAN SCHOOLS
t8S4
SON, PRINTERS
3
B','
Entoroa according to Act of Parliamrnt of Canada, in the year of OUr
Lord, 1H84, by
JAMES P. O'REILLY,
in tho Ottico of the Minister of Agiiculture.
1
J
PRIMARY
ARITHMETIC,
Introductory Definitions.
-:o:
1. Arithmetic is ilio mcncc »>r moiihem, and also the
art of compvtnlioH.
2. Number is tlio re^uU oi^ llu> row/>^mo« of a 7,/^;?.
tiiy witli //>/%.
3. Quantity is any iliinir that can 1>e in«^roase(l or
Jlimnnsliod ; as, <lio le.^rtk of a road, Iho .,,.>•. of a
body, \\m weight of an arf iclo.
4. AUnitisaqnantily will, which wo compnr(^
others of tlio same Jdnd.
6. The comparison ofquantity with unity produces
three kinds of numl,ers : hUegen, Fractiom and IMhecl
Jynvibers.
6. An Integer is anumber wliich contains its unit
m exact number of tim.. : as, 12, 15 ; G boys, 4 apples.
2
DRKTNITIONS.
a.-l.v,aed ml„ two classes; viz, ^/„/„,, and r'„«.
10 An Abstract Number is a numhor (he naluro
of whoso ,.„.t i, ,.ot .l..t,.,mi„,Kl ; as, ,r., 42r,, 7840
tIiO dol J::" "" *""""""'' ^ -■ "' men. 425 days.
NUMERATION AND NOTATION.
12. Nim.omtion i. the methcul of reading- num-
fnns <'xi)r('sso(l by .•haraotons.
13. N«»tatioii i.s Iho iiu'lliotl of wrilin^r numbers.
14. Numbers may be re])ri'.seiited as I'oHows :—
T. JJy jw/v/.s ; as, one, two, three.
11. y>y Ji^urcs, called the Arah/r Method; jis, 1, 2, 3.
III. IJy A7/o>-, called the Roimm Molhod: as Tv
15. In llu. Ai-al»ir Mt'tliod, numbers are ex-
pressed by tne lollowinii- ten
^is:un..s:,,2, 3, 4, S, 6, 7, 8, 9, O.
rV allies : One, Two. Throo. Four. Five. Six. Sovon, EiRht, Nine, Naught-
PRINCII'LE.
A simple name is ^nven lo enrh oj the first nine num-
bers, of which groups are formed. These groups also
receive, each, a particular name, and are numbered by the
simple names of the first numbers.
16. The first nine figures are called signifwant be-
cause they represent a value. But the tenth, by
itself, represents nothing. It is only an auxiliary
figure : its ofiice being to hold the place of any order
4 NI.M,.;li,AT^O^f ANl, NUTATION.
wh„tov..r, whoa thoro are ,k, unit., of that order iu
17. l^]a<liofthe/instuinenuia)H.r.s expresses sim
pie units, or u.nts ol' tiie.M/ ..v/...
18 The numl>er whi.-h follows the ninth is cdled
fen- r s represented by writinn- the il^are 1 with
a naugnt ui'ter it; thus, 10. '' ^
19. 7Vv. i« I he unit of the ,eron4 order und is eaunl
lo ten units of the,/,V.s/ order. ' ^ ^ ^
20. Tens are counted in tl»e same manner as sin^^lo
^nsUnn has rephiced these words by the followin<.- •-
^^^-^y' 20 Sixty, lo
Thirty,
Forty,
Fifiy,
30
40
50
Seventy,
l<:ighty,
Ninety,
70
80
90
NotM._The..,yuitl,..s,.wonl«sij^„i,iesten.
21. The names of the numbers included between
two <.onsecutive teiis. are formed ),y joinin.- to th
-neoftheiirst of tln.et.ns, the L;l.n^^^^^
the hrst nine numbers, sayin- :
Twenty-one,
Twenty-two,
Tvventv -three,
Twenty-four,
Twenty-live,
Twenty-six,
Etc.
21 '''
22
23
24
25
20
Thirty-one, &c.
Forty-one, &c.
Fifty-one, &c.
vSixty-one, &c.
Seventy-one, &c.
Eig-hty-one, &c
Etc. Ninety-one, &c. ^ ^, _^^
The highest number expressed by two fin.u^.s
being niuety-nine, 9<). ^ i^oUrts,
31, &c.
41, &c.
51, &c.
(51, &c.
71, &c.
81, &c
91, &c."
'esses Sim-
NUMERATION AND NUTATION. 5
22. But instead of saying ten and one, ten and two,
ten and three,... ten and nin(^ custom has adopted
the expressions :
Eleven,
Twelve,
Thirteen,
Fourteen,
Fifteen,
NoTK.-Tlie " toen •' in (lie wonJs liiirlee,,, etc., lo ninetpen, niPans
Im. bo lliat, strictly sj.eakints thirteen nipons llirce and ten •
fourleon, four and ten ; etc.
EA'EJWISES.
Copy and read the follovvinn-juunbers, namino- the
lena and units in each :
11
12
13
14
15
Sixteen,
►Seventeen,
FiulittMMi.
Xineteen,
1<)
17
IS
1!)
(1)
17
12
11
16
13
87
46
(2)
28
20
30
90
79
69
59
(3)
55
22
37
48
40
31
19
53
87
62
32
43
34
50
(5)
85
44
33
(>7
97
79
60
(6)
29
10
61
99
21
33
54
0)
70
89
64
23
14
74
82
Express the following- numbers by fio-u,.e,s ;_
73
98
72
27
58
80
49
1. Ten.
2. Thirty-seven.
3. ScA^enteen.
4. Fifty-eight.
5. Forty-three.
6. Twenty-one.
^. Forty-two.
8. Twenty-three.
9. Eighty-six.
10. Ninety-eight,
11. Thirteen.
12. Forty-live.
13. Thirty-six.
14. Forty-seven.
15. lilleven.
16. Ninety-seven,
17. Seventy-six.
18 Sixty-eight.
19. ]']ighteen.
20. Forty-four.
21. Sixteen.
oeve
nty.
23. Nineteen
24. Twelve,
25. T
26
NUMERATION AND N
enty-six. I 83. Eighty.
OTATION
26. Seven ty-ont
27. Fifty-one.
28. Sixty-three.
29. I'hirty-niiie.
30. Fifly.
Fifteeji.
41. Eighty-three
3J
34. Twenty-fonr.|42. Fifty-six.
3.). Thirty-seven. I 43. Fifty-nine
36. Sixty-two. 44. Seventy-eight
37. Twenty. 45. Forty-six
38. Twenty eighl 46. Sixty-three
two naughts after it ; thus lon. " '"'
24. 0,«/,Mrf,-,rfi,the unit of the «,>,/„,</„. ...j
's equal to ten units of the «.«„,/ „„/«• '
One hundred,
Two hundred,
Three hundred,
Four hundred,
100.
200.
SOO.
400
Five hundred, 500.
Six hundred, fioo.
Seven hundred, 700.
Eight hundred, 800.
Nine hundred, 000
26. The names of the numbers included between
two consecutive hundreds, are formed by io^I i^.;
successively, to the name of the first of therhuf
One hundred one, |qj
One hundred two, iq2
One hundred three
One hundred four,
One hundred five
103.
104.
105.
is*
manner as
NUMERATION AND NOTATION. 7
One hundred six, 106. »
One hundred seven, 107.
One hundred eight, 108
One hundred nine, 100.
One hundred ten, ] 10.
Two hundred eknen, 211
Three hundred twelve, 812.
Four hundred thirteen, 413.
' Five huiulred fourteen, 514.
Six liundred fifteen, 815.
Seven hundred sixteen, 7 If].
Eight hundred seventeen, 817.
Nine hundred eighteen, 018.
One hundred nineteen, 110.
Two hundred twenty, 220.
Three hundred tliirty-one, 831.
Four hundred forty-two, 442.
Five hundred iifly-three, 558
►Six hundred sixty-four, 0(14.
Seven hundred seventy-five, 775.
Eight hundred eighty-six, 88<).
Nine hundred ninety-seven, 00?.
Nine hundred ninety-eight, 008.
Nine hundred ninety-nine (000) is the liighcst
number that ean be expressed by three figures. °
27. The group comprising the first three orders of
units, viz., units, tens, and hundreds, constitutes the
first period, that of simple units.
1
J.
8
NUMERATION AND NOTATION.
hundreds, tens, and units in each :
(1.)
100
211
121
700
^{0«
420
900
040
728
572
248
300
(2.)
500
256
905
840
273
590
400
(334
777
308
407
863
(3.)
224
297
337
103
110
733
892
920
701
620
800
462
(4.)
861
598
250
305
606
467
850
670
999
202
706
501
(5.)
652
720
862
722
165
533
573
798
877
346
723
244
Express the followino- numbers in lig-ures ;
1. Three hundred seventy-six.^
2. Nine hundred sixty-eight.
3. Five hundred forty-three.
4. Six hundred eighty-four.
5. Six hundred twenty- three.
<5. Nine hundred eighty-three.
7. Eight hundred twenty-three.
8. Five hundred ninety-five.
9. Three hundred forty-seven.
10. One hundred thirty-eight.
11. Two hundred fifty-two.
12. Nine hundred sixty-one.
13. Four hundred ninety-seven.
14. Nine hundred eighty-two.
(<3)
278
122
972
605
334
407
863
580
121
313
816
911
[ON.
JVUMKUATHtN A IV 1) NOTATION
naminir the
•)
(«)
.2
278
122
2
072
2
005
5
334
3
<I07
3
863
J
580
1
121
>
313
} ^
81G
\
911
15. Throo hiiiidrcd forty-live.
l(i. Seven hundred nine.
17. Eiucht hujulred tv^'o.
18. Five iiuudred sovonty-two.
10. Seven hrimli-ed two.
20. Six hundred fii'ly-lbur.
21. One hundred seventy.
22. Three hundred twenty-nine.
23. Nine hundred nine.
24. Six liundred live.
25. Seven hundred .sixty.
2(). Four hundred seventy.
27. Three hundred tw^enty-seven.
28. Five hundred ninety-seven.
20. F\)ur hundred ninety.
30. Two liundred eighty-four.
31. Four hundred seventy-live.
o2. One hundred one.
33. One hundred two.
34. Seven hundred seven.
35. Seven hundred seventy.
30. Fight liundred eighty.
37. Five hundred sixty-one.
38. Nine hundred ninety-nine.
30. Eight hund.ed.
40. Three hundred thirty-three.
28. The number which follows 000 is called Hum-
mnd, and is represented by writing the figure 1 with
three naughts after it ; thus, 1000.
29. Thousand is the unit of the second period. The
period of thousands, like that of simple units, com-
10
N U ]\I E II A T I O N
A NM) N O T A T I
ON,
pi'Lscs uiiitis, t('n>
Jind limidn-ds. ^j^j.
lousamls, and hundreds or jh(
<on.sh(ul.,Mh(. iourlh, iinj,, ,,Hd
t' miilN of thou-
'UNiinds.
Tl
K' ninls of (ho
iKsjuids tin
«ixtJi orders oi miHi
One th«)ns;ind, (avo t}
1000.
JouNjiinl,
The lens ol' Hiousund
<»iiNand. hveniy jh
2000.
"iiio Ihousjind.
S:>000.
ton 111
y are
The hundre<ls onhou.san<i,s are ' ''*
onehnndredlhousand, two h,. wl- i *i
400000 ^^^" hundred thousand,
' . , 200000,
"^"^' hundred thousand.
900000.
^0; Tl,e names of! he numbers belvvecm two
«oeuhve onfc-s of thousands, an, lorn ed ' ^
sueeessively, lo ll^e name ohhe st oH '^^'^^^
*^''' "^""^"^ of all the nrnn 1 ? ''^''''^'*^^'^«'
In (his inanne; we "..r r;:: 'T ''"^ ^'^^ "•^-•-
w( iiatn the number yjMlDOj).
C'oi>y and n^ad
(he Ibllowinn- numben
(1)
1831
4785
TcMO
6837
8001
8788
2027
1456
(2)
1030
2686
1522
7403
5465
1401
6434
8573
I
(3)
0184
1025
2222
6807
5273
6600
1020
5409
(-1)
2040
3107
5043
7041
7856
4624
4862
4709
(5)
5083
3174
4065
7831
4563
4000
5980
1036
(6)
8800
5580
1001
2050
3307
3009
2010
3003
n
4
7i
21
8(
4;
riON,
NUMERATION AND N O T A T 1 o N . 11
mils oftliou-
"nhouNuiidN,
dvrti ol uiiiiis.
'u; fhouNund.
!»000.
y tlioiisaiul.
tl thousand,
)00,
'i two con-
>y joiiiinir,
lose orders,
this order.
(6)
8899
5580
1001
2050
3307
3009
2010
3003
154(12
21009
80450
78921
44383
(12.)
442839
750351
290420
807905
431900
(8.)
03041
79S25
3H(;78
10909
8000(1
(13.)
905497
080329
751341
008315
917823
Express in figures,
II.
(0.)
0848! >
73401
3!M;32
71854
27374
III.
(14.)
034584
100091
390400
745001
370492
the Ibllovv
I.
(10.)
25738
1050(1
8i!ni
i2i;u
io09(;
(15.)
25120(;
358192
870538
704115
171211
injj^ : —
(11.)
71392
59!»S9
0300i>
24784
87004
(10.)
9!K)098
431900
829473
110018
980703
1. One thousand eight liundred eighty-lwo.
2. Three thousand nine hundred four.
3. Two thousand, nine.
4. One thousand eight hundred sixty-three.
6. Seven thousand five hundred forty-one.
0. Nine thousand forty-seven,
7. Six thousand five hundred eighty-four.
8. Nine thousand one hundred twenty- seven,
9. Six thousand five hundred eighty-nine-
10. Three thousand one hundred five
11. One thousand one hundred twenty-two.
12. One thousand five hundred fifty-five.
13. Eight thousand eight hundred ninety-seven.
14. Six thousand three hundred forlv-
15. Eight thousand eight hundred ninety-six
12
"UMKnATION AN,, N,,,.....,.,^.
,;!• ^■'"^'''•""••""'"-""iKvo )„„„,, .,,.1.
--.Sovo„fy,l.o„„,„„,„i,,|,,.,.„„^
-A K.sl. y..,.v,.„ ,l,„„s„,,„l si,.
-^- ieii Ihoiisjmd, ono
25. Tw..,Uy thousand two h,„„l,,,„,,„,,,
^^•;;-. N,„o,y.„,„e thousand f„„,. ,„,„„.,,,, ^'I,,,,,,^..
^5. Ten thousand, (on.
J^-^Ki,Ut hundred .si'J'u.ou.sand nino hundred
l-,dJdUv!'"""""' '"--'y--" '"""-..1 oight
dreT '*'^'""'d-<Hwo„(y.fin. Ihon.and nine hu„.
Sa Six hundred Uvelvo thousand one hundred
#
*'
thirty.
TIOJV.
!veii(y-ono.
Hy-fivo.
I»ly-N«»v(»ii.
(1.
NTTMERATION AND NOTATION.
n
WO.
orly.
ivd Jiiiio.
^'<l ono.
sixly-ihroo.
lmI Ion.
t^l, hveiiiy.
iiiiioly-iiiiio.
t' iiiindred
::iii(l oiglit
iiino Juiii-
- liundred
40. Nine hiindrod Ihonsand, six.
41. One liuiidrod twon<y-ono tliousand lliroo lum-
urod iiinctoeii.
42. Eio-lit Inindrcd tliousand.
43. Eicrlit Inmdml Iwoniy-fivo llionsand i'i<r\it.
44. Sixhundr.'d olovon t^ionsand ninoty-fbirr.
45. Nino hnndrod Ibrty tlionsand thirty.
4(). Ei^lii Jiundrod nine tliousand.
47. Ono hnndrod sixty-ono thousand sovon hu.i-
arod cigiity-lour.
48. Throo hundred ninety ono thousand two hun-
dred eleven.
40. On«^ hundred nin,.ty.nine thousand nine hun-
dred ninoty-nine.
50. Six hundred forty- four thousand nine lauulred
31. (V)ntinuing- in the same manner, the next
In^^hor periods are formed, Mi/lionx, J3m>„s, Tril-
hotfs, Sec.
Million is the unit of the finrd period ; billion, the
niiU ol the./o//rM period; and trillion, the unil of
the /iff h period.
These three periods, like w.^V*- and llumsanth, com-
prise, each, three orders ; viz., the order of units,
that of tens, and that of hundreds.
32. The names of the various numbers included
between their several orders are formed in the same
way as those included between the several orders of
thousands.
PRINCIPLE.
Ever!/ figure placed to the left of anolher, represents
mils ten times greater than those of the other; in other
words, %t represents mils of the next higher order,
14
N U M K U A T ION AND N f ) T A T I O N
33. From this principle it loiJows :
I. A fi^raro 8tandin^r alono, or in the f.rst place at
the ri-ht of other li-ures, expresses units.
II. A fin-ure stjMulin- in the second place, counl-
ins irom the rioht, expresses tens; in the third
place, hundreds ; in the fourth ,>lace, thousands ; &c.
Til. It IS necessary to have one iigure to represent
a number having- only simple units ; two, for one
having fens; three, for one having hundreds; four
^' rone having thousands; &c, according to the or^
der ot the units.
34 ^^^'t^ry significant Jlgure has uvo values. One
Ls called Its smpfe, or nbso/uf, value ; and the other.
Its /oral, 01 re/afive value.
The Suupfe Value of a figure is that given to it by
Its lorm. •'
The W Value is that which it receives from the
place that it occupies in the number.
^^"" ^- ^^ e number 430G, the simple value of the
is 4
first figure to the left is 4 ; and its local
units of thousand
ocal value
PRINCIPLES.
/. Ten nnihnfam, order whatever Jorm one unil of (he
next higher order.
II. A th„,,,,u,,l „uih of „„y period, « equal to one unit
"I Itle next lugliei periml.
h-rs i.l,e hg,„es are divid.,1 into ;,«•/,.*, each of
which comprises three places. The//™/ ihne place,
T A T I O N .
> .
ho fiivst ])liu'(' at
mils.
id plaro, conn I -
; ill tho lliird
tliouKaiids ; &c.
nre to represent
> ; two, for one
lundreds ; four,
'ding- to the or-
• o values. One
and the other,
t given to it by
elves from the
le value of the
cal value is 4
N ir M E R A T I () N AND \ n T A T H ) N . IT)
eonstitule the first, or units perio<l ; i\u) secoiul llnvc
places i-onstituti! tlu^ sav/n/, or Ihonsotids \W\oi\ ; cScc.
36. The division of the periods will Ju. easily un-
derstood by a careful examination of tin; following-
NUMEUATION TaHLE.
Names
OF
OUDElliS.
* -/j CC
S s S '■ '• "' 1-> ii ^ 2 2 S
•2.2.2 5 3 n O O o ^ '/J S
:=:SS ■^■^■^ ^^;a '^ '^ '^
Hip^ §^S i5i5^ £^5^5
c-^HH p:;p;pq ^<=^?% H
c—i r-(
' ©oo ooo ooo --
n3
o
'/J '•^
OOO
0)
S2.5 15.5 I2.2 -2.2 -2^2
Sr''-* r-;^^ p-SZ- ^-"•'^ -"i;.~
fcljl'.^ u^O)"-" p^jTCI ST2 r-S^
HhP SHt^ ShI^ K^C KhLB
Names
OF
I'ERions.
Ni MHiai.
TriUiuns, P.illions, :Millioiis, Tliuiisimds, Vnxu,
S-^O 02o 0V4 .308
040
( one unit of the
lual to one unit
writing num-
riods, each of
St three places
Orders. 'ZlSS -^-tl-^ ^-d^
»o 't CO rM ^ o c: ■X' 1*^
Peiuo
ns.
5 S-^-^ r^^
.^ —^ ■"^ w 1/3
'•O -f iTO (? I rH
-2
>0
1<
CO
'd
<M
M
37. If it be required to read or write numbers
above trillions, the ibiiowing i, ,he order of some of
the next higher periods: Q„adntt,>ns, Quinmons,
kexlUlions, Septitlmns, Octillions, X-c,
16 NUMERATION AND NOTATION.
MA'i:iiCli6E8 f V NUMEUA TION.
AiU'i- tli(. ioiv-oinir (.xi.lanatioi.s, the pupils should
1).' able to remi any numlM>r whatever accorclin«r to
the ibllowiiig' "^
RULE.
/. Be<rinru\ir at the ri'^ht hmirf, arran^re the /ig-urcs in
periods of three Jig u res each
If. ThetK l)e<rin,n„o' at tlie left, read each period in sue-
cession, omittin^: to name the last.
NoTK.-If an onJer. or .von an entire period, be wantin^f, il is not
"•'"t.oned. 'Ih. name of the last or nuils period i8 also omitted
Jjecauso il is understood.
1. What number is expressed by 75346821 ?
SoLUTioN.-Separaling those ligures into periods acconling to the
rule we have 75. 3)6. 821. The third p-riod is Tf. .nillions ; the se-
cond is3/.(, ihonmnds ; and the first is 821 unils ■ hence the number
IS /o millions, 340 thousands, 8'M.
Read the following numbers :
I.
(1)
(2.)
(3.)
(4.)
75
972
1008
60001
63
840
5000
73182
37
569
6300
39502
25
708
2501
18007
X
411
15784
40905
r.u
1934
29092
56000
225
^o27
56311
171360
12 1
•025
12102
562984
305^
7690
20976
630192
(5.)
704«e5
O59037
954308
100716
536900
213472
360005
800001
780602
'^•^^T^Mt.v^tcaa
PAT I ON,
TJON.
10 pupils should
cr according to
'i^e the figures in
ich perml in sue-
je wanting, ii is not
0(J is also omitted,
•346821 ?
s according to the
/■r> millions ; tlit^ sh-
lionce llie number
(5.)
V
704«-?5
2
O59037
I
954308
J
100716
>
536900
1
213472
f
360005
800001
780602
f
NUMEKATION AND NOTATION. 17
ir.
(6.)
2l9M7»i5
377!t843
321167??
7864321
.>623102
54H220()
9180406
4706204
7601o;?6
4073208
14050(10
8880808
8006807
6000011
20!)0001
2390086
(9.)
4072634
82791640
7006
984270
400200
1807
62876000
900040
900000800
3742680002
8632073009
862794846704
2872819642
34006411H
(7.)
23 7s 2621
486:51425
77666555
43125789
52706000
60300001
72060:584
10010010
83000505
758(10207
31500004
90088050
60500283
200O2021
53700006
69014789
III.
(8.)
978564123
HO«;273S7l
55211S622
4H(;.37462H
1112223,^3
7090,S()O(;2
203100000
840601007
320000006
786400200
842900601
120340560
400300600
910004576
475462394
800006301
(10.)
S563400024
7462007302
82367400210
53024046070
86920000030
17629080406
294635112211
909009008007
842780062004
1303000170410
327864219741(3
14000075001004
167008634216786
3462184390075819
rl
18
N U :\I E 11 .\ T I O N ^ N D NOTATION
EXEllCISEH JN NOTATION.
R U I. I^ .
/. Be^-innin<i: at /lir Irfl, and ivi/h the hiirJiest period,
ivrite the hnndmh, Ict/s, (iii'l uiiil^ of each period in the
numlier.
If. Fill all vaennt /tldrcs with naui'hts.
1. Expivss in liguivs llio niiinber tteo thoumndfour
hundred three.
Solution.— 'I'liis minilpci' consists ol two piTioils, t/iunsuiuls and
ii/iits. In llio llionsaiids jierioii Uhto is Iml ono orJor, wliicli is '1
miils ofUiousaniLs. We, llicrcrorc, wrilo '2 tliousands in llio rourtii
place, 4 liuniin!(ls in iho lliird place, a nauglit (()) in Uio second
place, there l)eing no Inis, and ;{ units in the Ijrst place. Hence these
figures, 'MO.*?, are the jiroper expression I'or the given number.
Express the lollowiiig nunibi'rs in lii^uivs :
I.
2. Thirteen. Eleven. Seventeen.
3. Nineteen. Tliirty-four. Eighty-two.
4. Fii'ty-five. Ninety-lour. Forty-three.
5. Seventy-two. Twenty-nine. Thirty-one.
»>. J^lig-hty-eiglit. »Seventy-seven. Fil'ty-live.
1. Forty-nine. Twenty-six. l^lighty-nine.
8. Ninety-two. Thirty. Seventy-three.
• 9 One hundred five. One hundred eleven.
10. Three hundred ten. Two hundred sixty-five.
11. Four hundred nine. Three hundred twelve.
12. Five hundred thirty-eight. Six hundred eighty-
one.
1\ Nine hundred lliirty-two. Eight hundred
ninety-nine.
14. Three hun'.-red sixty. Five hundred eighty-two.
15. Nine hundred twelve. Three hundred fourteen.
10. Seven hundred nineteen. Nine hundred three.
ATION
WN.
". hiij^hcat periody
rh period in the
vo thonmnd four
Ills, thousands and
tie onJcr, wliicli is "I
isands ill llie Iburtii
L (0) in Uio second
t [liaco. Jlence these
ivcii number.
liguivs :
wo.
lireo.
irty-oiic.
il'ty-livo.
'-nine.
reo.
I olovon.
•ed sixty-five.
Ired twelve.
nndred eig-hty-
light hundred
red eighty-two.
idred fourteen,
liuudred three.
NUMERATION AND XoTATloN.
19
lY. Three liundred twenty-two. Two hundred
sixty-six.
18. Seven hundred eighty-eight. Four hundred four.
li». Five hundred twenty-eight. Eight hundrc^d
twenty- five.
20. Three hundred eigdity-five, Six liundred sixty.
21. Seven thousand, sixty. vSix (housiiiid, seven.
II
22. Nine thousand, seven hundred eight.
23. Three thousand, seven hundred fourtcHMi.
24. Three thousand, two hundred foriy-iive.
25. Seven thousand, six hundred ninety.
20. Three thour;and, seven hundred fifly.
27. One thousand, four hundred seven.
28. Two thousand, two hundred s(U'enteen.
20. S(»ven thousand, threi^ hundnnl twelve.
80. Two thousand, four hundred ten.
81. Three thousand, eight hundre<l twenly.
82. One thousand, nine hundred four.
83. Seven thousand, six hundred.
84. Six thousand, four hundred sixteen.
Sf). Four thousand, one hundred twenty.
80. Six ihousand, iwo. One thousand, one.
87. Eight(>en thousand, seven hundred. Foriy
thousand, six.
88. Fifty thousand, eight hundred forty-one.
39. Seventy-three thousand, one hundicd twenty-
nine.
40. Eig-hty-seven thousand, four hundred t\n3nty-
two.
41. Seventy thousand, one. Twenty-four thousand
20
W U M E 11 A T I () N AND NOTATION.
42. Twenty-four thousand, nine hundred sixty-
eight.
43. Twenty-nine thousand, two hundred.
44. Seventeen thousand, one hundred ten.
45. Forty thousand, three hundred ninety.
46. Twelve thousand, eighty. Six thousand, two.
4*7. Nineteen thousand, sixty-two.
48. Ten thousand, one hundred ten.
49. Twenty-three thousand, five hundred eighty-
nine.
III.
50. Sixty-three thousand, twenty.
51. One hundred forty thousand, five hundred
seventy-five.
52. Two hundred ninety-ono thousand, seven hun-
dred forty-six.
53. Nine hundred sixty thousand, ninety.
54. Nine hundred thousand, nine.
55. Three million, five thousand, one.
56. Five hundred million, five hundred.
57. Six hundred million, five thousand, four hun-
dred seventeen.
58. One hundred eleven million, one hundred
eleven.
59. Two hundred ninety-seven thousand, forty-one.
60. Four billion, six million, one.
61. Five billion, seven million, two thousand, five.
62. Eleven million, eleven.
63. Four hundred six thousand, seven hundred
eight,
64. Eight hundred nine thousand, sixty-five.
65. Two trillion, twenty-five million, five.
66. Sixty-six million, ten thousand, nineteen.
'•'■VilJWrW ^•''^*iK-bi*A;9liaiti\^-^t,\giYi
M T I O N.
hundred sixty-
undred.
trcd ton.
1 ninety.
: thousand, two.
n.
lundivd (Mghty-
. five hundred
and, seven hun-
ninety.
lie.
dred.
and, four hun-
one hundred
sand, forty-on
e.
thousand, five.
even hundred
iixty-five.
ri, five,
nineteen.
NUMERATION AND NOTATION. 21
67. Fourteen million thirty-five thousand, one
hundred ninety-four.
68. One million, three.
69. Seven million, three hundred thousand, ninetv-
[four. ^
70. Forty million, four thousand, seven hundred.
1h Six hundred three million, fifteen thousand,
sixty-one.
^^ 72. Fifteen billion, seventy-one million, six thou-
' Rand, four hundred.
73. Three hundred thousand, five hundred eio-htv-
I two. ° ^
' 74. Two hundred million, fourteen thousand, one
hundred.
^5. Eight hundred thirty billion, twenty thousand
twenty-two. '
76. Five million, two hundred six thousand nine-
teen.
77. Nine hundred billion, sixteen million, eiffht
thousand. ^
78. One hundred nine million, four hundred
twenty thousand.
79. Five hundred twenty-one million, three thou-
sand, ten.
JX^d''" ''""'''■"' '"""°"' '"'"''y "^»'«»>"i. '""«
83. Three trillion, one hundred twenty billion, two
milUon, five thousand, one.
00
NUMERATION AND NOTATION.
84. Thirty-sovoii trillion, one billion, ninety-nine
80. Four trillion, eighty-one billion, one thousand
two.
Roman Notation.
38. Tn the J^omm Method of Notation, numbers
are expressed by the Ibllowing- seveii letters of th.
Jvoman Alphabet :
Lrller,. I, V, X, U C 1), M.
^dho'^. 1, 5 i(>^ ,-^ 100,500, 1000.
PRINCIPLES.
I. The mine of the letter is repeated as often «.« the tetter
Itself I, repealed ; ax, HI expresses the numher three ; XX
expresses tinentn.
II. A letter placed to the right of one of ^greater value
adds Its own to that of the other ; as, X V represents f,J teen \
VII, seven.
Ill The valneofa teller plaeed to the left of one of
grenter value, must be subtracted from that of the other;
as, IV expresses four ; IX, nine.
IV. The value of a letter or a combination of letters, is
increased a thousand-fold by placing a dash over it. Thus.
X, LX, denote, respectively, ten thousand, and sixty thou-
sand.
NoTi.:.-l. Ifa lelK'r Ihat denotes a less niiinber be placed betwvrn
two that denote greater numbers, it diminishes the latter, but do,.^
not atToct the former. Thus in the combination LIX, the value of 1
must be lalven Irom that of X. Hence the number expressed is fiftv-
nine. (59). ^
II. It. must also be observed that no letter is written four limes
in succession.
T A T 1 N
NUMERATION AND NOTATION. 23
Ilioii, ninety-nine. 39. The application of tliese principles is shown
ion, one thousand, i» the following
roN.
otation, numbers
'en letters of the
1), M.
.^00, 1000.
as often as the tetter
limber three ; XX,
of greater value,
^ represents fij teen :
the teft of one of
hat of the other;
wtion of letters, />•
'ish orer it. Thus.
and sixt// thou-
erbo placed belwi'rii
tlie Jailer, hul diM-
LIX, liie value of I
>er e.xprossud is fifty.
TABLE.
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Eleven
Twelve
Thirteen
- Fourteen
Fifteen
Sixteen
Seventeen
• Eighteen
XIX -
XX
XXX ^
XL
L
LX
LXX .
LXXX
XC
C
CC -
CD
D .
DC
CM ~
M
MM -
MDCCCLXXXIII
19
■ 20
80
- 40
50
- (10
70
- 80
90
100
200
400
500
600
900
1000
2000
1883
wriWen four linicb
24
NUMERATION AND N () T A T I O'N .
EXERCISES.
Eoad ihe following lumibors and express Jhem in
figures.
(^•) (2.)
IV XXII
XV XXXII
XLIV XVI
LXXV LY
XXVIII LI
XXXIX LXII
XI XCI
XLIX LXXVIII
(3.) (4.)
LXXXIII LXVIII
XIV Lxxxrv
LXXXVIH XLII
LXX
LIX
XCIII
XXIII
XCVII
(r>.)
CCXLIX
DXXVI
CMLX
CDXXVI
(G.)
DCVIII
CXIV
DCCCXCI
DCCLXXVII
(8.)
MDCCCLXXII
MCDXXII
VDCCXI
IVXC
LXXIII
X
XIX
XLIX
XXXIII
il.)
CXVIII
DCLIII
DCCXLIII
CCCLXXXI
(9.)
MMDXCVII
MDCXLVI
LIXV
MDXLIX
(10.)
MMCXXIV
CIJXXXIX
XXVLX
MI
NOTATION.
lul ('xi)r(;s.s lliom
(4.)
II LXVIII
LXXXIV
an xLii
LXXIII
X
XIX
xux
xxxrir
CXYIII
DCLIII
DCCXUII
CCCLXXXI
(9.)
MMDXCVII
MDCXLVI
LIXV
MDXLIX
NUMERATION ANO NOTATION
or.
'rite tho following mnnbors })y the Roman Melhud •
■)
lo.
402
(2.)
24
18
64
38
27
13
(3.)
34
40
12
80
77
08
41
177G
18G0
1783
2570
(14.)
51
G3
42
80
14
15
80
(20.)
1342
]()35
1883
1206*
(15.)
02
10
48
25
01
20
02
(21.)
1402
1184
1203
1035
(4.)
30
07
70
82
00
00
2!»
(10.)
2132
8004
4040
7032
(10.)
£8
47
62
60
11
41
73
(22.)
5048
2732
1704
1500
(5.)
830
501
320
270
105
014
182
(«5.)
402
080
084
583
372
007
300
(11.)
2358
8422
4004
8743
(H.)
83
00
10
33
50
04
70
(23.)
3058
4032
0004
2801
(18.)
37
2r>
14
85
70
05
0)
202
100
470
324
712
410
007
(12.)
0008
12074
11402
21800
(10.)
40
68
13
55
87
38
44
(24.)
4010
0020
1000
5000
1;.
ADDITION.
-.o:-
40. A<l.liti«n i» th. proves, ollin.li,,.,,!,, sun, 1
ol two or more numbers.
and any number
Any number and
ADDITION TABLE.
make that nnmlier: and I ;
make tliai number: I and
"'t' I ; (I .md 2 are !?.
•'"•el ; 'J and iire 2
1 and
2 and
2 and
3 and
Sand
3 and
4 and
4 and
4 and
4 and
5 and
5 and
5 and
5 and
6 and
1 are
1 aie
2 are
1 are
2 are
3 are
1 are
2 are
3 are
4 are
1 are
2 are
3 are
4 are
3
4
4
f)
5
6
7
8
6
1
8
9
5 are 10
t> and
and
C and
G and
G and
G and
(T and
*7 and
V
1 and
7 and
7 and
7 and
7 and
8 and
8 and
1 are
2 are 8
3 are U
4 are 10
5 are 11
G are 12
1 are 8
2 are !)
3 are 10
4 ar(^ 11
r> are 12
G are 13
7 are 14
1 are (»
2 are 10
fr--S3&n^--^--,^^^-5^-3^^^..,
ADDITION.
27
ORAL EXEltCIHES.
nindinn- jIk, g^^,
' "ff I ; (' .111(1 2 aro ',\
8 and 3 aro
H and 4 aro
8 and 5 aro
8 and are
8 and 7 aro
8 and 8 aro
and 1 aro
^ and 2 aro
and 8 aro
and 4 aro
and 5 are
and (5 aro
and 7 are
and 8 aro
and 9 are
low manv
and 1 ?
and 8 i
and 1 ?
and 4 :*
and 'Z ?
and 2 ?
and 2 ?
and 1 ?
and 2 ?
I and i
aro
4 and 1 ?
•3 and 4 ?
3 and ?
n and 3 ?
7 and 2 ?
4 and 4 ?
and 2 ?
1) and 4 ?
3 and 8 ?
and 1 ?
II.
1 and 1 ?
5 and (> ?
4 and 5 ?
5 and 4 ?
1 and 9 ?
7 and 3 ?
(3 and 2 V
3 and 9 ?
'') and 7 ?
7 and ?
f3?
3
f-1?
5 + 8?
6-
|9?
G-
1-7?
4|G?
3-
[8?
f)
5?
7-
0?
5
6?
G and 4 ?
8 and 8 ?
7 and 8 ?
r> and 3 ?
9 and 7 ?
4 and 8 ?
and G ?
2 and 8 ?
9 and G ?
8 and 5 ?
4+7?
7+8?
4+9?
If 8?
2+6?
3+5?
2 + 7?
2+9?
0+8?
5+9?
w >l
28
ADDITION.
III.
1. (i })ats and -^ l)ut.s arc how luaiiy bats ?
2. 4 l)()y« and T) })()yN an; liovv many hoys ?
J3. V dollars and 2 dollars an; how many (h>llars ?
4. 2 (H'nts and T) i-cnts aro how numy ccnls ?
5. 4 g'irls and 3 girls arc how many <^irls ?
(). 7 houses and 5 houses aro kow many houses?
7. A fishes and 8 lishes are liow many lishes V
8. !) toi)s and 1 loi> are how many tops ?
A boy pnid 1 cent lor a slick of candy and 2
cents for an apple ; how many cents did ])oth cost ?
Sou;TiON.--If a stick of candy cost 1 cent, and ;iii applo cost i
CHiits, l)olli must cost the sum of I cent and 2 coiils. Tlio sum of I
com and .: conls is 3 ecu's. Tlicrcl'uro bolli cost 3 otiils.
10. John's lather gave him two ui>])les, and his
mother gave him two more ; how many ai)i)leB had
John then ?
11 George had 4 chestnuts and Joseph gave him
3 ; how many had George then ?
12. If a pencil cost 2 cents, and a co])y (5 cents,
how many cents will both cost ?
13. "William lost 7 marbles and has remaining ;
how many had he at first ?
14. There aro 8 birds on one tree, and on another;
how many birds on both trees?
ir>. There a-re 4 hens in one coop, and 5 in another;
how many hens in both coops ?
16. I travelled 4 miles one day, and 7 miles the
next ; how many rniles did I travel ?
17 There are G eggs in one nest, and 8 in another;
how many eggs in both nests ?
jj^
A D i:) I T I O X
29
ly biits '^
iiy ))«)ys ?
: iiuiny dollurs 'i
any rciitts i
11 y skirls ?
' many Iiounos?
laiiy lislies ?
T tops V
of ciuuly a I id 2
s did both cost 'i
and iiii ai'plo oost '2
ceiils. TIhj t-uin of 1
•I 3 oeiils.
itp])l(\s, and his
lany ai)[)les had
osoph i>'avo him
a copy coiits,
IS G remaining ;
ndOon another;
ind 5 in another;
nd 7 miles the
nd 8 in another ;
18. raid 5 cents ll.r a kit.., and '. cents lor some
String; how nmcli did holli co.st ?
I 10. A man Imu-ht ;| |,„rsc,s „n \Vc<lnc,sdi,y and !i
^n f^atuiday; liow many horses did ]„. |>uy v
L'd. .lames put S .hairs in the parlor, and C in (I,..
nt<-hen; )i<>\v manv <-}iairs did lie ■,u( ju the two
fooms ?
21. I paid n dollars for a hat, and ll dollars f<,r a
#airol pants; liow miirli money did I sj.end '^
I 22 Mi<hael ],oun.},t 8 niarl.les, aiul aln>rwards w<.n
f ; how many marbles had lie then >■
Add:
1 . 1 and 0,
12. 51 and 2,
f^. 2 and 1,
fl. /i;5and3,
|A. 4 and (J,
f <!. -i5 and 0,
*7. (Jandl*,
8.07 and 0,
10. 8 and 7,
lOand-S,
(>1 and 4,
12 audi,
G3 and 4,
14 and 6,
05 and 8,
l(>and8,
87 and 1,
18 and 3,
to. GO and 1, 1 50 and 0,
IV.
20 and 5,
71 and G,
22 and 2,
73 and 4,
24 and 7,
75 and 8,
2G and 7,
77 and 2,
28 and (5,
70 and 0,
30 and 7,
81 andO,
32 and 2,
83 and 5,
34 and 7,
85 and 0,
3G and G,
G7 and 3,
40 and !>.
1 and 0.
42 and 3.
03 and 5.
44 and 0.
05 and
4G and 5.
'")7 and 4.
38 and 8. | 48 and 4
80 and 2, | UO and 5.
HI-?
|2+6n=?
i5 + 0-='<»
64+3==.?
72-f-5--^?
60 + 7:::r.?
34-j-O:..?
88+4=?
f4+8--? 62+9=?
Gv I b=; o /+8^-?
47+7=? 63 + 5='?
11+8=? I 23+0=?
V.
01+ 9-.?
21+ 8=?
7+14=?
03+ 7--?
46+ 5=?
13+ 8=?
40+ 0=?
61+ 8=?
32+ 1=?
63+ 0--?
78+ 6--?
53+ 9-=?
82+ Q=--'i
9+31--?
8 + 12=?
00+ 7=?
68+13=?
40+ 7_?
02+ 7---?
86+ 3-?
72+ 9=?
6+12=?
7+99=?
55+ 2-=''^
93H- 9=?
27+ 6=?
7+84=?
I
fl
80
ADDITION
VI.
Add :
1. l^y thrct's, from '2 to 110.
Tluis, 2 and '? arc T), and H arc H, and ;'. aru 11, &c.
-. \)y twos, from .'} to 81.
3. By throes, IVoni 1 to 01.
4. J5y lours, from 8 to 115.
5. liy lives, from 2 io 11.
0. By lives, from 4 to 104.
1. By sixes, from 3 to 57.
8. By sixes, from 5 to 83.
9. By sevens, from 4 to 11(5.
10. By sevens, from G to 118.
11. By eiii'hts, from 1 to 80.
12. By eights, from 5 to 69.
13. By eights, from 7 to 55.
14. By nines, from 3 to 102.
15. By nines, from 4 to 76.
16. By nines, from 8 to 116.
17. By threes, from 11 to 44.
18. By fives, from 7 to 47.
19. By sevens, from 9 to 86.
vn.
1. A news boy sold 10 papers in the morning and
7 in the afternoon ; how many papers did he sell
during the day ?
2. If Joseph has 3 e»»nts in one pocket, and 10
yents in another ; how many cents has he?
3. AVilliam paid 12 cents for a slate and 1 cent for
a pencil ; what did he pay for boili ?
how
There are 17 trees in one field and 9 in another
many
trees in the two fields ?
ADDITION
Bl
I ;{ aro 11, &c.
he morning and
pors did ho sell
5. If there are 15 panes of jrlass in one window
and 8 in another ; how many panes in both windows ?
6. Francis had 2r> cents and liis uncle gave him 5
more ; how many cents had Francis then ?
7. Albert took 1 4 roses from a bush, and Mary took
j !• from the same bush ; how many roses were takeu
I from the bush ?
8. If John say (34 words in a minute, and Thomas
18, how many words will both say in a minute?
9. Thomas plucked 47 plums from a tree, and picked
off the ground ; how many plums had Thomas ?
10. In a company there are 50 private soldiers,
I and (i officers ; how many men in the company ?
11. How many cents must I pay for a pound of
butter worth 3G cents, and a pound of cheese worth
1 9 cents ?
12. llobert having 05 marbles, won 8; how many
I had he then ?
13. There arc 19 books on a shelf and 6 on a table ;
I iiow many books in all ?
14. During a recitation 25 queslions were an^
Bwered correctly, and 8 incorrectly ; how many ques-
jtions were asked ?
15. Aleicander is 3(1 years old, and Jacob is 9 years
roJder ; how old is Jacob ?
IG. During a game of base-ball, one side made IG
runs, and the other five ; liowmany runs were made
I by both sides V
17. In the park 45 boys were plnyin^ ball and 1
fwere playing leap-frog; how many boys were en-
gaged 111 both games '^
(, 14
n- I
82
ADDITION
iRWl,-,! '"'"""""I' '""».»» .0.1. JIJ
Ac
63
10
id;
42
25
57
30
54
45
39
60
2i
75
57
11
31
26
68
31
48
56
47
61
18
86
46
32
2!)
27
7!)
42
32
57
38
62
38
87
35
13
92
38
81
43
29
58
47
73
59
98
24
24
80 .
89
72
44
38
59
66
74
62
99
82
41
07
14
19
93
27
86
45
63
54
75
ADDITION.
3, and 9o cents for
)r both ?
^•^igo., and 38 milos
its, and sold it for
vv many cents did
S3
39
2i
00
75
47 .
18
61
80
38
38
62
87
47
50
73
98
66
71
02
99
45
G3
5t
75
IX
Find Ihe sum of
10 and 10 U4 and 10 132 ami 47
25andll 24aiid30 25and27 ...„uo4
J^ and 13 T3and38 02and37 07and58
J 2 and 27 -^ - '
14 and 40
';fandl2l39and32!04and48!88andI5
4/ and 10 J^5and27 49and50 12and03
^^^^iind39|92andl8
70 and 54
nand57 17and92 44and03
87 and 32
19 and 91
80 and 57
;:!!:;:J!fi!^»"^^^"-i2«i2«a;;a;;;
28 and 21
30 and 33
£7 and 12
80 and 40
47 and 52
77 and 07
-2and2o Iand27 29and34 .....,,
83 and 4 J 47 and 08 50 and 33 54 and 98
44 and 07 1 01 and 92 1 10 and 10 I 07 and 99
X.
1. William has 54 cents and James has 43- how
much money have both ? ' ^
2. A farmer havino- 47 /in/^l-c u i i .^
how many auofa,,i|ht\f,:tnr''' '«■"-;
■^U\onZ T7 t""'' "'"' "^*' *■"■ =' '^''"Wl worth
-7 do la,.s, and ,, divss worth 45 doUar.s ''
6 Purchased two tu],s of butter iho hv *
*-»i"S- 03 pounds, and the smalW 5 j ' f ' T'^"
--'h butter dKl I purchase ?' '"""'^ ' ^^^^'
7. A real estate agent sold two lots containino- on^
83 acres, and ihe othr^r j 1 • 1 "lauuiio^ one,
sell '^ '' ^ * ' ^'^^^ ^"^^»y a^'res did he
34
ADDITION.
9. In a school consistiiiR of two oIn<,<.„. ti. > « i
class has 42 p„pik, and *he secrd VT hoi '
Pnpils in the school '^ ""ona 71 , how many
bo'i'oitXnrr''^^'-'^''^''^'''''--''' »■'"'>«
11. Jeae's library contains 8r, books, and Charles'.
2. how many books in bolh libraries ?
were received by both ? ^ ^^^
IG. How much money will be ronm-r..^ + i.
a hat worth 65 cents a/d a ba^^Z^O '^I^"
17. Andrew bought a pair of skates for 95 eonfs
and sold them so as to gain IC cents ; what w^ h^
celling price ? vv"<^ii was nis
18. February has 28 days and M-iivfi qi i
days in both months? ""^ ^^'^^^^ 31. how many
19. A tailor sold 4G yards of cloth to ^VTr Q ui.
«.oMr.W;howmanyytd::f";,,^:^
lines has he to write ? " ^ ' ^'"""^ "^^"7
■i-j
classes, the first
^1 ; how many
how old will ho
v's, and Charles's
ies?
^ for arithmetic
ny good points
Ivanced Reader,
how much did
neck-ties, and
class ?
. one class re-
V m.any credits
fed to purchase
80 cents ?
for 95 cents,
what was his
31, how many
o Mr. Si^Ath
of cloth did
ADDITION.
35
25 lines im-
• ; howiiiuiiy
OPERATION OF ADDITION
^u™r"J::i::'';;i!^---^'^T5,854,and.oo.
854 wo hogin at f|,o ri.,, . ' '""" '°''"""'
(JOt; atdy. Tl, s ' 'r '■"''' ''''^' ^""""" ^^P'"-
— - and .0 „ s ,^," ,' 'T """ ' """^^ '^ "^ »"'^« ^
.0.5 -'-• - Ho;:;;;; rr w:^;r ;;'"^'* ^^^
"- ' ^eu wl,id. .0 car ," , 'unrJ"7 ''^ '^"^ ^^^"""'""^ -*'"
■«'"' '^ lens, is iOtons, an 5 is " r 7" '"" ^"" °' ' '"^^
l""«; t'-alis, 2 l,undro,ls and 2 f n W v ' '"Z' ' ^'"^ ''' ^
'"'"nH.oflons, we carry 11,02 1.,, '"^ "'' ^ ^«"^ '" "'«
''-tis.2t,,ousandslnd trr^^^^
-t 'lown Iho entire s„m. Tl, n ',., V'o! " ^ ? '''' -'"-" we
'/""■od sum, because it is the 'um n i "' ^''"''''''''^' ^''^ '^-
"'•l''e given nuuWs '"'''"•'"'" ^^^^''^ »"'t-S tons, and hundreds
412
348-
(5.)
542 feet.
717 "
203
!*71
<(
12087
(7.)
278 pounds.
24'8fcet. 1314 d„y,.
U
2293 pounds.
IiVTmn. Ti •'"■ -^-1^^ pounds.
^- 3t;J^liS;;^i:;;-;i|^'^^Jo.umn oniguros should be ab-
;'mp)e r,, the pupil should "a^^nl3^T,^ 'I'P- '^''"^' ^" e'^"
8(5
A D 1) I T I () N .
1 1 7t'/ TTEX EXERCISER.
Adtl the fjllowinir :
1. Tliroo Imiidrod uinoty ; eight huiKlred thirty-
six ; throe hundred tweiity-.six ; and two hundred
""^^ Am. nCl.
2. Tlire.> thousand, forty-eight , one thousand, four
hundred eighteen ; one thousand, two hundred fifty-
two ; and one thousand, nine luuidred ninety-one.
Ahs. 7700.
8. Eight hundred two ; two hundred seventy-two ;
tw^o hundred sixteen ; and five hundred thirty-nine!
Am. ISiiO
4. Six hundred ten ; one thousand, seven hundred
thirty-six ; four thousand, eight hundred ninety-se-
ven ; seven hundred one ; eight hundred thirty-
three ; and seven hundred ninety-six. An^i. 0573.
5. One thousand, two hundred tw^o; five thousand
live hundred five; six liundred seventy-eight; tw^o
thousand, fifty-on(,' ; and one thousand, three hun-
dred thirty-nine Am. 10775.
6. Two thousand, three hundred sixty-seven ;
eight hundred seven; five hundred twenty-four;
and three thousand, one hundred seventy. Am. G8G8.
7. Four thousand, five hundred seventy-eight;
nine huiulred sixty-one ; five hundred seventy-tw^o;
and three hundred sixty-three. Am. 6474
8. One thousaiul, three hundred nine ; four thous
and, three hundred twenty-nine ; one thousand, two
hundred sixty-five ; three hundred eight ; and four
hundred twenty-six. Am. \ 337.
9. Eight hundred ; four thousand, one hundred
ADDITION
luli'od thirty-
two hundred
Ans. 11GL
housand, four
luiidrod fifty-
L ninety-one.
Ahs. 7709.
soventy-two ;
d thirty-nine.
Ans. 1S20
'ven hundred
ed ninety-se-
idred thirty-
Ans. or) 73.
ive thouso,nd
^-eig-ht; two
, three hun-
Ans. 10775.
sixty-seven ;
twenty-four ;
y. Ahs. G8G8.
venty-eij^ht ;
leventy-two;
Ans. 6474.
; four thous
ousand, two
it ; and four
Am. \337.
ne hundred
eigrhty-three ; two thousand, one h
three hundred twenfv
37
10.
11.
12.
13.
14.
15.
10.
17.
18.
19
20,
17G
674
71.-)
33i5
643
496
1015
5434
3287
4906
7603
21. 2004
(22.)
3416
8743
2655
14814
(26.)
96327
86438
69476
(39.)
333355
766988
544375
und red sixty-four;
nnd eight hundred five.
jj Ah.^. 827e.
302
523
672
856
129
257
8037
2305
4662
879
46
5087
490.
241.
805.
274.
576.
490.
6191.
1140.
9315.
3402
709.
603.
Ilf.
(23.)
7422
8674
9830
25926
(27.)
37951
98029
96746
^31.)
45706
847687
(24.)
6089
7906
4078
(28.)
56789
37454
15079
(32.)
509234
767448
189979
Atfs.
A//S.
Ans.
Ans
Ans.
Am;.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
(25./
6780
3007
5944
(29.)
99777
55444
(OO.)
76815
274867
537967
968.
1438.
21!)2.
1465.
1348.
1243.
15273.
8879.
17264.
9187.
8358.
7694.
3g
ADDITION.
IV.
34. Three hundred sixty-five thousand, four hun-
dred sixty-two; five hundred sixty thousand, four
hundred twenty-seven ; four hundred five thousand,
seven hundred sixty-three ; one hundred thirty-six
thousand, one hundred sixty-six. A?is. 1467818.
35. Three hundred twenty; four hundred fourteen
thousand, five hundred ninety ; and eight hundred
seventy. Ans. 4151S0.
86. Two thousand, five hundred thirty-seven ; nine
thousand, three hundred eighty-one : six hundred
sixty-eight ; nine hundred ; and fifty-nine thousand,
seven hundred forty-four. Ans. 23230.
87. Seven hundred three ; one thousand, five hun-
dred ninety; one hundred twenty; eight hundred
thousand, sixty-six ; and three thousand, seven hun-
dred seventy-seven.
38. Two hundred ten thousand, three hundred
eight ; twenty-eight thousand, seven hundred fifty-
six ; three thousand, one hundred forty-two; and
thirteen thousand, seven hundred fifty.
39. One hundred nineteen thousand, ninety-four ;
two hundred fifty-five thousand, two hundred seven-
teen ; three hundred thousand, sixty-five ; and sixty-
eight thousand, six hundred. Ans. 946580.
40. Sixty-four thousand, four hundred sixty-seven ;
one thousand, five hundred twenty ; seven thou-
sand, nine hundred thirty-six; thirteen thousand,
seven hundred forty-four ; nine thousand, nine hun-
dred fifty-five ; and eleven thousand, eight hundred
twenty- two.
(42.) (43.) (44.
37 78 68
12 35
14 92
29 71
62 57
(51.)
91
65
42
39
11
13
(59.)
231
462
563
492
(65.)
893
491
682
963
421
506 -
30
34
79
57
(52.)
14
17
36
48
57
36
(53.)
93
12
49
67
82
91
(60.)
896
431
567
624
(66.)
321
402
913
806
201
497
ADDITION.
V.
(45.) (46.) (47.) (48.) (49
68 79 51 70
29 68
36 92
14 55
72 41
32
93
45
12
68
31
72
19
39
12
77
85
56
89
50.)
21
)
49
98
87
(54.)
63
47
93
25
12
49
(61.)
729
820
926
409
(55.)
38
48
72
96
57
43
(1^6.)
36
72
46
35
20
93
(67.)
482
371
206
431
502
739
(57.) (58.)
87 79
36
45
32
24
92
(62.)
302
921
426
526
(63.)
429
602
391
402
(68.)
803
413
516
796
385
402
63
45
33
29
64
(64.)
365
893
943
627
(69.)
234
964
757
813
405
691
-i^J
ADDITI
ON.
(70.)
.(71.)
(72.)
(73.)
(74.)
205
910
749
102.
482
431
796
322
893
396
304
804
416
421
410
276
510
702
605
516
153
312
512
734
503
421
406
614
896
912
089
527
•735
431
431
(75.)
(76.)
(77.)
(78.
4321
6-93
5002
7893
5078
405
3015
4821
3134
7931
6912
5632
50G3
3144
7896
345
2093
5689
4004
21
7215
3965
7965
4002
2653
£01
4689
3112
203
6009
398
705
5035
3965
4590
3456
UNITED STATES CURRENCY.
41. The Si}rn, $, written before a nnmbor signifies
do//ars. Thus, the expression $120 is road one hundred
twenti/ dollars.
42. DoUars and cents may bo written together, the
ccnis being separated from the dollars by a point.
Thus, the expression, $25.35 is read 25 dollars and 35
cents.
ADD I 'J" J ( ) N .
41
Ilxpio.s l.ypropor s.-ns niul fi-nivs. Il.o Tollovvin-
, ^, , /■:.\ /'-'/>'( 'I s/-:s. °
1. N'v<-n (i.'llius mid Iwvniy-ihuvvvuis.
2. Sixlccii (lolkirs iind I'orly cdiIn.
^. yoviy-swrn dollms aud'sixty-lluvo roiit«.
^. AiiH>ty-,ni,c dollars niul lourlvon conts.
T). ]*.mh!y-s('vcii c'nls.
<j. »S('vviily-liv(' (('Ills.
7. KIcvcii d(.l]:ir.s;ind('l,.vri, ..('iit.s.
«. yH'iy dollars and (wciily-five eonl.s.
0. NiiH'tciMi dollars Miidllnv.'cvnts
10. Fil'lycM.ls. Kiolny-livo cents.
11. ThriH' dollars and iil'ly ..•oiiis.
12. 8ixty-l\vo dollars and nine conls
13. Thirl y-soven conts.
14. Sixty-two oonts.
15. Thirty-lhroo dollars and one cent.
16. Seventy dollars and ivn cents.
n. T\nir cents. ]':iol,t cciils.
18. Thirly-tlnvo ccnis. Imvo ,'ents
IIX One hundred dollars and three'cents.
43 In writinn- dollars and cenis ibr the purpose
of adding them, the separating- points must stand in
the same column.
*'^^Tn^^^^'i^n'/.^" '""' °^ '^^^•-^' ^^23.00, .S20G.90
$>3.10, and $0.40 ?
OPERATION.
$10.27
123.00
o
206.90
3.10
0.40
$343.79
Soi.rnoN.-IIaving arranged llienumbors accor.l-
H.g to Art. 4,lw.ad,!tl,Pmhy the principles of
•■^inii)]*! addition. Tlio sr
in li
paratinjr point is f)lacH(l
numijors
'orosiiliimmodiulHj- under those of
tho
given
42 A p 1) I T nj N .
Ill the same maiiiuT add llie following:
(2.)
• (3.)
(4.)
!8;S1.05
1217.75
I78..50
54.02
83.10
151.03
125.84
55.32
90.18
370.(;2
13507
1203
!i!032.13
(5.)
(G.)
H)
$05.14
175.15
!ii!2245.70
91.73
207.45
791.18
182.04
1241.10
33.87
79.30
7907
0.75
20.37
34.81
050.37
11038.24
(8.)
(9.)
(lo:
15838.24
11840.25
I370C8.75
0183 42
30000.00
6000.00
981.3 I
4700.50
8337.25
89.05
373.33
840.16
320.10
870.45
73.82
4823.03
1950.55
10950.03
$58810.01
11. Find the sum of $75.85 ; $16.05 ; $123.25 ;
$475.00 ; $325.50 ; $110M6.
12. Find the sum of $3284.03 ; $87.24 ; $1325.55 ;
$1806.10
13. Add $26.45 ; $33.80 ; $70.67 ; $8.70 ; and $63.73.
14. Add $135.10; $0.17; $1.67; $1800.00; $3.60;
md $867.25.
ADDITION.
43
|H3o, toafor$10.5; InUtor for$l7.10; cheese for
$5.70 ; and egg. for $m. What was the amount of
his purchases ? , .^, '
10. A owes 1137,75 to B; .^207.25 to C; $0r>0.00
to D : and MUO to E ; what is his indebtedness V
17. A lady purchased a dress for |27.G0 • a shiwl
for 114.75 ; a bonnet for $(3,50; a pair of glovel'for
$l.1o , and handkerchiefs for 90 cenls ; how much
money did she expend ? Au^m^Q
.,lf,fl- ^^^^^^»«.bought a house for $3810.00; paid
§^I<o.7o for repairing it, and $200.75 for paintin- it •
then sold it at a profit of $575.50 ; what was hislell-
'''^' ''''''• Ans.$mS.
^^It ^n""'''^'?* ""^^'^^^ ^^^^•'^ *« ^he amount of
$^827,o0 ; paid duties $650.75 ; and freight $127 50 •
what was the entire cost of the goods ? ' '
*(^8?"o^ ^'T.' ""t.t" ^'"'^^'^"S- sales: wheat,
M7.00 poiatoes $(,7.00 ; corn. $180.75 ; cabbage,
ilO.80; turnips, $20.60; apples, $76.05; pears and
peaches, $99.18 ; what was the amount of the sales ?
21.^ How much will a pupil pay for the followino.
set 01 school-books : Intermediate Keader, 45 cents
Urammar, 36 cents ; Arithmetic , 40 cents ; Cate-
chism, 12 cents; Geography, 70 cents; and a U S
History, 25 cents ? ^^^^ ^,,^[
..?^-- ^" "" family of five persons, the flither ea:ns
^iJi.oO per week; the mother, $6.75; the daughter
$1.2c»; one of the sons, $10.00 ; and the other son '
f 4.65 I what are the weekly wages of the family f
W
m
44
AUDI T I O >r.
WIUTTEX AA /■:/,'('/ SKS.
(I.)
4i;
27
82
50
9i>
13
07
48
24
(18
52
n7
21
18
75
Ol)
37
12
(4.)
!»2
35
24
11
13
(10.)
53
4(1
02
38
84
75
00
(11.)
30
87
12
50
73
(50
(12.)
84
47
30
00
21
10
70
47
03
45
no
(13.)
■Id
13
04
21
37
48
(0.)
83
20
88
03
23
(14.)
70
20
18
32
47
53
01
(7.)
40
55
111
72
45
(!•'">■)
02
15
20
08
72
82
(8.)
82
41
8J)
20
73
(IG.)
13
93
00
GO
18
22
87
(17.) (18.) (10.) (20.) (21.) (22.)
214 182 831 231
031 003 477
1 03
(102
003
804
(153 750 022 510
701 411 500 872
502
508
r.ix;
201
roo
410 001 384 243
ix'J
.71
785 417 700 832
i<»7
10<)
802 103 402 714 572
831
382
405
o
17
203
(lO
« 'ad
031 400
317
508
704
(23.) (24.) (25.) (20.) (27.) (28.)
4'2 837 043 032 050 300
408
191
782
401
810 431 184 756
411 032 345 709 279 83.')
(8.)
82
41
8!)
20
73
(1G.)
13
98
22
CO
18
22
87
(21'.)
8I>12
7or)i;
28!>8
1702
410l>
(34.)
0132
421G
>842
7720
8054
0328
1217
5(580
(30.)
04781
04075
70807
84518
30572
04784
43002
14840
30047
28034
3005
2138
4700
0023
8107
(35.)
4502
3054
1804
0407
5074
3102
1804
5287
ADDITION.
(81.)
1045
3023
780 4
5231
2100
(40.)
38303
07084
37400
5 i507
02841
01950
80372
50841
61130
00 110
(30.)
0480
2447
5810
1234
9768
3521
7023
4210
(82.)
7432
5031
8470
0401
7108
(37.)
2345
£081
7108
5043
2731
1852
2040
1508
(41.)
20301
80734
50032
30:i7
400S2
50721
24002
00831
44765
ol3(34
45
(33.)
1000
4082
3875
4023
0742
(38.)
0784
4050
3027
5273
1450
2180
1355
0701
{42.)
80320
7201 ^.
40005
81707
34502
03140
00825
42023
18704
50348
SUBTRACTION.
-:o:
43. Subtraction is the process of finding the
difTerence between two numbers.
SUBTRACTION TABLE.
from any number leaves tliat number; thus, from 1 loaves I •
from 2 leaves »', elc.
1 FROM
1 leaves
2 leaves 1
3 leaves 2
4 leaves 3
5 leaves 4
G leaves 5
7 leaves 6
8 leaves 7
9 leaves 8
10 leaves 9
2 FROM
2 leave
3 leave 1
4 leave 2
5 leave 3
6 leave 4
Y leave 5
8 leave 6
loa.v« t
10 leave 8
11 leave 9
3 FROM
3 leave
4 leave 1
5 leave 2
C leave 3
*7 leave 4
8 leave 5
9 leave G
10 leave 7
11 leave 8
12 leave ^
SUBTRACTION.
41
4 FROM
4 leave
5 leave 1
6 leave 2
7 leave 3
8 leave 4
9 leave 5
10 leave G
11 leave ^
12 leave 8
13 leave 9
5 FROM
5 leave
6 leave 1
1 leave 2
8 leave 3
9 leave 4
10 leave ^
11 leave 6
12 leave 1
13 leave 8
14 leave 9
G FROM
G leave
7 leave 1
8 leave 2
9 leave 3
10 leave 4
11 leave 5
12 leave 6
13 leave 7
14 leave 8
15 leave 9
ding- the
t loaves I ;
^ROM
'ave
'ave 1
ave 2
ave 3
ave 4
ave 5
ave G
ave 7
ave 8
ave ^
7 FROM
7 leave
8 leave 1
9 leave 2
10 leave 3
11 leave 4
12 leave 5
13 leave 6
14 leave 7
15 leave 8
IG leaA'^e 9
8 FROM
8 leave
9 leave 1
10 leave 2
11 leave 3
12 leave 4
13 leave 5
14 leave 6
15 leave 7
16 leave 8
17 leave 9
9 FROM
9 leave
10 leave 1
H leave 2
1 2 leave 3
13 leave 4
14 leave 5
15 leave G
IG leave 7
17 leave 8
18 leave 9
48
SUBTRACTION.
OJtAL E.YERCISE8,
I.
"What remains after takinjr
6 from Y ?
1 from 8 ?
1 from 9 ?
4 from 7 ?
5 from 5 J
3 from 8 ?
1 from 1 ?
from 3 ?
2 from 2 ?
1 from 4 ?
f) from 1 ?
5 from 7 ?
2 from 6 ?
3 from 7 ?
3 from 8 ?
i from 9 ?
4 from 5 ?
7 from 9 ?
1 from G ?
8 from 9 ?
1 from 2 ?
2 from 4 ?
8 from 8 ?
from 7 ?
2 from 7 ?
from 8 ?
2 from 8 ?
6 from 9 ?
7 from 8 ?
5 from 8 ?
*7 from 7 ?
3 from 6 ?
1 from 7 ?
2 from 5 ?
3 from 4 ?
4 from 6 ?
1 from 5 ?
from 9 ?
3 from 5 ?
4 from 8 ?
2 from 3 ?
9 from 9 ?
5 from 6 ?
5 from 9 ?
6 from G ?
8 from 9 ?
from 2 ?
from ?
from 6 ?
2 from 9 ?
II.
15 7=?
15—8= ?
17—8= ?
18—8= ?
15-3 ?
10 8- ?
11—2- ?
14—7- ?
13 9_?
12—9= ?
12 3=-?
17—9- ?
11 Q=l
12—8= ?
11 1 ?
13— C= ?
13—5= ?
10—2= ?
14—2= ?
18 3 ?
10 9=?
10 6=?
16—7- ?
16—6= ?
11—3= ?
14—6- ?
12—5- ?
14 8=?
14—3= ?
18 7 ?
12 7-?
16 9-?
12 8 ?
17—6= ?
14—4=;?
13 4=?
11 8=?
18 5-?
16 2 ?
13—2= ?
11 0-?
15 9=?
16 4=?
17 9=?
15—4- ?
13—9=?
10—1- ?
17—5= ?
18—3= ?
16—8=5 ?
(
SUBTRACTION.
49
5 from 5 '?
1 from 4 ?
3 from 8 ?
8 from 9 ?
2 from 1 ?
5 from 8 ?
3 from 4 ?
4 from 8 ?
6 from G ?
2 from 9 ?
8+4—5=.?
9 + 2—6^-:?
•7+7—5-=?
8+6—3.=?
9+8—6=?
5+4—2=?
8+8—9=?
3 + 9—1=:?
14+4~9=?
16 I 2—7=?
13+3—1=?
12-f5— 4=?
15+0—8=?
9+9—6=?
16+1— 7, ?
11+3—5=?
III.
6—4+ 1^?
16—3+ 7=?
14—9+ 3=^?
9—8+ 6=?
11-
10+4—8=?
7+9— 6 =? 1 12+4— 'v^?
10— (3+5)=?
18-(7— 2)=?
9— (4+3)=?
15— (6-1)=^?
3+ 9=? 13— (7-j-2)=?
7—4+ 6=?
15—5 + 18=?
16—9+10=?
14—4+ 3=?
9—6+12=?
14— (5 + 4)=?
16-? =.. 9
10—? =,. 6
13_? == >j
18—? =11
15—3= ?
12—9= ?
11—1= ?
18—3= ?
11—3= ?
18—7= ?
14—4=;?
13—2= ?
15—4= ?
16-8= ?
IV.
76!"?!^''^ ^■'"' '' ^^'-^''^'^; 46, 56; 66;
^^2. S^ubtract 4 from 14 ; 44 ; 24 ; 94 ; 84 ; 61 ; 54 ;
3. Subtract 7 from 13; 33 ; 23; 43 ; 14 ; 24 • 64-
74. ' '
4. Subtract 9 from 18 ; 28 ; 78 ; 97 • 67 • 15 • 7^, •
85; 12; 62; 42. '> ^^, li>, 7o,
5. Subtract by threes from 29 to 2.
6. Subtract by sixes from 45 to 3.
7. Subtract by eights from 79 to 15.
8. Subtract by twos from 63 to 1
9. Count by fives from 6 to ^6 and back a.o...„-„
10. Count by sevens from 9 to 72 and back^again
11. Subtract by 9's from 100 to 1. ' ^
12. Subtract by 4's from 83 to 7.
50
S U U T K A C T I O N.
V.
- ]. Margaret >ought 7 cakes, and eat 4; how many
had she remaining- ?
Solution,— ir Margaret bouglit 7 cakes and eat 4 of tlioiii, she
must have remaining tlie clilTerence between 7 caltes and 4 cakM«,
wiiich is 3 cakes. Therefore, if Margaret bouglit 7 cakes and eat
4 of them, she has 3 cakes remaining.
2. George picked G quarts of strawberries find
William 4 ; how many more quarts did Creorge pick
th:m William?
3. A boy had cents and spent 3 for fire-crackers
how many cents had he left ?
4. Albert caught T butterflies, but 2 got away
how many had he then ?
5. Jane bought live oranges and gave away 2
how many had she for herself?
6. Henry sold for 1 cents a kite that cost him 5
cents ; how many cents did he gain ?
I. Charles rises at G o'clock and studies till 8 ; how
many hours does he employ in study ?
8. You have 8 fingers on both hands. Close 3
am' tell me how many remain open.
9. If I borrow $12 and pay back $5, how much do
1 still owe?
10. A boy had IG rabbits, 1 of which were killed
by a dog. How many rabbits has he left ?
II. Mr. Brown purchased $G worth of provisions,
and gave the clerk a |10 bill ; how much change did
he receive ?
12. In a class of f>5 boys, 9 were detained for bad
conduct ; how many were dismissed ?
SUBTR/ CTION,
51
i/ 'f!'''^"^^ ' ^ow many wore saved ?
July ? "^'"^^ '^^^''^ '"^"^ ^^^^ ^^h to the 27th of
15. I bought a harness worth $22, and paid S'i on
It ; how much do I still owe ? ^ ^
IC^ In a company of soIdi<>rs there wore 78 men
Ot those f) were Icillr^l nn,i t t ,
were fit for duty ? ' "'"' ' ''"'""^'''^ ' '^"^"'any
17. Abel is 8 years of 'in-,, tt
pass before he i.s\T;„lf ' """ '""'^ ^^^'^ ^'"
There torfstTt''' ' """" '""'■^ '^an boys,
incro w eie b7 girls ; how many boys 'i
fhem ■Ifn"' "":"'' '' '""^ °' ''"5' »»'! -M « of
'ntm , how many tons remain '
20 There were 16 persons in an omnibus After
;.^t^o.U...n.^3,ot in, how many persons w.eret^^
21. In a ring there were ]0 marbles. James shot
•.way C, and Edward 2 ; how many remained Inthl
22. Ri,hard had 21 marbles. He won 16 and lost
' ■ how many had he (hen ?
23 William had 1 cent and his unele s^ave him 8
nore. How mu,). does he still want to pureh sT a
pair of skates worth TO cents "
24. There wei. 8« peaches on a tree. The wind
"itw OH o ; how man^' - i
tree ?
91^
ly ponchos re
mained on the
n arithmetic is worth 70 cents, and a si
worth 8 cents. What is the dim
ate is
orence of their prices?
52
SUBTRACTION.
26. James had 17 oranges. He gave 4 to Mary, 5
to Esther, and sold the rest ; how many did he sell?
27. Oliver had 15 lines to v^rrite from his history.
He wrote 4 on Monday, and the same number on
Tuesday ; how many had he still to write ?
28. James is 14 years old, Emma 4 years older,
and Jessie 7 years younger than Emma ; how old
arc Emma and Jessie ?
29. 18 boys were going to have a swim ; 3 stopped
to hear a hand organ, and 5 ran to a fire. How
many went to swim ?
30. What is the difference between 16+11 and
2+8?
V.
From 20
From 47
From 69
From 74
From 63
From 15
From 37
From 99
From 86
From 28
From 74
From 27
From 83
take 15
take 21
take 36
take 23
take 31
take 11
take 16
take 63
take 74
take 21
take 25
take 19
take 57
From 87
From 43
From 62
From 39
From 38
From 95
From 37
From 46
From 73
From 92
From 54
From 38
From 70
take 36
take 29
take 47
fake 29
take ?9
tabe 46
take 35
take 38
take 66
take 78
take 48
take 36
take 16
From 84
From 56
From 97
Frojn 42
From 22
From 31
From 64
From 91
From 72
From 88
From 69
From 90
From 81
take 69
take e7
take 89
take 26
take 18
take 29
take 17
take 36
take 49
take 67
take 58
take 26
take 37
VII.
1. Martin had 25 cents, and spent 15 cents for a
lunch ; how many cents had he left ?
SUBTRACTION.
53
2. From a flock of 87 sheep a farmer sold 26 ♦
how many had he remaining ? '
3. Purchased p watch for $47, and sold it for $34
How much did . lose ? *
if' wu^'' ^' ^'^'' ^^^' ^^^^ his father 58 years
old What IS the difference of their an-es^ ^
5. A geog-raphy is worth 70 cents, and a small
grammar 36 cents ; how much moro i<\hn t
,, ,, ,, ' ""^*^ ^"^^i more IS the ffeosrranhv
worth than the grammar ? ° o^dpny
6. In the last examination James had 75 per cent
and Henry 38 per cent. What per cent, had James
more than Henry ? ^^®
7. A person spent 37 cents in a store. What
change did he receive if he gave a 50 cent piece r
8 Joseph ran 84 rods and William 56 ; how much
further did Joseph run than William ^ o.ymucn
9. The sum of two numbers is 75, and one of
them IS 25. What is the other ^^
more than i cost ; what was the cost price ?
12 John has 63 cents. If he spend i cents for
marbles, 25 cents for a ball, and 5 cents itr p Its
how many cents will he have Mi ?
13. A tree 58 feet high was broken off 46 ft. from
the top. How high is the remaining piece '^
14. A foreman receives $80 a month. He pays
f f ' *'^'^"'^' ^^^ ^"^ provisions, $3 for a pair
of shoes, and $14 for sundry affairs ; how much ha
he remaining ?
Iwo 110 bills. She spent #3 for ribbons, $6 for vel-
f)4
SUBTRACTION.
vet $1 for Silk, and |2 for linin^r. How many dollars
and she remainging?
16. A farmer having 04 sheep, sold 11 of them to
A, 36 to 13, and the remainder to C. How many did
C receive ?
n. IG. pupils were promoted from a class of 75 ;
and on the same- day 11 were received into the class •
how many pupils were then in the lass ?
^ 18. John had 26 cents, and his mother gave him
82. Ho then lost 17 ; how many cents had he left ?
^19. Sold a sled worth 87 cents for a penknife, and
15 cents ; what was the penknife w^orth ?
20. Mr. White had .$93 in bank. He took out $87
on Monday ; and put in $26 the .sai >e afternoon. On
Tuesday he took out $16 ; how much has he now in
bank ?
VIII.
1. To 5 add 7 ; subtract 6 ; add 4 ; subtract 9 • add
11 ; subtract 3 ; add 4 ; add 12 ; subtract 15 ; add •> •
what is the result ?
2. 7— 2f5— H-9— G^-l2^-l— 5 + 20— 37 = ?
3. 3+17-lH- 37-64-2-1-.- -25 + 7-30..'^
4. 18—12+4-10+1—1+0-3+7-?
5. 3-1 7-4+5— 1 + 10— 6 + 2-8+1— 3-G- '^
6. 3-2+8—8+6+3-2+10—6—7+4.-?
7. 17H 8— 6+10— 8— 3+74— 6:-?
8. 47+7+10-25+5-6-4+3-13-7+4-fo ,
9. 38— 1+3-30+17+3-10+2— 7 + 1-4-?
10. 67—8+1-50+47-6+7-8+32-2+3-'?
11. 46—26+17+7-8+3-16+2=?
12. 18+7—5+32-6+7-2-8+16-7+23=?
SUBTRACTION.
OPERATION OP SUBTRACTION
OPERATION.
Minuend, 837
Subtrahend, 564
order shall stand m the same column Bo-
. f "":7 «l «f'e right, we see that 4 unit; f,o,n
Remainder, 273 L'l"f '' c""'''' ^'"«'' ^^« ^^^'i« '" .ho
from 3 tens, ^ve add 1 hun. red oriot""'.' 'T ''""'' ''« ''^''"''
tens. Now, G tons from ,3 '^s leave 7^ ' ' '""'' '"'^'^'"^ '^
"^r t'.e tens. To compensat for the ,0 '"''" '"""' '"' ^'"''^ ""*
to the minuend, we dimin, Mhe « h . ."'' "' ' '"'"^''^"^ ^^"^'J
•^> "undreds taken from 7 ^^ d ^jt^^rf^ ^J^ ' ^-"-". Then
ton under hundreds ^^^ ^ J'undreds, which is writ-
responding P.HS or .b/:;;;':': ^Pri!;:!;;'",?;;"'' '■'" "■"-
Illustrations.
From 5786 5«tri'7o„i
take 3428 qq *7qp j iS">^-'J.o4
yd 736 yds. 2074.18
RemaindT. 2308 493 937 yds.
3746.36
Prool', 5736 '■^«*7 «^o i ^ "
o8< 673 yds. $5820.54.
WRITTEN EXERCISES
1.
8:
^.
6.
634—231.
•748—523.
542—132.
627—221.
876-525-
-^ns. 403.
-4^5. 225.
Am. 410.
^«.<f. 306.
^«5. 351.
- —■ '»Hi
56
SUBTRACTION
6.
8.
85.
895—371.
178—153.
387—152.
396—312.
297—174.
952—834.
733—214.
487—329.
877—593.
73G— 682.
758—378.
785—597.
476—284.
894—698.
943_»764.
587—364.
829—74.
700—309
186—98.
200—45.
10.
11.
12.
18.
14.
15.
16.
17.
18.
19.
20.
21.
22.
28.
24.
26.
26. 9084—5579.
27. 6240—4089.
28. 5089—3009.
29. 9001—2532.
80. 7689—2137.
81. 7224—973'.
82. 1096—982.
83. 4232—109.
84. 9624—4007.
7586—397.
Ans. 524.
Ans. 25.
Ans. 235.
84.
123.
Am
L«S.
Ans. 118.
Ans. 519.
Ans. 158.
Ans 284.
Ans. 54.
Ans. 380.
Ans. 188.
Ans. 192.
A
ns.
86. 3120—895.
JJ7. 6000—3006.
196.
Ans. 179.
Ans. 223.
Ans. 755.
Ans. 391.
Ans. 88.
Ans. 155.
ilws. 3505.
Am. 2151.
^w.s. 2080.
Ans. 6469.
^ws. 5552.
^«s. 6251.
Ans. 114.
^ws. 4123.
A?is. 5617.
ilws. 7189.
^w.s. 2225.
Ans. 2994.
SUUTKACTION.
88. 2364-
89. 5307
40. 4800
41. 9854
42. 44690-
43. 6T888-
44. 22003-
45. 48909-
46. 71968-
47. 70000-
48. 60901-
49. 91111-
50. 16843-
51. 57345-
52. 35123-
53. 82036-
54. 21185-
55. 58900-
5G. 353655-
57. 478547-
58. 847654-
59. 504245—
60. 642006—
61. 703901
62. 644305
63. 458724
64. 698447
65. 500702
66. 201006
67. 376210-
68. 709558-
69. 369636-
fit
1008.
-48.
■376.
■7926.
•9886.
8096.
10008.
—19898.
—50003.
—69999.
—8909.
-8908
-13959.
-2219«.
-112 ..
-4804.
-5706.
-46304.
-9447.
-92215.
-398007.
-102907.
-97719.
-65809.
-509709.
-417384.
-525809.
-309908.
-106207.
-265100.
■636900.
■84907.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
Ans
Ans.
Ans.
Ans.
1356.
5259.
4424.
1928.
34813.
59792.
11995.
29011.
21965.
1.
57992.
82203.
2884.
35147.
23916.
77232.
15479.
12596.
344208.
386332.
449647.
401338.
Ans. 544287.
Ans. 638092.
Ans. 134596.
Ans. 41.340.
Ans. 172638.
Am. 190794.
Ans. 91799.
Ans. 111110.
Ans. 72658.
Ans. 284729.
nni
^8 SUnTRACTION.
UNITED STATES CURRENCY.
To subtract dollan and renin \vrifo thorn as in
add lion, so that the .soparatinjv points may fall in
tho same column. Thus, to subtrart $17.(;7 from
$2G.03, we place the less numbor under the "greater,
taking rare to have the points in the same column,
and then proceed as in ordinary subtraction.
It-lustration.
Minuend, %2{)M
Subtrahend, 17.07
Remainder, $ 8,80
(!•) (2.) (8.)
From $39.02 $180.25 $170.00
take 14.37 40.75 37.83
$25.25 $180.50 $132.07
(5.) (0.) (7.)
$250(W)0 $300.01 $8100.75
1750.20 73.00 098.03
(4.)
$2084.02
1950.37
$134,25
(8.)
10700.00
8700.75
9. Turchased a house for $10787.99 and sold it for
$18000.00; what was my gain ? Ana. $1212 01
10. A tailor purchased cloth to the amount of
$03.25 and afterwards-sold it for $59 10 , what was
11. A and B began business with a capital of
$16000.00. If A .put in $9713.73, what was B's share
of the capital ? Ans. $6280.27.
12. A gentleman having $3800.25 in bank, drew
out $408.71 ; how much ha« he remaining in bank ?
Ans, $3331.54.
StJBTRAOTION. jg
-^la. receive i ' ' ''°"' ""'>='' ^'""'ff- Bhould
15 A ,„erc.,.a„t i„ one d V ' , , ^"''- *'*'«^-
Wlmt „.„. l,i.s 1,.,^, ■„, ™ V "'^«'- o-""! »».).XHO.
'«■ How much m„V, "'«• «2M1.00.
it «I000 y '""" ''" '"•<»« '" «'!7; 38 to u.ake
n. A man with iinnnn , . '^"■'•'- S324.(J2.
f ods b„.ine.s, pa,, .r C73t T""'; "' »"•' '''T
*-"-^ ^"' the ,„odi ?a;r h '::h't;'s'-!
18. If a man receives 41/,n no '^'"■' «'''-'9-25.
«32 1-c.r provision,, « /vf ■!,." Vn''"""""' ■•""' ""J'^
bo able to save each mLth ' ' '""' ""''' ""' ^e
19- A farmer sold h.v for *„• ,. '^'"- *^'-^'^-
20. An auctioneer reeeived Tn.. •. '^'''- ^^^■^^•
of ^7864, which he ai c o, . 1 a"'" *^ ^^' ^'^i"«
on the furniture v ^^^^' ' '''^^^ was the loss
''' ^ ' lo-ht a nair nf 1 . '^''^- ^243.25
'&"i- a pan ot horses for " '
for #60.50, and a <^arria.'
for both horses and haj
the carriage "?
^ .. 20, a harness
i- for ^300 less than I paid
"OSS ; what was the cost of
Ans. $380.50 .
60*
SUBTRACT ION,
WRITTEN EXERCISES.
X
I
(1.)
(2.)
(3.) (4.)
(5.) (6.)
(7.)
(8.)
93
47
82 51
67 89
21
50
86
32
70 49
52 28
19
42
(0.)
(10.)
(11.)
(12.) (13)
(14.)
946
423
482
703 681
732
817
206
379
486 397
489
(15.)
(16.) (17.)
(18.)
(19.)
3841
4928 9238
7678
87:8
19'74
2396 5373
6723
5921
V
(20.)
(21.)
(22.)
(23.)
47206
80129
79345
20001
39135
£6547
45678
19245
(24.)
(25.)
(26.)
(2t.)
8965
34527
57932
49345
492
10968
9682
30921
(28.)
(29.)
(30.)
(31.)
72145
30924
70093
64983
9062
8921
19027
35897
4
SUBTRAC
TION
•
32. 493 387.
Ans
106
33. 4061—289.
Ans
3772
(8.)
34. 537 29.
Ans
508
50
85. 601—482.
Am
119
42
36. 8971 896.
Am
3075
37. 4008 3196.
38. 2134 97.
Am
812
(14.)
732
39. 493 281.
40. 175 26.
489
41. 832-746.
42. 201-156.
43. 824—357.
(19.)
87:8
5921
44. 923—868.
45. 1002—491.
46. 796 485.
47. S71— 296.
48. 4321 3924.
(23.)
20001
49. 862—674.
50. 502—209.
19245
51. 738 21.
52. 892—406.
53. 56892—7964.
(27.)
54. 5394—4096.
49345
5o. 792—485.
30921
bQ. 6931—5076.
57. 392—289.
58. 702—498.
(31.)
59. 2020—1965.
64983
60. 70065—3962.
35897
61. 8434—7908.
62, 456-390,
ei
MULTIPLICATION.
i I !
44. Multiplication is the process of taking one
number as many times as there are tiiiits in another.
Multiplication Table.
Once is ; twice is ; taicen any nunibor of times is 0.
times 1 is ; limes 2 is ; limes Any niinrb.'r is 0.
ONCE
1 is
2 are
3 are
4 are
5 are
are
7 are
8 are
9 are
10 arc 10
11 are 11
12 are 12
1
3
4
5
G
1
8
9
4
6
8
TWICE
1 is 2
2 are
3 are
4 are
5 aro 10
6 are 12
1 are 14
8 are 16
9 are 18
10 are 20
Hare 22
12 are 24
3 TIMES
1 is 3
2 are 6
3 are 9
4 are 12
5 are 15
« are 18
1 are 21
8 are 24
9 are 21
10 are 30
11 are 83
12 are 36
4 TIMES
1 is 4
2 are 8
3 are 12
4 are 16
5 are 20
6 are 24
7 are 28
8 are 32
9 are 36
10 arc 40
11 are 44
12 are 48
1
1
li
1
2
3
4
5
6
7
8
9
10
111
12 J
king one
1 another.
5 TIME,3
1 is 5
2 are 10
3 are 15
4 are 20
!> are 25
are 30
7 are 35
8 are 40
9 are 45
10 are 50
11 are 55
12 are (10
^ULTIPtlCATlON.
6 TIMES
1 is G
2 are 1 2
3 are 18
4 are 24
5 are SO
fi are 3C
*7 are 42
8 are 48
^ are 54
10 are 00
1 1 are GG
12 are 72
7 TIMES
1 is 7
2 are 14
3 are 21
4 are 28
5 are 35
G are 42
7 are 49
8 are 50
are 03
10 are 70
11 are 77
12 are 84
I
63
8 TIMES
1 is 8
2 are 16
3 are 24
4 are 32
5 are 40
are 48
7 are 56
8 are C4
9 are 72
10 are 80
11 are 88
12 are 06
mos is 0.
4 TIMES
1 is 4
2 are 8
3 are 12
4 are 16
5 are 20
6 are 24
7 are 28
8 are 32
9 are 36
10 arc 40
11 are 44
12 are 48
TIMES
1 is
2 are
3 are
4 are
5 are
6 are
7 are
8 are
are
10 are
11 are
18
27
36
45
54
63
72
81
90
99
12 are 108
10 TIMES
1 is 10
2 are
3 are
4 are
5 are
6 are
7 are
8 are
9 are
10 are 100
|11 are 110
12 are 120
20
30
40
50
60
70
80
00
11 ^^MES
1 is 11
2 are
3 are
4 are
5 are
6 art*
7 are
8 are
are
10 arc 110
11 are 121
12 are 132
22
33
44
55
GG
77
88
00
12 TIMES
1 is 12
2 are 24
3 are 36
4 are 48
5 are 60
6 are 72
7 are 84
8 are 96
9 are 108
10 arc 120
11 are 132
12 are 144
*'
64
MULTIPLICATION.
ORAL EXERCISES.
How man
3 times 9 ?
2 times Y ?
5 times G ?
6 times 8 ?
9 times 9 ?
2 times 1 ?
9 times 7 ?
8 times 5 ?
2 times 2 ?
3 times 4 ?
y are
2 times 9 ?
7 ^ imes 4 ?
9 times G V
8 limes S ?
5 times 1 ?
2 times 4 ?
4 times 9 ?
G times 7 '^
3 times S ?
7 times 5 ?
I.
3 times 2 '?
2 tfmes 6 ?
8 times 3 V
8 time.s G ?
5 times 5 V
6 times 4 ?
5 limes 3 '?
7 times 7 ?
4 times 8 ?
8 times 2 ?
2 times 5 ?
9 times 1 ?
7 times 8 ?
4 limes 6 ?
7 times 1 ?
G times 6 ?
7 times 3 ?
9 times 5 ?
8 times 9 ?
4 times 4 ?
II.
13 X 4-?
16 X 5—?
11x10—?
18 X 2—?
15 X 2—?
12x11—?
10 X 10—?
11 X 7—?
12 X 7=?
18 X G— ?
18 x 9—?
16 X 7—?
14 X 3—?
17 X 3—?
14 X 7=?
14 X 5—?
11 xll— ■?
14 X 8—?
17 X 8-?
12 X 6—?
10 X 4=?
12x10—?
15 X 4—?
17 X 9—?
15 X G— ^
15 X 9—?
12 X 12—'^
10 X 2—?
17 X 5—?
18 X 4—?
13 X 6—?
15 X 8—?
]2x 9—?
16 X 8—?
16 X 3—?
13 X 5—?
13 X 7—?
13 k 9—?
14 X 2—?
18 X 7=-''
times 5 ?
times 1 ?
times 8 ?
times 5 ?
times 1 'f
times 6 ?
times 3 ?
times 5 ?
times 9 ?
times 4 ?
2kftJLTlPLicATlON.
65
6x9-i- 2=?
8x7-1- 9==?
7x9+17=?
12xll-f-8=?
15x6+ 9=?
8xG— 4=?
12x9—18=^^
7x6— 2=^?
13x8—12=?
11x11—71==,^
30—6 x4=?
19+11 X ]l = i
37—9 x4=v
III.
8X9-1 24=?
16x5—18=?
14x6+60=?
9X5—15=?
17x4—15=?
15x61+0=?
18x8-51=?
8x4—30=?
7x12+3=?
7x7+11=?
''2—12x4=?
28 I 6x16=?
^\ I 9 X8='^
(<5+7)x3--?
(14-3)X6-?
(l«-4)x9=.-?
(11— C)X7-?
^'20-2) X 5-^?
(13— l)x4.-f
(6+2)xll-- ?
(HO) xo---?
(28— 15)X2-'?
(21-6) + 5--'^
78—16x4=?
13-4-13x4=.?
99-17+5^?
8x
2—?
Ix
7-?
6x
7—?
4x
5—'^
2x
6—-?
7x
9—?
3x
^_?
5 X
8—?
3x
5—'^
^x
7=--
ly.
Multiply 21 l)v • 91 1 o
M
U tin V ,37 },v J . ro 1 / > ''MJ), /.
V 7 ; 27 hv '-, • n« J n !^ ' ^'^ ^'y '' ; 80
J '-*'>} o , 08 hv 9 : fin K,r Q
y ; 99 hv 8.
66
MULTIPLICATION
V.
33c»iits. ' " '^""'s •' iioiinds will cosl
2. What cost 2 .pool, of tl„.,.„d ,i 5 eent. a ,.i„.e ^
^^5.^mat. w.H . po„„„. of cheese oo.,t at 9 r^t „.
yo.'solr-nl'V' ' r,"f"'^ " '•''>'• '">- ™-y vvill
? A 9 ,"■'■'■' ^ '^•''>''' ^ ''"y^ ? 2 days ?
o James earns *C a week and Henry |3 ; how much
"•.1 both earn in 3 weeks ? weeks ? ]3 w"
ing if rZh'TsT "'^''-^^ '"" f-'' -^ ^oot contain-
11. John bought C rabber bUls at 16 cents each
How mud. change should he receive from a do itr
2. A man travelled by stage nt Ihe rate of 8 miles
nn hour. JIow far did he i.-avel in 't hours ? 1 1 t
16 hours ? 18 hours V '"'"'''■.
a,„n / !r""'f "^ r""''^ "'■ '*'f •■" ^^ """'-^ ••» POU'"'
aiHl 11 pounds of rice at 11 r',.nfc. „ ^
did both cost ? ' ^'''""^ ' ^^'' ^^^
H- What will be th. cost of 7 pounds of c.;, •. ^t
ii at 11 cents
pounds will cosl
'ich are 33 cents,
'ounds will cost
mih a piece ?
: how iiiaHV
311S ?
I any days in
' 15 wcnks V
it 9 ceiHs a.
many will
days ?
ners cost ?
liow much
weeks ?
'ot conlain-
' a Ion ? at
:'en(s oacli.
I a dollar ?
of 8 miles
11 hours?
s apouif
id ; vv' '■
r Cvi; "^ at
"• Joseph has I , /'" ■•'■"■''"■e for it <•
"-y '- 10 row :^^ J' t;';"" '^!-^ « ""'- -
i« Ti., "any nas Jleiirv ^
i». iwo meu start from ih.. ... .
m opposite directions one S4 tT ^'''"' '""^^ '^^^'^'^
«^hor2G; howiarapa'rtawh " ^^^Y^^^d the
1^- How many hand^^^^^^^^^^
tainino- 25 of them ? ^ ^^^*'^«' ^^'^^h con-
20. Two men traveJhvI i^. i
-i/-au ho„n and h ;1h: 7 ''Tr'r ?'«•• -'« -•
SK:::i:::S"'^^-'- Piece.
, 23. A boy earned 07 c™tfrr '' '^'"''"'^ " P«'' ?
inboard ; hov. much had he'!! "'"'r '" *^ "^ "
24. Bought 9 load. „ • u ""-" "'"' "''« J»ys '
f • A carpenter earned *lV '""■ '
™»k«' *n. How much more ..'"•''-T "'"' " ^^00-
"''11 the carpenter have e ",n d ■",'' ""^ ^''«™»k«-
20. If a man d,> -^b,,!' "' ^" ^"^k^ ?
how many will bi di.. in 6 I.? 'I"!''""' '" ""^ day,
2V. What is the am'ou^ of the' nf ^^^ • « ""V^'
Quarts of soft-soap at ,1 eel '^""wnig bill ; «
^'"*' » auart ; 7 cakes of
68
M U LT 1 I'L I (' AT lO N.
soap at 1> coiits eacli ; ami 2 brooms at 35 cents a
piece V
28 11' 1 men do a pieee of work in 10 days, how
long will it take one man to do it V
29 IIow many pounds of coffee in 4 bags, each
containing U] pounds? 3t pounds? 50 pounds?
30. If 12 men build a wall in 12 days, how long
will it take one man to build it ?
31. There are 16 ounc(?s in one pound ; how many
ounces in 5 pounds ? pounds ? 3 pounds ? 2 pounds ?
32. If 14 yards be required to make one suit of
clothes, how many yards will 5 suits nxpiire ? 3
suits? 7 suits ?
33. If a pound of butter cost 23 cents, what will
pounds cost ?
34. A farmer sold 10 bushels of potatoes to one
man, 20 to another, and 32 to a third, at $2 per bush-
el ; how much did he receive ?
35. William is 15 years old and his uncle Charles
is 4 times as old ; w^hat is the sum of their ages ?
36. A farmer exchanged 17 barrels of apples worth
$5 a barrel, for 12 cords of wood at $7 a cord. Did
he gain or lose, and how much ?
1 1
1. 6x4,— 3,-|-9,x2,— 10,+5,x4-«
2. 18— 8,xl0,—75,x2,— 50,-1-1=?
3. 37— 3,— 30,x6,-f 17,— 65,X8=?
4. 14x4— 6,+13, -1-17—65, y8,xll— 41=?
5. 12x9,— 90,x3,— 4,+ll,— 37,X5,— 16=?
6. 130— 75,+5,x8,— 400,-1-20,— 68,X3=?
7. 7+3,— 4,+27— 6,— 12,X8,— 26=?
cents a
fs, how
MULTIPLICATION.
8. 144-24, i80,~n0, x 2,+4,— 30, x 2-04 ?
9. 19 jY, X 5,_i2.-,,-f-0,__.'} :< ]2,— 32,— 1(>-^?
10. 33—18, X 8,-70, I 10, X 3,— 150.—' 2;-):-? .
69
^s, oarh
ids ?
)W loiii:^
»v many
)ouuds '^
suit of
uirc ? 3
it will
to one
er bush-
Charles
ges ?
?s w^orth
•d. Did
Case I.
When the multiplier contains only one flgure.
1. Lot it be Tvquirod to multiply 8!)o by 1.
Operation. Soi.rrtnx.— After writing the multiplier
Multiplicand, 805 ""'''''' ^''" '""'''^^ ord(.Toriii,> muiiipiicand
Multiplier, 7 "'"' ''''''^''nf? « I'ne. wo hcgiri to muiliply
at I 111- right. 7 times 5 units, are 3."i units,
which art' equal to ;{ tons ami 5 units.
We write ihe 5 in units j»iace,ami reserve
Mnltipiying 9
Product, 0205
the 3 le,is to be ad.l.-l to the ".r^iluj, iriUe'lZ. .nnup.ymg ,
give 00 tens, or G hundreds and tens. We set down the tens in
ens place, and reserve the f) hundre,ls to add to the next product 7
Umes 8 hundreds are 50 hundreds, plus the hundreds reserved
make 02 hundreds, or thousand and 2 hundreds. As wa have no
more orders to multiply, we put the thousands and two hnn.Ireds
m their proper places. The resulting number, G2G:., is the required
product. ■ 1"'"=^
Illustrations.
(2.)
213
1
(3.)
432
3
(4.)
341
4
(5.)
520
6
(6.)
17.43
7
213 1296 1304 3156 $52.01
'(7.)
$5.26
5
$26.30
10
MULT
ION.
wnrnEN exejicises.
Multiply :
8.
871) by 1.
Aus. 6153.
25. 604 by 8.
Am. 4832.
}).
()!)2 by (5.
yl//.s-. 4152.
26. 3'n; Ly 1.
Am. 1544.
10.
lm by 6.
Ans. 6368.
27. 915 by 7.
Am. 6615.
11.
47G by 3.
Am. 1428.
28. 776 by 6.
Am. 4656.
12.
582 bv 5.
Am. 2910.
29. 525 by 8.
Am. 4200.
13.
607 by 6.
Ans. 3642.
30. 378 by 7.
Am. 2646.
14.
840 by 3.
Am. 2520.
31. 267 by 9.
Am. 2403.
15.
736 by 2.
Am. 1472.
32. 156 by 5.
Am. 780.
16.
913 by 4.
Am. 3652.
33. 801 by 2.
Am. 1602.
11.
619 by 6.
Am. 3714.
34. 307 by 4.
Am. 1S28.
18.
495 by 3.
Am. 1485.
35. 471 by 6.
Am. 2826.
19.
856 by 9.
Am. 7704.
36. 167 by 9.
Aws. 1503.
20.
768 by 8.
Aui,. 6104.
37. 516 by 7.
Am. 3612.
21.
259 by 7.
Am. 1813.
38. 165 by 2.
il/«. ^ 330.
22.
387 by 6.
Am. 2322.
39. 722 by 8.
Am 5776.
23.
954 by 9.
Am. 8566.
40. 249 by 4.
il«i\ 996.
24.
832 by 4.
Am. £328.
41. 3807 by 9.
56. 90038
5 by 6.
42. 2918
5 by 7.
57. 783206
!by7.
43. 479$
!by 8.
58. 405185
!by6.
44. 7587 by 4.
59. 17842C
► by 5.
45. 631£
►by 6.
60. 218^9;:
;by5.
46. 905^
tby 5.
61. r. -/9?
Sbv9.
47. 811^
rby2.
^% 380697 by 2. |
48. 3948
5 by 3.
. 790]
. by 8. 1
49. 744.8
5 by 8.
4. . 490£
I by 3. 1
50. 2Y93£
> by 7.
65. 30216^
5 by 7. 1
51. 17092 by 9.
m. 235619 bv 6. |
52. 46181 by 4.
67. 81927^
J by 5. J
63. 31953 by 5.
68. 19311]
L by 4. 1
54. 67209 by 8.
69. 37495S
J by 8. 1
65. 36431 by 9.
70. 506044 by 9. 1
M U LTl V L I C A T 10 S.
71
-■s.
the;". : 'rv'"' *''"■ "■"■" ""' '•' '--- -«t ..t
baLfflh™' "' """^ ™^' *"■ «'"" "'■" -''«
ea4 r''"' "'"""'■"" ""*• "' "'" '•"« "'■ 4-'«»'^«
in « mili-" "'" ^^'*" ^"'' "' " '""^'' ''"^^ "'""y f>--^^'
8. How much wilf a grocer pay for 2504 hoads of
cabh, ve at 3 cents a head ?
coit' ? *^ ' "'"''^ ^^'''^ ^'^^ ^^^^ ^^^'^^ «t^ vvood
11. II it tak tailor 7 days to make a suit of
1 '"I'htratvo""" " '^"^^ ^™ '» ™'k: 42«z ,:
in Vyeat I ""'''' '" ^ >'""' ''''^ """'X ^^-k^
,„, . Case II.
one^gSre.*'"' ™»»'l>»«>- ^ontoli.s more tha..
1. Find the product of 643 by 58.
OPERATION.
Multiplicand, 643 Solution. — Having wnlirn
Multiplier, 58 ^''^ multiplier under Iho mulli.
plicand so that units stand Uii-
1st imrtial ^1 i/l n ay o
product '^144 643x8 . . --•
2nd partui 3215 ^43 ^ ^n ^c noginat the right liand an.
^ ' -^- ..' J muiiiplyalliheparlsoMhemu:
Prodtict 37294 643 x 58
5a is equal to 5 tens and 8 units, 58 limes m'n^Z^l^lufZ
der units, tens undo- tons, Ai-.,
at the right I
lUlheparlsot
successively,
term of tlie multiplier, Sin
f
72
MULTIPLICATION,
Itiis limofi Oi.] plus 8 units limos 543. Having found S unilft timfts
01.? ly lilt! riilt! uniler Cas.' l,io 1)C 5111, w« sol it down as
the lirst parliai product. To ttnil 5 lens times 613, we begin by
mulliplyinpS units liy 5 tons, which gives 15 tens, op 150 units,
Oinilling tho naught (or units place, we s^tt down the 5 tens in lens
pia<-e and carr-y tho I luuidred to I ho next |»roiluct. By multiplying
the remaining terms ol the multiplicand by tho T) lens of tho mnlli-
plier, and carrying,' as before, wo obtain the second partial product
:!•.'!.■)() ; which is equal to 5 tens or 50 times (113. Now, by adding
the partial products, :>\U and 3'!l,".0, we find the entire |irod)i(;t
37'2',)4. In like manner we may lind the products of any two num-
bers, being careful to place tho first flgupe of each partial product
under the corresponding figure of the mulUplier.
Illustrations.
(2-) (3.) (4.) (6.)
327 4<; 816 436
46 827 63 78
1902
822
948
3480
l.",08
92
1 i\R
1896
3045
ir)Oi'>
19908
33930
15042
(0.)
(t.)
(8.)
(9.)
(10.)
2(i3
425
548
318
862
32
21
4&
25
59
WRITTEN EXERCISES.
Multiply :
11. 354 by 19. ^Ais. 6726.
12. 295 by 23. .,is. 6785.
i:'>. 359 by 36. Am. 12924.
14. 487 by 28. Ans. 13636.
15. 546 by 32. Ans. 17472.
10. 674 by 45. Ans. 30330.
17. 906 by 53. Ans. 48018,
18. 863 by 25. Am. 21575,
19. 735 by 42. Ans. 30«70.
20. 683 by 56. .4, . 38248.
A ^
MULT I I' LI CAT I ON.
nilft lirafls
(luWIi US
begin by
loU UlillS.
IIS in Ituis
ull'plying
tho miilli-
tl product
l)y adiling
•0 |iruiliu;t
two mirn-
li product
(5.)
435
78
8480
a045
33930
(10.)
862
50
nz
30330.
48018,
2157rv
30«70.
38248.
21. 521 by ;{<). Ans. 20310.
22. 044 hy 7(5. /1«.s. 48044.
23. 078 by 41. /J/?.s. 400O8.
24. 872 by 47. yl//.s. 40084.
25. 7()1 by 58. Ans. 14138.
20. 408 by 00. Ans. 2Kl,-)2.
27. 007 !»y 78. Am. 47340.
28. 320 }>y 84.. Am. 27030.
20. r)341)y03. A„s. VMWyl.
30. 285 l)y 74. Am. 210!>0.
31. 802 by 40. yl//,v. 42238.
32. 704 by 24. Am. 10050.
33. 827 by 52. .-Ia/x. 43 .04.
34. 502 by 71. Am.^biJA'l.
35. 288])y42. /1«.s. 12090.
30. 830 by 80. yl //,s. 74071.
80.
75.
37. 310 ])y 75. Am. 23025. | tj7
38. 417 by 93. Am.mi>^\.
30. 523 by 87. Am. 45501.
40. 108 by 70. ^«.s-. 15048.
41. 879 by 34. yl/i.s-. 29880.
42. 725 by 77. ^//.s. 55825.
43. 300 by 37. Am. 11322.
44. 090 ])y 58. yl«.s. 40308.
45. 287 by 09. ylw.s. 10803.
40. 014 by 28. Ans. 25592.
47. 540 by 08. Am, 37332
48. 705 by 00. Am. 00705.
40. 307 by 52. ylw.s. 10084.
50. 497 by 44. Ans. 21808.
51. 447 by 03. ylf/A-. 28101
52. 310by 18.^/<.s-. ^(jyg
53. 8730) by m. Am. 838050
54. r>485 by 88. Am. 482080
55.^/l;}7by25.^1/y.v. nS425
50.8409by03.^/„.s.r,2J>707
57. ()523 by .'}5. Am. 228305
58. 0040 ],v 47. J A/s. 425102
50. 52877 by 28.
00. 018024 by .38.
01. 270301 by
02.105107 by
03. 2304 by 271.
3104 })y 815.
1282 by 430.
4730 by 810.
5321 by 427.
3240 by 245.
4871 by 502.
0547 by 374.
0293 by 853.
0785 by 070.
5482 by 735.
8073 by 103.
75. 007284 by 352.
70. 7S0ir25by 039.
77. 2842753 by 784.
78. 9310924 by 028.
70. 0454705 by 475
04.
05.
00.
08.
00.
70.
71.
72.
73.
74.
iii.
74 M U L
i
T I P L I C A T I N . 1
^^H
1
45. Aiinoxiiig" a
cipher to
a number moves each of
^^^H/
its digits one place
to the le
ft, thus converting units
H^l
into tens, tens into huntlrecU
&c, ; which is the same
^^^H
as multiplying the
number
by 10. Hence to multi- 1
^^^H
ply a number by IC
), wo annex one cipher ; to mul-
m^l
tiply it by 100, we
annex two ciphers ; and so on.
^^^H
I
r.LUSTRATIONS.
^^H
1. Multiply 35 by
' 240 2.
Multiply 3500 by 240.
^^^H
OPEliATIUN
OPERATION.
^^^^H
35
35 00
^^^^H
24
24
^^H
140
140
70
70
840
840 000
^^H
Multiply :
^
^^m '
3. 8607 by
10
Ans. 86070. 1
^^H :
4. 68038 by
100
Ahs. 6803800. 1
HH 1
5. 780 by
100
Ans. 78000. 1
6. 38600 by
10
Ans. 386000. 1
^^1
7. 37862 by
1000
Ans. 37862000. 1
^^H
8. 98630 by
1000
1
^^B
9. 86421 by
10000
1
HH
10. 378200 by
100000
11. 394 by
200
^^^H
12. 5860 by
320
^^^^M
13. 8790 by
4600
^H
14. 1576 by
3000
^H
15. 1700 by
16. 2030 by
4200
5000
■i
Ans. 10150000. i
■
17. 10800 by
250
Ans. 2700000. 1
■
18. 46200 by
7130
3S each of
ing- uiiitw
tho same
to multi-
to mill-
so on.
by 240.
).
15
MULTIPLICATION.
39. 47300 by 16000
20. 25000 by ](5500
21. 70500 by 40500
22 40000 by 82000
23. 08000 by 7(5000
24. 53200 by 10300
25. 386000 by 147000
2(1. 70200 ],y 20(J0
27. 4030 by 74000
28. 405000 by 3070000
UNITED STATES CURRENCY
46. When one of the factors contains cents or ./oA
/«- and ..nls, mnltiply as in simple nnmbers' ^nt
SourriON.— If one ton cost $5,75,
27 Ions will cost ^7 limos $5.75,
wl.icliis$l55.'.'5. Since Ihe mulli-
rlicand contains cents, ve must
point onriwo places in the product.
-.75
27
4025
1150
155 25
J^^Whai will 37 ),arrels of /lour cost at .*6.85 a
barrel ?
3. Multij)ly $472,06 by 27
4. Multiply }i^]826 37 by 160.
n Tir
Multiply 1802.06
by 327. A
-"Hiply ^20.!i2.25 ],y 1408. Aus. |4128G08
7. If an acre of land
462 acres worth ?
Aus. 1253.45.
Jns $12701.82.
Ans $202210.20.
$201703.62.
00.
IS worth $237.82, what
aro
4ns. $1146£9.2^
•76
MULTIPLICATION.
8. At $4.80 a bushel, what will 625 bushels of flax-
""^f Z^^ ' ^^'^- $3000.00.
9. What cost 83 bushels of corn, at 15 cents a
^"'^^^' Ans. 62.25.
10. What cost 145 yards of sheeting at 8 cents a
y^;t\ An.s.nSO.
11. At $4.03 a head, what will 378 sheep cost?
io wi, . ^//- $1750.14.
12. What cost 8 pieces of calico, each piece con-
taining 25 yards, at 7 cents a yard ? Ans. $14.00.
13. How much will a grocer pay for 2 chests of tea
each containing 65 pounds, at 65 cents a pound ?
14 Txri ^^*'- *i84.50
14. What will 19 hogsheads of vinegar cost, each
containing 63 gallons, at 23 cents a gallon ?
Arts. $275.31
15. Bought 9 cows at $30 each, 13 horses at $135
each, and 300 sheep at $3.50. each ; what was the
*'"*''^ ^««t ^ Am. $3075.
16. A merchant purchased 27 pieces of cloth each
containing 54 yards, at $3.33 a yard, and sold it for
$3.45 a yard ; how much did he gain ? Ans. 174.96
17. A Hour merchant bought 450 barn^ls of Hour
for $3262.50, and sold them for $8.63 a barrel • what
did he gam? .1/^... $621.00
18. A man earns $3.25 a day, and his daily ex-
penses are $1.89; how much will he save in' 365
'^""Z-, ,, ^//.v. $496.40.
19. I sold 13 bales of cotton cloth, each bale con-
taining 10 pieces, and each piece 19 y.ards at .05 iicr
^ard ; what did J receive for the whole {
ilsof flax-
$3000.00.
5 cents a
ins. 62.25.
^ cents a
ins. 11.60.
) cost ?
$1750.14.
iece con-
ta. $14.00.
L^sts of tea
I pouiKl ?
IS. $84.50
ost, each
. $275.31.
at $135
was the
IS. $3075.
oth each
'Id it for
s. 174.06.
of flour
3l ; what
$621.00.
Inily ox-
^ in 365
$406.40.
►ale con-
t .05 per
HULriPl.iCATlON
WRITTEN EXERCISES,
(1.)
356
7
(6.)
7002
28
(11.)
3063
49
(16.)
3073
42
(21.)
7006
235
(26.)
10034
• 806
(2.)
392
%
a)
5062
15
(12.)
7802
25
(17.)
4063
55
(22.)
8067
007
'27.)
4006
450
4
(8.)
7803
26
(13.)
5632
78
(18.)
0063
75
(23.)
4063
204
(28.)
70632
0/\rt
.(4.)
1056
(9.)
3056
88
(14.)
7032
51
(10.)
6803
123
(24.)
80{}3
204
'20.)
45632
6o7
77
(5.)
305
5
(10.)
4063
42
(15.)
5062
97
(20.)
4563
2')7
/25.)
7006
752
,'30. )
8963
404
is
MULTIPLICATION .^
Multiply
''H. 0G5 })y 1.
'iS. 805 })y 45.
84. •7302 ])y 71.
85. 062 by 15.
86. 2008 by 9.
87. 850 by 10.
88. 4000 by 21.
30. 70602 by 50.
40. 70032 by 01.
41. 80213 by 70.
42. 5008 by 101.
43. 0032 ])y 500.
44 7820 by 20.
45. 80032 by 108.
40. 7003 by 75.
8032 1]
y 270.
48. 8584 ])y 002.
40. 70021 ],y 008.
50. 50032 by 403.
r>l. 8084 ])y 132.
52. 28501 by 175.
53. 3002 by 581.
A4. 8008 by 705.
55. 7003 by 300.
50. 50002 l)y 280.
57. 85032 by 5003.
58. 7000 ])y 304.
>y 702.
/;q Anr.o-t i,
-X'JXJU i.
fO- 20068 hy 142.
Ans. 0755.
82. 1008 l)y 150. ' Am. 1
A
A
na.
05828.
10425.
m. 522702.
Am. 14480.
Am. 1S507.
Dimm.
47. I^ivisionis'th6-processofiindino. how inanv
^ one number i. contained in anot W of :L:;:!
DIVISION TABLE.
divided Ly I equals 0; div
any numbor equals 0.
ided h\
2 equals 0; () divided by
.V^-^^W-
■ .i TMfTMWIwWHwiT >| ii ii-. ^ ff ;^ | ,^|rt,^ fui ^
80
9-^9=1
18-:-9=2
27-9=3
36 ;-9=-4
45-^9=5
54-^9=6
63-^-9==7
72-^9=-8
81-^-9=^9
DIVISION.
10-HlO=l
20--10=2
30-10=3
40 -.-10=4
50-:-10==:5
60^10=6
70 rl0=7
80--10=-8
90-10=9
11^11=1
22--ll=:2
33-11=3
44-:-ll=:4
55--ll=5
m --11=6
77 :-ll=7
88-11=8
99-:-ll=9
12
24-
36-
48-
60
72-;
84
96
108
12=1
12=2
12=3
12=4
12=5
12=6
12=7
12=8
-12=9
OJiAL EXEMCISES.
6--2=?
8-1=?
9-^9=?
4-f-2=?
6-f-3=?
8-^4=?
9-^3=?
8-2=?
7-f-l=?
16
2 1
8 ?
8 •
24
3 •
36 9
4 i
24 9
6 '
f=?
16 9
8 •
14-:-2=?
18-3=?
16-f-4=?
15--3=?
12-^2=?
12--3=?
18—2=-?
25—.^=?
24-4=?
27-- 3=?
27.
28
30
33 9
11 •
35
42
45
t
56.
12
63
'=•?
II.
24-4-8=?
28-4=?
20-:-5=?
32-.^4=?
30-6=?
35_._7=?
36--9=?
32-^-8=?
36—6=?
40-5=?
72 ?
81.
84.
12-
=?
36 ^?
12 •
48 9
8—-,
3() 9
10-
i
10 9
5 — L
99 ?
11"^
80.^9
10—%
< I 12 — L
48
45
48
44
49-:
56
50-:
54
64
63
6=?
5=?
12=?
11=?
- 7=?
8=?
10=?
9=?
8=?
7=?
10 9
•2 i
54 9
6 1
91 9
12 •
72 9
8 •
40 9
5
iK) 9
10— i,
•am '
42.
:7-
:?
>' * •<
77 9
(11 •
18 *>
40 — ;
\ ^ V
12-^-12==:l
24-f-12=2
36-^12=3
48-12=4
60:-12=r)
•72-M2=6
84-:-12-:7
96-:- 12=8
08 ;-12=-9
i>ivisiojv.
8-;
5-
8-
4-:
d-
y
1
;- 6=?
5=?
12=?
:-ll=?
:- 1='?
8=?
10=?
9=?
8=?
J-f- 1=1
10
2-—'
54.
6-
<J1
12
8
5
?
«
?
=?
00 o
io— i,
18^'>
40 ?
8~v
15--5=?
16-^5=?
12-6=?
14:6=:?
21: Y=?
24-f-7=?
40-:-8=?
46-:- 8=?
18-9=?
26-^9=?
22-^2=?
36--3=?
48-^^4=?
55-^5=?
88-f-4=?
28^2=?
46-f-2=?
69-:-3=?
77-^7=?
64--2=?
(12+ 6)- 3=
(20+ 4)-^l2=.
(17-f 1])-- 2=
(26- 6)-^- 4=
Si
23; 3= ?
10 : 4=?
42:-8=?
17-^-6=?
12:-7=?
19-;-3=?
25 ^6=?
34-^5=?
43-^5==?
53-:-9=?
Ill
•37 : 10=?
73 : 8=?
GC) :- 7=?
69;- 8=?
95M1=?
87-:- 12=?
{]d~ 9=?
18--ll=.?
44-:- 7=?
' BS-r- 9=?
IV
03-:-3=?
68-; 2=?
50-:- 5=?
66^6=7
86-:- 2=?
8i-f-4=?
63-f3=?
06 : 8=?
44 : 2=?
I)f>-: 9='?
48-;-3=?
75^5=?
60v-5=?
96-:-8=?
84-:-7=?
91--7=?
78-^6=?
85-:-o=?
42-:-4=?
51-:-3=?
(47- 5)-:
;?
2^?
- 6==?
(19-1-17)-;- 5^? I ( 5
V
(37-1-16)-- 9=?
(29-13)-.. 6-?
(48- 7)-^ll=.?
( 7x 6)~- 3=?
( 8x 9)-- 6^?
( 6x 4)-- 2='?
X 8)--
(6
4S
72
X
-(
^(
81
82^10=?
74^11=?
35-:- 4='^
27 - 4=?
99 --12=?
55 ~- 7==?
81 :-12=?
75-- 9=?
63-;-lG=?
51-f- 6=?
78--7=?
43-:-S=?
61--4=?
79-f-5=:?
75-;-4=?
94-6=?
82-7^?
33-^2:^?
47-^^3=?
58-^4=?
^)^ 7=?
2X 6)=?
3x 4)=?
4x 2)==?
'^4^-( 3x 2)=?
4=? 84
96--< 8x 3)=?
-( 3X 4)^?
'Jj
ill
"mm
82f
(18- G)
(30— 9)-:
(84— 4)
(63— 8)-;
(76 + 12)-:
(36+ 7)-
(42+23)-
(80+ 4)-
( 7x 8)
( 8x 9)
DIVISION.
;-( 4+2)=?
( 1 + 4)-?
( 3+7)-?
(11-6)-?
(14-3)-?
-( 8—1)-?
-( 3 + 2)-?
-( 6+3)-?
-( 4X2)-?
;-( 4x3)-?
(47- 7)
(93- 8)
(43 I- 7)
(48+12)
( 8X it)
( V-^ 0)
( 8X11)
( 7X 9)-
(78-^- 6)
(93-^ 3)
( 3X1)-?
( 6x2)-?
-( 3X5)---:.?
( 6x4)---?
( 4X3)=?
( 9+1)=?
( 3 [6)-.?
(17-3)-?
( 3x4)-?
(72-: 9)=.-:?
VI.
1. At 4 cents a piece how many oranges can be
bought for 16 cents ? 28 cents ? 32 cents ? 20 cents ?
8 cents ?
2. A man earns 1^2 a day. How long will it take
him to earn ^18 ? $4 ? !^6 ? $12 ? $2'?
3. How many yards of muslin can be bought for 72
cents, at 6 cents a yard ? 8 cents ? 12 cents ? 9 cents ?
4. How many times can 5 yards of cloth be taken
from ii piece containing 25 yards? 45 yards? 60
yards ? 30 yards ?
5. By writing 8 lines a day how many days will it
take John to write 56 lines? J 6 lines ? 64 lines ? 88
lines? 40 lines ?
6. At 11 cents a pound, how many pounds of
sugar can be bought for 88 cents ? 55 cents ? 99
cents ? 22 cents ?
7. If one man can do a piece of work in 36 days,
how long will it take 9 men to do it ? 4 men ? 6 mer ?
3 men ? 8 men ?
8. Divide 24 into 3 equal parts. Into 6 equal parts.
IM V ' . : o N
83
3X1)--?
6x2)-?
3X5)==?
(3x4)-?
4X3)=?
9+1)=?
3 + 6) r:r?
3X4)-?
r2-;9)=n?
5 can be
!0 cents ?
1 it take
:ht for "72
9 cones ?
be taken
rds? 60
rs will it
ncs ^ 88
unds of
iits? 09
36 days,
(] Trin-ji ?
al parts.
0. How many dozen of Qo-crs at 9 ro.if^ o .i
lots ot 10 acres each can be sold '^ ^
14. In what nunil)or of davs will n ^ ^
miloa. at ,ho rate of 5 n.ilo.?;!;'" """ "''"■^■' ''
15. How many tim.-s 9 is times 1" '
for «3.'' WsTiro'A;^^"""'^ '^'^ '^"" ''^' ''"^'■''-<'
IT. Mr. Jolin-soii travelled 140 miles in T ,i
how many miles did he travel eaeh day , " ' '''"'^ ^
18. How often is 5 contained in T-fi ? ft,> ? co ?
l.». How many barrels of apples of sq , u . '
be purchased for m ? $i}r, ? |3o ,' * " ^''"'^' «»''
44Th'^ ["'T '""'°'" '''"''" '^ *«0. •-" 'he rate of
»4ahead. How many did he buy ?
ati^i^L:;:;7'^^^'^^^^^^^^'"--^-oid..ii2o
relsts^^""''''"'"^^^^**'^''^^'^^^-"'^
2a If a man earn $.x> in .» weeks, how much xvill
ho earn in ] 1 weeks ? ^^ "*
24. If 8 yards of cloth cost |48, what will 12
cost 1 Ir, yards ? 9 yards r 14
yanis ?
25. What will 5 tons „1 hay ci>st
^26? 118 ? 130? 36?
iftw
12 yards
ons cost
it
84
DIVISION
i i
26 How many bottles of mucilage at 10 cents a
bottle, will pay for 40 copies at 4 cents each ?
.7 At the rate of 28 miles in 7 hours, how far
o" V ""''" ^''"''^^ "' ^^ ^^^^'•« • ^1 hrs. ? 14 hrs ^
28 How many bedsteads at $6 each, can be bou-ht
or 11 boxes of oranges at $G each, and |18 worth of
lemons ?
2it How many fancy lead-pencils at 9 cents each
will pay for 5 tops at 6 cents each, and 11 three-cent
stamps ?
30. How many times can a father divide r
among his three sons, giving each |5 every time ?
VJI
1. 5x4,-2,+X.-.4i.;6,-f>4,+6,-ll,+4:= ?
^- ^^ 1^'X^' ^^^^-'- 5,X3,l-4,^7,-2,-|-8,x3= ?
3. 27-'3,^8,+« :«3,-r,0,X3,-l^,-f 25,-^8= ?
4. 48-^6,+3,X9+l~10,-4,X13,-8,-^7.-f4:^?
5- 144^12,-l,xll,--13,-^9,-5,XG,-2,^10:^?
6. VX9,-3,-^4,+3,X3,-4,X2-19,^9^?
7. 3C+9,-4-5.+2,-^3,+4,x5,-25,-^-8,+6= ?
8. 21-+9.X4,-10,H-ll,+iG,-^2,-3,-l,x9=. ?
1). ]08-f-12,+llH-4,^4,H--l,x7,-2,-^3,xY=^ ?
10. 86~.31,-^ll,+i7,_4,^9^_|.^X4H 11,-2= ?
) coiits a
how far
14hrs. ?
bought
worth of
its each,
ireo-cent
ide $90
time ?
3=?
= 7
10= ?
- ?
: ?
DIVISION. Q^
SHORT DIVISION.
1. Let it he required to divide 32540 by 5.
OPERATION. So^t;Tro^^^Traving•w^iUon the 'divisor at
_ . . Dividend ''« '^^^' 0' t"e dividend, with a .'' ved in
Divisor 5 ) 32540 'l'^^^^" l''^"'- we begin at Uw j.vide
'''. '^''^'''"' P°'-tB of the divi. M ,,e
Quotient (3508 '1^'%. ?"f ' '^ "^^ ^^"^"^'""^ '"3 we
a quoiienl and 2 thouonndir '' '^'"' ^''''''' ^ thousands for
sandsunder ho t "orand^anVrr'^^^ ""' ^^''^^ ^"^ « ^''-'•
annex the next i^J^^l^^^^^rtZ ' 'T''^'' ^
hundreds are equal to 25 hundred.^? .^^^^«"^«"''s and Hve
6 hundreds times LcVZt ^ '^ «°"^«'"ed in 25 hundreds,
than 5, there are no t n in tho "r '''"''"'''' ^"'^ «'"^« ^ '« ^^^
t"e pi;ce Of Is anr nn?x r flw•^^'""'°" "^'^« ' '"
'naking /.O units. Dividing ^n is bv 17 T' 'o '''' '°"'' ^^"«
ParJofthe^vri^K^-lr^^^^^^^
(2.)
4)672
Ans. 1G8
108
4
Proof
672
Illustrations
(3) (4.)
6)287 7)908
(5.)
8 ) 8145
475
47
6
282
6
287
129
129
903
1018>^
JWi
8145
IMAGE EVALUATION
TEST TARGET (MT-3)
/.
i<
&
^
1=
11.25
1^
12.2
2.0
1^
U 11.6
I
ihic
Sciences
Corporation
33 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 873-4503
'^^\
iV
:1>^
s>
V
;\
.1^>
I
<i
%
!
) I
86
D I V I S 1 iq" ,
WRITTEN
EXERCISES,
Divide :
. , . -
-
.
. , 6.840
by 4
Ans.
210.
•
7. 950
by 5
Ans.
190.
'
8. 834
by 6
Ans.
139.
9. 399
by 7
Ans.
57
10. 441
by 9
Ans.
49.
11. 392
by 8
Ans.
49.
12. 616
by 7.
Ans.
88.
13. 555
by 3.
Ans.
185.
14.
711 by 9
32.
24319
~ 9
15.
736 by 8.
33.
36848
-4- 6
16.
879 by 5
34.
20895
-f- 5
17.
384 by 6
35.
49763
-^-7
18.
472 by 4
36.
93007 -
^ 3
.19.
938 by 3
37
86214 -
-=-5
20.
477 by 2
38.
53720 -
-- 9
21.
2735 by 7
39.
38808 -
~ 3
22.
8945 by 6
40.
10738 -
^ 4
2.3.
2147 by 8
41.
345678 -
^ 9
24.
6092 by 9
42.
744018 -
T- 8
25.
8070 by 8
43.
456843 -
•■-7
2f).
6439 by 6
44.
945600 -
4- 6
27.
8296 by 7
45.
347017 -
-7
__28.
7350 by 5
46.
532801 -^
>- 6
29.
5837 -^ 4
47.
8077636 -
- 8
30.
4002 4- 3
48.
6300857 ^
- 4
31
73504 ~ 8
49 90437284 -.
-9
50. 76110884 -- 3
n
l"r
h(
w
of
cu
^lYlBlON.
87
x^- A gentleman divided Jisn »
P«reon», giving j4 t„ 2 h' "*>' """« P"'^--
were MieTc ? '' ' '"'"' ™*nr Poor persons
bu'/io^JTsV?""' ''^^"' """"^ ''""^ »f wood could .
55. At the late of T *v -i
-M u ,,, , ,„„/J, -'^^^ a„^ -. ^ho. ,o.,
«u 1820 days > ' ^*^^ '"^"X w^^^ivs
t>2 A 1.U ichaut yained 139875 dolk,, ,•„ ,,
what wa» his average yearly gainT"" " '"'"'
^'i- How many loads mav b.^ f ,t.„ r
oi gravel of 82806 cubic feel i' e, i in T ' '"'"
cubic feet ? - *^" ^^^^ contani 1 [
MM
88
D I V I S I O JT .
rh
LONG DIVISION.
1. Lot it be required to divide 50289 by 3t2.
Operation. Solution.— since 372 is not contained
in 5 tens of tliousands, or in 50 tliou-
santls any thousands times, there are no
tliousands 'n the quotient. Annexing
the next figure, 2, we have 502 hun-
dreds. 372 is contained in 502 hun-
dreds 1 hundred times with a remainder.
Write the 1 hundred in the quotient and
multiply the divisor by it, subtracting
the product from the 502 hundreds.
This gives for remainder J 30 hundreds;
to which we annex the next figure 8
tens, making 1308 tens for the next par-
bivifor. Dividend. Quotient,
372 ) 50289 ( 135
372 ,
1308
1116
1929
1860
69
Remnindert
tial dividend. The quotient of 1308 tens, by 372 is greater" "than 3
f.n.l less than 4 ; hence there are 3 tens in the quotient. Multiplying
"~^ by tens, we have 1116 tens, and this taken from 1308 tens
37
leaves 192 tens ; to which we annex the next figure 9 units, makin'^
1929 units. 372 is contained in 1929 units, 5 times with a i-emain"-
der. Writing Uie 5. units in the quotient, and multiplying and sub-
tracUng as before, we obtain the remainder G9. Hence the quotient
)s 1 hundred, 3 tens, and 5 units or 135, with a , ader of 09,
2. Divide 1062934 by 306, and prove ft.
Operation. Proof.
l>ivi8or Dividend Quotient.
306) 1062934 (3473
918
3473 QuoJent.
306 Divisor,
1449
1224
2253
2142
1114
918
Remainder 196
20838
10419
1062738
196 Homainder.
1062934 Dividend.
not contained
' in 50 tliou-
s, there are no
It. Annexing
ave 502 hiin-
in 502 Jiun-
1 a remainder.
5 quotient and
;, subtracting
02 hundreds.
30 hundreds ;
next figure 8
the next par-
reater than 3
Multiplying
n 1308 tens,
inits, making
ith a rema in-
king and sub-
the quotient
ler of G9i
3 QuoJent.
'6 Divisor.
8
8
6 Boniainder.
4 Dividend*
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
80;
31-
32.
^VlilTTEN KXEliciSEs.
89.
3- 888 --37.
4- 936--52.
"'• 975-25.
45G--24.
924-33.
54G-13.
804-G7.
946 :-43.
608-38.
894-76.
247-^19.
498-27.
816-80.
306-18.
537-46.
732-61.
364-29.
604-54.
477-^53.
836-44.
4214-49.
1335-15.
1617-21.
1081-^23
6184-:-58
8476-83
7581^-47
3544—93
6450-25
Aus.
Ans.
24.
18.
Am. 39.
Ans. l!>.
28.
42.
12.
Ans.
Ans.
A ns.
Am. 22.
Ans. 10.
Ans. 11^
An.-i. 18.
Am
I827.
^ns. 10^.
Ans.
Ans.
8^43-34 I 39
17.
^ns. 12.
^ns. 12]J.
Ans. llJJ.
Ans. 9.
Ans. 19.
Ans. 86.
Ans. 89.
Ans. 77.
8864-^92
5621-77
1209-31
2151-57
3864-86
12194-67
13314-42
lis
90
DIVISION.
it
fl
40. 38584---53
41. 1010(1 -2()
42. 70308: 37
43. 430501-95
44.
45.
40.
74009
04584
72259-
-83
:-7l
41
80819-:-
32406-f-
40950-:-
72828-:-
51084-^
47025-:-
47.
48.
49.
50.
51.
52.
53. 80257-
54. 74670-f
55. 145132-
56. 143082-:
57. 734530-:-
.■>,s. 350479 -
59. 504800:-
60. 3971954- 427.
61. 8450834 :-^ 889.
62. 1317296 : 232.
63. 6131043-- 681.
64. 1880810-- 397.
65. 4020621-5007.
66. 5718006: 6873.
67. 609960-:-1326.
68. 122031 3 -:-4503.
69. 4G05430--7663.
64.
33.
126.
867.
396.
627.
913.
108.
307.
462.
136.
320.
208.
Affs.
Am.
A /fs.
Ans.
Ans.
Ans.
Rem.
Rem.
Rem.
A as.
Am.
Ron.
Rem.
Am.
Am.
Am.
Am.
Rem.
Ans.
982.
325.
84.
129.
75.
70. 187790-:-2110
71. 273631-^-7329
72. 408576 ---4864
73. 1395940-3068
74. 2987620-:-6020
75.
76.
77.
78.
79.
826.
42.
228.
311.
5401
79.
192.
9302.
9506.
5678.
9003.
221,
803.
Rem. 6543.
Am. 460.
Am. 271,
Rem. 7630.
4268004:^5300
2462776-3709
846301--8219
11590744-1352
16815620->-3470
80.
81.
82.
83.
84.
85.
24L34744
32174272
12(Jr>5()9(>
t>3000180
7047400
5787088
UNITKD
;»IVlsiON.i
'^4072(86. 28898922
"77432 87. 7292924368
''5<5752 88 3289054376
86420 89, 10824675400
'^3400 90. 65642058
44671 1
STATKS CURRENCY.
88647
846007
' 13792
520117
326474
the answer in conK wi i '^"^^'^^"^ ^^^^^ ^o
dollars and CO s,;!,:!"/^ ^"^^^ ^^ -^«e.d to
places from the ri'ht ^ ' "^'""'^"^^ ^^^"^^ *^'<^
as ill simple nxunbers Th T"^' "^^ ^^^'^^«
required number " ^""''^"^^ ^^" ^^^^ ^^^
1 r^- •, . Jr.LUSTKATIONS.
]. Divide 1187 equally among 13 men
(1)
cents, cents.
13 ) 187.00 ( 1438
13
$14.38
57
52
50
39
110
104
(2)
^•50 ) 600.00'( 80 barrels.
3
92
PI VISION.
«
:- <
$5G.
908.
210.
47
12
2401.
30.
Ans.
Ans.
Ans.
Afis.
Ans.
Ans.
Ans.
Ans.
WMITTEN EXERCISES. >^
3. Divide $396.76 bv 28 a a,. ^
4. Divide 11308.24 by'': ^'^ ^^^-^^
•'>• Divide $0048 by 108.
«. Divide $'37806.2{) by 30'>
l V}''''^'' ^'^'^88 by ll^ents.
8. Divide $137.07 by 63 cents
9. Divide $15275 by $325
10. Divide $9672 by $806
11. Divide $0003.75 by $3 75
12. Divide $276.00 by $0 20. ^,,, o.
eo'A '''' "''' ''^""^ '''' ^''^^^ ^^-fwill laere
^^^^ If 516 cW cost $2012.40, what wia'^;!;!^
co:f$^:;r^^^^^^-^^^^i^^y^^^et^S
19. Bought a barrel of vinegar for iu!t ^^If
rate of 21 cents a o-ilinn -v. SI^-23, at the
barrel » ° "" ' ^""^ """y S»"ons in the
20^ How ^„ch does a laborer receive^r dafif
lor 42 days, he earns $56 70 'i . ^' "
21. A. $7 a barrel, how n,any barrels of L^'''-
be bought for $273 ? "^^rreis ol ilour can
22. How manv Trlr^e f i ,^ JlAm. 39 bbl.
=33.50 at .3 62 LrlV^'^'" ''^^ P^-^^-ed for
$633.50 at $3.62 per yard ?
^^. 115 ^ds.
«jf. §16.50.
«»■ 908.
210.
'47
12.
2J01.
30.
t will 1 acre
Ans. 1126.
^^l 1 chair
Ans. 3.90.
leep, if 280
^«.v. $;j 00.
iwd, when
^«s. o5t.
ohI ca^ be
«s- 13 tens.
>e bought
24 baskets.
'3, at the
>ns in the
^ 63^ra/s.
r day, if
^s. $1.35.
lour ran
s. 39 ^6/.
Glased for
175 2/ds.
Divide :
1
2.
3.
4.
5
6.
7.
8.
9.
10.
11.
12.
13.
14.
35.
DIVISION.
M'PITTJ'JN ILXEliClSES.
9&
408 by 2.
078 l)y 0.
525 by 7.
392 by 8.
504 by 9.
455 by 5
•792 by 8.
843 by 3
4080 by 4.
3961 by 12
4802 by 34.
39623 bv 61
43693 by 36.
35021 by 70.
49680 by 35.
16. 185952 by 20.
17. 38284 by 28.
18. 16967 by 47
96720 by 304.
8352 by 427.
6533 by 307.
18538 by 806.
32445 by 45.
4962 by 23.'
89322 by 756
4821 by 73.
19.
20.
21.
22.
23.
24.
25.
26.
34470
-'8. 53084
29. 41097
30. 57353
33. 0845
32. 23344
33. 26000
34. 8232
35. 25830
36. 3001443
37. 72072
38. 833405
39. 03045
40. 03984
43. 95048
42. 232002
43. 255045
44. 8430
45. 15341
46. 3450
47. 109440
48. 72134
49. 450203
50. 0024
51. 56396
by 08.
hy 831.
hy 57.
by 83.
by 07.
by 392.
by 208.
by 147.
by 246.
by 5789.
by 572.
by 6883.
by 791.
by 356.
by 98.
by 5740.
by 6b. 6.
by 1405.
by 529,
by 27,
by 608.
by 329.
by 856.
by 72.
by 184
H
INTKOPUCTOKV FRACTIONS.
i i
I- i
INTRODUCTORY FRACTIONS.
h
1 unit = I
*
I k
I 50. Ifa unit is divided into
two equal parts, one ol iho
parts is called one half.
f l^^^"" "»it is divided ipto
i\t\ '^'■^« ^*1"«1 parts, one of tho
M ""^^ =3 1 ^^'*' ^' ^'«IWonc third ; two
' ofthej.arts are called two
thirds.
inheunitis divided into
lour equal parts, one of the
i i
i — J-". 113, Kjuii oi ine
lunit = i ^^r'%V'"'^'"'^""^^^'
4 two of the parts are^ called
two fourths, and three, three
. lourths
OJtAL EXERCISE S^
1 How many halves in a unit ? in 2 units ? in ^
units ? in 4 units ? in 6 unit, f ''' ^
2. How many thirds in a unit ? in 2 units? in q
units ? in 5 units .? in 8 units ? '"^ ^
3. How many fourths in a unit ? in 2 units ? in 4
nnits ? in 10 unitt ? . "*
4. How many halves in a unit and a half? i„ o
units and a half? in 3 units and a half? '^ ^
5. How many thirds in 3 units and a third? in k
units and two thirds '•• ^^ * ^^ ^
oNa.
ONS.
i divided into
'i one ol ihc
>ne hair.
Jividcd into
s. oue of Iho
e ^hird ; two
called two
ivided into
one of the
5ne fourth;
are^ called
three, three
nits? in 3
nits ? in 3
nits ? in 4
alf ? in 2
ird? in 5
^NTRODUCTOKV FRACTiOI.s.
II
95
I Find i of 4, I of 8.
Solution To fin.? i ^r
2- Tim., j of 4=.4 J2I2 Z '""""'" ""■'''•' """ "">"'»r by
If. ^ of 8=r3 tinios 4 nf « *o-
S of 8=,3^4, X 3 j;/;f; •^...o... .t of 8=8^4, tloreforo
2. What is i of 6 ' of 10 ? r , ^ „
30?of50? '^"-"f^JofSOJofa^, „f
moT?:V'^"'''^°^^^^''f''5^ofl8,of04,of
ofteJ^'oti^^/^-^^^^^^'^^^^^ofso.or^s.
«o'ont^^*r/''^^^^»^^«?of.onofeo*of
7. At 20 cents a notind fm. i,
P'-^y for half a poundT '""'^^ ^^^^* ^«st you
8. When coal is worth « ^ n
IH' paid for i of a toll ? '"'' ^ '°"' ^^at ™„st
B. If tliere are 12 on i ■ <, ;„
onncesin jofaj,o„„d^ " ^"""''' ^<'"' Wany
eel- in foTa dll7^'="'^^" »'■«''-. W. a..,
.sLTtL^;i!tr:^:;^^i':ieo..at*4a,^
y«* will coat $288;i3rrMo™;lf "' *' ^ *'■ "-- ^^1
will «3 ix>„„d, of tea
j. At <iu cents a pound what
cost?
3. If
w"urpordf:sr»^-^^or^eet
what
ti:
i
96
INTIIODUCTORY PIIACTIO
NS-
4 AVhon rninins are worth fj of a (l«.]lar a boj
whjil will ].'{.-, 1
)oxes cost ?
•'>. WJiat must a n
ro(
toes at noj ,MMilsa }>iisli,.] ?
or pay for 3f) bushels of pot)
"• What will ;-,2
Ji ])()uikI
7. A
pounds of sunj-ar cost at 11 J centj
jnan havino- $uoo, si>cnt ^ of it. How much
Jiad he loft ?
S. AVhat cost 1L>!I7 (I
dozen ?
ozon of eggs at U)^ conis a
Ans. 1214.005
^' ^t <>| cents a spool, what cost <)245
thread?
10. IVliat cost 7842 yards of muslin at 33i
spools of
Ans. $r)77.H125.
yard ?
11 AVhat is the cost of 525 pounds .of
rents a pound V
12. Find the cost of 2500 melons at 2
cents a
Ans. ^2(J14.
sugar at 12 J
Ans. v$f35.025.
5 cents each ?
13. Wliut must be paid for bales of cotCoi'
tainin
120
Dound
1'.').
on, cou-
s eac
at 10 2 cents a pound ?
14. "WJinl will 18
45 yards co.st, at 25 vaut
pieces of calico, each cont
Af/s. |;420.
!unijij>-
15. If a wlieel turns 480 t
s a yard ?
Ans. $20-2.r)0.
imes in going- a mile, how
many times will it turn in going ;;. of a mi^le 1 Ans. 300.
16. At $2;^ a yard what will be the cost of 240
An.<i. 1600.
pages in a week, how
y pages can he write in 8/5 of a week ? An
30.
yards of silk?
17. If a boy can write 50
man
18. A boy sold 9^ dozen
He received m payment 6| pounds of ]>utter at 20
c^mts a pound, and 12= yards of ribbon at 3 cents a
yjird. How much is still djie hyij ?
ONS.
do/liir ii box,
shds ofi)ofa-
t nt 11? rents
How mmh
H)J conis a
h/s. !|214.00r>
45 si)0()ls of
s. $r,77.H125.
fc 33^ colli s a
Ans. $2(n4.
su^ar at 12 J
l«.s. .I65.G25,
cents er.ch ?
Ans. s|G2r).
cotton, con-
)ouik1 ?
^//.v. !ii420.
I contaiiiiii*'-
«.s. #202.r)0.
aniilc, liovv
e?/l/^.v. 300.
cost of 240
Ans. $GGO.
week, how
:? ^«.s-. 30.
ntsa piece.
Litter at 20
t 3 cents a
TABLES.
A
• I*
(Canadian Money.
''^ "'ills mako I ,-,.,,1 , ', .
JO corns .. ,:"' "'''"•'^"'' CI.
' nollar, « 0,
United States IVIonev.
I'Oonnls u i ,,. "Kirk.vl cl.
t').nn,os . r " .1.
c<-»ts ^ i„ eents ? in 8 cent. ' ',- t . "''"'" • "» ^
2. How many cents in? ?^^''^"''^-
^i«^^^« ? in dimes r ^^""^^ • ''' ' ^''^"-^ '^ in 5
5 "own,anymilIsi„5,ents^dn •
fonts m G dimes ? '^""^'''^ "> •' dollars ?
<^. How many dolJ-.i-v. ,„ i
12 eagles ? ^ '^''^' "^ ^ '^^^^"I^^^ ? in V eagles .> in
7. How many rent, i,, m i,
^« "^iiLs ? in 30 miJil , "'^^^'^ ' ^'" '^^ "^'"s ? in
97
niilh
m Jr "^"I-''^ -ul ,„,„.
9.- How
in o< mills .<'
in 98 mills
^^^ It) mills ?
cen
many dimes and
i^h}U,nuf^ '''''' '''''^ --nisi
in 8(>
m G3
98
TABLES.
• ?o ?T ""^"^ ^^^^^ ^'^^ dollars in 36 dollars ?
m 49 dollars ? in 72 dollars ?
English or Sterllxg Money.
4 faKhings, fur., make 1 penny, marked d.
-'shillings . ,gm„,^^
Mi
«■:
Oi?^Z EXERCTSES.
1^ How many farthings in a penny ? in 3 pence -
m 7 pence ? in 9 pence ? ^ J' m d pence .
andl^rj'""'^'™"^^^^" ^4. and .5s.. in £10.
•7. How many d. in 9s. 8d. ? in 12s Od v
J^.^Howmany pence in 20 forthings ? in 48 far-
ini}Z:r^"^^'^-^-^^^--^in9ed.
10. H(
low
shillii]
many .€ and s. in 25 shillirm-s ?
gs ^ m 14G shillings ?
gs V m 68
I 36 dollars?
EY.
Bdd.
s.
£
ill 3 pence ?
4 shilling's ?
n 5 pounds ?
1 6 guineas ?
fjir. ? in 8d.
*. '^ in £10.
? in 48 fai-
? in 96d ?
gs ? in 68
TABLES,
Troy Weight.
99
Tiie denominations of Trnv w„- i <
weights, and grains. ^ "^''^ ^'^ P^^nds, ounces, penay
Tl'opoun,, Troy c„„,.i„, 5,700 ,,.,„,. "■ ,
*.-M,
OiUL EX'-^CJSES,
3. How many trrains in „
l^eunyweights ? i„°6 dwt ^ P«"°y"'«Sht ? in 3
o..'"°iTrr'^«''-"—e. in, „,,,„,
3. How many ounces n, « v.
^^5.^Ho,w „.„, ounces i„ 10 dwt. Uu 80 dwt. i„
.rln~^r -•»«-.» 49 grains, in 8„
9. How many dwt \n 4 «-,
5 dwt. ? ^ • ''' ^ ^^- '-^^d 3 dwt. ? in ^ _
— ♦ vii,
XO. rintlir rv»r»«,— _
ounces m 6 pounds and
8
«z- ? in 5 lbs. 9 oz. ?
oz. ? in
i
iap
100
TABLES.
Avoirdupois "Weight.
Avoirdupois Weight is used lo weigh all common goods, such as
groceries, hay, grain, and ail nielals, exceitt gold and silver.
The denominations of Avoirdui)ois Weight are tons, hundred-
woiglils, quarters, pounds, ounces, and drams.
10 drams, ur,
IC ounces
25 pounds
4 quarters
20 Jiundredweighl
make 1 ounce, marked oz.
" 1 ])ound, " lb.
" 1 (juartor, " qr,
" 1 hundredweight, cwt.
" 1 ton, T.
The pound Avoirdupois contains 7,000 grains.
OliAL EXERCISES.
1. How many ounces in a pound ? in 4 pounds ?
in 8 pounds ? in 10 pounds ?
2. How many lbs. in 2 cwt. ? in 7 cwt. ? in 9 cwt. ?
3. How many cwt. in a ton ? in 6 tons ? in 9 T. ?
in 12 T. ?
4. How many ounces in 3 pounds ? in a hundred-
weight ? in a ton ?
5. How many pounds in 32 ounces ? in 64 oz, } in
128 oz. > in 144 oz. }
6. How many cwt. and lbs. in 120 lbs. .' in 260 Ibs..^
in 340 lbs. >
7. How many pounds and ounces in 39 ounces ^
in 84 oz. .' in 90 oz. }
8. How many ounce ■ in 5 lbs. 11 oz. } in 4 lbs. 12
oz. .? in 10 lbs. 3 oz. >
9. How many lbs. in 6 cwt. 25 lbs. ^ in "7 cwt.
36 lbs. }
10. Howmany tons and hundredweight in 45 cwt.?
in 92 cwt. ? in 130 cwt. ?
foods, such as
silver,
)ns, hundred-
oz.
lb.
qr.
cwl.
T.
4 pounds ?
in 9cwt.?
? in 9 T. ?
I hundred-
64 oz, ? in
in 260 lbs.?
9 ounces ?
n 4 lbs. 12
^ in *7 cwt.
in 45 cwt..'
TABLES.
Apothecaries' Weight.
101
This weight is used J,y apothecaries and nhvs'-ciin. in ,.;.• .. •
medicines, but medicines are generally .o 7 i ,, " """"
avoirdupois weight. ^ ^' '" ^'"' a"anl'ty. by
Its denominations ;fp nniin,io ^
grains. ' '""'^'' ''''''''' '^'^^^'' ^oruples, and
'^^0 grains, gr., make I scruple, marked so.
3 scruples <• i d,.am, - j^
8 drams, .- i ounce, « oz'
r:j ounces •< i pound, u j^'
C^^Z. EJCERCrSES.
1. How many grains in a scruple ^ in 2 s.-ruplos >
m 5 scruples ? m 7 sc. .?
2. How many sc. i,i a dram ? in 6 dr. ? in o ,],. ?
m 20 dr..? ' ^^- •
3. How many sc. in 40 g-rs. .? in 90 .-rs ? in 1^>()
grs. ? in 140 grs. ? ^^
4 How many drams in an ounce ? in f, oz ? in 8
oz. ? m 15 oz. ? ^- • in »
in s/^^'^T "'''''^ '^'''''' "' '^ '*'• • "' ^^ ■'^^- • i'^ '^^ «c- ^
6. How many ounces in 24 dr. .' in 48 dr ? in 64
dr. ? m 96 dr. > ' ' ^
7 How many ounces in a pound ? in .'} pounds >
111 5 pounds .' in 15 pounds > in 20 pounds ?
8. How many pounds in 48 oz. .? in 108 oz > in
240 oz. ?
9. How m-jny sc, in an oz. ? in a lb. ? in 1 Ih 6
oz. ?
10. How
'' \
dram
IS
many grains in a dram ? scruples in 4
drams in 5 lbs. ?
102
TABLES.
pi
WiJVE Measure.
Wine Measure is used for measuring all liquids, except ale, beer
and milk.
The denominations of Wine Measure are tuns, pipes, hogsheads,
tierces, barrels, gallons, quarts, pints, and gills,
4 gills, gi., make t pint, marked pt.
2 pints
'i quarts
31 J gallons
4'2 gallons
t)3 gallons
2 hogsheads
2 pipes
qt.
gal.
bbl.
tier.
hhd.
pi.
tun.
1 quart,
1 gallon,
I barrel,
1 tierce,
1 hogshead,
1 pipe,
1 tun, .
The gallon of Wine Measure in the United States contains 231
cubic inches, and is equal to 8,339 Avoirdupois lbs. of distilled
wafer, very nearly.
The English imperial wine gallon contains 277.274 cubic inches
and hence is equal to 1.2 times the wine gallon of the United States!
OliAL EXERCISES.
1. How many gills in a pint > in 4 phits .? in 6
pints ? in 12 pts. .? in 20 pts. ?
2. How many pts. in a qt. > in 6 qts. .? in 8 qts >
in 15 qts. ? * ^ •
3. How many gallons in a barrel ? in a tierce } in
a hogshead } in a pipe > in a tun >
/ 4. How many pints in 12 gills ? in 26 gi. } m 3t
gi. } in 50 gi. .?
5. How many quarts in 10 pts. } in 24 pts. > in 50
pts. ? in 84 pts. }
G. How many gallons in 1 hhd. 10 gals. > in 2bbls.
15 gals. }
7. How many quarts in a barrel } pints in 2 gal-
lons .? gills in 6 quarts ?
8 How many gallons in 72 quarts.? in 104 qts..?
in 4 bbls. 4 gals. ? ^
9. How many pts. and gi. in 18 gi. .? in 31 m. } m
53 gi. > in 74 gi. }
10. How many hogshead
gals. } gallons in 3 pipes
s in 6 tuns.? pint-s in 8
cept ale, beer
s, hogsheafJs,
contains 231
. of distillod
cubic inches,
Jniled Stales.
■nts? in 6
n 8 qts. ?
tierce ? in
ji. ? in SI
ts. ? in 50
in 2 bbls.
in 2 gal-
104 qts.?
31 gi. ? m
inis in 8
TABl^ES.
Ale or Beer Measure.
103
By this measure, beer, porter, and milk are measured.
ThodenommotionsofBeer Measure .re hogsheads, barrols gal-
lons, quarts, ana pints. . ••"Ills, gai.
pmt
2 pints, pt.,
4 quarts
36 gallons
make 1 quart, marked qi.
" 1 gallon, « gal.
" 1 barrel, << |j^)|
1J barrel or 54 gals- » i hogshead, •< hhd.'
OJiAL EJiEIiCJ8E8.
1. How many pints in a quart ? in 3 cits. ? in 8
qts. ? in 12 qts > i ■ i o
2 How many qts. in a gallon > m 5 gals. > in 7
gals .Mn 22 gals. .? ^ ^
3. How many gallons in a barrel } in 3 barrels >
m
5 barrels > in 8 barrels >
4. How many gallons in a hogshead > in 2 hhds >
m 4 hhds }
5. How many qts. in 10 pts. > in 19 pts. > in 31
pts. > in 56 pts. >
6. How many gallons in 11 qts. } in 32 qts. > in 2
bbls. 2 qts. ^ ^
7. How many qts. and pts. in 17, pts. > in 73 pts ?
in 85 pints > ^ ' '
8. How many barrels and gallons in 75 gallons '
in 110 gallons }
9. How many gallons in 2 bbls 5 gals > in 2 hhds
8 gals, ?
10. How many quarts in 18 pints .? gallons in 68
qts. J barrels in 144 gals. ?
5 i
104
TABLES
Cloth Measure.
Clolh Measure is used for measuring goods sold by the yard. Jts
denominations are ells, yards, quarters, nails and inches.
^ inches, in., malio
4 nails ••
4 quarters "
3 quarters "
5 quarters "
6 quarters "
nail, marked na
quarter, "
yard "
Flemish ell, "
Knglish ell, "
qr.
Fi. e.
E. e.
Frencli ell, " Fr. e.
OJiAL EXERCISES.
1. How many inches in a nail > in 4 nails } in 6
nails } in 8 nails > in 10 nails >
2. How many nails in a qr .? in 5 qrs. > in 6 qrs. }
in 12 qrs. .? in 20 qrs. }
3. How many qrs in a Fl. e. > in 5 Fl. c. > in 10 Fl
e. > in 15 Fl. e. .?
4. How many qrs. in an E. e. } in 8 E e > in 30 E
e .? in 50 E. e. >
5. How many quarters in a Fr. e. > in Fr e ? in
25 Fr. e. } in 40 Fr. e. >
6. How many yds. in 20 qrs. .? in 56 qrs. } in 96
qrs. } in 124 qrs. ^
1. How many quarters in 1 Fr. e. and 5 qrs ? in
9 E e. and 2 qrs. .?
8. How many English ells in 25 qrs. > in 30 qrs. ?
in 65 qrs. ?
9. How many nails in 3 Fl. e. .> in 6 Fr. e. ? in 8 E.
e. .'
10. How many quarters in 5 yds. and 2 qrs. > nails
in 1 qrs. and 3 nails ? inches in 2 Fr. e. ?
yard. Jts
s? ill 6
6 qrs. ?
u 10 Fl.
ill 30 E.
'. e ? in
? in 96
|rs. ? in
qrs. ?
inSE.
? nails
TABLES.
Long Measure,
105
b.e':z.f;r;;' ""■' '^ '"^^^"^'""^ ^^-^^^^ -'^'^-^ -^-'^ to
Us denominations are circles, degrees, leagues, miles furlom^s
rods, poles or perches, yards, feel, inches, and barleycorns ' '
3^barleycorns, b. c. make 1 inch, marked in.
12 inches
3 feet «
r)J yards, or iq iVet, "
•40 rods a
8 furlongs <<
3 miles «
C9J statute miles "
CO geographical miles "
360 degrees •<
1 foot,
1 yard,
I rod, pole or perch,
1 furlong,
1 mile,
I league,
I degree,
1 degree,
I circle.
It
ft.
yd.
rd.
fur.
m.
lea.
deg.
deg.
cir.
OUAL EJCEMCISES.
1. How many barley corns in an inch.? in 3 in-
ches .? in 10 inches .? in 20 inches }
in 9 ftHiATy""^"' "' ^ ^""^^ ■ "^ ^ ^^- • ^^ ^ ^t- •'
int fdr; rrjyt' r ^^ ^-^^^ • "^ ^ ^^« • "^ ^ y^- -^
in 63^tT '"''''^ ^^''^' '" ^^ ^- • "' -^ ^*- • "^ 57 ft. .?
in.'p inT^ T>\^^1 '^^ "^^^^^ "^ -^^ -^^- -^ "^ 3«
in 49?tTr62Yr'^ "^^ '^^^^^ "^ ^^ ^-* ' "^ -^9 ^^- -^
8. How many furlongs in 12 miles > leagues in *>!
miles ? degrees in 360 geographical mileK ? ^
J. IIow many rods in 2"miles ? in 3 leagues > in
16 furloncrs } m 1 miL. a«/i .i f.,..! ^ ^^^^ " "^
furlongs > in 1 mile and 4 furlon^« .
.0. How many feet in 16 yds. 2 ft. } inches
!l
10 in. }
in 8 ft.
106
Sq,uake Mkasubb.
This measure is used for >»>asurinp all kinds of surfaces, such
as land, boards, plaslcring, and every thing elso in which length
and breadth only are considered.
Its denominations are square miles, acres, roods, scpiare rods or
poles, square yards, square fret, and square inches.
Ii4 square inches make t square foot, marked sq. ft.
•J square feet " I square yar.i, " sq. yd.
30^ square yards, " I sq. rod or pole " p.
40 sq. rds. or jioles '< t rood, «
4 roods " I acre, «
640 acres " l square mile, "
A.
Sq. M.
ORAL EXEUCISEfi.
1. How many sq. in. in a sq. ft. ? in 4 sq, ft. > in 6
sq. ft. } in 8 sq. ft. ?
2. How many sq. ft. in 288 sq. in. > in *720 sq. in. .?
in 1008 sq. in. .?
3. How many sq. in. in 2 sq. ft. 12 sq. in, > in 5 sq-
ft. 80 sq. in. .?
.' 4. How many sq. ft. in a sq. yd. .? in 12 sq. yds. .?
in 20 sq. yds. }
5. How many sq. yds. in 36 sq. ft. } in t2 sq. ft. .?
in 99 sq. ft. .?
6. How many sq ft. in 4 sq. yds. Ysq. ft. .? in ^ sq.
yds. 8 sq. ft. >
Y. How many sq. yds. in 5 sq. rds. .? in t sq. rds. }
in 10 sq. rds. }
8. How many sq. rds. in 3 acres ? in 6 roods > in 5
acres
?
l\ How many acres in 2 sq. m. ? sq. yds. in 81
sq. ft. } sq. rds. in 5 roods ?
10. How many sq. ft. in 5 sq. yds. 4 sq. ft. ? acres
in 640 sq. rds. ? sq. it in '720 Bf^. in. ?
Cables.
107
Surveyors' Measure.
TI1.J Surveyoi's or GumUt's chain is generally used in surveying
land. It is 4 poles, or fiC feet, in lenglli, and is divided into 100
links.
7 95/100 inches, in., make I link, marked li.
25 links << j rod or pole, " p.
4 poles, or 100 links « I chain, «< cha."
10 chains « 1 furlong " fur.'
8 fur. or 80 chains " 1 mile " M.
10 square chains " 1 acre, '< a.
acres
OMAL EXERufSES.
1. How many links in a rod ? in 4 rds. ? in 8
rods ? in 10 rds. ?
2. How many poles in a chain ? in 3 chains ? in
5 chains ? in 20 chains ?
3. How many chains in a furlong? in 4 furlongs?
in 15 furlongs ?
4. How many furlongs in a mile ? in 12 miles ? in
20 miles ? in 30 miles ?
5. How many square chains in an acre ? in 7
acres ? in 12 acres ?
6. How many acres in 120 square chains ? in 150
s luare chains ? in 200*square chains ?
7. How many links in 2 furlongs ? chains in 2
acres ? poles in one furlonjr ?
8. How many chains in 5 furlongs and 6 chains ?
in 7 furlongs and 8 chains ?
9. How m.any acres and chains in 37 square
chains ? in 86 square chains ?
10 How many poles in 2 chai
6 chains and 2 poles ?
ns and 3 jioles ?
11^
108
TABLES.
Solid or Cubic Measure.
I '.
This is used for mensuring solids, llmt is, things tiut liavo thro.)
dimensions, viz., lenght, breadth and depth or lliickncss ; as wood,
limber, stone, masonry, etc.
1728 cubic inches, c. in. milie I cubic foot, cu. ft.
V cubic feet " t cubic yard, cu. yd.
40 cubic feet round timber " I ton, T.
4'2 cubic feet of shipping " 1 ton, T.
1)0 cubic feet hewn timber " 1 ton, T.
16 cubic feet " | cdd foot, c. ft.
8 cord feet or 128 cubic ft., " 1 cord of wood, C.
OMAZ EXEJiCISES.
1. How many cubic inches in a cubic foot ? in 2
cu. ft. ? in 3 cu. ft. ?
2. How many cu. ft. in a cu yd. ? in 3 cu. yds. ?
in 10 cu. yds. ?
3. How many cu. ft. in 2 cord feel ? in 10 cords
of woo<l ?
4. How many cubic feet hewn timber in a ton ?
in 3 tons ? in 4 tons ?
5. How many cu. ft. of round timber in a ton 7 in
5 tons ? in 6 tons ?
0. How many cord feet in a cord of wood.? in 3
cords ? in 12 cords ?
7. How many cu. ft. of shipping in a ton ? in 2
tons ? in 4 tons ?
8 How many cord feet in 48 cu. ft. ? in 04 cu. ft. ?
in 96 cu. ft. ?
9. How many cu. yds. and cu. ft. in 03 cu. ft. ? in
85 cu. ft. ?
10. How many cords of wood in 25G cu. ft. ? in 50
CU. ft. ?
TABLES.
Dry Measure.
109
salT!'ioal! o"r' '" '"^'''^"'•'"^ "'' ^--y '"•^'•^'««' «"«^" «« grain, fruit,
quirt;: anrpints""' "' ''"''' '^"'"'^«"' '="«'"'*°"«' »>»«''^"^ P-ks,
2 pints, pt.,
4 <|uarts
H quarts
-4 p<!Ck8
30 busliels
5 bushels
5 quarters
inarkt'd
«i
II
II
qt.
gal.
pk.
bu.
ch.
qr.
iuad.
make ] quart.
" 1 gallon,
" 1 pock,
" 1 bupbt'i,
t chaldron,
1 quarter,
orT^;;^;sj;"';^ is^Sj:^:!!';^S;;i^S i^i^ the winch;ster bu.hei
mchHs deep, and contains 21^0 rrbiilnch'rnearlv'"^!'^ T' '
77.G274 pounds -ivoirdupois ordislilled water. ^' ^^ '°"'"""
OliAL EXERCISES.
1 How many pints in a quart ? qtiarts in a gallon '>
pecks in a bushel i f,«»*"u .
V^^Sr^^^^' quarts, bushels in 32
els'. hTo busYelir "'^ '^ '' '"^'^^« ' "^ '' '^^^'^-
b/ ? ^^u'c b?'"v^ ^"""'^^ '" "" ^"'^''^ • "' ^ ^''- • ^*" '^
6 How many pks. and qts. in 42 qts. ? in '^ ots ?
in 50 qts. ? in 37 qts. ? M'^- • m .7 qts {
pk
pts
7. How many pints in a peck? in 4 pks.? in G
2 pks. i m 10 pks. ?
many quarts and pints in
in
39 pt
s. ? in 43 pts. ?
pints
in 2i
9. How many gallons in 16
in 64 pts. ^ in 72 pts. ? in 80 pts. ?
10. Hqw many quarters
pints? iu 48 pints?
iu IS loads and 2
in 10 loads and 3 quarters ?
f jn ^Q iQadg and i (juarter i
110
TABLES.
CiRCL TiAR MeAHUUE.
Circular Monsiire is applied to the divisions of the circle, and is
iisnd in roclconing latitude and longitude and tho motion of the
lii'uveniy bodies. It is often called Angular Measure, and is chielly
used hy astronomers, navigators, and surveyors. Its denominations
ure circles, signs, degrees, minutes, and seconds.
on seconds,", malte 1 minute, marked '.
()() minutes " 1 degree, " **.
30 degrees " 1 sign, '< s.
12 signs, or 300", '< 1 circle, " c.
OBAL EXERCISES.
1. How many seconds in a minute? iu 3' ? in 4'?
in 6' ?
2. How many minutes in 120 seconds ? in 240"?
in 360" ? in GOO" ?
3. How many minutes and seconds in 245 seconds ?
in 195"? in 370"?
4. How many minutes in a degree ? in 4° ? in 8°?
in 10° ?
5. How many degrees in 300 minutes ? in 420' ?
in 480' ?
6. How many minutes in 5 degree^s and f!0 mi-
nutes ? in 4° 15' ? in o^ 35' ?
7. How many degrees in a sign ? in 4 s. ? in 6 s. ?
in Os. ?in 12 s.?
8. How many signs in 150 degrees ? in 270° ? in
o'0ovin90°?
■. Ecv' many .sifrns in a circle ? in 6 c. ? i]
10 c.
j»i ti c? in 30 .?
!
lu. How many circles and signs in 20 signs ? iu
S s. ? iu 63 s. ? iu 74 s. ?
:lo, and is
Lion of iho
(I is cliii'lly
oniinalions
?in 4'?
1 240"?
econds ?
n 420' ?
•?0 mi-
in G s. ?
?0° ? in
1 10 c. ?
JUS ? ill
BlSTANCE—DEPTHfti—IlEiailTa.
Ill
\ inches malcc 1 liand, used for measuring tho Im^ihi of hor^os
6 points " . I line, for measuring lengll. of pendulums for .looks
1 geometrical pace, used for moasuring uistancos.
I laUioui, for measuring depths ai s.-a.
I league, for measuring distances at soa.
VI lines
5 feet
<i feet
3 miles
(I
0/?viZ E.XERCISE8.
K
1. How many inches in a hand? in 3 hands ' in
8 hands ? in 10 hands .'• in 20 hands i
2. How many points in a line ? in 5 lines ^ in 15
lines ? in 25 lines i
3. How many feet in a pace ? iu 8 paces ? in 30
paces V in 10 paces ? in 21 paces ?
4. How many feet in a fathom ? in 12 fathoms '' iii
20 fathoms ? in 50 fathoms ?
5. How many miles in a league ? in 5 leagues '>■
in 8 leagues ? in 15 leagues ? in 30 leagues V
6. How many lines in 24 points ? in 18 points ?
in 48 points ? in 30 points ?
•7. How many flithoms in 36 feet ? in 60 feet ^ in
47 feet ? in 108 feet ?
8. How many paces in 35 feet ? in 60 feet '? in tS
feet ? in 00 feet ?
9. How many inches and lines in 4" lines ? in 65
lines i in t8 lines? in 17 lines ?
10. How many leagues and miles in 22 miles ? in
M miles ? in 58 miles i
-flp
112
TABLES,
Time.
1 hour,
h.
Iday,
d.
1 year,
Y.
I week,
w.
1 month,
mo.
1 year,
Y.
1 month.
nio.
1 year,
Y.
1 century,
C.
This is reckoned by centuries, years, months, weeks, days, liours,
minutes, and seconds.
CO seconds, sec. make I minute, marked m.
GO minutes "
24 hours "
305 days '«
7 days '<
■4 weeks (com. reck'g) "
52 weeks " " *<
, 30 days '" " "
12 months ' "
100 years '<
The following are the numbers of days in each montii :
January, 31 days. July, 31 days.
February, 28 days. August, 31 days.
.March, 31 days. September, 30 days.
April, 30 days. October, 31 days. ^
^- May, 31 days. November, 30 days.
June, 30 days. December, 3 1 days. '
The days in each month are often expressed thus : —
Thirty days hath September, April, June, and November.
February hath twenty-eight, and thirty-one the others rate, ^
Except in leap-year, happening once in four,
When we give to February one day more.
"^ A natural day has 24 hours.
A Lunar month has 4 weeks, or 28 days,
A Solar year has 365 days, 5 hours, 48 minutes, 48 seconds, nearly,
, A Civil year has 12 calendar months, or 365 days.
A Julian year has 13 lunar months, 1 day, 9 hours, or 365J days.
ORAL EXERCISES.
1. How many seconds in a minute ? in 2 min. ? in
4 min. ? in 8 min ? in 10 min. ?
2. How many minutes in 360 seconds ? in 120
seconds ? in 240 seconds ? in *720 sec. ?
3. How many seconds in 4 minutes and 12 sec-
onds ? in 3 min. 15 sec. ? ;
.TABLES;
118
4. How many noUrs m 120 minuteslin 360 min-
utes ? in 420 min. ?
5. How many minutes in 3 hours? in 5 hrs. ? in
8 hrs. ? in 12 hrs. ? in 30 hrs. ?^
6. How many hours in a day ? in 3 ds. ? in 6 ds ?
in 9 ds. ? in 12 ds. ?
,7. How; many 'days in 3 weeks? months in 5
years ? years in 3 centuries ?
8. Howjmany'days in' May ? in August? in
March IJii January ?^in June ?
; 9.^ How many years and months in 15 mos.? in
29 mos. ?^in QS mos. ? in 42 mos. ?
-^lO.^How'many weeks and daysjn 25 days ? in 34
days^?_in G9 days ? ' " -- -
, Books and Paper.
^The terms folio,' quarto, octavo, duodecimo,' etc., indicate'the
number of leaves in which a sheet of paper is folded. f"
A sheet folded in two leaves is called a folio..
\ four « quarto, or 4to.
<4
<l
U
eight
ti
*' octavo, or 8vo.
twelve " a i2mo ""
sixteen " a IGmo.)
eighteen '< an I8mo
twenty-four is a '24mo.'
thirty-two << a 32mo.
24 sheets of paper make I quire.'
20 quires '« , '^ i ream.\
2 reams " << i bundle.
5 bundles « « i bale.^
•
OBAL EXERCISES.
1. How many sheets of paper in a "quire? in 2
quires ? in 4 quires ? in 6 quires ?
I :^
114
TABLES,
2. How many quires in a ream ? in 3 reams ? in
6 reams ? in 10 reams ?
3. How many quires and sheets in 30 sheets ? in
20 sheets ? in 80 sheets ?
4. How many reams and quires in 28 quires? in
44 quires ? in 72 quires ?
5. How many reams in a bundle ? in 5 bundles ?
in 8 bundles V in 20 bundles ?
6. How many bundles in a bale ? in t bales ? in
9 bales ? in 25 bales ?
1. How many bundles and reams in 9 reams ? in
15 reams ? in 37 reams ?
8. How many bales and bundles in 19 bundles ?
in 32 bundles ? in 53 bundles ?
9. How many quires in 2 bales? sheets in 2\
reams ? quires in 4 bundles ?
10. How many bundles, reams, and quires in 63
quires ? in 189 quires ?
MiSCELIi
12 units, or things, ma
12 dozen •<
12 gross, or 144 doz,, "
20 things "
100 pounds f'
I9G pounds "
200 pounds "
18 inches "
22 inches nearly, "
14 lbs. of iron or load "
21 J stones «
8 pigs «
7^ lbs. "
lOJ lbs.
ANEous Table.
ke 1 dozen.
1 gross.
1 great gross.
1 score.
1 quintal of lish.
1 barrel of flour.
1 barrel of pork.
1 cubit.
1 sacred cubit.
1 stone.
1 pig.
1 fother.
1 gallon of train oil.
1 stone of wire.
TABLES.
116
ams ? in
eets ? in
ires ? in
>undles ?
ales? in
ims ? in,
undies ?
its in 2*
;s in 63
14 lbs.
" t peck of salt.
" 1 lirkin of butter.
" t fagot of steel.
" 1 barrel of potash.
1 barrel of raisins.
" 1 barrel of soap.
" 1 barrel of shad or salmon.
" 1 gallon of molasses.
" 1 stone of meat.
" 1 tod.
" 1 firkin of soap.
" 1 sack.
1 barrel offish.
" 1 barrel of cider.
" 1 barrel of herring, Engl.
" 1 hogshead on shore.
" 1 hogshead at sea.
" 1 bushel of oats.
" 1 do. of buckwheat or barley.
" 1 do. of Indian corn or rye.
" 1 do. of wheat.
OEAL EXERCISES.
1. How many dozen in a gross ? nnits in a dozen ?
things in 2 scores.
2. How many pounds in a barrel of flour ? in a
bbl. of pork ? in a bbl. of raisins ?
3. How many pounds in 2 gallons of molasses ?
in 3 stones of lead ? in 5 stones of meat ?
4. How many pounds in a firkin of soap ?^ in a
barrel of potash ? in a bbl. of shad ?
5. How many pounds in a bushel of wheat ? in 4
bu. of oats ? in 2 bu. of rye ?
6. How many dozen in a great gros.s ? inches in a
cubit ? pounds in a peck of salt ?
•7. How many gallons in a barrel of cider? in a
"bbl. of fish ? in a bbl. of herring ?
56 lbs.
120 lbs.
200 lbs.
112 lbs.
250 lbs.
200 lbs.
11 lbs.
8 lbs.
25 lbs.
94 lbs.
364 lbs.
30 gallons
32 gallons
32 gallons
7J bushels
8 bushels
30 lbs.
46 lbs.
50 lbs.
60 lbs.
116
TABLES
10 cwt. :r= J ton.
5
4
2
1
Table of Aliquot Parts.
Aliquot parts of Avoirdupois tveight.
121 lbs. == 1 qr.
^ " -= i "
8 oz. = I 11).
4 " =j »
2
1
1
= 5
1
= 10
__ 1
— 20
2 qrs. = 1 cwt.
1 " =4 "
Aliquot parts of time
6 months ~- J year.
4
3
2
1
8
<(
u
<<
= i
1
= 6
1
— 9
1
— 12
15 days, = J month.
10
6
5
3
o
1
1
= 5
1
— 6
1
= 10
1
= 15
1
— 30
ORAL EXERCISES.
^ 1. How many cwt. in i of a ton ? in J of a ton ?
m jig ot a ton V in ^ of a ton ?
• 2. How many lbs. in | of a qr. ? in | of a qr. ? in
I ot a qr. ? ^
3 How many ounces in I of a lb. ? in J of a lb. ?
m /g of a lb. ?
4. How many months in i of a year ? in I of n
year ? in J of a year ? .^ ? u,
5 How many months in \ of a year ? in ?, of a year ?
in jig of a year ? j i >
6. How many days in | of a month ? in i of -i
month .^ in J of a month? ^ ^ •"
7. How many days in ,], of a month ? in ,\ of a
month ? m J^ of a month ? i5 "^ •*
TABLES
IIT
Aliquot parts of American Money.
PAHTS OF
!|1 IN NEW YORK
l^ARTS OF $1
TN
N.
EN-
CUIlRENCr.
GLAND CURRENCY
r.
50 cents
— 4s. —
%l.
3 shil
$2-
33J
— 2s.8a. —
%h
2 "
V3*
25
— 2s. —
41
Is. 6d.
«•
20
— ls.7id-
-%
Is.
t;,-
16s
— Is. 4d. -
- $(■>•
[) ponce
$8'
121
— Is. ~
n-
6 "
•iPl2*
^
-8d. =
'Pi 2*
6 "
|s.
6J
— 6d.
(ft]
•IPltJ'
4 "
is.
4J
•<
-4d.
* 1
3 "
is.
3|
li
— 3d.
(ft 1
^^ —
i«.
Aliquot parts of
Sterling Money
10 shillings —
£1
6 pence
I
shil.
6s.
8d.
£h-
4 "
*
((
5 shillings —
£k.
3 "
i
it
4
((
4-
2 "
1
ti
((
3s.
4d.
4-
n "
i
((
2s.
6d.
£1
1 "
1
12
<(
2s
hillings
£^Q.
2 farth's
iP
enny
Is.
8d.
12*
1 " '
i
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ORAL EXERCISES.
' 1. How many cents in 4s. ? in 2s. ? in Is. 4 d. ? in
8d. ?
2. How many cents in 4d. ? in 3d. ? in 6d. ? in Is.?
3. How many shillings in $i ? in li ? in |J ? in $i ?
4. How many pence in is. ? in }s. ? in Js. ? in Js ?
5. How many shillini^s in £\ ? in £\ ? in £l ? in
Xi?in,i„?
10
12
6. How many farthings in | of a penny in J of a
penny? ^'
118
1^
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I
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W
X
H
O
TABLES
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(ago)
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TABLES.
119
I
Rule /or fmdmg the number qfdai/s between any given
periods by table on opposite page.
Find the first given month on the horizontal litie
in the left-hand column, and the other given month
in the line at the top of the table, and to ifee number
Oi days found at the intersection of the two Wnes
add the difference between the days mentioned in
the two gi\^n months.
NoTE.-n must be observed, however, that when the number of
tZT'^l- T '^ "''' mentioned month is greater than the given
number of days In the second month, then the difference of days
Zles '"'**'^''*^ '^^'^ «he number found at the intersection of
Example l.-How many days from March ICth to
the 24th of the next July ?
The number of days at the intersection of the lines
IS 122, and 24- 16:=: 8. the difference of days in the
two given months.
Hence, 1 22 + 8 = 130 days.
Example 2.— How many days from the 25th of
June to the 18th of the next April ?
The nnmber of days at the intersection of the lines
IS 304, aiul 25-18 = 7, the difference of days of the
given month.
Hence, 304 — 7 = 297 days.
3. How many days from May 15th to the 22d. of
the next September ?
4. How many days from August 6th. to the 18th
of the next October ?
5. How many days from January 10th to the 14th
of the next July ?
120
MISCELLANEOUS
WRITTEN EXERCISES.
1. How many pencils in a box containing' 2 great
gross? An$. ll'2H pencils.
2. What cost 2Y boxes of writing ink, each 2J
dozen bottles at 9 cents a bottle ? Ans. $72.00.
3. How many reams of paper in 40*78 sheets ?
Ans. 9 reams, 15 ouires, 18 sheets
4. "What will 1 reams of legal cap cost at 35 cents
a quire ? Ans. $40.
5. What cost boxes of fancy pen-holders each
containing J gross, at 2J cents a piece ? Ans. |1G.20.
6. What cost 2 oz. of gold, if 3 dwt. cost !|2.*70.
*7. What will 2 quarts of kerosene cost at 40 cents
a gallon ?
8. What will 3 quarts of tomatoes cost at $1.20 a
bushel ?
9. How many feet high is a horse IG handsxhigh ?
10. What is the difference between two square
feet and two feet square ?
11. At 8 cents a peck, how many bushels of apples
can be bought for $6.00 ?
12. If 25 lbs. of flour cost $1.25, what will 2 cwt.
cost ?
13. How many half-pint bottles may be filled from
2J gallon of wine ?
14. What will 7 quires of paper cost at $3.20 a
ream ?
15. What will 8 eggs cost at 18 cents a dozen?
IG. If G oz. of tea cost 3G cents, what will 3 lbs.
cost ?
17. What will a gallon of molasses cost at 5 cents
a pint ?
18. At 8 shillings a pair, how many pairs of shoes
can be purchased for 2 sovereigns ?
M I « C E L 1. A N E (J U S ,
1^1
>• 2 groat
18 penrih.
oach 21
. 172.90.
3ts?
18 shce/.s
35 ceiiis
4w.s'. $40.
ers oach
S-. $10.20.
12.10.
40 cents
11.20 a
IsJiigh?
) square
of apples
1 2 cwt.
led from
$eS.20 a
)zen ?
1 3 lbs.
5 cents
of shoes
19. At what price must J dozen of chairs, worth
|1 o.OO a dozen, be sold in order to gain 50 cents a
piece ?
20. How much will a peddler gain by selling 3
dozen combs worth 30 cents a dozen, at 5 cents a
piece '?
21. What will f of a lb. of candy cost at 2 cents
an oz. ?
22. How many tablespoons each weighing 2 oz.
can be made from 1 lb. 8 oz. of silver ?
23. How many leap years in a century ?
24. How many pills of 5 grains each can be made
from J an ounce of quinine ?
25. If a gallon of wine cost |5.00, what will 3 pts<
cost ?
26. What will it cost to paint a ceiling 12 ft. by
29 ft., at 25 cents a square yard ?
27. How many yards of Carpeting, a yard wide,
will cover a floor 20 ft. long and 21 ft, wide ?
28. How many quarts of milk will a boy drink in
a week, if he drink a pint a day ?
29. What is the weight in tons, &c. of 3 loads of
potatoes, averaging 22 bu. each ; 1 load of wheat, 19
bu. ; and 4 loads of oats, each 25 bu. ? Ans. 4t. Scivt.
30. What will it cost to ship 75 t. 8 cwt. 70 lbs. of
freight at G cents a pound ? Am. $9052.20.
31. How many farms of 75 acres oach in a tract of
land 6 miles long and 5 miles wide? Ans. 2i)C) farms.
32. What is the height in ^eet of a horse 17J hands
^^S^ ^^ Ans. 5 ft. 10 in.
''?''* 'X
I
CONTENTS.
SIMPLE NUMBERS,
Introductory Definitions.. 1
Numeration and Notation. , 3
Arabic Notation ' 3
Numeration Table 15
Eoman Notation 32
Addition 26
Subtraction 46
Multiplication.. 62
Pivision ,...' 79
Introductory Fractions.... 94
TABLES.
Federal Money
English or Sterling Mo-
' ney
Troy "Weight
Avoirdupois Weight
Apothecaries' Weight
AVine Measure
Ale or Beer Measure......
Cloth Measure
Long Measure
Square Measure
97
f<
98
99
100
101
102
103
104
105
106
Surveyors' Measure 107
Solid or Cubic Measure... 108
Dry Measure 109
Circular Measure HQ
Distances — Depths — .
Heights Ill
Time 112
Books and Paper 113
Miscellaneous I14
Aliquot Parts 116
Given Dates .7.... 117