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4k^^^
II
SCHOOLJiEi^SoSCRIES.
ARITHMETIC
EXERCISES
FOR THIRD BOOK CLASSES
av
G. E. HENDERSON,
E^Ucrof" TH. Canadian T^^-' ^,.. n. E^ra«^
AMD
E. W. BRUCE, M.A.,
P^**'i/^l Huron Street Public School, Toronto
Wc«. 16 cents; T-ehew' Edition, with An.wer..
20 Cents
•■I
"" """"^no-A^ POBUSHIKO COMPANY. U„nW.
TOROKTO, M07.
M
v^
PREFACE.
The aathora of this series of Arithmetic ** School Helps "
offer no apology to the school public for the placing of their
books as candidates for popular favor. The several numbers
of the series are prepared t^ teachers actively engaged in the
busy work of the schoolroom, and as teachers they know the
great difficulty that the' average teacher encounters in the
presentation of new and crisp problems for his Arithmetic
classes.
The authors would most respectfully request a consideration
of the followmg points in connection with their series :—
I. Mechanical Work. After pupils have passed the
Second Reader the usual text books provide but very scanty
practice in the mechanical operations. Pupils instead of
becoming swifter and morie accurate as they advance in years
frequently lose the speed and accuracy which they had acquired
in the lower forms. To meet this difficulty the present series
proviues over 5,000 operations in mechanical woik, which the
teacher will find tested for him without the labor (and loss of
time) of performing the work himself. This feature alone
should commend the present series to every teacher of the
subject
II. No Answers. In the Pupils' Edition no answers are
provided ; the Teachers' Edition alone contains the answers.
lit Saving in Time. The time of the teacher 3s too
valuable to be taken up in the dictation of problems to a class,
when for a mere trifle each pupil may be provided with a set
of exercises for himselL
- .h. pupil'. n.tad .L^„";.'SS:;^1"»«™««< '• fi.
fenmofAriUimetic. ^^ """•'""""»« of the lodaicl
•tocolyped ptoblen* '^' «-"wi«Mw,t of old,
«P«,™« find. «,l,rf ,0 u„ lUIH?^"^ *• "-i^.
IX. Book of Butel.M. m ._■ T^
TocobUh August, i8^.
Tmt AuTHois,
•et bjr the
■vvenU (h«
'"ff formal
cted to fix
e technical
» problems
"School
' of old,
arranged
grouped
hgree of
•tionsof
• pupil's
^•Cher's
lyiense
edtext.
ken for
I hand
iching.
oit.
MECHANICAL WORK.
(I)
625456
31221S
763617
513315
767806
123432
(5)
361 22 I
212133
622331
524123
458416
468495
697261
644605
329185
518768
ExercUe l.-ADDITION.
(2)
279807
502136
796736
452432
967875
23434s
(6)T
642272
347447
872638
615465
421 64 I
879848
956925
508575
467259
752342
(3)
(4)
876390
507648
763769
727659
507648
307523
727659
423237
432140
876948
541546
768275
(7) -r
(8)
423426
782167
7091 5 I
4813"
820737
591479
253897
611512
541111
703608
422343
122291
735625
914572
156851
234210
481318
357444
423805
452468
Without putting the figures down.
(9) Adc 4's (the same number of 4's in each successive
Ime as there are figures in the line they are being added
ARITHMETIC
rSfli^^ t 552729 + 526063
578834 + 218272 ^. lyBS.t
121268 + 73956, + 366721
J76277 + 395587 + 821,85
810468 + 404432 + 4,5075
+ 169962
+ 827946
+ 143478
+ 434747
+ 382427
+ 6789,3
(19) 848703 + 7225,4 + 6353,3
22i7i| + 823135 + 288.74
34227^ + 68471? + 583.86
l^^fi i 5'68'3 + 642082
820818 + 902802 + 7C2.06
. 237833 + 6J6913 + 8743M
(30)
^
+ 433827
+ 563725
+ 434958
+ 367624
+ 233647
+ 454739
285135
472244
318217
187149
735846
+ 722445
+ 182174
+ 714924
+ 358462
'+ S13534
^S»353 + 224456
+ 82.745 + 276287
+ 714924 + 762875
+ 584627 + 875697
t ^47287 + 7C6978
+ 728733 + 7^3457
+ 873346 + 875438
_
('
(>
(•
of
re
be
7's
ca
ca
ca
ExercUe II.-SUBTRACTION.
(I)
625456763
3122155,2
(2)
876390763
432137698 **
(3)
825721423
376948768
811
(8)
(12
(4)
825125427
327587998
(7)
514723272
278976785
MECHANICAL WORK
(5)
823012345
759158576
(8)
62721 1335
378589657
(6)
713627230
273976735
(9)
914232013
267548129
Subtract 213987854 from each of the following :
(10) 373967873 ; (I I) 972725879 ; (12) 958378327 ;
13 7212851 13 ; 14) 813246201 ; htS 5?23;65i3
(16) 931467842 ; (17) 712353768 ; (li) 472651997 ;
(19) Without putting the figures down, subtract lines
of 3 s successively, from 62447901 224, as far as the seventh
remamder.
(20) Subtract in succession 4's from the above num-
ber as far as the seventh remainder.
(21) Subtract .5's* (22) Subtract 6's. (23) Subtract
7 s. (24) Subtract 8's. (25) Subtract 9's.
(26) Find by repeated subtraction how often 73869745
can be taken from 592410478, and give the remainder.
(27) Fmd by repeated subtraction how often 41689754?
''*Mx*S*'5 ["*"" 3966641 141, and ^ive the remaSicIcr.
(28) h md by repeated subtraction how often 975318643
can be taken from 10187754329, and give the remainder.
Exercise lll.-MULTIPLICATION.
Multiply each of the following by 357 :—(i) i8otd2 •
<^,) 3^3^456; (3)2705.3; (4) 36^4;% 541(^61^(6)
Multiply each of the following by 468 :-<7) 122553 ;
(12) 735318 ""' —-'— ' ^--/ j-^/^y/t \»*/ ^yw-j^i ana
8
ARITHMETIC
each 'of Z ''mZll"^'Jrj''!. ■""■•'P«ca.ion of
and 87468. ^ ; "^^' =9"S6 ; 43734 ; 65601 ;
Ustf i S a fecSr r™ """'"'ive times.
Us nf A rf J " **'^" consecutive times
(29) Usinf 8 S a fSr ^f" '^""secutive times.
U Usi^^|Sa^S;iS:ScZ1c\".t t'E
eighT-il^ r ??/; 'SN'-^'-r »« consecufVe," ;; the
(32) 17676 • /«\ ofirr. ^'/ ' ?' *^ '^'^tO" :— (31) I32C7 .
3950. ; (4<) /,Ul7ISd (46?^7Sf' <«> 39336; (44)
number lll^JJT'msV' L% '^.1, '**, "'v *« ''<•"'>'''"?
'8432 ; f572457W«S itS.8 3/^^' ^«> '6384 i (5o3
(55) 49152: aSd (56) 5^2^*^^' (53)32768; (54)368&,;
Exercise IV.— DIVISION.
Dittde Jach ofthl mI, ^'^^ t"**^'" ; (16) 802^4^^
(.8) :27^5<,^f .°[,'^,« fo«o.mg by 437 M_.;/,8657l%
/4oa9M2 ; and (32) 83957751^"' ' ''"'' 5dy/*o34i (2I>
'i3) 132456;
794736 ; and
'J9) H3712 ;
574848 ; and
plication of
34 ; 65601 ;
times,
times,
times,
times,
times,
times.
elv by the
30 132??;
>77i; (36)
39) 13112;
'336; (44)
following
J84 ; (50I
4) 36864 ;
3769154;
3598120 ;
J370832;
'4; (13)
0224992.
>657278 ;
4; (21)
MECHANICAL WORK 9
(23) Divide 8635547648 consecutively by 4 for 8
quotients.
(24) Divide 5123828125 consecutively by 5 for 8
quotients.
(25) Divide 39430665216 consecutively by 6 for 8
quotients.
(26) Divide 81422872867 consecutively by 7 for 8
quotients.
(27) Divide 394969219072 consecutively by 8 for 8
quotients.
(28) Divide 506573812728 consecutively by 9 for 8
quotients.
(29) 3552714396-^726.
(30) 3489514378^406.
(31) 445886497875-^4875.
(32) 5963879065-^9307.
v(33) 2975019839-^5423.
^(34) 11516639848344-^704006.
Ekercise V.— REVIEW EXAMPLES.
A.
(i) Multiply the difference between 4396408 and
9206000 by 346.
(2^ What is the product of 67489 and 758 ?
(3) Find the quotient and remainder when the product
of 86947 and 496 IS divided by 387.
(4) A man bought.26 cows at $32 €ach, and 1 17 sheep
at $6 each. How much less than two thousand dollars
did he pay out ?
(5) A man earns $22 a month and spends $14 of it.
How long will it take him to save as much as he earns in
a year ?
4-(6) Multiply the suhi of the numbers between 38 and
52 by 769.
(7) In an orchard there are r rows of trees and 18 in
each row ^iive barrels of apples are got from every two
irees. What is the crop ?
10
ARITHMETIC
» A'gr '-">• *'^-nce. p^duc. ana <,„„««„. «,
B.
««n>^ foi^"^ ?'*''5 " •'»y> ho" much will ,5 „«, '
foriV,s'"H",te°;:^e5'.W.andayofc.„fox«,
Sheep cost ? payment 80 sheep. What does a
(io> Divide the sum of 7i8co .,/i,^ . j
"' 73359, 4637 and 59428 by 684.
REVIEW EXAMPLES
II
quotiem of
es loo steps
m hour?
nts a yard ;
re stockings
she receive
rth Si,52i.
each cow
»d forty IS
nd ending
[containing
ime at 35
>Tnent 146
h does he
^at is the
ust I sell
» 16 years
r did he
15 men
5 of oxen
t does a
by 684.
(2) If II men can sod an acre of ground in I2 days,
how many days will 4 men take to do the same work ?
($) Multiply 76493 by 8973.
(4) A man sold chickens that cost him 35 cents each,
for 76 cents a pair, and gained $2. 7a How many pairs
did he sell ?
(5) What nimiber subtracted 88 times from 80005, ^^^
leave 13 as a remainder ? *
f^{6) Write in figures : seventeen thousand and eight;
nine hundred and one thousand six hundred and four ;
eighthundred thousand and two ; XCVII.; CD.; CCCV.
and XLIV.
(7) Divide 121 marbles between John and Tom, giving
Tom 19 more than John.
(8) What will a telegram of 44 words cost, if you have
to pay 25 cents fo^ the first 15 words and 2 cents for each
of the remaining words ?
(9) ^. boy was told to multiply 720 by 304, and gave as
liis answer 24480. By how much did his answer diffef
from the correct product ?
(10) How niany bushels of wheat at 69 cents a bushel
rhouldbe^ven for 6210 pounds of sugar ft 5 cents a
pound ? '^
I Iambs,
get for
REDUCTION.
BssreiA
• VI.-OOLLAR8 AND CCNT8.
9; How many ten.r#.nf «: ^ff /^^
J9; How many ten-cent pieces in Lq \
^ ('o) How many fiv#» I.o«l -^^ *98.9o ?
S3.3o+$4.4c? ^"y «^«-cent p.eces in $,.,o+$,.2^ +
4«»»9 cents ; and 1908190 cents ' ^ ^ °°°^ ^'^^^^ J (9)
Exercise VII.-TI we.
f '? Write the table,
in /h^o5°lrhi; -onds in 6 minutes ; in ,3 „.•„„,,, ^
(12)
REDUCTION
13
ITS.
87.04 and
'7?
?
i-$?.2<} +
ints ; (2)
^4 cents;
tnts ; (9)
(3) How many seconds in i day ; in i week ; in 19
•lays ; in 2)4 weeks ?
(4) How many seconds in 5 hours, 7 minutes ; in 12
hours, 51 minute^, 37 seconds ?.
(5) How rtiany seconds from 6 o'clock a.m., to 7 o'clock
p.m. ?
(6) How many minutes in a year ? How many minutes
in a leap year ?
(7^ How many seconds in tlie year 1897 ?
(8) How many hours in the month of January? in the
month of September ?
(9) How many days in the spring months? in ther
summer ? in the autumn ? in the winter ? j
(10) How many iiays are there in four centuries ? ~^ ■;
' B.
(i) How many seconds in 17 days, 5 hours, 15 min-
utes and 35 seconds ?
(2) How many minutes in 180 seconds? in 1980
seconds ?
(3) How many hours in 10800 seconds? in 183600
seconds? » -
^4^ How many hours, etc., in 34896 seconds ?
(5) Reduce 28974 minutes to days, etc.
(6) How many weeks, etc., in 2308589 seconds ?
(7) How many days from August 24, 1896, to January
7, 1897?
(8) How many Saturdays in 1897, Friday being the
first day of the year ? How many Fridays ?
(9) If a clock ticks seconds, how many times did it
tick in February, 1896 ; in February, 1897?
(10) Reduce 8 years, 340 days, 17 hours, 57 minutes
to seconds, reckoning 365 days to the year.
mutes ,
BxerciM VIII.— DRY AND LIQUID MEASURES.
^1} Write the tables.
(2) How many pints are there in three quarts ? i gal-
1 5 - 1. i . 1 u-i a
^
. AWTHMETIC
cents a peck? ® ®' '7i3 bushels of potatoes at 9
fro.iVirge"'^"^^?':^^"^^^^ o' berries could L ^Hed ■
gallon ? ^ ^^''^^ containing 2 bushels, 3 pecks i
gain on at 15 cents a quart; find hil
^"«4{?^t'Z.?^.S^^^, »'<« for $,6. What
ii.i.xt5:?arn-r-r-i:«
chete';'ct^»ut' ""^"'"^ ^ l-*'. ' gallon. „,
a. f i ^ITshef ~^' °' - ""'h^H ^ pecks of g„«s seed
cenjVhe'';r^':""«'°f 'S bushels of cn.b apples at .
(6) Find the value of re t^^i
- -ts a pound, assl'^-^f ^- 3,uans.f^^^„ ,.
« ■•tttlT/effs'TiiS.it'^ P»'^ of ™">- and wia,
>?
REDUCTION
15
(8) How many pint bottles will be required to hold 6
gallons, 3 quarts, i pint of vinegar ?
(9) A grocer bought 2 bar»^ls (31 >^ gallons each) of
syrup for $1 5. He sold half of it at 18 cents a quart, and
the remainder at 22 cents a quart. How much did he
gain ?
(10) Find the cost of 23 gallons, 3 quarts of vinegar at
five cents a quart.
(11) If $10 was paid for a barrel of molasses, which
was retailed at 20 cents a quart, find the gain.*
Bxerci8C<(^— AVOIRDUPOIS WEIGHT.
much
A.
(i) Write the table.
(2) How many lbs. in 4 cwt.? 7 cwt.? i ton ? 8 tons ?
6 cwt., 53 lbs.? 14 cwt., 90 lbs.? 14 tons, 13 cwt., 79 lbs.?
in 14 stone?
(3) How many ounces in 8 lbs.? 25 lbs.? 3 cwt.? 2 cwt,
15 lbs.? II cwt., 82 lbs., 14 oz.?
(4) How many lbs. in i bbl. of flour? i bbl. pork or
beef? in i bbl. salt?
(5) How many pounds in a bushel of each of the fol-
lowing: Wheat, peas, potatoes, clover se^ com, rye,
barley, buckwheat, timothj^ seed, oats ?
(6) How many grains in i pound avoirdupois ? in i
ounce? in 8 ounces? in half a pound? in i}4 pounds?
(7) How many ounces in 19 tons, 12 cwt., 73 lbs., 15 oz.?
(8) Reduce 3 cwt., 1 5 lbs., 8 oz. to grains.
(9) Reduce 13579 ounces to higher denominations.
(10) How many bushels of wheat in 3 tons, 4 cwt.,
20 lbs.?
(11) Bought flour at $7 per bbl., and s.>ld it at $4 per
cwt. Find the gain on 27 bbls.
(12) Find the cost of 1365 lbs. of hay at $12 the ton.
(13) If an ounce of sugar cost half a cent, what will
2 cwt, 15 lbs., 12 oz. cost?
16
ARITHMETIC
(i) How many cwt t»ti^iJt
, ^ Find the value of .^^^"^^ ^767 ounces ?
(2; 2750 lbs. of wheat 'af rv^
(3) 2584 Jbs. of oats at i.^ "^t"*' ^^' ''"^hel.
(4 2704 lbs. of bariey a1^6^?'%P^'-b"«heJ.
(5 1896 lbs. of timothy seed ^ri ^^' ^'''^^^'
(6 1896 lbs. of clover seed i«r^'*^' ^^' ^'''^^^'
(7) 73 1 5 lbs. of Indian coi^ \ ^^' '"^ P^^ bushel.
(8 8964 lbs. of peas at ?c^..^'' ""'' P^' bushel
,. (9) Find the worth of 1 tc?/^ ? ^' ^"^''^J-
ibs.at96 3perbushelV°^^°^-^eat weighing 4,85
'95 pounds.. Findtysumofthdr^dXs?"" "^'^^^^
Exercise X.-TROY WEIGHT.
jl) ^"te the table.
- 3 oi^7wtT.r ^"' '" 7 dwts. ? in ,3 d^ts. ? in , ^z. ?
\3) How many o^r«i m ^ ^
■j^s; j?EJK ""■•»■.,-..«.„„
f1^?\S?'"'^'''^°8ST"' '*^'' ashing. „.., can
0') Reduce .23 lbs. ,og,i
REDUCTION
.IT
fi2) Which IS the heavier, i lb. of feathers or i lb. of
gold ? I oz. of feathers or i oz. of gold ? How much
heavier, give your answer in grains ?
(13) How many pounds Troy, in 15 !!>s. Avoir., and
how many grains over ?
(14) How many pounds Avoir, in 15 lbs. Troy, and
how many grains over ?
"^Exercise XI.-APOTHECARIES' WEIGHT.
lib.?
(1) Write the table
How many grs. in 2 scr. ? in i dram. ? in i oz. ? in
(3) Reduce 6 lbs., $ drs., i scr., 19 grs. to grains.
(4) In ten thousand grs., how many lbs., etc. ?
(5) How many grains of calomel in 1 1 oz., 2 scr. ?
f6V Find the number of lbs., etc., in 791 scr. ?
(7) How many morphine powders of i gr. each can be
made from 2 lbs., 2 oz., 3 drs., 2 scr., 7 grs. ?
(8) Which is the heavier, i lb. Troy, or i lb. Apoth. ?
(9) How many pounds Apoth., in 20 lbs. Avoir., and
how many grains over ?
Exercise XII.— LONG MEASURE.
(i) Write the table.
(2) How many inches in 2 ft. ? in 7 ft. ? in S ft. ? m 14
ft. .<•
(3) How many inches in i yd. ? in 5 yd. ? in J^ a yd.?
n sH yd.?
(4) Express in yards i rod ; 4 rods ; i mile ; iX miles.
(5) How many feet are there in 3 miles ? in 5 miles ?
^16 miles ?
(6) How many inches in 3 yards, 2 feet, 1 1 inches ?
(7) Reduce 6 miles, 24 rods, 3 yards to yards.
(8) How many inches in 25 miles, 78 rods, 4 yards, 3
fcct, 5 inches of distance ?
^-:.i
18
AKITHMBTIC
.Jn) Reduce 4 miles. 4.5 yards, . fee,, 4 i„che, ,0
4 yi^t "Z^rJkSr '■" ^ ■""^'- 5 f-'-S^. 3^ rods,
B.
Express 1239 inches in yards fr^f o«^ • u
f xSr''' r^98 yards in mUe 'and y'ardr^"''
•fc-xpress 64016 inchi»«s in «,:i /^ras.
Reduce a/^f inchesNo m eTy'^l^' !''•
H^^ress .He ^di^^X"^ ^^ ii:oaf„arcJ-.S.r^^^
Exerctae XIII.-SQOABE MEASURE.
m a square foot. number of square inches
in i?,u?ryi^t «lr ^^Sr 07"""°^ ^«--^«'
square rod. ' "i" <ne number of square yards in a
squ^^aM?""*""""^" '»=■'« i» a square foot? in a
, (s) A table is 10 feet hv c a><>» . 1.
of surface ? How ma^Ts, Ja^etnU^^^^^^ «-ny square fee,
o.hUAc^'r.filn'X'^i^ '/ii-"" "y*'-"?^ and an-
inches m each board ? "°^ "*^'' "^Juare
•■i."'^
REDUCTION
feet, ^I
iches to
32 rods,
>9
1 wide,
dsand
nches,
feet.
iches
5 feet
in a
in a
feet
an-
Liare
(7) How many square inches in 5 square yards 8
square feet, 73 square inches? ^ ^ '
(8) How many square yards in 4 square rods ? in 6
square rods? m 12 square rods ? ^
59) Reduce 2 square rods to square inches.
lon^'^d";;^ k:tll^:r '"^'^ •" ^ ''*^''*"*^'- ^6 feet
I
B.
How many square yards in i acre ?
C2) Express 8 acres in square rods.
(3) A cellar is 36 feet long by 24 feet 6 inches wide.
How many square yards in the floor ?
(4) What is the difference in square feet between 10
:?«:;: ya^is?"' " '^^^ ^^"^^^' •" ^^-- -<^-" ^«
hoifll?Ti*"^y ^3"**^ ^^^^ of carpet are required fora
yalds? ^ ^"^ ^^ ^^^^ wide Thow many square
^6) Reduce to acres and square rods each of the fol-
l^owmg: 1000 rquare rods; 1250 square rods ; i32Ssquare
(7) How many acres and square yards in each of the
squrTaid'sl?' ^"""^ '^' ■• '-'a/square yards, ^^
(8^ How many acres in a lot 200 rods by 80 rods ?
(9) A ten-acre field is 80 rods long. Express the dis-
tance around the field in yards. » f «« ui*
(10) Reduce 8642898 square inches to acres, etc.
^ [i) Findthe number of acres in the following fields ;
rorf. t..^ ^V^^'lJ^ T^' ^y 32 rods ; 80 rols by 36
rods ; 140 rods by 96 rods ; 100 rods by 96 rods. ^
■i\. ^^2 .**°^«»any acres in fields whose dimensions are:
^23 chams by 10 chams ; 32 chains by 2? chains: ^o
-^ f byls'chains?''^"''' ^^ "^""^ ^^ ^^ '^*'^' ' ^^ ^^"^
'vi n:
ARITHMETIC
(3) How ,„anya^T«8 in fields whose length md^Mdths
respectively are : 26 rods by lo chains ; 64 rods by «
chains ; 240 chains by 96 rods ; 100 chains by .44 rods^
100 rods by 144 chains? ^ ^^ •
mnm^Vj^"."/^"^ ^'^"f *^ y^?"?^ ^'^ *^"« '" the walls of a
poom, 21 feet long, 15 feet wide and 13 feet high ?
h\A^^ m'*^"" " ^^ ^^^* '°"^\ '^.^^*^' ^'^e and 15 feet
c^liiig ? "^^ '"^"^'^ ^^''*' ^'^ ^^""'^ •" ^*^^ ^*"s and
AcJfl7Kl^'7^^^' ""^ I rectangular plot of ground is
f^Jf \ t ^'^^•■ence between the length and breadth
^t\^i """^ T'^y '^"^'^ '"c^es are in the plot ?
squl?e;^er. ^Ct fs ttU^r '" "^'^' ^°"^^'"^ '°
co.i'^osTua"VaUr?'^ °' ^^^* ^^ inches wide will
, ) A souare yard of paper is cut into rectangular
pieces 3 inches by 2 inches. How many pieces are there ?
D.
(i) How many pupils would a rectangular school-room
40 feet long, 32 feet, 6 inches wide accommodate, allow-
'n&/o square feet of floor for each pupil ?
» JaIJ^'^IT^^ ^""I^^J ^^*'» ^""^ t^e*'^ »n a square field,
a side of which is 7260 feet ? 1 . «= ".
vai^^ Ji"'l*^-'^°^*^^*°**^'"«fa ^awn 66 feet long, 16
yards, 2 feet wui •, at 6 cents per square yard.
(4) Reduce 7964820 square inches to acres, etc.
make 6 > '^ ^ ^^^^ ^'^®' ^°^ "^^"^ ^^""^^ °^'* '^'"
rnH^il"^* ^'55 an acre, what is the value of a farm 240
rods long and 90 rods wide ?
(7) At 2 cents a square foot, find the cost of fencing i
mile of a railway track, both sides, with a close board
fence 4 feet high.
oni^.l y^¥^ •'^'" '* i. '* ''^ P^''« a roadway 2 miles long
and 15 feet wide at $( ^ qu.of.« yard ?
(9) Find the prit< >: p,. - ^ of land 86 miles lon^ and
4 roqs wiae, at $44. k> •::, r,? n
I
f
s
c
REDUCTION
BzerclM XIV.-CUBIC MCa^URC.
at
I
(iVWritc) he rnhle of cubic or solid ini„«sure. *
(2) Show by diagrams the number of cubic feet in a
and the
cubic ynrd ; the number of cubic feet in icord
number .i ubic inches in a cubic foot.
(3) Jiovf many cubic in. are there in « cubic ft. : m x
cubic ft. ; m 17 cubic ft..> ^
(4).How many cubic ft ir^ 3 cubic yds.; in 7 cubic
yds. ; m 23 cubic yds. ? / . / .^
(5) How many cubic in. in a cube, one edge of which
IS 2 ft. ? ' o
(6) What is the volume of a solid 8 ft. long, 5 ft. wid«j
and 3 ft. thick ?
(7) How many cubic ft. of earth must be removed ii'
digging a cellar IS u. long, lo ft. wide, and 6 ft. deep?
How many cubic yds. ?
(8) How many cubic yds. in a cellar 27 ft. long, i ? ft
wide and 7 ft. high ? / »» a
(9) How many cubic ft. in a block of stone 13 ft. Ion?;
II ft. wide and 17 ft. thick? ^'
(10) How many cords of wood are in a pile 242 ft
long, 28 ft. wide and 12 ft. high ?
(i i) A sleigh upon which 4-foot wood is piled is ib ft
long. How high should the wood be piled to make a
cord? '^
(12) How many bricks are required to build a wall ii
ft. long, T2 ft. high and 2 ft. thick, if 21 bricks with the
r-ortar .o'M make a cubic foot of wall ?
B. ,
(1 ) Find the value of a pile of tan-bark 1 28 ft, long, 40
ft. wide, and 16 ft. high, at $3.25 a cord.
(2) How many cords of wood can He piled into a wood-
shed 20 feet square and 16 ft. high?
(3) A box 24 in. long, 16 in. wide and 18 in. deep will
contain about •» bushfils. Hn«, _
ve in a bin lalft. long, 6 ft, wide and'5 ftrdeep?
Wiicai
33
ARITHMETIC
.6 feet thick and jjfcethi^li','' "»""•"• "' » ■*"« long!
avei^in^ 8 in dSp ?' ^™' '° ''= ^'^ ' «• *We and
7Xya,5scost%' °' *««'"«f » «"" 35'X24'X9', if
teni'°A^KnV6ltig'^V/t.r1r"''"""J «^ ^•^
cords, and %% ■h » ,.™U i- .? getting $4.25 a cord for u
he re^elJe foi'Se Z^ j*^"' ">« «" "fit- Ho» much di^
%i\o>crtiTStS"--^^^
< I
. ' c.
maif cIJdThl' thl'L"! T?""'?' -•»' X t' X * • How
SaUons doe? the cistern hpld? " ^ x 4 x j . H"w many
™. by 5 in.,
mile long,
i required
wide and
'7 ft. long
ng, 12 ft
ng, i8 ft.
I?
24' X 9', if
"f 64 ft.
rd for 14
nuch did
I ft. high
5 a cord.
>ng, 4 ft.
ft. long,
trd, and
square
»od, the
:?
nd 6 ft.
How
ay $18
a rec-
quarts.
many
REDUCTION
23
.f/^^-^** T^*.^^ ^**® ^^""Sth of a rectangular bin
4 ft. wide by 5 ft. 4 ,n. deep to hold 300 bushels ?
W A gallon of water weighs 10 pounds Find th*.
weight of water in a rectangullr cistern 6 ft. long and !
ft. wide, the water in the cistern being i ft. 4 in deeo ^
(9 There are 31^^ gallons in a Lrre .^ How £anv
barrels of water are there in a rectangular waTer ta^k 6
ft. 9 in. wide 7 ft. long and 5 ft. 4 in. deep? ^
(lo) A cubic foot of water weighs 1000 ounces How
many pounds are there in a rectangular cistern 9 ft long .
4 ft. wide, the water in it being 2 ft 6 in. deep?^ ^'
^ (u J ,." a swamp in Dereham, the townshin
council had a ditch dug one mile long, 3 ft deepTnd 6
ft wide at the surface, and 4 ft. wide at the bot?om^ Find
the total cost at 9 cents per cubic yard.
Exercise XV.-BOARO MEASURE.
• A.
How many feet, board measure, are th^re in :
Vol I u J '^ ^'•i'*".8^' '2 in. wide and i in. thick?
h\ ? UA^' i^r^• ^°"«^' '^ •"• ^»^e and I in. thick?
}i{ l^K^'^5' '^ ^h ^?"«^' 9 in. wide and i in. thick?
}il \l t'^''^^' '^'^^i^onS^' 'o>n- wide and i in. thick?
(fl f. K "^'f'' 'V\ '°"«^' ^ '"• ^>«*e and 2 in. thick?
(6) 24 boards, 12 ft long, 12 in. wide and 2 in. thick?
(7) I plank, 12 ft long, 8 in. wide and i^ in. thick?
S L^if ^u' 't./-i^7^' 9 in. wide and 2 in. thick?
(9) 20 planks, 8K ft long, 16 in. wide and 3 in. thick ?
o ,3 planks, 16 ft long, ,3 in. wide and I iS. thick ?
(Vl I f ^" .'"8^' »2 ft ong, 3 in. wide and 2 in. thick?
J ^{ 1 ''^"^Ir^' 'l^t l°"8^' 4 in. wide and 3 in. thick?
J^ !« f an 1"&. 16 ft ong, 5 in. wide and 4 in. thick ?
(14) 48 scantling, 18 ft. long, 6 in. wide and 4 in. thick ?
*
B.
(1) How manv KoarJ faa«. «r 1
'ong, 14 ft wide and i inch thick?
.. 1
a floor iS ft.
H
ARITHMETIC
ft lln^K»d'.'Si"?'/rul^V""'"' "" "'^^ °f "■"''" -
(7) Find the cost of the lumber for a nlatf««,, ^.^
«W "^ "'''" 1"^ ^ '"• 'hick at $.2 Ar'^AouSid '
. (8) How many feet long will a plank ?o in wiS- »nH
.ain'IUtaSLl^'"• P"""^ '^ ■»• -"e, will con-
per M.; all the boards are 14 ft. i„ lengih ' ^ °'^°
BxercUe XVI.-GENERAL TABLES.
ill ?°1 '?*">' ""''5 '" ' gross ; in 3 CTOSS 7 dozen ?
^c^ SS''.** E"" °' '"° *'»"« of flour at $3 percwt
each" " ■""' °f "• '■"«" brooms at ,8^0™!*
cos^^f's^eatsl"^'"'^'' -^""^ '* ''■"^- What is the
.aii?g'?rsh'i"oV"'''°'"'"P '" 5 fl"*^. «>* con-
REDUCTION
25
(8) Ifa box of pens be bought for 80 cents and the
pens sold for a cent each, find the gain on 2 dozen boxes
(I box contains i gross). ""xcs,
cents a tenT^ ^""°"' '"" ^' P"^^^^^^*^ ^«^ ^ ^' ^S
(10) In 105 12 pens how many boxes ?
honlV? H^.r"'?? fu*"* ^472 eggs at 9 cents a dozen, and
bought cloth with the money at 27 cents a yard. How
many yards did she buy ? ^
VUJ
terclse XVII.-STERLING MONEY.
S
fi) Write the table.
^i i in" gT^inet? ^"'' '" ^ '**"""^' ' '" '" ^^"""^^ ' '»
p) pP^ess 96134 pence in pounds, etc.
rl u ^ Sru'neas how many pence ?
in ii.iinp'!,'^ J"?T^i,""*' '" ^ shillings; in 12 shillings;
in 2 guineas ? (Taking 24 cents to a shilling). ^
ios.^?\".°r$r86^t"^"^'^^^^^ -^^9; in ^3
?«^ p T ""^r^ ^"'"^^.^ '" ^42 ; in ^147 .?
M S-^*!,"''^ -^'3 4s. 8d. to farthings,
guineas d'^erence in pence between ^109 and 89
(10^ Reduce 76841 halfpence to £, etc.
pieces ? ""^"^ P""""^"' ^*''' '" 3927 three penny
(12^ Reduce ^13 19s. 7d. to halfpence.
{13) How many shillings are there in /? ics • 2
^"Tfri' \f^TT^^: ^ ^^^^"u^ .' ^"^ =^ six-?encei ? '
our money f^^^^^'^°^ '"""^ '^ -^^ '«*• «q"^» *<> »>
(15) How many pence in ^63 9d.?
I Ini Hour mii<->h ...III iU— Ti i ^ .». »
•--,- »....-,xi n^jn i«u X3uiiiv or loronto charpp to
discharge a debl of ^,59 in .Liverpool at $^88 ^rT?.
36
ARITHMETIC
Bmrcise XVUL^ARTICLES SOLD BY THE 100.
Find the value of;
7250 lath at 30 cents per hundred.
2900 pine apples at $13 per c.
2425 lbs. sugar at $3 per cwt.
8175 lbs. cheese at $16 per cwt.
275 lbs. of beef at $6 per cwt.
2160 lbs. of pork at J8 per cwt.
15 bbls. flour at $2.50 per cwt.
47800 bricks at $8 per thousand.
47200 shingles at $3.50 per M.
' 4320 feet of plai.k at $40 per M.
20750 ft. of lumber at $16 per M.
25500 shingles at $4.50 per M.
B.
3500 lbs. of hay at $18 per ton.
25360 ft. of lumber at $27.50 per M.
0400 lbs. of hay at $9 per ton.
8 tons, 1000 lbs. coal at $5 per ton.
6325 bncks at $8 a thousand.
thicWar$??pe? m"' " ''' *°"^' " '"• ^'^^ -d 3 in.
(7) Find the cost of 17640 feet of lumber at $11.50 ner
^•Vt?l368o lbs. of coal at $5.50 per ton. ^ ^
(8> How much would it cost to shingle a roof 40 feet
long, each side bemg 15 feet wide at $2.65 per M ^ (i«S
shmgles cover 10 ft. square) .> ^
i^L!?!?'^^*"/ l^'^u*^'.^' V^} *^°^«^^ t^« two sides of a
Jf, each side of which is 27' by 14' 6"?
t«n^',^^«iJ??** i^^r!''*!*''''^ ^^^^4o lbs. of coal at $6.25 a
ton, 17860 feet of lumber at $13.50 a thousand.
C.
ill Kinrf th#» ffict- nf istM lU- ~et . mt^
roo
REDUCTION 2'-
th^^^l^Jtl^ 'f ^? y^/^^ *°"8^ *"^ 220 yards wide. Find
It $5? ^r M.'^ ""^^ ^°'* * '^^'^ ^*»*'^ *^"" 6 ft. higl^
(3) Find the cost of inch flooring at $17. so oer thou-
sand for a floor 28 ft. by 16 ft. '^ ^
t^J^^ :^ ^M^!*" P"ic»»ased 4250 lbs. of hay at $10 per
ton and sold it at 68 cents per cwt. ; find his gain ^
^ll Al"?tl l^'^fi! ''^^''op Dine apples at $12^ per C.
r^Jf , P^*^ thousand, liow much will the lumber
cost for a close board fence 80 rods long and 6 ft. high ?
i6'x\^^!^^?or^ """ " T* *^ '^y ^^^ ««o^ of a room
?«\ \A * ^^ u ^"l"?!®. (a square = 100 square feet) ?
(8) How much would it cost to lay a floor 7 yards long
by 5 yaMs wide, at Su^sH a square ? ^ ^
(9; How many bunches of shingles will be required to
7f^? «°^ ^"^ ^ J^ • • ( J' ^^^^^ 4 bunches to the square ?
(ip) How much will it cost to shingle a roof, theJenffth
ofthe rafters on each side being ,5 ff. and the bSng
35 ft. long ; the bunches costing $1.16 each? "'"'°'"«
i'i.
COMPOUND RULES.
Exercise XIX.— ADDITION.
$987 63
. 429.92
38.34
927.74
9.00
$ 96.24
198-78
647.92
68.34
928.87
$719.43
921.99
86.86
50.00
9-37
(4)
$9836.74
968.10
91.98
7.54
.87
. <5)
yds. ft. in,
23 2 7
34 I 6
52 I II
74 2 7
61 2 9
miles.
18
73
196
584
762
(6)
yds.
897
936
1042
1 197
1264
miles, chams. yds.
6 40 II
7 29 19
8 37 8
7 16 5
3 74 21
miles. rods.
6197 50
8193 47
604 123
897 235
68 39
mileSi ehains. rods.
16 13 2
12 22 3
»7 15 3
26 73 2
59 68 2
(28)
COMPOUND ADDITION
(lo)
miles, yd*.
17
8.7
918
69
8
94
832
912
1013
in.
II
7
8
9
6
sq. yds.
56
48
20
39
M
(n)
sq. ft.
4
5
8
6
7
sq. in.
76
23
38
96
(12)
sq. mis. acres.
817 89
76
934
518
72
104
216
317
94
29
rods.
138
147
25
16
118
(13)
sq. miles, acres, sq. yds.
87 39 193
92 217 763
31 318 1082
986 169 2162
14 4 894
(I)
ttjns. cwt. lbs.
18 7 37
17 18 45
9 12 53
8 16 61
26 18 77
(14)
acres, sq. rods.
186 89
175 76
123 94
loo 123
98 119
B.
(2)
tons. lbs. oz.
719 187 4
816 913 II
43 486 7
219 1732 9
8 58 8
(•5)
acres, sq. ch ins.
114 8
96 5
l^-K 7
64 9
257 3
(3)
lbs. oz. dwt. grs.
5 9 II
18
17
29
26
7
4
6
38 II
17 13
6 21
14
3
6
8
IS. rods.
2
3
3
2
2
(4)
;£ s.
27 16
81 17
93 9
67 9
72 14
(5)
d.
£
8. d.
3
9
4
5
7
W
86
72
474
79
6 8>^
13 9>^
15 7
9 7X
9 83i<:
(6)
;£ s. d.
987 15 4H
764 17 7X
.99 9 9K
87 II iiX
986 13 io>^
30
ARITHMFTIC
<7)
wlu. d«yi hi*, rain. m&
8
I
9 32
27
9
2
II 36
31
'9
4
17 40
35
17
3
19 44
39
26
5
21 48
(9)
43
tons
cwu
qrt. lbs.
oz. drs.
14
12
I 13
5 9
23
13
I '5
7 8
37
17
3 9
9 6
iS
19
2 17
S 7
8 4
68
8
2 ^16
(")
CnatRToss
grou. dos. nnits.
IS
7
5
6
13
8
6
7
29
9
4
8
76
5
9
10
13
4
7
[I
(8)
y^ da3^ bn. mltu mc.
98 217 12 47 28
87 221 16 51 36
76 318 18 55 42
35 247 24 49 48
42 108 29 43 24
(
.0)
bus. pks.
gals. qts. pt
897 I
I
2 I
26 3
I
2
3 2
3 I
41 I
I
3 I
768 2
I
2
(12)
thous'd. hund'd.
tens
• units.
6
9
1
4
7
3
5
S
4
8
6
2
6
9
7
I
7
5
4
a
amiiiu r iJr the "Ter "=Mof°1 " 'Ijl ''"'"""■'^
J..3..8 ; frui't, $168 JSd ,u„dri« Volk ' 'h^"""""?;
did the whole come to ? ='""™«s. W9-«i. How much
L\
COMPOUND ADDITION
3<
MC.
28
36
42
48
34
I
o
I
I
o
(3) A farmer sold 6 loads of wheat, the first contain-
ing 1 819 lbs., the second 2037 lbs., the third 2036 lbs., the
fourth 1926 lbs., the fifth 1673 lbs., and the sixth 2162 lbs.
How many bushels did the six loads contain ?
(4) A merchant sold the following quantities of mo-
lasses : on Feb. 1st, 15 gal. 3 qts. i pt. ; on Feb. 2nd., 23
gal. 2 qts. I pt., on Feb. 3rd, 31 gal. 3 qts. ; on Feb.4lh,
9 gal. I pt. How much did he sell in the four days ?
(5) A grocer sends off the following quantities of
butter : 47 cwt. 56 lbs. ; 83 cwt. 86 lbs. ; 26 cwt. 34 lbs:
How many tons did he send off?
(6) A man has owing to him the following sums :
;6i3^ips. 7d. ; £^6 5s. 8Xd.; and ^49 19s. 5>^d. How
much IS owmg altogether ?
(7) A jeweller receives on Mon., 16 lb™. 4 oz. gold; on
Tues., 9 lbs. 5 oz. 18 grs. ; on Wed., 6 lbs. 15 dwt. 2ogrs.-
on Thur., 5 oz. 10 dwt. ; on Fri., 13 lbs. 3 oz. 16 dwt. 16
grs. How much does he receive in all ?
(8) Three fields have an area respectively of 17 acres
139 sq. rd.; 16 acres 76 sq. rd. 25 sq yd.; and 9 acres 12?
sq. rd. 18 sq. yd. What is the total area ?
(9) What is the entire length of a railway consisting of
4 different lines, measuring respectively 189 miles I76rd.
2 yd. ; 85 miles 60 rd. 4 yd. ; 100 miles 224 rd. 3 yd. •
and 59 miles 174 rd. 4 yd. ?
(10) Find the total quantity of wood in 4 piles con-
taming respectively 20 cords 1 5 cub. ft. ; 23 cords 59 cub.
ft. ; 16 cords 68 cub. ft.; and 29 cords 125 cub. ft.
Exercise XX.-SUBTRACTION.
$8976.43
987.49
A.
$3427 63
2197.21
$1600.87
384.93
ja
ARITHMETIC
(4)
JS s. d.
1089 12 7
423 IS 9
(5)
I ■. d.
784 14 8>^
457 16 11^
(6)
^ •. d.
563 IS (>A
138 19 7X
(7)
cwt qrs. lbs.
200 2 20
99 3 21
.(8)
miles yards
8943 67
4817 943
(9)
miles rods
1376 21
987 237
(10)
tons cwt, lbs. oz.
714 13 y? II
286 17 49 13
00
lbs. ^z. dwt. grs.
576 9 19 4
89 10 16 15
(12)
y«. da. hr. min. sec.
4083 200 10 30 15
2186 319 19 39 34
0)
ac.
sq.rd
197
57
103
96
B.
(2)
•C. sq. yd.
283 1239
118 3674
' (3)
cords cub. ft.
893 76
275 127
(4)
miles rd. yd. ft,
768 29 5 2 5
94 138 3 2 7
in.
(5)
ac sq. rd. sq. yd. sq. ft. gq.in
I30I 31 29 3 23
423 38 13 8 76
(6)
bus. pk. gal. qt. pt.
710 2 O 2 O
186 3 I 3 ,
(7)
tons cwt. qrs. lbs. 02. drs.
716 13 2 16 2 7
176 16 3 20 9 8
COMPOUND SUBTRACTION
33
I
^r. min. sec.
lo 30 15
»9 39 34
(3)
Is cub. ft.
J 76
; 127
<l' ft. sq.in
3 23
8 76
drs.
7
8
(8)
f rest ijroM gross dot. units
576 3 4 5
289 10 9 8
(9)
thousand hund. tens units
76 4 7 ^8
17 5 8 ^9
(i) A merchant has 219 casks of butter, weighing 397
cwt., 64 lbs. He ships off 173 casks, weighing 214 cwt.,
76 lbs. How many casks has he left, and what is their
weight ?
(2) A farm contains 769 acres, ^^fooj i^, 20 rods, of
which 473 acres, Xj^3S^3 rods are under cultivation.
How much remains untilled ?
(3) A merchant has $5947.87 in the bank ; $3789.63
in stock; $9419.15 in property; $2684.39 on his books
against his customers. His debts amount to $8762.49.
How much IS he worth ?
(4) How much must be added to 6 tons, 1419 lbs., to
make 10 tons ? > -• y 1
(5) I started for a walk 3 hours, 37 minutes, 29 sec-
onds after noon, and returned at 9 p.m. How long was
I away ?
(6) From 15 years, 3 days, 16 hours, 29 minutes, 6
seconds, take 9 years, i week, 3 days, 22 hours, 50 min-
ates, 40 seconds.
(7) A wagon loaded with hay weighs 34 cwt., 72 lbs •
the wagon alone weighs 9 cwt., 96 lbs. Find weight of
the hay. **
(8) A barrel hoWs 31 gals.; there was poured into it
14 gals., I pt. of vinegar at one time, and 3 gals., i qt. at
another. The barrel was then filled with water. How
much water was poured in ?
(9) A farmer had 1000 bush, of wheat. He sold 249
bush., I peck at one time, 448 bush., 3 pecks, i gal. at
ano'her, and kept the rest for flour and seed. How much
did he keep ?
(10) A man travels 8 miles, 216 rods by railway and
17689 yards by boat. Which way does he travel the
farther, and how much ?
34
ARITHMETIC
ions 4 cwt. ; 2 tons m cwi co Ih. ',"*^ respectively j
lbs How much is K';h'-'s't''o"i; ?""" ' """ '^ ^'^'- M
3sq*;?i^,^:;7^:\'^;;- f"--.'>.e firs, has 75 acn=s
yds^ and the^thirda; muchasth^"''!."'^ ' "?' "*• '» "*•
3 3,. rds. .,s<,. yds. Horurh'lrnS'iL'L'SaS
Exercise XXI.-MULTIPLICATION.
((
«(
• ••
Multiply $573.52 by 49.
13 cwt. 5 lbs. 6 oz. by 12.
13 bus. 3 pk. , gal. 2 qt. i pt. by 57
&'^5'^:-b7r-'-'''-^y37.
/4911S. 8^d. by8.
6 days 15 hrs. 32 min. 17 sec bv ^71
23m,les,76rds.4yds.by22. ^^^^•
olbs 30Z, i5dwt. i7grs.byiQ
12 miles 560 yds. by 23 ^ ^'
17 miles 83 yds 2 f^ 1 1 ir, u .:
J /us. 2 It. 1 1 ,n. by 63, using
30 rods 4 yd. 2{!^Xd" "^ * ''"'^"' «^'d
avejie'?„',.^,^i«^^^,^,^9 r^iles in length, and its
road. =*P"'^ 35-37. J* md the cost of the
•aini'ni^tihe'sVp^cL-l'Kn."' t'H- -^h ™"-
.5 ^itf i-ht -r'-" 4 -^^^^^^^^^^^ peas a.
COMPOUND MULTIPLICATION
35
A, 9LI . iV^^^l f'^'i''^ '^ ^"^^^ '6'^*- ba^'ey at
45 cents a bush. ; 56 bush., 45 lbs. wheat at (/, cent, a
bubh., and 10 bush., 17 lbs. oats at 40 cents a bush.
^^^(8) Find the value of 7683 lbs. of cheese at $12 per
bushd/'""^ ^^^ """'^ ""^^'^^ '^'- b^^l^^heat at 72 cents a
(10) If I silver spoon weigh 3 oz., 8 dwt., n ers
what IS the weight of 8 dozen such spoons ? ^ ^ '
(11) A man travels 24 miles, 6 furlongs, 3 rods in a
day. How far could he travel in 2 weeks ?
C.
(1) Find the total length in rods of 48 pieces of wire
each piece being 35 yds., 2 ft., 3 in. long. '
(2) A wagon wheel 15 ft., ,0 in. in circumference
makes .634 revolutions in an hour. How far in miles
yards, etc., does the wagon go in 5 hours ? '
in„^!l;^.K"^ "^""^H-^ "'''^' 15 yards to school each morn-
ing, and the same distance home each afternoon, for 208
time?" ^ ""^ ^^' ^""^^ ^^ ""^^^ ^"""& that
(4) A farmer plowed i acre, 160 sq. rods a day for 2^
days. How much did he plow ? «* ^lay lor 23
Ion r? ^^^^ '^ *^^ ^^"^^^ ""^ 3°°° '"'''''^' ^^*^h '6 ft- 8 •"•
(6) The fore quarters of a lamb weighed 6 lbs. 2 07
each and the hmd quarters 8 lbs. 5 oz. each. How much
did the lamb weigh .* "lum
tir/7^'^,'^''^" '^ 35 ft. II in. long and 7ft gin wide
What is the length around it ? " 7 u. 9 m. wide.
(8) How much coal oil is contained in 29 bbls., each
containing 29 gals., 3 qts., i pt..> ^ '
(9) Multiply 89 miles, 119 rods, 4 yds., i ft., 8 in. by 7.
,«./i°^r •*'''°*'-^ •^'''".^ 3 min., 15 sec. per day. How
much will It gam m a fortnight ?
r
I
I
36
ARITHMETIC
i\
ExerciwXXII.-DIVISION. DIVISOR ABSTf,M*T.
27 lbs. 12 oz.^3.
39 lbs. 5 oz. 4-4.
$7624.53-^9.
^'713-^4.
3ogal.3qt ipt. .^7.
68bus.2pk. igal. 2qt.-j.8.
31 days 5 hrs. 15 min. 10 sec.^12.
84 yds. 2 ft. 9 in. -^ 5. "'
v^, 13 miles 945 yds. 2 ft. 6 in.-rr
00)^157 15s. 8d.-M3.
yO 73219 tons 15 cwt. 89 lbs 6 07 ^v.-*^
('3) 287 acres 469 sa. vds.*r
(14) 47 thousand, 8
(15) 5 million, 3 ten
9 tens, 8 units -^ 79.
B.
,„43) D.v,de a legacy of $,<«| e,ua5irrot/,79 per-
sacf^ >t-io?hLts°/cSo1i? ^™'='^"^'' '-<"'-
eacl'^o^tlEf ;- eTlS'srrd%'^T^ °f -«,
into 108 lots, and sold them 1, «. *'f"''"' ">« '«''">'e
did he get for each lot ? ' "^^ "''• «'"' "^W"*
}i) 287 acres 469 sq. yds -s- ?
14) 47 thousand, 8 hundred, 7 tens, 1 units--8 '
1^5)^5 m.lhon, 3 ten-thousands' 6 thiisa"nTshu„d,.d,
COMPOUND DlVISIOJi
37
IS gllsJloftT °^^""°"' ^^'^ ^2 '^" «o^ much will
(8) Seven horses eat 15 bus. 2 pk. 3 qt. of oats in a
^eek How much is that for each horse ?
(9) A father who had a 200 acre farm, gave his onlv
son 80 acres, 100 sq. rods, and divided the remainder
t^^'j,!::^.l,^i::r Find to a square
yds^r^^ o^Pa^pe-f?u^& tSe'o^f 1^; !^ i^
''9 acres 18 sq. yds., 7 sq. ft. less than 9 times as mud^
asB's Fmd the amount of land in the three farms
-y Si: f J"^!? T? ^.^ ^^'■^^' '24 sq. rods, 28 sq. yds.,
vds^* Ln ff"^- A^% ^T. ^i^''^'^ '37 sq.'rods, 29 sq
yds., 6 sq ft, and divided the rest among his 4 sons
How much did each get? , ^
Exercise XXIll.-DiVISOR CONCRETE.
JO $43.50-;- $8.70.
' $20024-13 cents.
$444o-^$3.7o.
IS lbs. ID oz. 4-3 lbs. 202.
4days,4hrs.-^5omin.
., 9702 gal. ^31 gal. 2 qt
(7) I mile-r2 ft 6 in.
(8) i6yds. 4in.-r4ft 10 in. '
(9) 50 miles, 200 yds. ^2 yds., i ft 6 in.
(10) 68 tons, 1594 lbs. 10 02 -r 152 lbs. 6 oz.
(11) 20 lbs. 8 0Z.-rI2 0Z.
(12) 26 weeks, I day -h 3 hrs., 50 min.
B.
acri;\39rq.td"?" " '""' '' ^^^ ""^"^ ^^^^^'"^^ '» 36
3«
i
ARITHMETIC
«vi?o\^°'^ long will it take to plow 147 acres 10; so
rods at the rate of 4 acres, 35 sq. rods a day ? ' ^ '^•
W How many turns will a wheel ia ft -.;«;« •
cum erence „ake in rolling a distencTofI J m'ile"? " ""
,^A" i'"" "^"y '""«■=. each containine I bnsh ,
null?to ^sT"'' ''^'" '*<* " '*■ '°"f ""' "casure 2
cwt 2 a«°'in£'',ir5l!''*''! "f ^^«"' ^^"^^ containing r,
cu^l^flS: rn"X-?.t- ^ «• « ">• '" ci.
(12) Assuming that a person's steo « 2 ft ft ?n f
many steps does he take £ walkfug'Tt^fiu's^o y'Js! ?''°"'
C.
9xi'^2V^5Ttt''n;S„'r^'^^ '•• ' '"'" "-y "-ks
bin 8l?xTf?T,''"'K''r'«''«" *<">'d it take to fill a
man^ miles will a steambSt'^^t ^ « 'd^s^Tthe s2S:
(4) A cask contains 64 ffal i nt t »^f u«
may a vessel holding i at ^ m \« ^,1^^"^'°'^ "J^"^ ^"^*'^^
^c^ TK- r ""'"'"s/ V. I pt. be filled from the cask?
. (5) The fore-wheel of a carriage whirh 5« ^ r . •
:res, 105 sq.
3 Jn. in cir-
liles ?
I bush., 3
124 bushels
I measure 2
>ni a hogs-
ntaining 13
of 341 tons
in. in cir-
d 80 rods
ning from
urs each.
> in., how
► yds. ?
COMPOUND DIVISION
39
h^ i^l ^'"? *^/ number of bushels of wheat in a bin 6 ft.
bTches: ^ "^"'P' '^ ' ^^^' '' "^"^^ *° ^''^"^ ^77 cuWc
is th^fidd /^^^"^ ^° """^^^ ^°"^ contains 10 acres, how wide
arotto'ds^loll^r'^' °'"'^^ ' ''' ^ '^' -" ^^ -^ -^
One^UJZ^}'''^^' '°? ''**^!.°*" ^'""^ f^«^« 6 wires high.
Afi Jt"i How many bushels of oats are equal in weieht to
68 bushels of barley and 51 bushels of wSeat? ^
o«^^ v^J" *^® ^^'"® °^ * ^'n of wheat 6' long, 4' wide
?ufr?s) ^'P' ^' ^' '^"'' P"^ ^'^^^^^^ <' ^"bfj ftlls
ny bricks
:e to fill a
5?
Is. How
the same
my times
e cask ?
7 feet in
the hind
nference
ining 15
s of car
rd?
MISCELLANEOUS.
Exercise XXIV.-AVERAQE8.
A.
« oii^^^f '^ *^® "^^^" between 10 and 80 : between
o and 90 ; between 76 and 182 ? ' oeiween
7 ft.? ^^^' '^ ^^^ ^""^'^^^ ""^ *^'^^ ^^"&ths of s ft.. 6 ft.,
-lit'J^^ltl^sVr/r^^^' '^^ "^'^'^^ °^^ ^*^^"
buslf^Yhn^h ' i^^, ^T^8^« Of four loads of wheat of 40
Dush. 45 bush., so bush., 55 bush.? ^
VS) What IS thi» averacro. «<■ tu^ r»n-_ •
rifle match: 72, 73,"79,"iS,Y3; g^'T ™"""""^ '""'*' "' '
40
^ITHMETIC
dailv receipts for the week ^^ '^^' ^ '"^ ^^^ average
vearf ^ TK* *""^* *8« "f A, B, cf D, E Knd F is ,.
pM'
^ B.
(0 2.3 cows and i6 horses together cosr t^cfj^ tu
cows^ cos, J.6 each. Find .hfTve'rage'cSi''^f elc'h
33 K. ® 5«'' 2Ubr^*!r°'' Pf;"'- of ••>« following :
® 14c.? * ' ^ ^'- ® ^*^-' ^3 lbs. @ 3,c., and ,y Ihs.
a Ih^"*^, AS""'.?'"" '"Ke*" 9 lbs. tea worth ,2 ccnt^
(S) A grocer mixes 15 lbs. of coffee (cb 'ynr -, ik ^
^nSeltewtlS ^' -« --faTaif Votdl
long and 36 "^s m¥e" 4nd ,he .k';?^'*'""^^"'"'-"'''
"'t)'^r'"= -»"t buTo'nSXXSg"5^« ^° '"^^
the fou„h 'rlrd— '-'-t:^'"^'' "'^'^''^ => ">»• '«^^ "ha"
* -^^ "'^ i"c weight 01 eaca.
AVERAGES
41
s 1896 lbs.
Jay, $200 ;
'day, $325 ,
le average
ps. Wliat
1 ; 2 at $23
2. I sold
id F is 31
s 28 years.
5O6. The
: of each
bUowing" :
s J 24 lbs.
allowing :
id 17 lbs.
32 cents
Find the
3 lbs. @
f pounds
irms, the
200 rods
r 20 rods
pounds ,•
ond, but
ess than
15
@ 17c.
(8) Fihd the average price per lb. of the following :
lbs. @ 15c.; 16 lbs. @ 14c.; 18 lbs. @ iic, and 13 lbs.
Exercise XXV.— APPLICATION OF SQUARE
MEASURE,
(i) Find the area in square yards of the following
square fields, whose sides respectively are : 15 yds., 24
yds., 37 yds., 59 yds. :» ^ » 'f
(2) Find the area in sq. yds. and sq. ft. of the follow-
ing square fields, whose sides respectively are : 9 yds
2 ft.; 12 yds. I ft.; 17 yds. I ft.; 25 yds. 2 ft.
(3) Find the area in sq. yds., sq. ft, sq. in. of the fol-
lowing square fields, whose sides respectively are : 4 yds
2 ft. 5 in.; 7 yds. 2 ft. 8 in.; 9 yds. i ft. 9 in.; 15 yds.
2 ft. 10 in, * ^ J J
(4) Find the area in sq. ft. of rectangular fields having
respectively the following dimensions in feet : 24 by 20 •
27 by 18 ; 33 by 27 ; and 1 12 by 97.
(5) Find the area in sq. yds. and sq. ft. of the follow-
ing rectangular fields : 5 yds. 2 ft. by 7 yds.; 3 yds. i ft.
by 10 yds. 2 ft.; la yds. 2 ft by 12 yds. i ft; and 26 yds.
2 ft. by 24 yds. 2 ft
(6) Find the area in sq. yds., sq. ft., and sq. in., of the
following rectangular fielcis : 2 yds. i ft. by 4 yds. i ft 3
in. ; 5 yds. i ft. 4 in. by 5 yds. 2 ft. ; 6 yds. 2 ft 8 in. by
3 yds. 2 ft ID in.
(7) A plank is 18 in. broad, find what length most be
cut off to make a square yard.
(8) What part of an acre is a field 120 yards long and
25 yards wide?
(9) A street is a quarter of a mile long ; find the
number of square yards in the pavements 3 feet wide on
both sides.
42
ARITHMETIC
ing II inches by 8 inches ' ^P^n^'neasur-
wi,/a JSjXX7'l^-Vk'^ 9 in. wMe
meSn^'gls'ft.VfcTt 1un„"' •"""■ "t"" '" " ^oon,
qui«asp\cepf27i;,?by'.8gr""«^ '*"='' P'"°" "> «■
aveiage four treeVo^ o^eaAl^r^ chjir"^ "" -
widl''^<JJ',o'^„'dl"^4"„t"'L**,hT'%=^.''=''»'''.yds.
many stones i ft. 4 in ?on7hv o n °f '"'•I;- '''»<' h""'
to pave the path. * ^ ' '"• "'"'« *'" ^ "equired
(5) How many rails 11 ft. Ion? w„„u i,. ■ ,
enclose a rectangular field 30^5 by .8 ,„'^'''""^1'<'
straight fence 5 rails high ? '^ ■• '°^^ ""'' a
d'------S'8--^^^^^^^
s^SaSil=^^:"oSc^:ir-
<eoiSJi?'iS"rJndZ"wSb°''- "^ " «•• «"<• «■=
wm<u1ot.\rsrdVr»h\^;f^^™Tr„^^t'^^-^-'".-H
by 2 ft. 5 in.,
ane measur-
will be re-
in, by 4 in.,
t. 8 in.
9 in. wide
in a rcK)m
"son to re-
ood half a
>ing on an
path 2 yds.
Find how
e required
iquired to
Is, with a
land 4235
by 12 ft.
sr square
J^ yards,
se a rec-
find the
'w much
i&i wide?
CARPETING
Exercise XXVI. -CARPETING.
43
A.
Find how many yards of carpet running lengthwise
will be required for rooms of the following dimensions :
(j) 18 ft. by 15 ft., carpet a yard wide.
(2^ 25 ft. by 18 ft., carpet a yard wide.
(3) 18 ft. by 12 ft., carpet 27 in. wide.
(4) 21 ft. by 9 ft. II in., carpet 27 in. wide.
Find the expense of irpeting the following four
rooms, the dimensions and cost being :
(5) 24 ft. by 21 ft., carpet a yard wide and 90 cents a
yard.
(6) 30 ft. by 15 ft., carpet a yard wide and $1.20 a
yard.
(7) 18 ft. 6 in., by 13 ft.^ in., carpet 27 in. wide and 75
cents a yard. ,
(8) 43 ft. 4 in. by 24 ft. 9 in., carpet 27 in. wide and 99
cents a yard.
(9) How many yards of stair carpet will be required
for a straight stair of 21 steps, 11 in. wide and 7 in. high,
allowing for 2 extra yards ?
(10) How many yards of carpeting 27 in. wide will be
required for a room 17 ft. 4 in. by 14 ft. 5 in., if the strips
run length-vise of the room, and 8 in. per strip be wasted
in matching ?
(11) How many yards ot carpeting, i yard wide, will
be required for a room 30 ft. by 16 ft. 10 in., if the strips
run lengthwise of the room, and 9 in. per strip be wasted
in matching ?
(12) Find the cost of carpet for a room 22 ft. 7 in. by
14 ft., if the carpet be 27 in. wide and cost $1.20 a yard,
and 6 m. per strip be wasted in matching, the strips
running crosswise of the room.
B.
(l^ How manv varHs of thicl*- r»ar»»i- ^/> :« ...:^« ...:!!
cover a floor 20 ft long and 18 ft. wide ?
44
ARITHMETIC
?i^ FinTSf "^"."'"Z lengthwise of the room:'
ry X«,!)^o •.? '^ *^°^^ ^° ^^^Pet a room 2?' 6" lontr mH
wide and tunnfJhnl^wi^f'u^ ""T",? ''''■'« '7 in.
• at 87>i cents a yird^ . """^ """* "<""'' " <=«'
in. widens «".s a 'v^rr *° "'"' ^-^Sthv,'^' carpet 3>
-IK--^^^^^^^^^^^^ to
cheaper, and how much, to fa ' tht 4/4 ^Jh '' *'
p./aprde'in'd''c;f.i^;'^,r<^,^7/4«' I* car.
each case? *"™'"^ ""^^"^ ^nd matching in
Exercise XXVII.^PAPERING.
A.
folln^'.T;i5°£ °"_,"l»'^h ;M« exercise is worked is .s
-— - . . ... 3u,» ux «ie wiaiiis of doors and windows Ts
PAPERING
45
5 required
5 '"• rise,
long and
8o cents a
if
t 85 cents
long and
)6 cents a
long,
long and
r $ .44 a
/ise?
•ed for a
»g 27 in.
Id it cost
carpet 32
2at$i a
iiore ?
ie be, to
arpet 27
^ IS the
iwise or
?
ith car-
' 12" per
:heaper,
■ much ?
hing in
i is as
lows is
deducted from the perimeter of the room, And the number
of strips is obtained by finding how often the remainder
contains 18 inches (The width of Canadian and American
paper). The length of a single roll of paper is 24 feet.
Note. — Paperhangers have a special rule : Deduct
half the area of the openings (in square feet) from the area
of the walls, and divide the remainder by 30. This gives
the approximate number of rolls.
(i) How many widths of paper will be required for a
room 18 ft. by 1 5 ft., no allowance for doors and windows ?
(2) How many strips will go round a room 19 ft. by^
24 ft.?
(3) How many strips are required for a room 31 ft. by
24 ft., if there are 4 windows and 2 doors each 3 ft. wide ?
(4) How many rolls will be required for a room
21' 5" by 13' 4", with 2 doors and 2 windows each 3' wide?
(5) How many strips are recjuired for a hall 26 ft. long
and 6 ft. wide, papering the sides only, on which there
are 4 doors, each 3 ft. 3 in. in width ?
^6) How many rolls will paper a ceiling 24' x 18' ?
(7) How many rolls of paper are required for the walls
of a room 2 1 ft. long, 1 7 ft. wide and 9 ft. high ?
(8) Ho\ ' many rolls will paper the walls of a room
12 ft. by 16 ft. and 8 ft. high, allowing for i door and 2
windows each 3 ft. 4 in. in width ?
B.
(1) Find the cost of paper for the walls of a room 17
ft. by 13 ft. and 9 ft. high, with 3 openings, at 36 cents per
double roll (each opening 2 ft. 11 in. wide).
(2) Find the cost of paper 21 in. wide for the walls of
a room 35 ft. by 20 ft. to the height of ^jS^ ft. at 65 cents
per double roll; 1 foot on each strip is allowed for
matchings, and the border costs 8 cents a yard.
(3) If the paper-hanger charges $2.50, the border cost-
ing 8 cents a yard and the paper 1 5 cents per roll, find
the cost of papering a room 22 ft. by 14 ft. and 12 ft. high,
with paper 30 in. wide, allowing 12 ft foi doors and
windows.
46
ARITHMETIC
r^Sf ^'1? ^^^ -"'i °/^^® wallpaper 21 in. wide, at 25
cents a roll, required for a room 20 ft. 8 in. by 15 ft. 4 in
eacM it. wiSe' "^^ ^ ^' ^ '"• "'^" ^"^ ^^indowi
r.ntcl^'n'^ ^^®u°'i °. *^® ^^" P^Per, 2r in. wide, at 20
cents a roll and bordering worth 10 cents a yard for a
^A? K ^^ • u,"^^' ^""^ 1 ^'"do^s each 3 ft. 10 in. wide.
dJull^^ A ^ rollmake only 4 strips, and 8 strips be
deducted for doors and windows, find the total co t nf
papenng a hall 30 ft. long and 8 ft. wide, with paper wort^
62 cents a roll and bordering worth 12 cents a yard ; the
on the border i cent a yard. H»<^""b
(7) What will it cost to paper the walls and ceiling of
a room 27 ft by 33 ft. and 18 ft. high, at 35 cents ner
square yard ? ' s > «>■ js t.cius per
Exercise XXVIII.-PLASTERING AND PAINTING.
A.
«,ni^°J^~^* '^ customary in plastering or paintin? the
walls of a room to deduct half the area of all ooenfnl^s
etc and take for the required area the number orsquare
yards nearest the remainder. ^ ^
(i) Find the cost, at 20 cents per sauare vartl «f
plastering the walls and ceiling of a mom% ft Lnl' 16
ft. wide and 10 ft. high, allowin^g for 2 Tors^ each ^ ff
by 3 ft., and 3 windows, each 6 fl. by 3 ft ^
(2> Find the cost of plastering the walls and ceiling'
of a room 16 x 12 x 9 feet allowing for 2 doors, er.ch 7 ff
by 3 ft. 6 m., and 2 windows, each 6ft bv 4 ft anH 1'
skirting board i ft. high, at 15'cents per squLt yird. ^ ^
(3) How much will it cost to paint the ceiling of a
box wid^^Hd ! f^f ^T Z^ P^;"*'"«^ *^« outside of a
squirryard ' ^ ^' ^^ ^ ^' ^^ ^ ^'' ^^^P' ^^ '^ <^-«ts .per
PLASTERING AND PAINTING
47
(5) Find the cost, at 10 cents a square yard, of paint-
ing boti sides of a close board fence 4 ft. high, round a
rectangular lot 132 ft. by 66 ft., allowing $3 for painting
posts and scantlings.
(6) How much would it cost, at 20 cents per square
yard, to paint the walls of a room 20 ft. by 17 ft. andf 9 ft.
high, deducting for 2 doors, each 7 ft. by 4* ft., and 3
windows, each 6 ft. by 3 ft., and also paint the ceiling at
30 cents per square yard ?
(7) Find the cost of plastering the walls and ceilings
of a room 24 ft. long, 18 ft. wide and 15 ft. high, the
skirting board being 18 in. high, at 22 cents a square
yard, three coats being put on the walls and two on the
ceiling.
(8) Find the cost of painting the walls and ceiling of
a room 26 ft. 6 in. long, 18 ft. wide and 14 ft. high, at 34
cents per square yard, allowing for 2 doors 7 ft. 6 in. by
4 ft., 2 windows 6 ft. by 4 ft., and i smaller window 3 ft
by 2 ft.
(9) What will it cost to paint the walls and ceiling of
a room 18 ft. long, 15 ft. wide and 12 ft. high, at 2% cents
a square foot ?
(10) Find the cost of painting the walls and ceiling of
a room 15 ft. 6 in. long, 14 ft. wide and 10 ft. high, at 36
cents per square yard, allowing 80 square feet for doors
and wmdows.
(11) Find the cost, at 6 cents a sq. yd. of painting a
fence 6 ft. high around a lot 22 rods square, both sides.
B.
(i) What will it cost to plaster a room 32 ft. long, 18
ft. wide and 13 ft. high, at 12 cents a square yard, aUowing
200 square feet for doors and windows ?
(2) Find the cost of painting the walls and ceiling of
a room 18' 6" long, 14' wide and 10' high, at 23 cents per
square yard, allowing for 2 doors 7' x 4', and 3 w^-dows
6'X3^\
48
ARITHMETIC
Of a cistern 8 ft. bv 12 f' S 8^ hLk '^^ ^"^ ^««°»"
square foot. ' ^ "' "'«^^» at 9 cents per
(7) How much white learf n ;n> ;« • , ,
coat on a fence ,87 yards lonir Ld 6 ft ^^^"^^ ^" °"«
covers 4^ square yidT? '' '• *""''■ '' " •"""d
B number
ong and
veiling of
'ith four
rd.
bottom
-nts per
for one
I pound
feet by
t. by i6
Fence 5
^ts per
(0
76894
68317
34567
89123
45678
91234
56789
12345
67891
23456
78912
34567
(6)
49867
71386
23456
78912
34567
89123
45678
91234
56789
J2345
67891
23456
MECHANICAL WORK.
Exercise XXIX.-ADDITION.
(2)
31467
28913
45678
9 '234
56789
»2345
67891
23456
78912
34567
89123
45678
(7) •
76413
31982
34567
89123
45678
91234
56789
12345
67891
23456
78912
34567
(3)
82154
67418
56789
12345
67891
23456
78912
34567
89123
45678
91234
56789
(8)
45128
81476
45678
91234
56789
12345
67891
23456
78912
34567
89123
45678
149)"
(4)
98621
94628
67891
2^456
78912
34567
89123
4S'^7-
234
56789
12345
67891
(9)
12689
82649
56789
12345
67891
23456
78912
34567
89123
45678
91234
56789
(5)
73409
37645
78912
34567
89123
45678
91234
56789
12345
67891
23456
78912
(10)
90437
54673
67891
23456
78912
34567
89123
45678
91234
56789
12345
fiTRni
'{
»)fi/.'
50
ARITHMETIC
Exercise XXX.- SUBTRACTION.
(4) 4533599 ;(sl^lUU)^ti''^' ' <3) 449o6i. ,
(10) 5664169 J (}; ^^^If' ^?>>*gf44i ; (9) 6068767;
in succession: (n) 7i7ijci • ?..\ ., l°°^'«n times
06) 7076,73; (4^,11 U^l otll'Xll' ('5>7»7^73-.
(38) 945677. ; ^.fe^'j g ^^9^3 ' ^''^ '''''^' '
in srst^n\°'^5f)1'oT.'i|« times
•0376794 ; (34) 49^!,°;-(5tf.i5i|o1. ;'°5^^Ut^
Exeretae XXXI.-MULTIPLrCATION.
.«8lf(T)'';3l^^°[3"°-[n? numbers by 4.7 : (,)
34576 ; (7) 3686^ i i,??^ ,' /l> '«43^ ■ (S) ^7648 ; (6)
-7«f(TIf:^4°7!-3V:i;ii"f/ mte^^ by 568. (,o)
(^9='^ '^^^« ' (») '^464 ; kY^e^l (~r--e
(35)';'?5Vf (.6?.^^ r (^^) '^"[^(^"sntri ■■ h} '^* ■'
MECHANICAL WORK
Exercise XXXII.-DIVISION.
51
Divide each of the following numbers by 284: (i)
36261 12; (2) 4079376; (3) 4834816; (4) 5439168; (5)
7252224; (6) 8.58752; (7) 10878336; (8) 14504448; (9)
1 63 1 7 504. J t^t , VW
Divide each of the following numbers by 9 ten con-
secutive times : (10) 21527406891774 ; (i i) 28703209189032;
(12)43054813783548. J -V y-j ,
Divide each of the following numbers by 8 ten con-
secutive times : (13)1457067655168; (14)2914135310336;
(15)4371202965504.
Divide each of the following numbers by 7 ten con-
secutive times : (16) i;35535453564 ; (17) 2303303180346;
(18) 767767726782; (19) 3454954770519; (20) 1 151651-
590173.
Divide each of the following numbers by 6 ten con-
secutive times : (21) 5826157922304 ; (22) 8739236883456;
(23) 3884105281536; (24) 971026320384; (25) 2913078-
961 I 52. N .// 7 J /
Using factors, find the result of oach of the following •
(26)8396741^63 ; (27)893749847^72 ;(28)8967459.^56;
i,29) 9876402^84 ; (30) 45296787-J-72. .
Bxerclse XXXIII.-GENERAL REVIEW
PROBLEMS.
(i) Divide 84 miles, 240 rods, 2 yds. by 13, and re-
duce the quotient to inches.
(2) A man paid$38.75 for cloth, 7 yds. costing $10.8?.
How many yards did l^e buy ? o ^
(3) A boy counted the number of square inches in 4
times I acre, 49 rods, 3 yds., 7 ft., and his brother counted
the niimnpr nf rmnooc ir» r^»» ^^.^^ \iri-:_i- 1 .
— „„.., .^^ .„ ^^^ iwii=. Willi;!! uoy countea
the greater number, and how much greater?
52
ARITHMETIC
(4) John and James started to walk from Tni.rt«f« «♦
noon and walked until 20 min. af^r one ?clodc T„hn
wagon going ? ^ """"''• ""^ ">»">' ">"« ^ hour is the
ani^i ft "x'';!!'^ -2" °? pT«ing a room 20 ft. 6 in. lone
?!?{ Sfu ""^ • 7 miles 4 rods to iiches.
ton) ^ ^^' '' '^^ ^^^"" °f "°° lbs. of hay at $8 per
ills An oK?^"^i"/i^?' ^^^^ ^'■^ tl^ere '» 746859 inches?
anilhi tos?s"ar2o 'rod's'S'' "^ '=™'^ '' '""""^
hour doeMhe trih, go? ^P^"" "°" """y "i'*^ »"
MoXlo6.3r;^.'^nn-sJk7 *- '- -S a.m.
wi./^^Jl'Jri/i^^irga-^tr '"' °'"^ ^'"
s,u^\ot"'i1ot3ira^n-r!--=-^!;"«" ^3
GENERAL REVIEW PROBLEMS.
oronto at
:k. John
?2o yards,
aart were
the rate
ains long
ch plank
wide.
:tangular
deep?
lakes 48
ur is the
in. long
costing
of each
$8 per
sd 3 in.
inches.?
Is wide,
cents a
4 qts.,
econds
iles an
5 a.m.
What
«n 23
53
(20) riow often can 2 gaL i qt. be subtracted from 36
bus. 3 pks. ?
(21) A man travelled 32 miles 217 rds. 4 yds. 2 ft. on
Monday, and 43 miles 276 rds. 5 yds. 2 ft. on Tuesday.
How far would he have to go on Wednesday to go 100
miles altogether ?
(22) A man paid for a piece of land 32 rdg. wide by
giving 240 cords of wood at $4 a cord. Land being worth
$40 an acre, find the length of the piece of land.
(23) Find the cost of carpeting a room 30 ft. 6 in. long/
by 18 ft. 6 in. wide, with carpet 27 in. wide, at $1.17 a
yard, allowing 6 in. for matching— the carpet running
lengthwise.
(24) Find the total r ■.■ , ,f 12 scantlings 24'x3"x4'' ; 30
planks 2 xi8"x24', and ft. of lumber at $15 per M.
(25) A road is 4 rods wide and contains 32 acres, how
long is It ?
(26) How high must wood be piled upon a rack 12 ft.
long and 4 ft. wide, so that there may be one and a half
cords ?
(27) Find the cost of the boards for a close fence 7}4
ft. high around a school-yard containing one acre, at $12
per M., the yard being 8 rods wide.
(28) Find the cost of 3 loads of wheat containing : 54
bus. 26 lbs. ; 49 bus. 54 lbs. ; and 51 bus. 30 lbs., at 60
cents a bushel.
(29) A gravel bank has a surface area of one acre, and
is 3}4 ft. deep. What length of road 14 ft. wide and 9 in.
deep will it gravel?
(30) Divide 279 acres, 139 rods, 26 yds., 3 sq. in., by
68. .
(31) Find the difference between 99 miles, 319 rods,
25 yds., 2 ft., 1 1 in., and 100 miles.
(32) Find the cost at 12 cents per sq. yd. of plastering
the walls and ceiling of a room 2 1 ft. long, 1 2 ft. wide and
9 ft. high. It has 4 openings, each 8 ft. by 4 ft.
.(33) How many yards of carpet 30 in. wide will be re-
quired to carpet a room 18 ft. long and 15 ft. wide. What
will It cost at 95 cents a yard ?
54
ARITHMETIC
wil/iit^gt ,vUf4pf? "' " ^'^P ' ""^ ■"-y -"«. etc..
tons and iK each ? ^*^"^^ P^'^'^"^* «°^ "^*»y
(37) Subtract 16 bus. % nk i nt frr^r« «, u
q... and d^ide tU. imJ^^nT^^^Jl^"^^'^ '
\ 30) Reduce 75614c inches tn 'nicrU^r. ^ ^. " .
K', ^ater wpicrh Tr» iko I, »* ^°"" oz., and a erallon
(4-) Exp„sf^8399Tyards in'rJJiletSd™?"'
a J^th r^^vW^^^^
J12.50 per M * '• '"'^'' *'* P'*""^ 'fi in. tfiiclc, at
staii^'if^''sUps'^ch'\?!i?^ "'".^'"T?' <■"' " fligh' of
/'^A\ T J- P?' ®^<^" io>2 m. wide and 7 5/ in hJifh ?
.on^f?8r':'iii?„^d?aird:^r'''""*°'^"'-''^^
busS.'S^ andT;5;rbs'^/'°i''|V f, *"»' '" 9^ cents a
spent 60 cents Md with .^ ' ?6 cents a bushel j he
ceV. a cwt" ' Vo^'r^tn^r Efh^u^;'^'" <=-' ^' 3o
(50) A farm containing co acr^s •" ^r r-- J- • '
v\
\
GENERAL REVIEW PROBLEMS.
55
rnd"w?^t wiS^thr/'^^' ^'"'^ ^'^ '/^"■'■^^ *° go around it,
and what will the fence cost at i >^ cents a foot ?
V5i; A stick of squared timber is i8 in. by 15 in., and
measuri?"^' ' '' '' ^^"^ ^' ^^^ P^'^ ^., boarS
(52) A half acre lot is 10 rods long. A 5-strand wire
fence IS put round it. How much wfre, at 5 cems alb
will be required if 2 yards cost 3 cents.? ^ '
2bbl. nf hf /^^ total weight in lbs. of: 3 bbls. flour ;
I hulh if ^ f ' ''°.^"?- u°^ P°*^^°^« ' »2 bush, of rye
5 bush, of oats, and 9 bush, of barley. ^
f^J^^^i^?^ "^*?y ^"'"'^^ pickets placed 3 in. apart, will
fence a half acre lot of 66 feet frontage ? *^
;n.Cr.^°'^T^"y^^^'°^'"'^^^^ are required for a 12-
mch baseboard around a field 40 rods by 30 rods ?
h*» ri^ i **if°°";^ '^^ ^^ ^^' ^S^^"*^' ^hat must its height
square ya'rds?^' ' ^''^ '^ ^^ ^""' '"">^ ^"^°""^ ^^^
(57) Find the value of a pile of wood 40 ft. long, 24 ft
^'*^; ??i^ ?• ^'8^^' at $575 a cord. ^ ^' ^
«^i^^^^'"^ t^® ^a^"e of a field 50x32 rods, at $95.50 an
(59) Allowing 90 cubic feet of air for each pupil, how
many pupils could be accommodated in a school-roim 27
ft. long, 18 ft. wide and 10 ft. high ?
ma K^fwJ. '5,^^"*^ a square yard, find the cost of paint-
Lnd2ift tlde°°''^^ ^ ^^^^^^^°^^ room 27 feet long
r«,/k^^ A bag of grain weighs i cwt. 45 lbs. 3 oz., how
much less than 45 tons would 18 bags of such grain weigh.?
^.-^i^K^ ^. ^"^"^T ^""^^"^ ^^*^' °^ ^3 rods I ft. 6 in. on each
side, has trees planted aL around it. There is a tree in
!?S''T!u°^*^^ ^'*^' ^"^ along the whole length of
!«?!," V^^''^ ^'■^, 9 trees. How many trees are there,
and how far apart ? '
(63) To pay his rent on 75 acres at $2.75 an acre a
.!IIfrK^^u^°*'^^35olbs.ofbarleyat78 cents a sack of
100 lbs. ; how many bushels of wheat at 8« rent<z aK,
wiii he need to sell to make up the balance ?
n
56.
>iRITHMETIC
(64) How many times must a boy walk round a nlav
ground 140 ft. long and 70 ft. wide, L order to w^kseve'n
o„it^^ ^ ^**?^'" ^9'd peas in a field containing 10 acres
a b1,.h JP^"i ?5.75 inlabor. He sold the peasit 85 cents
!2S Y?^'^^ ^^\ "°^ "^a^y bushels per acre had he?
(66) Make out thefollowingpay sheetriohrs J^day:
A..
•B..
C
D..
M.
9
10
.8
10
T.
W.
h
9
9
10
9
ID
ID
ID
10
10
10
8
10
10
8
6
5
4
5
$2.00$
$1.90
Si. 80
$1.60
$
Exercise XXXIV.-BUSINESS TRANSACTICNS.
A.
iowL" nili^^xTmptsT °' ''' ^"""'^^ '" ^^^^ '' '"^^ '^''
aJ^I ^^^ '^^- ^""erat i8c.; 103 lbs. cheese at 14c • 112
at 4Qc^?and S^'h' '^^ ^''- "^""^ ^' ^''' '^S bush. plSatoe'
at 49c., and 87 bush, carrots at 58c
^6 hn.T? «ij"'^- "^^^^^^ \* ^?^-' ^7 bush, barley at 6^ •
corS at 77c ^^'•' ^^ ^"'^- P"^^ ^' 57c., and^3 busli:
iJuJu ^"^^- *"™'S^ ^''♦^c; 84 bush, beets at 7?c •
Wh »' 'Pf'^^'P'^^^^c.; 137 bush, onions at 82c.; 20
bush tomatoes at 50c., and 85 doz. cabbages at 53c. ^
U; 137 bbls. apples at S2.M : f>A h..=K «i „ „": *
BUSINESS TRANSACTIONS.
57
id a play-
alk seven
lo acres,
1 85 cents
of labor,
i had he?
= I day :
3$
3$
ICNS.
the fol-
jc.; 112
otatoes
tt 6^c.;
3 bush.
•t 75c.;
2c.; 29
c.
r- _-
108 bush, peaches at $1.87 j 93 bush, cherries at $1.40,
and 85 bush, pears a^ $1.95.
(5) 26 lbs. rice at 4c.; 34 lbs. tapioca at 13c.; 42 lbs
sago at I2c ; 25 lbs. barley at 5c.; 39 lbs. dried apples at
8c., and 22 lbs. prunes at 9c.
-^(6) 25 bbls. flour at $5.50 ; 36 bags flour at $2 80 ; 18
bags bran at 85c.; 15 stone oatmeal at 37c.; 17 stone
commeal at 36c., and 29 lbs. wheat meal ?,t 5c.
- (7) 27 lbs. pork at 14c.; 35 lbs. beei at 12c.; 19 lbs.
mutton at 1 6c.; 14 lbs. veal at 12c.; 17 lbs. lamb at 15c ,
and 24 lbs. ham at 13c.
(8) 13 tons hard coal at $6.25 ; 17 tons soft coal at
S4 50 ; 19 cords maple at $3.75 ; 24 cords oak at $3.60 ;
16 cords pins at $4.25, and 23 tons coke at $3.70.
^9) S4yd3. cotton at 12c.; 41 yds. cashmere at 57c.;
3 ? ^ -Is. flannel at 35c ; 56 yds. muslin at 17c.; 67 yds.
.xmt at 1 8c., and 52 yds. lace at 99c.
"^10) A man exchanges 14 lush, wheat for 24 bush of
barley, when 12 bush, wheat are worth $1 1.52. Find the
difference between the prices of 7 bush, wheat and 7
-, .bttsh. barley.
(11) A milkman bought 40 gal. of new milk at 16
cents a gal., and 60 gal. of skimmed milk at 2 cents a
quart. Having mixed together, he sold the mixture at
24 cents a gallon. Find his gain.
-<I2) I bought 167 bush, wheat at $1.65, and 287 bush,
oats at 37 cents. I sold the wheat at a loss of 4 cents a
bush, and 34 bush, oats at a gain of 18 cents a bush.,
and the remainder at a gain of 13 cents a bush. What
was my gain on these transactions ?
B.
*(i) A farmer bought from a merchant 1 1 yds. of cloth
at $1.2$ a yd; }4 doz. ties at $4.12 a doz.; 17 yds. of
print at 23 cents a yd , and 3 collars at S2.40 a doz. He
handed him in payment $25. How much change did he
get ?
(2) A merchant bought 13 doz. oranges for $3.75. He
cave aw»V nin*»- anH cnlH tVi*» rprnainrlor of tUa m*^ nf t
oranges for 10 cents. Find his gain.
58
ARITHMEIIC,
^\
'™;f»d^owt foX?„t1''ei° P<'S„^^ of hay a, S,o a
^ (4) How many loads of Z^, , ""^ «^"'-
exchange a tufo^bu/.L weighL%^'?^- ^""^^^^^n
, (6) Find the total cost of • sTf ' '' ^' '^ « "'•
■°&> pencils at$,.sorgro3A°P^"\«7for2;^cents;
J"oa ream, and 7»exfrdse'bSat ,T~ "^P^P" ="
■hs/S^&r^fTot-'^l.'oadtftLl^l^^^^^^
S-. 5 cents .a Ibf VhttVere^l-^s'^ri
(8) A paid $i6 for 20 mt „r
■°gal. worth 60c. affaf ^H»^ fPT- ""d mixed it with
a quart. Find his gffn: "^ '"''' ""= "''ole at 25 c«2
busl'l I^'^ t. ^^^ at /*|~ b'^ "^ "-- « «°c. a
wheat at $,.00 a bushel ^ * '"'"'•' *"'' 47i9o lbs. of
He<patJ$taf„'„Zp';"e^S.'/75.on-fhayat $,a .„„.
How much must he cSaiS Ir '" ° ^'f "^ " "»■ each
the ostofonebaleonev^'ry.hS'Uf^^,'^ ,0 gain
J.f 'iAK^"\?;^^ -^^ .0 r^e'rchant the
|5445: •68oIbs.ofhayTt^$°' fon'',T■''''^^'^~™' "'
itm^t °"' •'■--""-wi^^ t^taic\rrd^
so.il« rittra";ir«^tf ^^•i'* 'r,"'^ ^-"- He
Of "heat. How much Per%ZZ^^^i,tf,^^^^i
BUSINESS TRANSACTIONS
59
(i) Bruce Duguid bought 7 qts. coal oil at i6c. a gal.,
I lb. 8 oz. tea at 40c. a lb., 10 lbs. flour at $2.50 per cwt.,
6M lbs fish at IOC. a lb., 48 oz. of butter at 17c. a lb
l ind the amount of his bill.
^xr ^u^ ^^^® °"^ ^". P""®?^^ ^°""» supplying dates : Mre.
Walter Jessop took to Chas. G. Eraser's store, 16 lbs
butter at /Sc. a lb., and 14 doz. eggs at 13c. a doz. She
bought 4^A lbs. cheese at 13c. a lb., 6 lbs. biscuits at 3 lbs.
for 25c., 14 yds. print at i ic. a yd., 10 lbs. teaat 35c. alb.,
*u un^/^"^'"^^ ^°*^^ °^ s"fi^ar. How much will settli-
the billr
(3) Make out a bill of the following : You sold Frank
Dickson 146 yds. cotton at 7c. a yd., 156 eggs at 14c. a
doz , 17 pairs boots at $3.50 a pair, and 98 lbs. of salt at
4c. a lb.
(4) A grocer mixed 15 lbs. of tea worth 40c. a lb., 8
lbs. worth 60c., and 1 2 lbs. worth 30c. He sold it to gain
•97 '3o ; nnd the selling price per pound.
(5) A drover bought 27 cows at $29 each, and 39 cows
at *37 each. Find how much he must sell each cow for
to gain $480 on the whole.
(6) Bought 75 cows for $38.25 a head, fed them 9 tons
of hay at $16.25 a ton, and sold them at J60.20 a head.
Find my gain per head.
(7) Find the total cost of the following : 19 lbs. 12 oz
butter at 28c. per lb.; 1848 lbs. of hay at $15 per ton ; 49
bush. 24 lbs. barley at 30c. per bush., and 65 geese at
$1.40 a pair.
(8) Find the total cost of: 26 yds. silk at $1.45 ; 4 yds
linen at 15c.; 2}4 yds. lining at 20c.; 4 yds. muslin at
lie; 2 doz. buttons at 25c.; 12 yds. flannel at 38c.; 5 yds
cotton at 14c.; 2 pairs gloves at $1.25 ; s}4 yds. ribbon
at 42c., and a silk handkerchief for $1.45.
(9) What is the cost of: 560 lbs. hay at $9 a ton ;
4320 lbs. of wheat at 65c. a bush., and 325 ft. of lumber
at $11 per M..?
(10) A^man bought 4750 lbs. hay at $20 a ton, and
solw it at 4" i. 15 pc^ cwt. What aid he gain .-'
6o
ARITHMETIC
(n) Make out the total cost of- ->««/> ik t .
79C. a bush.; 612 lbs. oats a 28° a bush -^i en ik^^* ^*
at 42c. a bush., and 518 lbs. com at ^c a b'u's'h ''" P'"'
D.
bush ^ ^2/'"?'^!; ^°^^ 40^ bush, of wheat at 80c ner
^9.bs af .raCnXailS.e^m.'™'' ^^^^ ^^^^^
t^tanf^'ral.; .'ShSef VF =• ^ >^ ■""'
white lead at J245 a can • ,r ft „f h':"^ ^*'='' ' ^ cans
.«.n^H„gs at«.ir.^'rvL?»o:t^i^-^.f-s
botfit''-^o wi''""^'" l8«>«les of wine at 70 cents a
« f ^zla^^n.^-'^in'-dttVlL"^ ^°"' """"^^^^
ar.ili^7~ lbs' ^ur «t' f „"'" <■" '"e following
J. 50 eaci; .~ ft ™b?lr*L^r.™aV^.'''''?„",r
above account $20 was paid. '" °" *«
(0) Find the total value nf rtn^., a ^ * i_
V7; A grocer sold •? oz of te-a fr»- .r !.
■""* cheaper is this thin li plr pound fi ^T "°"
WAGES.
6i
(lo) A grocer bought 3 bbls. vinegar, each containing
jio gal. 2 qt, 4 pt., at 32c. a gal., and sold it at 9c. a quart.
Find his profit.
Exercise XXXV.-WAGES.
(i) A man earns $2.15 a day. How much will he
earn m the month of August, the first day of which is
Tuesday ?
(2) A man working 9 hours a day at 27 cents an hour
will earn how much in 3 weeks ?
(3) How much will a boy earn in a fortnight, who
earns 1 5 cents an hour and works ten hours a day ?
(4) A carpenter worked a certain number of days, and
received $41.25 ; if he had worked 22 days more he
would have received $6875. How many days did he
work?
(5) A man receives a yearly salary of $700, paid
monthly. Haw much does he receive each month ?
(6) A man earning $2.50 a day— ten hours— lost 15
hours in one week. What were his wages for that week ?
(7) A man receives a yearly salary of $1196, paid
weekly. How much does he receive each week?
(8) At the rate of $2.61 a day of nine hours, how much
should a machinist receive for 143 hours' work ?
(9) If a man receives $1.95 a day, how much will he
earn in the month of June, the first day being Sunday?
(10) A paper-boy buys 3 papers for 2 cents, and sells
them for a cent each. On Mon. he sold 64 papers, on
Tues. 60, on Wed. 69, on Thur. 74, on Fri. 83, and on
Sat. 112. How much did he clear during the week ?
B.
(i) If 20 men can do a work in 12 days, and 40 boys
ran tin if m R rloirc . urKi/>K Mtlll K*. ♦!>« <iUn-,_ — x_ ..
62
I I
n
I*'
AP?THMETIC
as much as A a„7^ ,LX™ a,fd " rf •5°- ^ ^ '•"^•^'"^d
day m„^ than A. HotTXtlZlZ'^'l dT> '
ceive f„. ,8 futeX, h^oS:; re-^A^f ?' *■= •" -
ho{i, J^^'SsT- f t„^/ ^y and spends $4 a wee,,
(9) A boy wSfo earn «^ =A ? «^"u 5'=- " I""-"-'-
fifths of .his''s„„,trm^S t^rLtiiream r ^ '"'«-
n>uc^rld\'yTef;^crrnt?^p-"-*S8.48. How
shoi'i U,f Kef r?cei!f for-h*'" " ^^ "°" ""ch
nuni&r^fX"-Tf lelad'l'-'e ^ "°?'"^ " «««'"
would have ,e^;ed^^V*:5t 7Kis'i?,na?er "^
con^dtol.'raMil^tLrm/"'""?^-- "Pon .he
month. If he receiS! ro .i» «^.^'' ''5 «"'=> «^ach
his entire wages amount .of ""' """""^ *>«' '^i"
or men at
it takes a
$36, how
ges for 13
?ether for
I received
'•S cents a
ir day ?
s, and 3 c
he to re-
jow much
♦ a week,
lies for a
i quart,
ns three-
j8. riow
ek, how
it worth
wmuch
y, if the
certain
lore he
es.
)on the
s each
iftt will
WAGES, 63
(5) A man agreed to draw 129 loads of gravel for
road purposes at $1.45 a load ; he paid a boy 15 cents a
load for helping him with 87 loads. If it took hnn 40
days to do the work, how much did he make on an
average per day ?
(6) The wages of 1 7 men for a week are $ 1 59. 1 2. How
much did each man earn in a day ?
(7) A contractor engages 3 men and 5 bov ; ^ do a
piece of work, giving a man 60 cents a day ir ore th n a
boy. They are engaged nine days at th^^ work, . nd
all together receive $70.20. Find their daily wi-es.
(8) A boss carpenter agreed to build a woi. («!ied ior
iT' ^^e employed two men for $1.25 a day v :h, and
they hnished the job in 15 days. How much per day did
the carpenter make ?
(9) A man engaged with a farmer from the ist of
May to tho 29th Nov., inclusive, at $1.25 for every day he
worked. Allowing 33 days for Sundays and holidays
during this time, find how much he earned.
(10) Make out the following pay sheet; a dav==io
hours. '
M.
T.
W.
T.
F.
S.
I
«
" '
A. . . .
B....
C...
D...
£. ..
10
10
8
9
10
6
10
7
10
5
10
10
5
9
10
9
9
10
10
7
10
9
ID
8
10
5
4
5
5
3
$2. 50
$2.00
$1.80
$1.60
$1.50
$
$
$
$
$
$ .
64
ARITHMETIC
E«ercl.e XXXVl-PROFIT AND LOSa
- 4A9';c!'a7u?TiKr^,?! ««- ^ "--.and seU
Wa/w^°sXVai^ '^ o' '>"«- ««■■ -c. and sold i. a. ,;c.
J4.i|;peJJ„1d^Vsir,>^a'.tf8r^ "'"^ "^ ^"^ -
gain? » every »ioo worth. How much does he
pm^?o^e^%'rlf?~-°J*'>f .ea,^d '"^'-^ J^5
tea for? ' *'«> <>' cost. How much does he sell the
aii>?an''d?rfb\''"rrtV'?A*"''5'^/°«'« -"h «c.
to gain $1.94 ? ^^ ^''°"''» he have sold it for
foron2yl'™rcasht'Dlns'.T/"*5*°= "e fed them
the entire he?d for $27^o1ach n^-t ^* ^^' ''^«* »"
how much? """^^^'-Soeach. Did'he gam or lose, and
exp^n'ls\e?eVr,';' ^'nf-' *= ''~^? "' *^-75 each, his
.™^df^«-So-^S^^..a
PROFIT AND LOSS.
65
B. ,^^
(1) A fruit dealer bought 243 dozen of oranges at
ijc. a doz.; 102 oranges were spoiled. He sold the rest
at the rate of 14 for 25c. How much did he gain ?
(2) A man bought a house and lot for $8375 ; he built
an addition to the house at a cost of $1735. The house
was d^^troyed by fire, and he received as insurance
$4560 ; he then sold the lot for $2045. How much did
he lose?
(3) A grocer bought 49 loads of potatoes of 20 bush,
each at 60c. a bush. Allowing 15 bush for waste, would
he gain or lose by retailing the rest at 25c. a peck, and
how much ?
(4) A boy bought 210 apples at the rate of 3 for 5c.,
and traded them for 150 oranges, which he sold at the
rate of 3 for 8 ^ents. How much did he clear ?
(5) A farmer bought a horse for $125 cash ; he traded
him for a yoke of oxen, and gave $13 into the bargain.
One of the oxen died, and he sold the other for $72.
How much did he lose ?
(6) A man bought 223 head of young cattle for $27.50
a head. He paid $1 1.35 a head for fattening them, and
then sold the entire lot for $6150. How much did he
gain or lose ?
^^ (7) A drover bought 247 sheep ibr $5 each. It cost
•^149 to get them to market, and 8 sheep died onxtfiewayT
He-5old the remain4«^^«;~^.75 a head. How/inuch did
-"iTe^aiM ,/^ ^\ /-^
(8)3 Jjtt cKer pays $1 1 9. 25 foT^i 39 , t tirt i£ys,,At how
mudlapair must he sell them to gain $41.34? ~^"
(9) A fruit dealer bought 9 bushels of cherries at
$3.50 a bushel, add sold them at 20 cents a quart. Did
Jift-i^ain or lose, and how much ?
(10) A grocer bought 12 bbls. of pork at $14 a bbl.,
and retailed it at loc. a lb. Find his gain.
(i i) A farmer bought a 2d-acre field of ripe wheat for
$250. He paid $1.45 an acre for cutting and saving, 4
cents a bushel for threshing and cleaning, and $2 a load
[46 bushels) for teaming. The wheat yielded 23 buS;^ to
66
ARITHMETIC
*d Sa™er"Sl/,f "" *'-^7 a bushel. How m„:h
'^ak^.^s.Sfk whTh cn^f " ^5 '^?"" "» Ae dollar a
half of ft cle^ng 5c o^'eTiT'^V^J^So. He sold
gain of 7c. on the I and ,hl f • ,* ""''d of it he sold at a
the $. bid he glin or tie on ,h"",?',* '»= °f '^-^ on
. .(13) A man buys a tenkmot s?o'::£°'^' ^"dhowmuch?
which cost $2500 per invo^™'^\fi°''''„^S7c. on the $.,
of 7SC. on the $. How mirhV t*"* " *' an average
and how much does he gaS ''^»' '^ ">* S""^^
ExeroUe XXXVII.-ANALVSIS.
I A.
cosfP IfS yards ofcloth cost $8.40, wha". will ,4 yards
^ J2) If ,0 yards of cbth cost $,4.50^ what will ,9 yd,
ml^s c^^Tctnrs'PP'*^ '"• *« '»-'<fh. for Ji.ja, if ,3
wilgtIp^.8TS,et t^ote^-* -n 5. d^^s, how long
"lS?™-"i-Tda?F^^
(6) If 5 bbls. of flour cosf «/S?^l
""wlf'lhVr^f ptiF"^ ^'^ °^'«-"^ '"^'^ "'
»ilgf hors^sXllf^f.^Vsr '" ^ '"'^' ••- ">-h
J'.L'L''.'?'" bought 468 turkevs a", J, .„ , .... .
a man
at 20 cents a dozen SselC thenff' ''^ ^"^'"^ P^P^^s
How many papers did he seS? °' ^^ ^^n^^ a dozen.
r^t^lnJIleVpeilZ^^ «^^o»<^' -hat is its
ANALYSIS.
67
fow mu.;h
> dollar a
He sold
sold at a
f 1 2c. on
Jwmuch.?
n the $.,
average
e goods,
* yards
J 9 yds.
>r if 23
w long
mount
rds of
much
It will
I, and
apers
ozen.
s its
(12) A woman sold eggs at 10 cents a dozen, gaining
thereby 2 cents on each dozen. How much did 600 eggs
cost?
B.
(i) If 40 men can do a piece of work in 60 days, how
long will 15 men take to do half as muclis^
(2) Three turkeys cost $2.25, an'B three geese cost as
much as two turkeys. Find the P^^ce of 5 turkeys and 4
geese. ^
(3) If6mendiga trench 34 yards long in 10 days,
how long a trench can 20 men dig in 1 5 days ?
(4) A father earns $6 while his son earns $2.75.
When they both have earned $105, how much will belong
to each ?
„„**^5) If 3 horses cost $192, and 2 horses cost as much
as 16 sheep, find the combined cost of 5 horses and 6
sheep.
(6) If II men build a wall in 18 days, how many men
will it take to build a wall three times as long in half the
thetivse?
(7) A man can buy a white hat which will last him 4
months for $1.76. He can buy a black hat which will
last him 9 months for $5.67. How much will be, saved
in 6 years by buying the cheaper kind of hat ?
(8) if the yearly rent of a farm of 187!^ acres be
$450, what will be the rent of a square mile for 20
montl ?
(c, j A piece of work is to be done by 25 men in 16
days ; after 4 days 15 men go away. How long will it
take the rest of the men to finish the work ?
(10) A clock which loses 4 min. in 12 hours is 10
min. fast at midnight on Sunday. What o'clock will it
indicate at 6 o'clock on Wednesday evening ?
^^11) The weekly wages of 4 men and 5 boys are
558/50. If a man earns twice as much as a boy, what are
the daily wages of each ?
,>*<I2) A case of oranges containing 36 dozen was thought
for 97.20, and sold at the rate of 12 for a quarter of a
dollar. Find the gain on it.
\'
68
ARITHMETIC
c.
soli 34 VS^^lteSl;?;//^'^ f- H- He
cost of5, sheep and 9 lambs **'^«« between the
and^sint tte.'a7th'° °ri^- ?' '"'' '^"= "'^ for 8 cents,
does he gain ? * ™ 5 for 14 cents. How much
find the value of thlpuiS " *= "" "f thepurst;
four<^^°r'tt^t'„=;h'?;-™4?"'™'«'™^<'"e three-
n.iles^forc^rl:r4'^c^?A«"V "■■'' f" «•« first 50
every 4 milesTfond°ie fifty ~Wh«'' ^'i''" ^ ""'^ '"r
250 cords 90 miles ? '^^ "^^' *'" " tost to carry
w!^el's"o?tur cl^'t"ml5| f'° '"'• i"' "o"- ""w
wheat? "^ ■'^ "ade from 4263 bushels of
,. (9) Jf a boy walking at the rate ,^f . •■
takes 18 minutes to get to sclLTh^i"* ""'^^ »" hour.
he walks 3 miles an hour ? ' ""' '""^r wi" he take if
p4« onX' $.l^T tl^ '»1.«>"' «°n.ake$3o
. (• A man bo^hra farS^ f^' I'll! *« §»<«'' sold for?
.^S»5 on eve.. ,.«, pt^hTs et^^ -^fn^l^J'sel'llS^-
h;slL'rli^e"sSir,;o^\"^:-l'- %^^ -"^ f-
the owner receive ^ *'°°- ^^^ much did
D.
paySii2h%|;ri5"Slowe?oVr^^^^ °^ ^^75, and bv
much do I pay? ^^^^"'^^^off every $ioo worth. How
SHARING.
69
SO
(2) If the tax on every dollar's worth of property is 2
cents, find the taxes on a house and lot valued at $4600.
(3) A man's property is assessed for $7200. How
much taxes does he pay, being charged 2c. on the dollar?
(4) If the rate of taxation is 3c. on the $, what do the
taxes on properly worth $^500 come to?
(5) If the rate of taxation is 2c. on the $, what do the
taxes ou property worth $2345 come to ?
(6) $3645 is to be collected in a township to build a
school-house. The property in the township is rated to
be worth $370170. What will Frank Connery have to
pay, whose property is worth $4570?
(7) A money lender receives 6 cents for loaning $1
for one year. What does he receive for loaning $200 ;
$350 ; $475 ; for one year ?
(8) If the money lender received 5 cents for the loan
of $1 for one year, what would he get for the loan of S250
for 2 years ? for the loan of $300 for 4 years ? for the loan
of $425 for 3 years ?
(9) If he received $5 for loaning $100 for one year,
what would he receive for the loan of S630 for 2 years ?
'k74i for 3 years? $500 for six months? $224 for i}4
years ? and $360 for 2 years 8 months ?
(10) A boy puts $25 in the Dominion Bank for a year.
He received for the use of it at the rate of $4 for $100.
How much money did he withdraw at the end of the
year?
Exercise XXXVIII.-SHARING.
A.
(1) Divide 16 apples between John and James, giving
John 4 more than James.
(2) Divide 60 marbles between Thomas and Henry,
giving Henry 10 more than Thomas.
(3) Robert has 6 pigeons more than William ; together
thev have 22. How manv has ea<^ ?
70
ARITHMETIC
"7, f" fiid he g» each day? ' ** '^"°"d ^ay-
VS; Divide $1000 hpfw«>ir> *
^ (9) Divide Si amon^ Fri^u ', ' ^ ^^^'''^^ ^ >
{. =) A man sold ? sheen %T '""2 ">« 'hird.
eac^J.^r^/ht^.S^eXiLr™'"^ 37 boys, so d.a.
„ (6) Divide Jgo ,6 am«n„ .1 " P""^*" « a boy.
Robbie, so that ?ge fim to? lTt.^^\ ^H'- »«« and
the second, but 80 cents hS;S ,tV^'* »»« *»?
./"I
— _ _. Jiiifet.
SHARING.
7<
(7^) A mixt M re of green and black teas is made, 3 ounces
of green £o tvi^ry 5 ounces of black. How much of each
kind will be in 5 pounds ?
(8) Divide 36 apples among 2 boys and 3 girls, so that
each boy may receive 3 apples more than each girl.
(9) Divide $398 among A, B and C, giving B three
times -AS much as A, and C $6 more than B.
/^!o> Eiiiest has $1000, Warren has as much as Ernest
ks.^ $82, John has as much as Ernest an,d Warren and
$"04 besides. If the whole of their money were divided
equally among them, how much would Warren have more
than he has no«v?
(11) A man spent $240.25 in cloth at $1.55 a yard, and
sold it to three men. The first man bought 35 yards more
than three times the second man's purchase, but 22 yards
less than the third man. Find how many yards each
bought.
C.
(i) Divide $840 among A, B and C, giving A three
times as much as B, and $70 more than C.
(2) Manly, Ernest and Beulah had $1800 divided
among them, Ernest got twice as much as Manly, and
Beulah got twice as much as both Ernest and Manly.
How much did each get ? -
(3) Divide $973 between A and B, giving A $57 more
than B.
(4) Divid^ 27 bushels potatoes between A and B,
giving A 2 bus. 3 pks. more than B.
(5) Divide S500 among A, B and C, so that A will get
$75 more than B, and C $50 more than A.
(6) A calf, a cow and a colt were sold for $110. The
colt brought $15 less than the cow, and the calf $25' less
than the colt. What did they each bring ?
(7) A woman sold two tubs of buttei: weighing together
60 pounds, one being 5 lbs. 8 oz. heavier than the other.
How much did each tub weigh ?
(8) In a basket there are nuts, oranges and apples,
135 in all. T^.ere are 35 apples and oranges, and no
nranerf^a ttnA nutS Hq*" rnanv ar^ thf>r«> of *»arK ?
/
72
ARITHMETIC
'he^ httt^X'/eT^^jSli? r '=""1*3. When
to each ? *io98.32, how much will belong
', 1
Exercise XXXIX.-CANCELLATION
A.
What is the Quotient of:
,[) 42x13x6x22 divided by 4x6x7X1^?
,,, 55X2ox8T?39x,4X4ii;^
(6) 3«^138x39Xiox42X44X45x49x ,,0
3ox3ox57x78x7Jr24X99x35l?r
(7)Sox5;j<54X56x5^58x6rx63x64X4
m „'*°'''*°''*5x='7X48im;?^^8^4r^
W iixi3xi4xisxi6 X35 x »x 2, x 2 'x 24
/^\ .., 39x56x40x30x70x33x48
f.o^ 7f'''*''33x72x45x6w5;rFSS856r^-^
conlZ4 ." pL?« 7;i ''^1 "*" 15 •»'« °f -^'oth, each
4 «;»hXn^ *?,^S^^^^^^^^^ -^^ ^ «• Wide and
/
y\
CANCELLATION.
73
(3) Nine pieces of cloth containing 30 yards each,
worth $5 a yard, were exchanged for 1 5 pieces of cloth
containing 45 yards each. What was the second cloth
worth per yard ?
(4) If a farmer exchanges 25 bushels wheat at $1.28 a
bus. for cloth at 40 cents a yd., how many yds. does he
get?
(5) A tailor bought 24 pieces of cloth, each containmg
22 yds., worth $2.25 a yd. He made 54 suits of clothes ;
how much must he get per suit, so as to make $3 profit
on every suit ?
(6) A brick is 9 in. long, 3 in. wide and j2 in. thick ;
how many of such bricks will there be in a pile 12 ft. 6 in.
long, 10 ft. 8 in. wide and 6 ft. 9 in. high ?
(7) A pile of bricks is 40 x 27 x 1 5 feet, how many
bricks 8x4x2 inches are there in the pile ?
(8) A pile of bricks is 8' 6" high, 14' long and 15' wide
(each brick is 8>i" x 4" x 2^"); What is the pile worth at
$12.50 a(^ thousand ?
(9) Find by cancelling the simplest value o f 6950
45x25x3.
MECHANICAL WORK.
Exercise XI — ADDITION.
(0
47658
76584
65847
58476
84765
47658
76584
65847
58476
84765
47658
76584
(6)
56987
69875
98756
87569
75698
56987
69875
98756
87569
75698
56987
69875
(2)
76584
65847
58476
84765
47658
76584
65847
58476
84765
47658
76584
65847
(7)
69875
98756
87569
7569^^
56987
69875
98756
87569
75698
56987
69875
98756
(J)
65847
58476
. 84765
47658
76584
65847
58476
S476S
47658
76584
65847
58476
(8)
98756
87569
75698
56987
69875
98756
87569
75698
56987
6987.
9875b
87569
(4)
58476
84765
47658
76584
65847
58476
8476s
47658
76584
65847
58476
84765
(9)
75698
56987
690/5
98756
87569
75698
56987
69875
987^6
87569
75698
(5)
84765
47658
76584
65847
5i»47^
84765
47658
76584
65847
58476
84765
4765;?
0^ .
7569.'
56987
6987 c
9875^
87569
75698
56987
C ?75
9 56
8. ,69
75698
56987
/-.\
^/■s/
(5)
«4765
47658
SUBTRACTION. 7$
Exercise XLI.-SUBTRACTION.
Subtract 487569 ten times in succession from each of
the following: (i) 5221368; (2) 5332473; (3) 5443524;
(4) 5554035 ; (^) 5^59146.
Subtract 57 864 ten times in succession from each of
the following: (6) 5934432; (7) 6156564; (8) 6377886;
(9) 6591 108; (10) 6723321.
Exercise XLII.~ MULTIPLICATION.
Multiply each of the following by 6 ten times in suc-
cession as a factor: (1) 16209; (2) 21612; (3) 32418;
(4) 48627 ; (5) 64836.
Multiply eac'^ by 7 ten times in succession : (6) 12708 ;
\j) 19062; (8) 25.116 (9) 38124; (10) 57186.
Multiply each I S ten times in succession: (11) 1 1427 ;
(12) 15-16; (13) 2- ;4; (14) 34281 ; (15) 457o8.
Mulupiyeach by 9 t^^n times in succession: (16) 10608 ;
(17) 15912 ; (18) 212' . (19) 31824 ; (20) 42432.
Exercise XLf DIVISION.
Divide each of the following numbers by 6 ten times
in succession: (i) 653397497856; (2) 980096246784:
(3) 1960192493568.
Divide by 7 ten times in succession : (4) 1794847732146;
(5) 269227 1 5982 19; (6) 3589695464292.
Divide by 8 ten times in succession : (7) 817976521 5 232 ;
(8) 12269647822848 ; (9) 24539295645696.
Divide by 9 ten times in succession : (10) 27740856-
694356, (II) 36987808925808 ; (12) 5548 1 7133887 1 2.
Divide each of the following by 29 three times ii suc-
cession : (13)278424824; (14)417637236; (15) 556849648-
(16)835274472.
Divide each of the followmg by 347 three times m
succession: (17) Q02Q9oq 19876; (18) 1354486379814 • '''9)
1805:981839752; 20)2708972759628.
/ ,
/
u
FACTORS AND MULTIPLES.
Ex.rcl« XUV.-PR,Me AND COMPOSITE
NUMBERS.
. (0 Which of the fnVn^,;^^
Which are composil^: 3 c Tf "1^^''' ^'"^ P""»« ^"d
45, 5r, 57, 63 and 75 ? ^' ^' ' ^' ''' '5, 27, 35, 39, 4,, ^3^
and 50. '""" °^ ^*^« P"me numbers between 30
(4) Find the sum of thp /-««,« •.
35 and 55. """ °' ^'^^ composite numbers between
. (5) Fmd the sum of hnth tu^
numbers between fo and & ^' ^"""^ *"<' '^^ composite
.0 if ^ "^"'^ ""«'" ^" '"' integers less than .; and prime
.ha[l'';,f„'e^^,„^"^''f 'he '""sers between 80 and .00
,„ .(8) Write down the integers .ess than .4 and prime
.«>;t"5^[tr p-.J.i'JVr"^'- -'egers between
3 aiil ? ^' "-"''^" '-^ '"- '50 are divisible by both
5 ald^'^'"^' """"^^^ '«' «•-" '75 are divisible by both
3 aii's f"^"' """^'^ '7;,^ n ^» are divisible by both
PRIME FACTORS. 77 '
Exercise XLV.-PRIME FACTORS.
Resolve into its prime factors each of the following
numbers: (i) 30 ; (2) 36 ; (3) '08 ; (4) n2 ; (5) '28 ; (6)
210 ; (7) 324 ; (8) 504 ; (9) 555 ; ('o) 728 ; (II) 1024 ;
(12) 1000; (13) loii ; (14) 1050; (15) '320; (16) 1768;
(17)1848; (18)2934; (19)3456; (20)32320; (21)345345;
and (22) 456456.
What prime factors are common to: (23) 440 and
231 ? (24) 650, 635 and 540? (25) 55> 66, 77 and 121 ? (26)
42, 70, 156 and 210? (27) 256, 320 and 336.'' (28) 144
and 180?
Find the product of all the prime divisors common
to : (29) 16, 24, 40 ; (30) 108, 81, 54 ; (3O '44, 180, 216 ;
(32) 64, 96, 112, 136 ; (33) 75, 125, 165 ; (34) 306, 408,
(35) The product of 2 consecutive numbers is 750.
Find them.
(36) The product of 4 consecutive numbers is 1680.
Find them.
(37) The product of 3 consecutive numbers is 2730.
Find them.
(38) The prime factors of a number are 2, 3, 5, 7 and
li. Find the number.
(39) The prime factors of a number are 2, 2, 3, 3, 7,
13 and 19. Find the number.
(40) The prime factors of a number are the prime
numbers between 10 and 30. Find the number.
Exercise XLVI. -GREATEST COMMON
MEASURE.
A.
Find the greatest common divisor of each of the
following : (i) 546 and 462 ; (2) 394 and 672 ; (3) 735 and
770 ; (4) 2 121 and 2626 ; (5) 232 and 160 ; (6) 1628 and
4543; (7) '2341 and 30401 ; (8) 15561 and i35»5 U9^
34, 100 ftnd 120 ; (10) 32967 and 50061,
78
ARITHMETIC
B.
(0 279lrt\'nlT5f ft^^^^^^ of the following-
*333 and $851 • U) 2Rfil^ ^"^ ^^s- and 634 rodr. ^^-^
ft. and 2788 rods%fol^e^ ^"^ 4543 gals^f (7) , ' ^;/
«M63 and 11,75' ^em?- mX^"^ "43r m nutes 'It
marbles; (9) 11592 hTrse/^> ^,9 ^^^^^^ and 2 j J-.]
bs and 20539 ounces ;('o 7"?J?^9 horses; (,0/987
('2) 2769 tenths and 3195 temLl'"^' ^"^ 2057 thirds;
(0 What is the leno-fK ^r ^u .
exactly measure the Sth anH^^"^-' '^^^'" ^^^^ ^i"
land 312 rods lone anrfn& ^"^ ^^^ ^'^th of a oier^iJ
(2) Three sSltn ^ """^^ ^'^e? ^ P'^^® ^^
ft. aU 20 ?t, were cEto ?f ?"^ respectively ,2 ft ,6
equal length. Wh^r.^r.^^tXcV^''^^^^^^^^^^^^^^ o'f
(3; Two cisterns hoW 11^- ,^P'ece?
ga Ions. Find thTlargH h!^T'''Kf^72 and 5088
both cisterns. ^^^'^ ''^rrel capable of measuring
(7) Three lots mt^a^,,^^
>°4.ft. by u8 ft! fnd "^f^KT'*' »< ft- by .44 ft
out in square beds of .JJ i "'^ 9* f'- 'f these be l,L'
""^-f-^f beds tel'cht '''^"' P»-ib.e si^e^find '"he
58VW"« ^-S^rsT/n^r -" "'vide 600 and
. ('o) What is the I^n^ffc r I ■■''^P«<:l>vely.
«t.ck that will „^,2l '|,T\2^."'-«_ J°"««' measurin.
GREATEST COMMON MEASURE.
79
following •
f«ds ; (0
(5) 12341
lutes ,~ (7)
nd 23023
('o) 987
;7 thirds ;
that will
piece of
[2 ft., 16
ieces of
d 5088
asuring
rtioned
ney.
can be
n 3588
ed for
1 from
h 7 is
44 ft.,
2 laid
d the
4180,
and
inne
V
(11) Find the length of the longest chain that will
exactly measure both 7308 in. and 8004 in. Give answer
in feet.
(12) Three drovers, A, B and C, bought sheep at the
same rate per head. A's drove cost $102, B's $138, and
C's $99. Find how many each bought.
Exercise XLVII.— MULTIPLES AND COMMON
MULTIPLES.
Form a table of the first nine multiples of: (i) 13 ;
(2) 14 ; (3) 15 ; (4) 19 ; (5) 21 ; (6) 25 ; (7) 30 ; (8) 36 ;
(9)50; (10)57; (11)63; (12)75.
Find three common multiples of each of: (13) 3 and
4; (14) 5 and 6, (15) 7 and 8; (16) 8 and 10; (17) 12 and
15 ; (18) 16 and 18 ; (19) 11 and 12 ; (20) 15 and 20; (21)
25 and 30 ; (22) 18 and 24.
Of what two integers are the following common mul-
tiples : (23) 30 ; (24) 35 ; (25) 42 ; (26) 56 ; (27) 84; (28)
96 ; (29) 121 ; (30) 132 ; (31) 187 ; (32) 119 ; (33) 169 ;.
(34)289; (35)631 ; (36)221.
Exercise XLViil.-LEAST COMMON MULTIPLE.
A.
of:
Find the L. C. M.
(i) 4, 8 and 12.
(2) 12, 18 and 30.
(3) 21, 28 and 35.
(4) 2, 3, 4, 5 and 6.
(5) 9, 12, 22 and 33.
(6) 15, 18, 21 and 24.
(7) 9, X2y 15, 18 and 20;
4, 5, 9, 12, 15 and 20.
10, 16, 24, 40 and 64.
[10) 36, 45, 60, 75 and 84.
[11) 25, 40, 75, 100 and 120.
80
ARITHMETIC
M l\^^ 26, 39, 46 and 78.
J 3; 4, 6, 8,9, 12 and 15.
f 4 f, 52, 36 and 156.
05) 3, 5. 6, 8, 15, 2olnd 24.
yj 5040, 7770 and 1848
3 ?8''3fA'^'^--^48.
(6) 6 rods and 66 ft?
(85i^f/./.^;-<^'ogaI.
(»; $6o6r and $73,7
(9) I acre and 1 •»-« =«
<>'> .6 days, ,8 hour^S.. minu.es.
"TftH"''-^ 5-^^^^^^^^^^^ 'hat can be
(9) What IS the lekst weirf.t\? -^5 cent pieces ?
r^fwr'^'-°f''"'heWw?eafr,"'"' will „^e
LEAST COMMON MULTIPLE,
8l
D.
(i) What is the smallest sum of money that can be
paid all in $3 bills, in $4 bills, in $5 bills, in $6 bills, or in
4)io bills?
(2) Find the least number which, divided by 6, by 8,
by 15, or by 21, leaves in each case the remainder 3.
(3) What is the least number which, divided by 16,
by 18, or by 24, leaves in each, case the remainder 7 ? '
(4) Find the prime factors of 126 and 1^60; using
these factors, find the L. C. M. of the numbers.
(5) What is the least number from which 1224 and
1656 may each be taken an exact number of times ?
(6) Find the L. C. M. of 7, 9, 11, 13, 15 and 21 ;
divide the L. C. M. by each of the given numbers, and
find the sum of the several quotients.
(7) What is the smallest sum of money with which a
cattle dealer can buy sheep at $4.50 each, or pigs at $7.50
each, or cows at $45 each, or horses at $135 each, and
have no money over ?
(8) A farmer's wife found that whether she counted
her eggs by 6, or by 8, or by 9 at a time, she had an exact
number of counts. How many dozen had she ?
(9) What is the smallest quantity of wheat that can
be carted away in either 20, 25, 30, 35 or 40 bushel carts .-•
(10) When a certain number of dozens of oranges are
counted by fives, or by sevens, there are three over. Find
how many there are.
(11) A battalion of soldiers numbering rather less
than 1000 can be divided off into companies of 60, of 72,
of 80, or of 90 men. Find the number in the battalion.
MISCELLANEOUS.
Exercise XLIX.-ON THE SIMPLE RULES.
A.
^l\ Th^ ^^!,^a''-«e Of 9087064X89706^336.
(S) By what number must iggg be dividsH tl,,. ,1,
quotient and the remainder iS? b| the ;»^» S*
quonen. and the remainder in Si vision ofTo^ bJ ,?f
of t^^i ISS °/e1iS rA"t L'«^^«^ ' f .™«
the result is 7 times whit numte?? ^^ "^ '" '""^^'O".
fact|^,t^Vv%e1„-^Vth°i:to^S "^ "^^
^evi ije™tars"?.t"nrda"„'it';r;4^^^^^^^
one hund'-ed thnncar.^ ^ j • =>*=^«="iy-inree millions,
r^^p^S^^ M^tiply the
timS\he' fjil :„Tr 1 "..6^'""^"i>. 3784875ranT seven
(lo) Multiply, using factors 766485 by 63.
B.
0) Multiply 83102254 by 7090.
(ll FinH ?/^'°"54 by 19435.
W i' ind 78 times the sum of 894967,
8a
38730. 6q3Q7
LV I
ON THE SIMPLE RULES.
83
PLES.
and half
fourth of
*■ is 343.
70 times
seventy-
that the
as the
» by 1 1 ?
If one
cession,
by the
nd and
lillions,
aly the
•
seven
of the
10507
MDCCXCVIL, 467896, and divide the resuh by the
.factors of 48.
(4) The quotient of two numbers is 498 ; one of the
numbers is eighty-nine. How much is the other less
than one million ?
(5) What number must be subtracted from 461634 to
make it exactly divisible by 126?
(6) Ho V many times must 720 be added to 514 to
make 987634 ?
(7) The divisor is 63875, the (quotient 46938, and the
remainder the largest integer possible. Find the dividend.
(8) Find the smallest number that must be added to
461633 to make it exactly divisible by 758.
(9) Multiply 867349278 by 70908, and divide the pro-
duct by 23636.
(10) Divide 9 times the product of S9496 and eight
thousand and seventy -four by LXXVIII.
(i) Multiply 4786926 by 7869 and divide the projcluct
by 23607.
(2) Multiply 976531 by 999, short method.
(3) Add 3456 to the product of 8347 and eight, and
then divide the result by 1 2.
(4) Find the value of (36380250^ 125) -(4024 156-!-
8903).
(5) Add together 95949, 67896, 8939, 667586,
738496 and 89496. Take 59497 from the sum, multiply
the difference by 98, and divide the product by 47.
(6) The dividend is 74198, the quotient is 2005, and
the remainder is 24 less than the divif or. What is the
divisor ?
(7) Divide one billion by 256.
(8) The sum of the remainder and s',bt va'vjnd is 100-
190801. Find 20504 times the minuend.
(9) Multiply 4567895 by 192648 h- short process.
(10) Square 6384 and divide the product by 3192.
84
ARITHMETIC
D.
by ^jL""'"'"'' ^^^'^ ^y 7869, and divide .he product
.hS' The quotient is 908 times 987, which is 227 tim.=
the remainder. If the renai.H.r i. , 1 ■ ." '""^'
divisor, find the dividend ™"*""'*'^ '^ 5 less than the
and^iS"''"''^'^?'''^"'^" '«''»'«» *e squares of 7684
divi^ll'rh^°:;:"j '^^7, *« remainder 2,9, and the
''7^^ti£S9¥r":^^^^^^^^^^^
1809 ? ' ^ ^ ^^ """^^^'' "*"^* ^ multiply
e:,
(i) Divide 1084197160c: by 1874800C
(i Oft'JfJr'7l543>y 2r'6546%S
(aI TK 5^i """"H" '" 7006 both divisor and quotient ?
(4) The difference between 8^^72 anH tiTl ^"?"^"* ;
.sll^d^oLS'^fiL*^^^^^^^^^^ "•« -""^end
«maild?r% To be^»H'A^*.'"'°'r' •««. «"d the
how mul/Jthe'di^id^dlnctas^edr" "''"^ *^'«' '^^
oJillt,'"""'^"' of 595 divided by 59S lives as
ON THE SIMPLE RULIia.
35
5 product
the result
'ove the
otient of
57 times
lian the
of 7684
and the
ifty-two
visor,
nultiply
otient ?
iuct of
bsrs is
'abend
id the
ee, by
■ their
7 and
'es as
(10) Subtract 123456789 from 987654321 and prove
the result by addition.
F.
(i) Add together 678, 593, 457» ?^9» t^ginning at the
hundreds, next the tens, and lastly the units.
(2) Add together 12345, 23456, 34567, 45678, 56789,
beginning at the left hand column and adding towards the
right.
(3) The divisor is 54321, the quotient 12345 and the
divident 670605090 ; find the remainder.
(4) Multiply 507308 by 4620, and verify the result by
dividing the product by the factors of the multiplier.
(5) Multiply 2468642 by 29 in one line.
(6) What number increased by the difference between
23089 and 196 1 2 will make the sum of 20948 and 45021 ?
(7) Find the remainder in subtracting 6633 as many
times as possible from twenty millions.
(8) If2i7 be added to a certain number it will contam
231 just 1 296 10 times. Find the number.
(g) What number divided by 537 will give 129 for a
quotient and leave 76 as a remainder ?
(10) Find the quotient obtained by dividing the pro-
duct of the seven whole numbers next in order after 30 by
the product of the first seven whole numbers.
G.
(i) Find the product of 897643 and 999998, short pro-
cess.
(2) Find the. product of 11 881 321 2 and 234567891,
having six Unes of figures when the solution is complete.
(3) The divisor is 17 times the quotient and 34 times
the rem- nder. The remainder is 358, find the dividend.
^. (4) The product of two numbers is 760669388, and one
of the numbers is 26078. What is the quotient when their
sum is divided by 72 ?
(5) Subtract 97864 nine times in succession from one
million.
^ (6) The sum of the quotient and divisor is i43/»b«
86
ARITHMETIC
^^Jh2':t' "•'"• '■' '<>"^' •» 'heir diffe^ce. Find
"y 8, by how much will th^n.^Pl'^S"'^ '^^^<='^ increased
- (8) If the divisor were hS"ofwh\^'!;'^'^u"''?
would be 64.84. The divideni is 5?L'Ut' '^^^T'""'
niamder 193. Find the divisor '^''^^ and the re-
-vSh'^^he'Sr^lTenyr?*! '^ {,'''"' ""« °--
rhe^divU^teti:y:h^°3i„a^^<,3«^^^^^^
H.
smaVlLrSl!!;^^ <f^[-ce ".t '"e largest and
75120. ""K '" 357 between TO867 anH
"''^ml^thXZesTlT^ri^'^ ^'"'^ 764., and the
dividend. ^ "^'"""^ ""'"'»'• possible. Find the
as the divisor, fed the dividend''™"™' '^ ^' '"»« ^^^i"
woii*d\S;roTucrhavf boTn i"frr' ■,-,--• What
Plicand haS been iTtimes i LtT^^'P"" ^^ '■>"■"■
635r4t'o"^: f^' '^4"^ fots'l'-''^ ^""'-in? "umbers :
add the re.naind^S^'; short prSetr' "* =»"'«».'»''
and;tedt^'.-;he.vi^^^^^^^^^^^^^ , ,,^^3
■-- ffi/ri,. ^ . • ^""' ">e fourth addend
fi-ifi S'.heTuin"' V''!."="'=!'"'i^ ''"d subtrahend is
..Ssf^.'^SthTremabder""'"'' ""^ ^'""^^'«"<1 i'
x
\\
GENERAL REVIEW.
«7
(9) How many times must 347 be added to itself to
make 98895 ?
_(io) How many times must 127 be added to 59 times
231 to give 24170/
Exercise L.— GENERAL REVIEW.
(i) A farmer gave 49 bus. of oats for 196 lbs. of cheese
at 9 cents a lb. ; how much did eacl buihel of oats sell
for?
(2) A contractor requires two million bricks. He has
560085 already. How many loads of 437 bricks does he
need to complete the full number ?
(3) A farmer bought 20 steers at $33 each, and after
keepmg them 4 weeks at a cost of 50 cents each per week,
two of them died. At how much each must he sell the
rest to gain $56 on the^ transaction.''
(4) When 4 li. 3 in. oTErass wire costs 22 cents more
than 3 ft. 4 in., what is the price of wire per yard ?
"^ (5) A woman sold 16 turkeys and 16 geese for $23.20,
getting 25 cents more for each turkey than for a goose.
How much did she get for each ?
(6) A grocer mixes 12 lbs. coflfee at 28 cents and 26
lbs. at 23 cents, with 10 lbs. of chicory at 8 cents. At
what price per lb. must he sell the mixture to gain $4.50
on the whole ?
'"^(7) A drover bought a number of cattle for $4050.
He sold 34 of them for $1926, gaining $396 on those sold.
Find how many he bought, and the cost of each.
(8) A woman sold two tubs of butter, weighing to-
gether 75 lbs., one being sH lbs. heavier than the other.
How much did each tub weigh?
(9) A butcher sold 8 turkeys and 8 geese for $12,
getting 30 cents apiece more for a turkey than for a
goose. What did he get for each ?
(10) Find the value of 57 cows, when 3 horses worth
$120 each must be given in exchange for 18 cows.
(11) A fanner bought 75 tons of hay at $16 a ton, and
SB
.-AITHMETIC
SkbKe"p^tr„T„,tt!? =« *3.75 each. The re-
lbs. of buttef were ^S« cents per lb. Ho* m...y
diff^releinThTcosfif i";" f"^ '"" fe-™^. and the
of the farm for whTch he naid Z '"" f,^^^^' The pr «
an acre, and the other JST^an acre " ni'"' '"■" '^••» »4
both farms ? * ' *" ^""^ "ow many acres in
lbs/4i.\:avS\tVro'."er''S " '"'V"- "-"« 3
weigh ? " ^"® °*"e'^- How much does each
-^^^ Which
^ 06) On the firsrof April L 1 nf T?^^' ^^ fi^^^'
for $37 50; he sold her onlht/i ^^""^ ^^"^^^ ^ ^^^^
her milk during that t;m« '^ -^^^Ptember for $20 •
Bland's gain ^^.^t^tJ^'^'h^''' 'f^'
month. ^^°' ""^ ^' '- < est of her keep per
(17) Find the daily wa?e« nf -
hours per day, and who ^ e? L 1, ''*^" ^ho works 10
a ditch 3 ft. iide and 4 ft ^deeriA?'!? ^''' '1 ^^"^^^ "^
per cubic foot. ^ ^P' " "® charges half a cent
.hriijiccePirthi stiro"'v"'™^;'' "- ™' -'o
second; but ^ yards lonL fu ^ P"""^^ shorter than the
length of thls^cond ? "^ '^^" '^" '^''^' ^^^t was the
and;^?|4 '^^rattfe'L^I^^^^^^^^^^ ^-d for $.5200,
(20) A and B had II^o?? a '"4 S^^m or loss.
$315. ThenAhadlwlT^mlh^a^R^^'j""^^ «P-"t
each at first? '^ice as much as B. How much had
J4o!^ai,^d1 JdTitcf msVerr;n3' ''r °' ^^^^ ^^
gam? y ^^"ts per pound. How much did he
expenses. How long win it til^\^ .^^ ^ "^7 ^°^
(23) A farmer nafd fo. ' '!!^.^.^'"^.*« ^ave $972 ?
^ ,0. „ ^v^v ana a sheep with th^
n
GENERAL REVIEW.
89
J
pnce of.2 tons 8 cwt. of hay at 60 cents a cwt. The cow
' ost seven times as much as the sheep. Find the price
of each.
(24) At $175 a rod what will it cost to fence a field
660 ft. long and 264 ft. wide ?
(25) A street one mile long and 66 ft. wide is to be
built. On it there are to be 40 crossings costing $15.80
each; two bridges, one costing $6840, the other $1650;
a sidewalk on each side costing $4 a rod ; and 16 lamp-
posts at $3. 50 each. If the cost of grading and pavmg be
$10 a sq. rod, what will the total cost of the street be .''
(26) Howmany feet of lumber are required for a 12-
inch baseboard for a fence around a field of 20 acres,
having a frontage of 40 rods ?
(27) On every square inch of the floor of a room, 60
yds. I ft. long, and 5 y 2 ft. wide, a 25-cent piece is
placed. How much money is on the floor ?
(28) A clock strikes all the hours in February, March
and April. How many strikes does the hitffimer give the
bell in that time ?
(29) From a lot 80 rods square I sold 80 square rods ;
what is the value of the remamder at $80 per acre ?
(30) A cellar is 18 by 20 feet, how many bricks 8 by 4
by 2 inches, laid on their sides, will cover the floor, and
what is their value at $14 per thousand bricks ?
(31) Find the cost of building a six-rail fence round a
field 65 rods long and 40 rods wide, the rails being 1 1 ft.
long and costing 8 cents each.
(32) What would it cost for stone to pave a walk
round the outside of a yard 40 rods long and 66 yards
wide, if the walk be 5 feet wide and the pavement cost
10 cents per square foot of surface covered ?
(33) A gentleman sells at $3.60 a square foot a town
lot 60 ft. wide and 120 ft. in depth. Find what he should
get for 3 acres at the same price.
/^ A A <^^i,ora KiooL" ■sAr* fppi- to the side has a Sidewalk
of two-inch plank around it. The sidewalk is 4 ft. wide.
Find the value of the plank at $1 5 per thousand.
IMAGE EVALUATION
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<^
/A 4
1.0
Im
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U£
Ut
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I.I
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1.8
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— 150mm
V'
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7
/IPPLIED^J INA4GE . Inc
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^^^- Rochester. NY 14609 USA
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^V
^\
Ak
■ '*
^\ ^3. n^
'^i^>>
'^
^t^
90
AftltHMETiC
f"^,',rF^"l"''™^fe«"cer" "■"" '"<= "i"" one.
. ^ . (38) Ho«r many cubtc iLh '• '«■■<;''''!': yard. *^'
each at first? ^"*^" ^^ A. How much had
•s ^f^^o^^^^^^ P^ed m a car which
. (44) A farmer sold a ho^I ? ^'2 '4 cords?
fi4-2S each, and 180S. lbs £1 ?or^i^^-^°' '^cows for
the proceeds he bought sheen /f il P'^"" ^ *°n- With
^ar^s sold the sheep for c'^ai^^u^ *^^"^' ^"^ after-
gam ? i' 'O"^ »S each. How much did he
8 in'^U^^^^^ box 3 ft. 4 i, long, , ft
30 hours. For how mariv df v. JIP' * '*°^« running for
the stove running ? ^ "^^y' ^'" ^5 cords of wood keep
-:^^^^&z^!r'^^'-^i - -i^e, is
mai^cords' of w^^^^^ T""} ^^ *°"^ °f coal, how
of coal in a yeaT? "'"* '^'* ^ ^»"^''y ^^at bums 26 tons
dozif Lll J' ^PP'"^ ^°^t 8 cents, what will a h.^.i .r . ,_
GENERAL REVIEW.
9«
(49) If 50 men do a piece of work in 12 days, working
8 hours a day, in how many days would 30 men do the
same piece of work, working 10 hours a day ?
(50) If 2 men or 3 women earn $1.80 a day, how much
should 19 men and 27 women earn in 1 5 days ?
(51) A factory tailor can make 10 shirts in 4 hours ;
whether will be more profitable for him, to be paid 18
cents an hour or 8 cents a shirt ? -~
(52) Two railroad trains are 5000 miles apart, and
approach each other, the one at the rate of 19 miles an
hour, the other 24 miles an hour. How far will they be
apart in two days ?
(53) If a boy waste on the average 2 minutes ev«:ry
hour, how many minutes will he waste in 4 years ?
(54) If 3 horses, 4 oxen, or 5 cows can be pastured for
one month for $6.60, what should be paid for pasturing
3 horses, 4 oxen and 5 cows for one month?
(55) How often does the L. C. M. of 4, 21, 36, 45, 91
and 180 contain the G. C. M. of 5642 and 7462 ?
(56) Divide the L. C. M. of 18, 21, 42, 45, 90, 180 and
640 by the G. C. M. of 3232 and 1952. •
^ vSTT^ftheareabfa field is 326700 square feet, and
the length 540 rods, what is the width ?
(58) Find the value of the rails in a straight fence 40
rods long,' each rail being 11 ft. long, and the fence 7
rails high, at $22.50 per M.
(59) In eight equal loads there were 9 tons, 10 cwt.
32 lbs. How many tons, etc., were there in 5 loads ?
(6b) A can do a piece of work in 6 days, B can do the
same work in 8 days. If both work at it for 2 days, how
long will it take A to finish the work ?
(61) When hay is selling at $6 a ton, and oats at 30
cents a bushel, it costs a man $9 for hay and $6.75 for
oats to feed a span of horses for one month. How much
will it cost him when hay has risen to $8 a ton, and oats
to 34 cents a bushel ?
(62) How many feet of lumber in a plank 18 ft. long,
12 in. wide and 3 in. thick?
//i^\ A ^nw^oM io jQ <r/1c- Irtnrr onrl -jn vAa iirir1(>. There
\Uj} .^x gaiiii-ii ts ij-j' j^fj: t--"ji •"• —7 ; - — -- -
aiv two paths, each 6 ft, wide, running across each other
c
93
ARITHMETIC
X.
through the centre of th« ^
/i Y V," ^°s' to diV all thAo\? * *^^"t the square
-^(64) How many cS,^ vds^nf''"" ^^^«P^ *»»« Ss?
tnefoundatbnofalin,,=f ^u • . °/ "masonry are thVr«?
wide? Ti,« r ' . "ouse which s -ya ft / '*'e mere in
^/<V A sack of neasp ^^Lu ^^ thousand ft
cents, and each word over Sn '^"' ^^ ^^'^ff'-^Ph cost 2c
ateWram and calcutt^ThfcoroV^^nd-^^"^^^^""- «"
-«rWA man's mnn^t, J ^Z*^ sendin^f u.
-. «^ .nude U|, of ^,-doIlv bill,,
>^,
\\.
V.
GENERAL REVIEW.
93
> side and
he square
>e paths?
' there In
md 1 8 ft.
nd 18 in.
:h would
el?
will pro-
h. is that
yard, to
n. wide,
unds, of
els will '
long, 8
» and a
^much
deep. ■
iioved
for a
>f the
des a
I day
i^ould
•ning
oing
t2S
out
•iil^
i
4.dollar bills and bo-cent pieces. Tnere are five times as
many 5's as 4's, and twice as many 50-cent pieces as 5 s.
Altogether he has $102. How many of each kind has
h"* ?
' i'77> How much must be added to the product of the
suni and difference of 8976 and CDIX. to make it exactly
clmsible by 37^^^^ loooo lbs. hard coal. What must be
the Jepth of my bin, which is 1 1 ft. long and 5 ft. wu'e,
to hold^it ? A ton measures 33 cubic feet.
(79) Reduce to acres, yds., etc., 11 128767 square
-TSSTwhat is a bin of wheat worth, if its length be 14
ft.. Its width 7 ft., its height 5M ft, and its cost 64 cents
*^(80 A house is 44 ft. long and 21 ft. wide, outside
measurement. What will it cost to put two floors in it
of 1 /z inch lumber, the walls being 18 in. tnick, and lumber
beine wdrth $15 per thousand ft. ? ' '
(82) A square block of land is i mile 80 rods on each
side Th3 road around it is 4 rods wide. Find the number
of acres in the block of land, and also in the r-ad.
(8^) A school-room is 40x28x14 feet, there are b
windows and 2 doors each 3 x 6 ft. Find the cost of plast-
ering the walls and teiling at 12 cents per sq^^"^ /J/"- ^
(84) There are 6 ft. in a fathom, how many fathoms
deep could a cable la rods long reach ? „,^j„^t
^8i;> There are three prime numbers. The procUict
of the first and second is 2537, of the ^^rst and third is
2881, and of the second and third is 3953- F'^^ them.
(86> Divide sixty thousand and sixty- nine by 420,
using all the factors of the divisor, and find true remr mder,
(87) A field is 9384 ir^ches long and 73 H inches wide.
Find its area in acres, ya»-ds, etc. '
(88) A cistern contains 2500 gallons If it measures
^ ft. 4 in. by 6 ft. 3 in., find its depth.
(Rn\ A nlate o! couper 3 ft. wide, 3 ft- 2 in. long, and
half-an-incii thick, is rolled' into a sheet 2 inches liucKana
ft 7 in. wide. Find its length.
94
ARITHMETIC
'■uls were taken %?'?'" containing , ^4 ballon o '
water still remai Jl .*^\PaiI held 2 ^ll f ^J*' 28 pail-
„ (96) TheXeUfV^ '^'^^^''"^ ^ ' ""^ "^"^^
PouSHa^dtTa'K y' '"- of bu«era. .8
"lany Ib^ of io 7^- ^f cheese at o cenVc T '^ ^ents a
»«oney aherrS ^^ ^^ ^«"^s a pound c^l'u'' ^u''''"^- How
ij_„„^---"~ ■'^■f""
^"\,
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