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1
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6
t^^^^^ SCHOOL HELPS" SERIES jlSSS^t
|-J rithmetic
*^^ Exercises
FOR THIRD BOOK CLASSES
•Y
G. E. HENDERSON
AND
E. W. BRUCE. M.A.
♦♦♦
JPILS' EDITION, 15 CENTS
• nt buvCAtlONAL PUBLISHING COMPANY Xf
TORONTO, lacr - *
''I
1
\.l
1 M
5
l^'
Njajona, Ubrary B«haque na.ionale
Of Canada
LL
i
1
SCHOOL HELPS" SERIES.
]
ARITHMETIC
EXERCISES
FOR THIRD BOOK CLASSES
BY '^
G. E. HENDERSOxN,
£di(or of" The Canadian Teacher " and ♦♦ The Entrance:*
AND
E. W. BRUCE, M.A.,
Principal Huron Street Public School, Toronto.
Price, 16 eents ; Teachers' Edition, with Answers, 20 cents.
THE EDUCATIONAL PUBLISHING COMPANY,
Toronto, 1897.
PREFACE. .
e year one
:rson and
The authors 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 by teachers actively engaged in the
busy work of the schoolroom, and as teachers they know the
great difficulty that the average teacher encounLs in the
presentation of new and crisp problems for his Arithmetic
Cl&SS6S«
The authors would most respectfully request a consideration
of the following 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 more accurate as they advance in years
frequently lose the speed and accuracy which they had acquired
m the lower forms. To meet this difficulty the present series
provides oyer 5^00 operations in mechanical wo.k, which the
teacher will find tested for him without the labor (and loss of
time of performing the work Hmseh". This feature alone
should commend the present sed.s to every teacher of the
subject.
II. No Answers. In the Pupils' Edition no answers are
provided ; the Teachers' Edition alone contains the answers
III Saving in Time. The time of the teacher is too
valuable tn hp talr<.n .,n 5" ♦»-" J-"-^--: ' .-
, , P '" "'^ "itiaiion or problems to a class
when for a mere trifle each pupil may be provided with a sei
ofexercises for himself.
IV. Wilting. The possession of these exercises by the
scholars will tend to preserve his handwriting-it prevents the
mad rush in copying questions from dictation.
V. Ur^derstanding of Termr. Without giving format
definition..! of terms, problems are specially constructed to fix
m the pupil's mind a thorough understanding of the technical
terms of Arithmetic.
VI. Nsw Problems. The great majority of the problem*
of the series have been written specially for these " School
Helps." They are not simply a rearrangement of old
stereotyped problems.
VII. Problems Grouped. The problems are not arranged
in the ordinary "hit and miss" fashion, but are grouped
according to types, and carefully graduated in degree of
difficulty.
yill. Time Tests. The purely mechanical operations of
addition, subtraction, etc., are intended to be done at a pupil's
best speed, a specified time being allowed as the teacher's
experience finds suited to the ability of his class.
IX. Book of Exercises. This series is not in any sense
designed to displace either the teacher or the authorized text.
There is no attempt to show how to teach ; this is taken for
granted. It merely furnishes ready to the teacher's hard
bright,, crisp, new problems with which to enforce his teaching.
The Authors.
Toronto, August, 1897.
es by the
events the
ng format
;ted to fix
: technical
problems
" School
t of old^
arranged
grouped
legree of
rations of
a pupil's
teacher's
iny sense
zed text,
aken for
r's hand
caching.
HORS.
Arithmetic for Third Book Classes.
(I)
625456
312215
763617
512215
767896
123432
(5)
361
2121
6222^1
22 1
2
J'
524123
458416
468495
697261
644605
329185
518768
MECHANICAL WORK.
Exercise I.— ADDITION.
(2)
279807
502/36
796736
452432
967875
234345
(6)
642272
347447
87263S
615465
42 164 1
879848
95^^925
508575
467259
752342
(3)
876390
763769
507648
727659
432140
541546
(7)
423426
7091 51
820737
253897
54'ni
422343
1 5685 1
481318
423805
(4)
507648
727659
307523
423237
87694S
768275
(8)
782167
4H 1 3 1 1
59 '479
6 1 1 5 1 2
703608
122291
914572
234210
357444
452468
Without putting the figures down.
(9) Add 4's (the same number of 4's in each successive
Ime as there are tigures in the line they are being added
to) successively ten times, beginning with the line 9684^
(5)
ARITHMETIC
(lo) Add
7's. (I
Add 5 s to the same line, (ii) \dd6\ fj',\ \^^
, . 3) Add 8's. (14) Add Q's Virf A n , (^2) Add
alternately. (16) Add L-. iV' f'5) Add 4's and q's
6's and 7's alternately ^ ' ""'^ ^' alternately. (,7) A^d
(18)
26q?6- i r'^'^J "■ ^78831 + 827946
I21268 + 739561 + 266721 + a-kVis-,
676277 + 395587 + 82i;85 + %^A^i
810468 + 40^433 + ^,^o^\ X fyll~^^
09) 84870
2217
03 + 732514 + 6353,3 + 433827
12 + 823135 + 288174 + ?6^7'^
342277 + 684718 + 583,8^6 + S^:^
-?8 ? 1 .^A^°- + 752196 + 233647
2^7833 + 656912 + 874314 + 454739
+
(20)
l7-^i i ^q'^-^^ + ^-^745 + 276287 =
^?8"'?7 1 i^"74 + 714924 + 762875 =
i87;]o i ^ f7-^ "- 5S4627 + 875697 =
187149 + 358462 + 647287 + 756978 =
73^846 + 51353^ 4. 728 ^^^/^
85:353 + 224456 -I- 873346 + 875438 I
+
+
Exercise II.-SUBTRACTION.
(I)
625456763
3'22I55I2
(2)
876390763
432137698
(3)
825721423
376948768
, (12) Add
s and 9's
(17) Add
(4)
825125427
327587998
MECHANICAL WORK
(5)
823012345
759158576
(6)
713627230
273976735
(7)
514723272
278976785
(8)
62721 1335
378589657
(9)
914232013
267548129
^3^7
Subtract 213987854 from each of the following :
(ro) 373967873 ; (I i) 972725879 ; (12) 958378^
(13) 721285113; (14) 813246201; (15) 512346513;'
(16) 931467842 ; (17) 712353768 ; (18) 472051997 ;
(19) Without putting the figu- down, subtract lines
of 3's successively, from 62447901 2-4, as far as the seventh
remainder.
(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 S's. (25) Subtract 9's.
(26) Find by repeated subtraction how often 73869745
can be taken from 592410478, and give the remainder.
(27) Find by repeated subtraction how often 416897543
can be taken from 3966641 141, and give the remainder.
(28) P^ind by repeated subtraction how often 975318642
can be taken from loi 87754329, and give the remainder.
Exercise III.— MULTIPLICATION.
!3
>8
Multiply each of the following by 357 :— (i) 180342 ;
(^2)^240456; (3)270513; (4) 360684; (5) 541026; (6)
Multiply each of the following by 468 :— (7) i2-'553 •
(8) 163404; (9) 245106; (10) 367659; (11) 490212; and
8
ARITHMETIC
each ;„? Z StL|':^';f8^™'\ '-, "ul.,p,ica,io„ of
and 8746S. "^ ■ -'«'^7 ; 29156 ; 43734 ; 65601 '
&') Ust"! t a^ a ^ IT'" ™"^ecu.ive times.
(27) Usi„5 I as a factor i " ""'"=™'"e times
(-'8) UsinJ 7 as a ftr n^ f" ™n==<=cutive limes
(^9) UsingSasaftrni ™"™"'""'''<= '""S
(30) Usint. 9 as a fac S I,!;!" ""^«u.ivc .i.nes-.-
. Multiply each of -he f , ""^'="'">'= times,
(32) 17676; At) 26-,,/V'?'"* factors :--(3,) t'.y,
3950,|(4 ) 5t^6V/ifdV4t^7^\^^^ <'^^ ^''3^6? :>
Exercise IV.-DIVISIOIM.
Divid(
Divide each of thet^u' '^"'^ (^) 9i79436o.
Oo) 15042,86; (n I^^^eZf^'^'r-^^^ '337083..
401,2496; (14) 53^8 j-^°°^6^^^^^^ 2674.66^; ^%{
D,n_ie each oflh^fLn^ij.^lty f.744 ; 06) 80224^92.
;Z^-'^'y"'59i7; (19) 37^, a;r"6. l^^-~^'7) '^'657278;
746291,2; and (22) 8395775,'^^' °^ 5597r834; (2,)
13) 132456;
794736 ; and
/9) 143712;
174848 ; and
plication of
34 ; 65601 ;
times.
times/
times.
times.
times.
times.
-ly by the
^3257;
771; (36)
9) 13112;
536; (44)
following
84; (50)
36864 ;
769154;
598120;
570832 ;
^- ('3)
224992.
57278 ;
; (21)
M^aHANICAL 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) 34895 '4378^406.
(31) 445886497875-^4875.
(32) 5963879065-^9307.
(33) 2975019839^5423.
(34) 11516639848344-704006.
Exercise V.— REVIEW EXAMPLES.
(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 each, and 117 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.?
(6) Multiply the sum of the numbers between 38 and
52 liy 769,
(7) In an orchard there are 7 rows of trees and 18 in
each row ; five barrels of apples are got from every two
trees. What is the crop ?
lo
ARITHMETIC
^e^^^LIlfst' '""• '^''^""'"' P™"!"" ^"d quotient of
. (9).A boy Steps twofeet earh fi.^^ j ,
•7 yds. of calico at72^cen s a V 'd "^ ^ ''"^' ^ >'^''^ '
at 45 cents a pair. How much tlf' ""^i P^''^ stockings
out of a $io bill ? ^""^ '^^'^"^'■e does she receive
B.
If tf;e^^e^rr;\^rnh\T:irVo' ^'^^^.^^-^^^^ ^^521.
worth? -Jj each, how much is each cow
the?i"onhelmbers'h""-''°"'' "'°"^™d and forty is
with 259? '"•'""'"bers begmnmg with 24S and ending
cents a pound. Wh'LUrhtgat ^'^ "'<= =-'<= a, 3*5
, (4) A farmer owes S:o T-r/^ ' •
bushels of oats at 27 cents a bu^f^ '^P^^' P^>'"^^"t 146
still owe? /cms a bushel. How much does he
(5) If the doors of 6 hoii^^c ^^.^ (t
costofonedoor--tlJrebeinfoin ^^^-5°.' ^''^^^ '^ the
-Sr-F'SiS? "■••■-
V/^* *^ iiiiam was born n iSt-^ . t 1 ,
sooner, and died at the as" if-' ' ''i '"' 'P' ^°"' "^y^^^^
die? "ieat,eot,2. In wliat year did he
earfi!,t,r we™s ?'^^-'5 ^ "->-. ""'v much will ,5 men
for t.t "hI ?ats\rp?yS;cSVo''t' '"' ^r"^^ °f »-
sheep cost .? Payment 80 sheep. What does a
Co) Divide the sum of 73859, 4637 and 594.8 by 684.
c.
Heyit^rrfniiTitSr. t-^' ^^rj^"" « -ambs.
a sh^ep.? ^^'"'^^ ' 1^0^^ "luch did he get for
REVIEW EXAMPLES
II
d quotient of
kes I oo steps
an hour?
ents a yard ;
•irs stockings
she receive
orth $1,521.
s each cow
md forty is
and ending
» containing
same at 35
ayment 146
ich does he
■vhat is the
nust I sell
rn 16 years
iar did he
ill 15 men
ke of oxen
lat does a
:8 by 684.
(2) If II men can sod an acre of ground in 12 days,
how many days will 4 men take to do the same work ?
(3) Multiply 76493 by 8973.
(4) A man sold chickens that cost him 35 cents each,
for 76 cents a pair, and gained I2.70. How ;.iany pairs
did he sell?
(5) What number subtracted 88 times from 80005, ^^'1^
leave 13 as a remainder ?
(6) Write in figures : seventeen thousand and eight ;
nine hundred and one thousand six hundred and four ;
eightjiundred thousand and two ; XC^VII.; CD.; CCCV.
and XLIV.
(7) Divide 121 marbles between John and Tom, giving
Tom 19 more than John.
(8) What will a telegram of .14 words cost, if you have
to pay 25 cents for the first 15 words and 2 cents for each
of the remaining words ?
(9) A boy was told to multiply 720 by 304, and gave as
his answer 24480. By how much did his answer differ
from the correct product ?
(10) How many bushels of wheat at 69 cents a bushel
should be given for 6210 pounds of sugar at 5 cents a
pound ?
43 Iambs,
le get for
REDUCTION.
Exercise VI.-DOULARs and CENTS.
(r\ Tjr. '^ ' 4)iS7.04 and
(7> How many cents in fh !,'" ^9-4o?
%3o + $4.45? > ^^^cent p.eces in $1.10 + $. 25 +
800 cents l^'fV." ^°"^'"^ ^"^ -ents -rD .r8
^-089 cents ; %%lr^\ZT ' ^'^ ^^ol'^'nTni')
Exercise VII. -TIME.
m
0) Write the table.
6 minutes ; in 13
(12)
minutes ;
REDUCTION
13
ENTS.
?nts.
ems :— $7.63,
5?
$187.04 and
81.17?
'i]Is ?
lO+$2.25 +
5 cents ; (2)
6004 cents ;
i cents ; (9)
(3) How many seconds in i day ; in i week ; in 19
days \ \x\ 2% weeks ?
(4) How many seconds in 5 hours, 7 minutes ; m 12
hours, 5 1 minutes, 37 seconds ?
(5) How many seconds from 6 o'clock a.m., to 7 o'clock
p.m. .''
(6) How many minutes in a year ? How many mmutes
in a leap year ?
(7) How many seconds in the 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 the
summer ? in the autumn ? in the winter ?
(10) How many days 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 18360a
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 bemg 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.
minutes ;
Exercise VIII.— DRY AND LIQUID MEASURES.
(i) Write the tables.
(2) How many pints are there in three quarts ? i gal-
lon? I peck? I bushel?
I I
14
AHlTHiMETIC
quattf^rn/r"" P'"' "- "^ berrte in 6 gallons, 3
cents a peck? °^ ^7i3 bushels of potatoes at 9
gam. '"*"> at '5 cents a quart; find his
Vr^^°^^^J^Z^ soM for S.6, .vha.
whi^.teT;t":Vd^a^r^'-^ - '- a Horse
B.
chegeilf/etr^lr^ut^ """'*' ^ P^*^' ' ?«"»„, of
how many'Xndl of wheaf ar^"if ^^^ 8^="'™^ "f wheat,
oats ? ™«a. are equal to 1870 pounds of
.heJ'LJtr.a^.Cun.fj-- worth 48 cents, what is
at i^{ bu"tf ~^' "' -■' •'"^h^l^. ^ pecks of grass seed
cen('.L'';"'irf '°^' °' " ""^hels of crab apples at ,
•o ^SJs'l'ZTLViir?'' 3 'l-"3 of berries at
pounds. ' '''■'"'"'ng 3 quarts to be equal to 4
is it Ir^hltT/ent a gail"o^',^.P'"'^ "^ »'"<• -^ what
REDUCTION
in 6 gallons, 2
n 2774 quarts ?
5 of potatoes at 9
^ could be filled
hels, 3 pecks, i
2 pails, if each
cherries at $2.25
quart ; find his
[ for $16, what
tts last a horse
M for 42 cents
peck, find the
Its, how much
5, I gallon, of
ons of wheat,
70 pounds of
:ents, what is
>f grass seed
apples at i
3f berries at
e equal to 4
Ik. and what
(8) How many pint bottles will be required to hold 6
gallons, 3 quarts, i pint of vinegar ?
(9) A grocer bought 2 barrels {31 }4 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 (4uart.
(11) If $10 was paid for a barrel of molasses, which
was retailed at 20 cents a quart, find the gain.
Exercise IX — AVOIRDUPOIS WEIGHT.
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 seed, corn, rye,
barley, buckwheat, timothy seed, oats ?
(6) How many grains in i pound avoirdupois? in i
ounce ? in 8 ounces ? in half a pound ? in i >^ pounds ?
(7) How many ounces in 19 tons, 1 2 cwt., 7;^ lbs., 1 5 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 sold 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?
I
! ! I
16
AkJTH.METIC
B.
^'^Sr;^r;;;^^-'-^e 5767 ounces P
(3) 'llVlhl' of "^'" ""' 9o rents per bushel
4 ^oi bs nf?'''1 '"' '^^ ""'■'''' per bushel
(6) 1896 lbs. ofcloverL'l ' i- "^^ P^"'; bushel.
foni'°\.1t™:;;;^!ir.„'2;nr3f "7- ^ >- >oad as
■95 pounds. Kind the'sZ of thei? ,ve"i^f;r°" ''"'•'"""'
Exercise X.-THOY WEIGHT.
(i) Write tlie ta'ule.
in 3l"ZTr '-'"■ '■" ' <'"'^- •' '■" '3 d"'^- •' in , oz. ?
• . -.! "T^^Zll; ■" ' °^" 5 'l^-. -3 .T. ? in 5 lbs.,
.3iil!'a'r^;!7^';e?J,":.°?™''™--'- -i,hin,3 0.
, fe/Vdt/numt;„7rrr-n™-5LfV'o .
2 grs. ? . *»'^- >" ^2 lbs., I oz., 10 dwts.,
aO "^^.-^I^^fbT °if ™7" a .quanerofa pound..
bei?id"?.r?3"Vs%rr' '^^"^ -■?"i"^-^.. can
(11; Reduce 123 lbs. to grs.
REDUCTION
•7
ounces ?
" bushel,
'uslicl.
' bushel,
per bushel,
acr bushel,
ts per bushel,
'ushel.
■ \\(--ighiny 4185
■ of his load as
^ '^•'^«' ; 153 lbs.
"f barley at ;->
e for all }
"ei^rht, said he
)anion weighed
its.
HT.
^vts. .? in I oz. ?
^"rs. } in 5 lbs.,
weighing 3 oz.
oz., 10 dwts.,
'of a pound.?
ing 2 oz., can
t weighing i
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 lbs. Avoir and
how many grams over .? '^vuir., ana
(14) How many pounds Avoir, in 15 lbs. Trov and
how many grams over } ^' "
Exercise XI.-APOTHECARIES' WEIGHT.
(i) Write the table.
(3) Reduce 6 lbs., 5 drs., i scr., ,9 grs. to grains.
4 In ten thousand grs., how many lbs., etc. ?
I( S"'y '^^'^"y ^''■^'"^ of calomel in 1 1 oz., 2 scr >
(6) Fmd the number of lbs., etc., in 791 scr ?
m-irU frnn^Ju*'"^' morphine powders of i gr. each can be
rR^ V l- J^'-'u '','■' 3 .^'"'•' 2 sen, 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 .? ^voir., ana
Exercise XII LONG MEASURE.
A.
(i) Write the table.
^^ ^^(2) How many inches in 2 ft. .? in 7 ft. .? in 5 ft. .? in 14
(3) How many inches in i yd. .? in 5 yd. ? in ^ a yd.?
'"5/2 yet. t ■'
(4) Express in yards i rod ; 4 rods ; i mile ; iX miles.
in 16 mile'T?"'^"^ ^''^ ^^^''^ '" ^ '"'^^' * '" ^ "'"'^^ •''
(6) How manv inches in ^ I'^ar^c -, fp^... ,, :__l-_ 5
(7) Reduce 6 miles, 24 rods, 3 yards to yards.
(8> How many inches in 25 miles, 78 rods, 4 yards ^
feet, 5 inches of distance .? ' ^ ^ ' ^
; I ! 'li
18
AKMHNfKTIC
H
(9) Reduce 19 miles, 200 rods to rods.
Wi°l ^^''u'^^ "^3 '""'*'' '50 rods, 3 yards, 2 feet, 11
mclics to inches. '
inchJs.^ Reduce 4 miles, 425 yards, 2 feet, 4 inches to
(r2) How matiy inches in 3 miles, 5 furloni^s, 32 rods
4 yards, I foot, 7 mches .? ^ ' -^ ^'
B.
(0 Express 1239 inches in yards, feet and inches.
(2) Express 76298 yards in miles and yards.
(3) Express 64936 inches in miles, yards, etc.
(4) Keduce 64789 inches to miles, yards, etc
(5 Reduce 321467 feet to miles, yards, feet. '
(6) Reduce 8647 rods to miles and rods
(7) Reduce 4708937 inches to miles, yards, etc
(8) Reduce 75680 inches to miles and inches
(9) A held IS 9876 inches lonjr and 7964 inches wide
Express the distance around the field in tenns of rods and
(10) Reduce 9482067 irdies to miles, yards and inches.
UU Express twenty thousand feet in miles and feet.
Exercise XIII — SQUARE MEASURE.
A..
(i) Write the table of square or land measure,
in 1%!:^^:' '•''^^""^ '''' """^^^'- ^' '^--^- inches
. (3) Show by a diagram also the number of square feet
m a square yard ; and the number of square ^ a'drin a
square rod. ^ " ^
(4) How many square inches in a squj-r- foot? n\ a
square yard.? ^ ^ i. * ui a
(5) A table is 10 feet by 5 feet ; how many square feet
of surface ? How many square inches ? ^ ^ ^ "^ '^'^^
(6) A piece of board is 12 inches by 6 inches, and an-
ther p.ece IS 16 inches by 5 inches. How many square
1-: ! "^ n each board ? '■
REDUCTION
19
ds.
yards, 2 feet, 11
feet, 4 inches to
furlongs, 32 rods,
et and inches,
d yards.
;irds, etc.
iirds, etc.
ds, feet,
"ods.
yards, etc
d inches.
7964 inches wide,
tenns of rods and
yards and inches.
I miles and feet.
EASURE.
measure.
3f square inches
ber of square feet
[uar' \ards in a
lu: '•:; foot? m a
many square feet
I inches, and an-
)w many square
m
5 square yards, 8
square rods 1 in 6
(7) How many square inches
square feet, 7;^ square inches }
(8) }low many square yards in
square rods? in »2 square rods?
(9) Reduce 2 square rods to square inches.
loni'?. «*>;r''^«'»»y square yards in a blackboard 36 feet
long and 4//, fec^ wide ? ^
B.
(i) How many square yards in i acre?
(2) Express 8 acres in square rods.
IHow many square )'ards m the floor ?
I (4) \yhat IS the difference in square feet between 10
(5) How many square feet of carpet are required for a
jhall^39 feet long and 24 feet wide ? How mJnytill^^re
1 (6) Reduce to acres and square rods each of the fbl-
^lowmg: 1000 square rods; 1250 square rods ; I325sqaare
kii^'''^- ^^o^' "^^"y ^^'-es and square yards in each of the
squ^rr>?irdt?^ ''^"'''' ^'^''^' ' ^''^^^ "^"^^•"^ ^'''''^' ' ^3040
(8) How many acres in a lot 200 rods bv 80 rods ?
(9) A ten-acre field is So rods long. Express the"dis-
ftance around the field in yards. ^
(10) Reduce 8642898 square inches to acres, etc.
C.
u) Find the number of acres in the following fields •
rods T n^ ^° '^,'^' '/5 rods by 32 rods ; 80 rods bv 36
rods 140 rods by 96 rods ; 100 rods by 96 rods '
U. u "o^y many acres in fields whose dimensions arc:
Jrh. T%^J° chains; 32 chains by 25 chains; 49
by 85 chains } ' ' ''""' '^ ^^ chains ; 48 chaij?
III!
ARITHMETIC
(3) How many acres in fields whose lengths and widths
respectively are : 26 rods by 10 chains ; 64 rods by 3^
chains ; 240 chains by 96 rods ; 100 chains by 144 rods
100 rods by 144 chains? ^^ '
(4) How many square yards are there in the walls of a
room 21 feet long, 15 feet wide and ijfeethigh? (
(5) A room is 24 feet long, 18 feet wide and ic feet ("
iiigh. How many square yards are there in the walls and ^"^''
ceiling .'' num
^ Jw^^tCT^ ^' ""^ ? rectangular plot of ground is (:
f^Jf\ i difference between the length and breadth *^"^!^
iS3() eet How many square inches are in the plot ? ('
(7) rhe top of a table 30 inches wide, contains 10^^^-
square feet. What is the length ? uauis 10 ^ ^^
(8) How many yards of carpet 27 inches wide will ^ ^ ^
cover 30 square yards ? uc xmu ^^
. (9) A square yard of paper is cut into rectangular *"d ;
pieces 3 inches by 2 inches. How many pieces are there ? (/
diggi
P> How
u. ^g
(1) How many pupils would a rectangular school-room ^'"^f
40 feet long, 32 feet, 6 inches wide accommodate, allow- i i^
ing 10 square feet of floor for each pupil ? P ft.
(2) How many acres, etc., are there in a square field J ^'
a side of which is 7260 feet.? ' ^<>"g>
v.rH? J]"'l^^^''°'^^^''''^'^'"^^ ^^^" 66 feet long, 16 I ^'
yaids 2 feet wide, at 6 cents per square yard W*"-
(4) Reduce 7964820 square inches to acres, etc T""^ •
(5Mf a road is 4 rods wide, how many yards of it will i /' '
make 6 acres.? ft. Ion
(6) At $125 an acre, what is the value of a farm 24a '^"''^^
rods long and 90 rods wide ? ^ I
(7) At 2 cents a square foot, find the cost of fencinjr i
Z'^r.. f ?K-"ty ^'^'''' ^""^^ ^'^e^' ^ith a close board
tence 4 feet high.
(8) What will it roQf to pa^ro n rna^'vni- - -,-;'-- 1
o„^ ,V r ^ J " ^""^ '" I-"'-- <^ roaoivay ^ riiiicb long
and 15 feet wide at $1.75 a square yard ? , .
(9) J ind the price of a piece of land 86 miles long and i ^^<
4 rods wide, at $44.50 an acre. ^pntai
Tie in«
(0
wic
(2)
|hed :
(3)
►se lengths and widths
ains ; 64 rods by 35
chains by 144 rods;
REDUCTION
Exercise XIV.-CUBIC MEASURE.
21
A.
there in the walls of a / v „r • ,
13 feet high ? y) ^yite the table of cubic or solid measure.
et wide and 15 feet .\^^ ^^how by diagrams the number of cubic feet in a
there in the walls and ^"'^'^ ^^^'^J ' V^.^ number of cubic feet in a cord ; and the
number of cubic inches in a cubic foot,
ar plot of ground is , (3) How many cubic in. are there in 2 cubic ft. : in ;
2 length and breadth cubic ft. ; in 17 cubic ft.? ^
i are in the plot ? , (4). How many cubic ft. in 3 cubic yds. : in 7 cubic
ss wide, contains 10 X^^^; V" 23 cubic yds. ?
;: (5) How many cubic in. in a cube, one edge of which
27 inches wide will ^ ^ *\- \„,
(6) What IS the volume of a solid 8 ft. long, 5 ft. wide
cut into rectangular ^"*^' 3 ". thick ?
any pieces are there .? ,. (?) How many cubic ft. of earth must be removed in
digging a cellar 15 ft. long, 10 ft. wide, and 6 ft. deep'
Jiow many cubic yds. ? ^ "
(8) How many cubic yds. in a cellar 27 ft. long, i; ft
angular school-room ^'^f ?"/,• 7 ft. high .?
ccommodate, allow- . ^^ !1"^^' "V^"^' ^"'^'^ ^^- ^" ^ ^^^o^k of stone 13 ft. long,
pil? ' ^i ft. wide and 17 ft. thick.? ^'
re in a square field. 1 ('o) How many cords of wood are in a pile 242 ft.
' f ng, 28 ft. wide and 1 2 ft. high ?
m 66 feet long, 16 I ^' '^x^ ^'^'K^^ "PO" ^^'^ich 4-foot wood is piled is 10 ft.
re yard. f"^;- How high should the wood be piled to make a
to acres, etc. f 7 ' , „
lany yards of it will A ^ "' ^T \^.''^">' '^'"'^'^^ ^^^ required to build a wall 3;
ft. long, 12 ft. high and 2 ft. thick, if 21 bricks with the
due of a farm 24a '^"'■^^'' ^^'o^ld make a cubic foot of \\'all ?
hie cost of fencing i ^ /,n tt' , .,
kvith a close board a y\ t^'n« the va ue of a pile of tan-bark 128 ft. long, 40
ft. wide, and 16 ft. high, at $3.25 a cord.
dway 2 miles long i^ V^ ^^^^^ '"^^^y cords of wood can be piled into a wood-
d ? F*^" 20 feet square and 16 ft. high ?
d 86 miles long and J ^^^ ^}^°^ ^4 in. long, 16 in. wide and 18 in. deep will
^ntain about 3 bushels. How many bushels of wheat
|-e in,a bin 12 ft. long, 6 ft. wide and 5 ft. deep ?
i
I Mi
22
ARITHMETIC
(4) How many cut stones, each 8 in. by 4 in. by 5 in.,
will it take to construct a wall a quarter of a mile long,
10 feet thick and 24 feet high ?
(5) How many cubic yards of gravel will be required
for 4)4 miles of road, the gravel to be laid 9 ft. wide and
averaging 8 in. deep ?
(6) Find th value of a pile of cordwood 87 ft. lonjj
and 3 ft. 10 in. high, at $2.75 a cord.
(7) Find the cost of a pile of wood 32 ft. long, 12 ft.
wide and 5 ft. high, at $1.75 a cord.
(8) What will it cost to dig a cellar 20 ft. long, 18 ft
wide and 6)4 ft. deep, at 24 cents per cubic yard ?
(9) Find the cost of digging a cellar 35' x 24' x 9', i
7 cubic yards cost $9.
(10) A person sold a pile of wood measuring 64 fi
long, 6 ft. high and 6 ft. wide, getting $4.25 a cord for Ui
cords, and $3.75 a cord for the rest of it. How much di.' '
he receive for ^he wood ? *
(i i) A woodshed 24 ft. long, 20 ft. wide and 8 ft. higl I
is half filled with wood. Find its value at $3.25 a cord I
(12) What must be the width of a box 6 ft. long, 4 ft
high to contain a cord of wood ?
C.
(i) Find the total cost of digging a cellar 48 ft. long
30 ft. wide and 6 ft. deep, at 20 cents per cubic yard, am
flooring it with Portland cement at 10 cents per squar
yard.
(2) What is the value of a pile of four-foot wood, th
pile being 6 ft. high and 20 ft. long, at $4 per cord ?
(3) A pile of cordwood is 7 rods, 6 yds. long and 6 ft,
high ; find its value at $1.60 per cord.
(4) There is a pile of cordwood 48' x 4' x 6'. Hov
many cords has the owner left after taking away $1
worth, wood being worth $2.25 a cord?
(3) How many bushels of wheat are there in a reo
tangular bin 8' x 4' x 6' ? A cubic foot contains 25 quarts.
(6) A rectangular cistern is 4'x4'x3'. How manf
gallons docs the cistern hold? ,
8 in. by 4 in. by 5 in.,
arter of a mile lony,
ravel will be required
be laid 9 ft. wide and
cordwood 87 ft. lonjj
I.
)od 32 ft. long, 12 ft.
liar 20 ft. long, 18 ft \
er cubic yard ? 1
cellar 35' x 24' x 9', i
ood measuring 64 ft ,;
ig $4.25 a cord for 14
of it. How much di<I'
ft. wide and 8 ft. high
value at $3.25 a cord
■ a box 6 ft. long, 4 ft ;
REDUCTION 23
(7) What must be the length of a rectangular bin
4 ft. wide by 5 ft. 4 in. deep to hold 300 bushels ?
(8) A gallon of water weighs 10 pounds. Find the
weight of water in a rectangular cistern 6 ft. long and 3
ft. wide, the water in the cistern being i ft. 4 in. deep.
(9) There are 31;^ gallons in a barrel. How many
barrels of water are there in a rectangular water tank 6
ft. 9 in. wide, 7 ft. long and 5 ft. 4 in. deep,?
(10) 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 ?
(11) To drain a swamp in Dereham, the township
council had a ditch dug one mile
long,
3 ft. deep and 6
ft. Wide at the surface, and 4 ft. wide at the bottom,
^he total cost at 9 cents per cubic yard.
Exercise XV.-BOARD MEASURE.
Find
ng a cellar 48 ft. long
ts per cubic yard, an|
10 cents per squar |
af four-foot wood, tht|
at $4 per cord ? a
i, 6 yds. long and 6 ftl
od 48'x4'x6'. Hov|
fter taking away $i|
rd ? _ I
c are there in a rec-f
)ot contains 25 quart- 1
X4'x 3'. How man/
A.
How many feet, board measure, are there in :
(i) I board, 12 ft. long, 12 in. wide and i in, thick.?
(2) 3 boards, 14 ft. long, 16 in. wide and i in. thick?
(3) 4 boards, 16 ft. long, 9 in. wide and i in. thick?
(4) 12 boards, 14 ft. long, 10 in. wide and i in. thick?
(5) 42 boards, 16 ft. long, 8 in. wide 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}4 in. thick?
(8) 2 planks, 14 ft. long, 9 in. wide and 2 in. thick?
(9) 20 planks, 8)4 ft. long, 16 in. wide and 3 in. thick?
(10) 13 planks, 16 ft. long, 13 in. wide and 2 in. thick?
(n) I scantling, 12 ft. long, 3 in. wide and 2 in. thick?
(12) 6 scantling, 14 ft. long, 4 in. wide and 3 in. thick?
(13) 20 scantling, 16 ft. long, 5 in. wide and 4 in, thick ?
(14) 48 scantling, 18 ft, long, 6 in. wide and 4 in. thick ?
B,
(i) How many board feet of lumber in a floor 18 ft,
long, 14 ft. wide and i inch thick?
24
ARITHMETIC
; i \
(2) How many feet of lumber in a sidewalk 200 yds.
long, 6 ft. wide and I'A in. thick? . , . .• 1
(3) How many feet of lumber m a stick of tmiber 21
ft. long and 20 in. square ? . , j r
(4) How many feet of inch lumber m a board fence
•?o rods long, 6 ft. high ? , „ . • j • a
(5) A bridge 144 yds. long and 18 ft. wide is covered
with plank 3 in. thick. How many board feet of plank ?
(6 How many board feet will be required to make a
walk 3 ft. wide around a garden 300 yds. long and 240 yds.
"^'^(7) Find the cost of the lumber for a platform 250
ft long, 7; ft. wide and 2 in. thick at $12 per thousand.
■ (8) How many feet long will a plank 10 in. wide and
3 in. thick require to be to contain 45 ft- board measure?
(9) What length of 2 in. plank, 16 in. wide, will con-
tain 64 ft. board measure? , •„ 1 • 1 f^..
(10) How many feet of 2 in. plank will be required foi
2 miles 80 rods of sidewalk, 6 ft. 6 in. wide ?
(11) Find the value of the plank for a sidewalk 100
yds long, 6 ft. wide and 2 in thick, at $20 per thousand.
( I -) Find the total cost of 8 boards, each 1 1 in. wide ;
7boarcls9 in. wide and 6 boards 8 in. wide, at $10.50
per M.; all the boards are 14 ft- n\ length.
Exercise XVI.- GENERAL TABLES.
(i) How many articles in 19 dozen ; in 17 score ; in 3
score and ten ? . j^^„„ ?
(2) How many units in i gross ; m 3 gross, 7 dozen .--
(3) Find the cost of 120 gross of spools at 40 cents a
°^a) Find the price of 1 120 stone of flour at $3 percwt.
(5) What is the cost of 14 dozen brooms at 18J/2 cenis
^'''''(6) If a quire of paper costs lA rents. What is the
'''''(7") Hownmny score of sheep in 5 flocks, each con-
taining 160 sheep?
REDUCTION
25
alk 200 yds.
f timber 21
board fence
I is covered
et of plank ?
;d to make a
and 240 yds.
jlatform 250
thousand.
in. wide and
rd measure ?
de, will con-
required for
sidewalk 100
er thousand.
1 1 in. wide ;
le, at $10.50
LES.
7 score ; in 3
)ss, 7 dozen ?
at 40 cents a
at $3 per cwt.
at \?>y2 cents
What is the
ks, each con-
(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 contams i gross). ' '
(9) How many buttons can be purchased for $6 at ^1;
<:ents a dozen } -^ t -3
(10) In 105 12 pens how many boxes }
(11) A woman sold 2472 eggs at 9 cents a dozen, and
bought cloth with the money at 27 cents a yard. How
many yards did she buy 1
Exercise XVII STERLING MONEY.
(i) Write the table.
(2) How many pence in 8 shillings ; in 12 shilhngs ; in
i,i ; m I gumea.? ** '
(3) Express 96134 pence in pounds, etc.
(4) In 768 gumeas how many pence ?
(5) How many cents in 3 shillings ;' in 12 shillings;
2 guineas .? ( 1 akmg 24 cents to a shilling).
V/t?°'''.'^^">''^^""^''^a"<^l cents in /6; in /g ; in /15
IDS..? (^ I =$4,862^). ^ ^V ' '" ^3
^l\ i?"7 "''^"y guineas in ^42 ; in /147 ?
(8) Reduce i;i3 4s. 8d. to farihings.
(9) i" md the difference in pence between ^109 and 89
(10) Reduce 76841 halfpence to £, e^
r,\oJX ^""'^ "'"""^ Vovmds, etc., in 3927 three penny
(12) Reduce ^13 19s. 7d. to halfpence,
(13) How many shillings are there in /7 i:s • 2
guineas ; 3 sovereigns ; 4 crowns ; and 2 six-pences.> '
U4; It i,i =$4-86, how much is £2 los. equal to in
(15) How many pence in ^63 gd ?
.lic^^'^ How much will the Bank of Toronto charge to
discharge a debt of ^159 in Liverpool at $4.88 per £ ?
ARITHMETIC
ii
Exercise XVIII
-ARTICLES SOLD BY THE 100.
A.
Find the value of : , , ,
(i) 7250 lath at 30 cents per hundred.
(->) 2900 pine apples at $13 per c.
(V\ 2425 lbs. sugar at $3 per cwt.
(i^ 8175 lbs. cheese at $16 per cwt.
(c) ''7C lbs. of beef at $6 per cwt.
(6) -160 lbs. of pork at $8 per cwt.
(7) I c bbls. flour at $2.50 per cwt.
8) 47800 bricks at $8 per thousand.
(9 47200 shingles at S3-5o per ^I-
o) 4320 feet of plank at $40 per M .
(I ^0750 ft. of lumber at $16 per M.
(12) 25500 shingles at $4.50 per M.
B.
(I) 3500 lbs. of hay at $18 per ion.
W) 25360 ft. of lumber at J27.50 per M.
(V) 8400 lbs. of hay at $9 per ton.
(4) 8 tons, 1000 lbs. coal at $5 per ton.
(c) 6325 bricks at J8 a thousand. .
(6) 20 planks each 12 ft. long, 12 m. wide and 3 m.
^'"(^V^Fhif t'h'cost of 17640 feet of lumberat $11.50 per
M.,.md 3680 lbs. of coaAat $5.50 pej-t^^^^^ ^^^ ,^^,
.on^l^HirSei;:;?"^^^^^^ (-
^^^'ir^ ma^Ssl;.ill cover the two sides of a
nTFin^^^S^o-^X:;^lVofco^at^
ton, 17860 feet of lumber at $13.50 a thousand.
(i) Find the cost
of 4444 lbs. of hay at $8.50 a
ton.
k
■ ■ ■ U
REDUCTION 27
(2) A field is 330 yards long and 220 yards wide. Find
the cost of the lumber for a close board fence 6 ft hiLdi
at $15 per M. ^ '
(3) Find the cost of inch flooring at $17.50 per thou-
sand for a floor 28 ft. by 16 ft.
(4) A dealer purchased 4250 lbs. of hay at $10 per
ton, and sold it at 68 cents per cwt. ; find his gain.
rll a'"^ ^^^^ ^°^* of 2700 pine apples at $12^ per C.
(6) At $12 per thousand, how much will the lumber
cost for a close board fence 80 rods long and 6 ft. high ?
(7) How much will it cost to lay the floor of a room
fex'^Lj^^ ^'^^ ^ square (a square = 100 square feet) ?
(8) How much would it cost to lay a floor 7 yards long-"
by 5 yards wide, at $1.33 >^ a square.?
(9) How many bunches of shingles will be required to
cover a roof 50' x 24', if it takes 4 bunches to the square ?
(10) How much will it cost to shingle a roof, the length
of the rafters on each side being 15 ft. and the building
35 ft. long ; the bunches costing $1.16 each ?
I
i !
i'!i j i
tl !
COMPOUND RULES.
E
xerci
se XIX.-ADDITION.
A.
(I)
(2)
(3)
$987.63
$ 96.24
$719-43
429.92
198.78
921.99
38-34
647 92
86.86
927.74
68.34
50.00
9.00
928.87
9-37
(4)
(5)
-, (^> .
yds. ft. in.
miles. yds.
$9836.74
23 2 7
18 897
068. 10
34 I 6
73 936
91.98
52 I II
196 1042
7-54
74 2 7
584 1 197
.87
61 2 9
762 1264
(7)
miles, chains.
(8)
(9) ;
yds.
miles. rods.
miles, chains, rods
6 40
11
6197 50
16 13 2
7 29
19
8193 47
12 22 3
8 37
8
604 1 23
17 15 3
■ 7 16
S
897 235
26 73 2
3 74
21
68 39
59 68 2
(28)
COMPOUND ADDITION
(lo)
miles, yds. ft. in.
17 94 2 II
817 215 2 7
918 832 I 8
69 912 I 9
8 1013 I 6
(II)
.sq. yds. sq. ft. sq. in.
56 4 76
48 5 23
20 8 15
39 6 38
14 7 96
817
76
934
518
72
89
104
216
317
94
29
(12)
sq. mis. acres, sq. rods.
138
147
25
16
118
(3)
$719-43
921.99
86.86
50.00
937
(6)
niles,
yds.
18
897
11
936
[96
1042
;84
II97
762
1264
(9)
es. chains, rods.
6
13 2
2
22 3
7
15 3
6
73 2
9
68 2
(13)
sq. miles, acres, sq. yds.
87
92
31
986
14
39 193
217 763
318 1082
169 2162
4 894
(I)
tons. cwt. lbs.
18 7 yj
17 18 45
9 12 53
8 16 61
, 26 18 77
(4)
s.
16
17
9
9
72 14
27
81
93
67
3
9
4
5
7
(14)
acres, sq. rods.
186 89
175 76
tons.
719
816
c
147
474
79
123
100
98
94
123
119
B.
(2)
lbs. oz.
187 4
913 II
43
486
7
219
1732
9
8
58
8
(5)
s. d.
6 8K
86 13 q^
72 15 7
o 71/
9 8j
(15)
acres, sq. chains.
114
96
123
64
257
8
5
7
9
3
(3)
lbs. oz. dwt. grs.
iS 5 9 II
17 7 17 13
29 4 6 21
26 6 14 6
38 II 3 8
£
987
764
99
986
(6)
15
17
9
II
13
d.
1%
iiX
^., ^Jtm!T^<i^^m».m--
M'< ^ 1
■i
ARITHMETIC
(7)
(8)
wks. days
hrs. min.
sec.
yrs.
days
hrs. min. sec.
8
I
9 32
27
98
217
12 47 28
9
-7
II 36
31
87
221
16 jl 36
19
4
17 40
35
76
318
18 55 42
17
^
19 44
39
35
247
24 49 48
26
5
21 48
43
42
108
29 43 34
(9)
(10)
tons
cwt
. qrs. lbs.
oz. c
rs.
bus.
pks. gals. qts. pt.
M
12
I 13
5
9
897
112 1
23
13
I 15
7
8
26
3120
37
17
3 9
9
6
3
2031
45
19
2 17
6
7
41
I I 3 I
68
8
2 16
8
4
768
2120
(II)
('2)
great Rroas gross, doz.
units.
thous'd. hui.i i. tens, units
15
7 5
6
6
5 4 3
13
8 6
7
9
8 7 5
29
9 4
8
5
486
76
5 9
10
2
697
13
4 7
II
I
7 5 4
c.
(i) A merchant in Toronto sells goods to ^he following
amounts during the week: Mon., $41 /•96; Jues.,
$738.46; Wed., $608.^2; Thurs., $976.50; Fri. $1087.63;
and Sat., $2109.75. Required the amount of the weeks
sales.
(2) My last month's expenditure was as follows :
Baker's bill, $3.16; Butcher's bill, $26.85; groceries,
$13.18 ; fruit, $3.68 ; and sundries, $29.68. How much
did the whole come to ?
COMPOUND ADDITION
3i
(8)
brs. min.
sec.
12 47
28
i6 3 1
36
i8 55
42
24 49
48
29 43
34
(lo)
pks. gals. qts. pt.
I I 2
I
3 I 2
■
203
I
I I 3
I
2 I 2
(12)
lUi.'i i. tens.
units.
5 4
3
8 7
5
4 8
6
6 9
7
7 5
4
)ds to *he following
$417.96 ;
Tues.,
50; Fri., $
1087.63 ;
unt of the week's
I was as follows :
$26.85 ; groceries,
29.68. How much
(3) '^ fanner sold 6 loads of wheat, the first contain-
ing 1819 lbs., the second 2037 lbs., the third 2036 lbs , the
fourth 1926 lbs., the fifth 1673 H^s., 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. ist, 15 gal. 3 qts. i pt. ; on Fob. 2nd., 23
gal. 2 qts. I pt., on Feb. 3rd, 31 gal. 3 qts. ; on Feb. 4th,
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 •
^13 JOS. 7d. ; ^"46 5s. 8;id.; and ^49 19s. 5;^d. How
much is owing altogether.?
(7) /i jeweller receives on Mon., 16 lbs. 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 dwi. 16
grs. How much does he receive in all ?
(8) rhree fields have an area respectivclv of 17 acres
139 sq. rd.; 16 acres 76 sq. id. 25 sq'yd.; and 9 acres 125
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 respectivelv 189 mik"^ 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-
taining 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.
(I)
$8976 . 43
987.49
A.
$3427.63
2197.21
(3)
384 -93
^ looo . u7
^ ^
■ " ■■■ ■■: (..- ■ -■.:-,..=^:':-^ =
ARITHMKTIC
(5)
C s. d.
784 14 8K
457 '^> "/4
(8)
miles yards
8943 67
4817 943
(n)
lbs. oz. dwt. grs.
576 9 19 4
89 10 16 15
B.
(2)
ac. sq. yd.
283 1239
118 3674
ft. in. ac.
2 5 1301
27- 423
32
(4)
£ s. d,
1089 12 7
423 159
*
jC s. d.
5^)3 15 6'/
138 19 7*/2
(7)
' cwt. (irs. lbs.
200 2 20
99 3 21
(9)
miles rods
I 376 2 I
987 237
i
■ i ;
. 'I
(10)
'[ tons cwt. lbs. oz.
714 13 37 II
286 17 49 13
(12)
yrs. da. hr. mifl. >ec.
4083 200 10 30 15
218C 319 19 39 34
: i ! ; i i
i ■ -ti
(I)
; ac. sq. rd.
197 57
103 96
(3)
cords cub. ft.
893 76
275 127
(4)
miles rd. yd.
768 29 5
94 138 3
^5)
sq. rd. sq. yd. sq. ft. sq.in
31 29 3 23
38 13 8 76
1
i
(6)
bus. pk. gal.
710 2
186 3 1
qt. pt. tons
2 716
3 I '7^
(7)
cwt. qrs. lbs. oz. drs.
13 2 16 2 7
10 3 2u 9 <J
(6)
c «. d.
5^'3 « 5 6 yi
I3"'> '9 7>2
(9)
miles rods
1376 21
9«7 237
(12)
yrs.
da. hr. mift.
>ec.
4083
2186
200 10 30 15
3'9 '9 39 34
(3)
cords cub
>. ft.
893
275
76
127
sq. rd.
(5)
sq. yd. sq. ft.
iq.in
31
38
29 3
13 8
23
76
(7:
wt. qrs.
1
lbs. oz. drs.
13 2
t6 3
16 2 7
_
zu 9 "
CO.MJ.OUND bUUlRACTlON
(8)
great gross gross do/.
57^^ 3 4
289 10 9
units
5
8
(9)
thousand hund. teni
76 4 7
'7 5 8
units
8
9
33
'6 lbs. How manyTsks h Ph?f ?; "■^^'^^'^i"^' ^'4 cu?.;
height? ^ "^'^^ '^'^^ ^ic left, and what is their
.(2) A farm contains 76() acrrs -, -^ i
. liHh 473 acres, 2 roods, ^/ r'! ,- "f"' -° '■"^'^' ^'^
low much remains untilied ? ""'''-''" ^"'^'vation.
.all^\o ..L?"" "■"« "-^ ^"ded ,„ 6 tons, ,„<, ,b,, ,„
(5) I started for a wi It -> k^
^-^.er noon, a,., ^^^^^'^^l^'.^^^
conL^^Clkc'U:^^ ,\S%'^ >-urs ., „,!„„„,, ,
es, 40 seconds. ' ^^ ^ ''»>'*' " ''Ours, 50 niin-
2 hay. ^"^ 9 cwt., 96 lbs. Find weight of
(8) A barrel holds ^ i o-alc . fi,„
&';^ls., I pt. ofvinegara^t on; t^m' ^''! P""'-"^ '"to it
#>ther. The barreUvas then filled """^^ ^^^^^•' ' ^^^ ^^
'ch water was poured in ? ^'^ ""'^^ ^'''^^^- How
(9) A fa.Tjier had looo bush, of whe-it H. ,^
'"•> I peck at one tim^ . .» u ,^^^' "e sold 240
>ther, and kept the re Tfo/fl^f. ^"''> ^ P^^^s, , gal. ft
he keep ? ^ '^'^ ^°^ ^°"^ ^^d seed. How much
|0o) A man travels S n,;i„. ^,, , .
i«9 yards by boat: Which wav'n '\'^'^^^y and
her, and how much ? ^ '^''''^ ^^ travel tie
1
i!lt
Hill
ARITHMETIC
/ A n ,^ nf n Stack of hay containing i6 tons 9 cwt.
f''\hreXds were sold^ containing respective y 3
Jc^nsl-'cw" 2 tl^sT9 cwt. 59 lbs. , and 3 tons 13 cwt. 14
s. How much is left in the stock r
(,.) A man «-- .^^J^^, ^ond 27 ac^^^^^^ '^- ^9 sq-
3 sq. rds. 17 sq. yds. ; ^1'^,'^^''"!},: 'other two, less 4 acres
Exercise
XXI.-MULTIPLICATION
A.
(i) Muhiply $573-52 by 49
(2)
(3)
(4)
(6
<7
(8)
(9)^
(10)
(n)
(12)
factors.
1^:; cwt'! 5 'lbs. 6 oz. by 12.
i"^ bus ^ pk. 1 gal. 2 qt. i pt. by 57-
^c^tm"si2?wt.23lbs.4oz.6drs.by37
/2 3 7s. 6,'^d. by 6.
/4911S. 8i4^d,by8.
6 days 15 hrs. 32 mm 17 sec. by 374.
23 miles 176 rds. 4 yds. by 22.
18 acres 29 sq. rds. by 914-
10 lbs. 3 oz. i5dwt. i7grs. by 19-
12 miles 560 yds. by 23. . -^
17 miles 83 yds. 2 ft. n m. by 63, usin
B.
a
30 rods 4 yd. 2 ft^y m long. .^ ^^^^^^^^ ^^^
(4) 1 he (.. W . K> • 's "9 ^ J ^^gt of t
average cost per mile is ifcOi 135. 37-
road. . ^fAimrls of wheat, each c(
/r\ Whnt is the value of 6 loads 01 ^^ , ' _, ^
1 5 cents the peck.
lU
!
■'IV
aining i6 tons 9 cwt
taining respectively 3
; and 3 tons 13 cwt. 14
tlie first has 75 acres
>7 acres i sq. rd. 19 sq-
• other two, less 4 acres
nd is in the third farm?
PLICATION.
COMPOUND MULTIPLICAT/ON
z. by 12.
al. 2 qt. . r- '^ ,-"
6 drs. by 37-
oy !-•
[. 2 qt. I pt. by 57.
lbs. 4 oz. (^ f^rs. bv
6.
8.
imin. 17 sec. by 374-
, 4 yds. by 22.
ds. by 914-
Iwt. 17 grs. by 19.
5. by 23. ^ • S
2 ft. 1 1 in. by 63, usm|
J u T^ m y^ ^"c 'Ore qu£
5q. yds. by 12. ■ach, and tho hin,i
m'dred 9 tens 7 units by|id ,],, j^^wS
enclosing a square fief^ ,^^ . _"-• v^cign
miles in length, and
37-
s in lengui, miv^ ,
Find the cost of t
oads of wheat, each c
,6 cents a bushel ?
ihels 6
oads ot wneai, cav-i^ -^
,6 cents a bushel ?
ihels 6 gallons of peas|y
bush., and ,o bush./,;' ,", ';;4' ' «; "beat at 96 cents a
(8) Find the va ue of 76S n .""" ''' '^"^''•
"«• ""^ 7*3 lbs. of cheese at $,3 per
bti?/'"" ""= -^' °'3>S7 lbs. buckwheat a, 7. centsa
oay! Lwrc^si^e .^;r;'i?/„SsT' ^ ™''^ - ^
ea4f"t •Jlr;-;!:^ j^^^^^^ pieces of ...e,
y) A wagon wheel t- ff , ' • •"
makes 1634 revolutions in an h^ '"• tP circumference
I >-;'^ -c^, does ..e u4c^^^> - ^ How far in mile^
I. {3) A boy walks I mile ,c ,.. ^ *
'ng, and the same distance j/ome / '? '?°°' ^^^^^ '"oni-
p^-^^eyearP Ho^^^^'Z:^ ^IPZl^^ ^
a^f^H^-J^lS'^X^-e, .60s, rods ^
|4f What is the length of 3c^ rails, each .6 ft. 8 in
;ac V^!? U^ l^r^^Jj: ^ Ir'^ -^^'-^ 6 lbs. 2 o.
I'd the lamb weigh ? ^ '''^- ^ «^- each. How much
(7) A hall is 3c ft r, • ,
hat isMhe length Lound it ?■ ^"^ ""^ ^ ft. 9 in. wide.
hf '"i^rVS!, 3'^ts.?'! ;^,?"^-"ed in 29 bbls., each
' (9) Multiply 89 miles, no rod. ,.^
10) A clock trains . ' "* ^''^'•' ' ^'-^ ^ '»• by 7-
-^-villitgaini^^Ujgiuy'"^-P'^^^^>'- i'oi
i' I
i 1 \'r
i!
in
i i
li 1
I
! ii
i
'ill,
Mi ' ^ '
\
1
ii 1 !
"
36
Exercise XXII
ARITHMETIC
-DIVISION, DIVISOR ABSTRACT.
(i) 27 lbs. 12 02.-^-3.
(2) 39 lbs. 5 0Z.-J-4.
(3) 57624.53-^9-
(4) $1713-^4.
(5) 30 R^^i- 3 qt- 1 pt- -^7. .
(6) 68 bus. 2 pk. I gal. 2 qt.-T-».
(7) 31 days 5 hrs. 15 mm. 10 sec.-ri2.
(8) 84 yds. 2 ft. 9 m--^ 5;
(9) 13 miles 945 yds. 2 ft. 6 m.-3.
(f-{\ 287 acres 469 sq. yds.-r3. . ^
9 tens, 8 units -r 79.
B.
n^ A farm of 250 acres is surveyed off as a village site,
''"4"The"RWe°aJ Canal is ,26 miles long, and cos.
*3#£rat^ai*oiirsv.srroL^^
'""(4) 65 bus. 3 pk. 2 qt. of vvhea. is contained in a dozen
sacks' What does each sack ho d ? ^^^^
K^ If n men can mow 27 acres 1 50 14.
in a dW, 1K>- mud. can one man^^^^^^^^ ^^ ^^„d,
(6) A speculator bought ^^ adjo.ning^.P.^^^ ^^^^^^^^^
each contaimng 4 acre* 80 sq _ru^ --^^ ^^^^^^
into 108 lots, and sold them at :j>3 a sq. ruu
did he get for each lot ?
►OR
ABSTRACT.
-rI2.
OZ.-r427
19 minutes 30 seconds
ens, 3 units -r 8.
) thousand, 5 hundred.
yred off as a village site, ^
as streets, and the re-
equal size. What is
miles long, and cost
cost per mile ?
squally among 279 per-
is contained in a dozen
I?
IS isosq. rds. of grass
mow ? r ^ A
joining pieces ot land,
YIq fiivided the whole
"asq. rod. How much
COMPOUND DIVISION
(7) If 7 gross of buttons cost /-. tAc u
15 gross cost.? -^ '^•' '^'"'' "^"ch will
(8) Seven horses eat i;bus ^ nk 7 nt ^f . •
equally arnV^sn'iv'e'ru"J^.te;r'''^^i„r.oT""'"
inch a daughter's share ''"^"^ers. i- md to a square
IS 9 acres, 18 sq vds 7 sn ft i« *i ^^^ s ; C s farm
yds%sq. ft.,ld"clinri'irr;"^^ 2L:?;T'^' '' "'•
How much did each get.? ^ ^"^ ^ ^""s.
Exercise XXIII.-DIVISOR CONCRETE.
A.
(0 $43-5o^$8.7o. «
(2) $2002^13 cents.
(3) $4440 Tf- $3. 70.
(4) 15 lbs. 100z.-f.3lbs. 20Z.
b; 4days, 4hrs.-^5omin.
(6)97o2gal.-3igaI. 2qt.
(7) imiIeH-2ft. 6in.
W 16 yds. 4 in. 4-4 ft. 10 in.
(I2)26weeks, iday4-3hrs., somin.
B.
(r) How often is -> arrp-^ ->- c >. 1
cres, 139 sq. rods.?" ~ ' "^ ^' "'^^ contained in 36
(2) How many sleeners o f f a ;„ ■,, ,
""■ed for a r.n.iy ,^^,; ,tt - ■;;!;;-;« -" be re-
>g"
I ! I.
, !
I+!
Iii:
|i 1,1 a ^■'
.1 i
ARITHMETIC
;n U take to plow i47 acres, 105 sq.
(3) How long will It take I \
rods at the rate of 4 acre^'^33 ^^- ;,,eel 14 ft- 3 Jn- m cir-
(A) How inany turns ^^"' ,.._„.£ of 19 miles?
c Jfcrence make in ro mg a * a ue^^^^, ;^^ ^
pec^i r^LSrS'afSl::e. require .0 pacU .4 bu.hel.
f°' ;Thow ™„y chains ea* 66 ft. Ion, .,.1 measure a
miles 80 rods ? ^e filled fro" a hogs-
(7) How many p.m boti es ca ^^^ ^
head holding 2 '^rrels of ^ /^ fe- ;, eontammg 1 3
(8) How many hogsheaclsof^sj^,^^^,^ ^ ^^.^ „, ^^. ,„„,
cwt. 2 qrs. 14 IDS. uiciy "^ r
burden? ..ni a bicycle wheel 7 ft. 6 in. ni cir-
(o) How often wul a oicyi-iy ^
curriference rotate in gomgr.^^;^,- ,„„^, ,„d So rods
widi'f iaUs it^vorth at J 5° an ac^re ? ^^^^^_ .„^
(, ,) Divide 4 years 2 nwnt ns i ^^^^ ^.^^h.
the^firs\dayof .S93";«ope,;od%o^ ^ ,^ , ; „o..
<'^-\''l'res he tale nx^alking 3 miles 7^° V^-?
many steps does ne laivc
C. .
(I) A wagon-box is 12x4 x- i
9x4x2 in. will It contam ^^^^^^^^^ . ^ ^^^ ^o fill a
(3) How maiy bashe^^^^^^^^
bin 8 X 4 X 3 ft., if '^ '^^^ ^o^ vards in 10 seconds Hoxv
(3) A man can run ]^J^'\ ,. ^ays at the same
many miles will a steamboat go m ^ . ) ^
rqte? , 1 o ..t I nt how many tune^
^'' U) A cask contains 64 g^ .3 It- Pj"' °^,, ,^,, ^isk?
may a vessel holding i qt. i Pt. be h i .^ ^ ^ ,,,^
(c) The fore-wheel of a ^a -^; ^^^.^.^ than the hincj
circmnference, makes 440 ^^ f ^^^Ve circumferenc"
vvhci'l in going i mile 240 ^o"^'
of the hind wheel ? f^^.^tnrs each containing r
(6) How many loads «f f ^ "'^.^Vfor 12 rolls of ca
bushels, at 42 cents ^ bushel u 1 1 ^Y ^^^^^^ ^ ,^ p
pcting, each containing 5^^ )aras ai /,
COMPOUND DIVISION
39
:)W 147 acres, 105 sq.
Is a day? .
eel I4ft-3i"- 1" '''^'
-eof I9"'i^^^-
ontaining i b^^^V.ii
•e to pack 124 bushels
t. long wiU measure 2
be filled from a hogs-
each ? ..-,,,
. ar each contammg 1 j |
oardashipof34it»"^ j
,eel 7 ff- 6 ^"- "' ""'''' i
llns long and 80 rods
lo days reckoning from
,f 7 days 2 hours each.
stepis2ft. 6 m how
ng 3 miles 7^0 V^'^' •
, ft. ; how many bricks j
eat would it take to fill a
mains 25 quarts r
U in 10 seconds. Uo^^
in 5', days at the same
, qt. I pt., bow many time'
be filled from the cask?
,laoe, which IS 7 feet u
ons more than the hm(
Find the circumferenc
aoes, each containing j"
illpayfor 12 rolls of ca
Is at 75 cents a yard? 1
(7) Find the number of bushels of wheal in a bin 6 ft
by 8 ft. and 4 ft. deep, if i gal. is equal to about 277 cubic
• l^K^^,^f^^^ 5° ^^^^ '°"^' contains 10 acres, how wide
IS the field ?
(9) How many pieces of wire 3 ft. 5 in. can be cut off
a roll 40 rods long ?
(10) I have built 102 rods of wire fence 6 wires hi^h
One pound of the wiro is 1 7 feet long. Find the value of
the wire at 3 cents a lb.
L /"^ How many bushels of oats are equal in weight to
|68 bushels of barley and 5 1 bushels of wheat ?
(li) tind the value of a bin of wheat 6' long, 4' wide
ind3 6 deep, at 72 cents per bushel (i cubic ft =->;
yuarts). • -^
MISCELLANEOUS.
Exercise XXIV.— AVERAGES.
A.
(i) What is the mean between 10 and 80 ; between
and 90 ; between 76 and 182 ? 'Jciuccn
^^(2) What is the average of three lengths of 5 ft., 6 ft.,
' Ibi T-M "'tS n^ ''''^';>^^ °^ ^''^ '''^''^^''' "^ 8 lbs.,
■ JOS., 1 5 lbs., 18 lbs., 22 lbs.?
(4) What is the ave-age of four loads of wheat of 40
/'\ \xru ' ^^ '^"^"•' 55 bush.?
(5) What is the average of the following scores at u
e match : 72, 73, 79, 80, 83, 87 ? ^
ilHI
40
ARITHMETIC
What
' (6) The aggregate weight of 12 men was 1896 lbs.
Find their average weight.
(7) A grocer's daily receipts were : Monday, $200 ;
Tuesday, 51180.50 ; Wednesday, $214.75 ; Thursday, $325 ;
Friday, $240.10; Saturday, $416.27. Find the average
daily receipts for the week.
(8) A man walked 373 yds. i ft. in 480 steps,
was the average length of his steps ?
(9) I bought 5 cattle for $72 ; 2 at $17 each ;
each ; 2 at $20 each ; i for $16, and i for $22.
them all for $347. P^ind my average gain.
(10) The axerage age of A, B, C, 1), E and F is 31
years. The average age of A, B, C, D and E is 28 years.
Find the age of F.
B.*
at $
I sold
"3
(i) 23 cows and 16 horses together cost $2566. The
cows cost $26 each. Find the average cost of each
horse.
(2) Find the average cost per lb. of the following : ;
32 lbs. of tea at 46 cents a lb.; 28 lbs. at 25 cents ; 24 lbs.
at 30 cents, and 18 lbs. at 15 cents.
(3) What is the average cost per lb. of the following
32 lbs. @ 50C.; 25 lbs. @ 26c.; 23 lbs. @ 31c., and 17 lbs.
@ 14c..''
(4) A grocer mixes together 9 lbs. tea worth 32 cent-'
a lb., 12 lbs. worth 41c., and 15 lbs. worih 56c. Find the
value of I lb. of the mixture.
(5) A grocer mixes 15 lbs. of coffee (o 27c., 3 lbs. f'
35c., and 3 lbs. @ 40c. What are two and a-half poundr;
of the mixture worth ?
(6) What is the average acreage of three farms, th
first containing 100 acres ; the second measuring 200 rod
long and 36 rods wide ; and the third measuring 20 rod
wider than the second, but only half the length ?
(7) The average weight of 4 horses was 1287 pounds
the first horse weighed 10 lbs. more than the second, bu
16 lbs. less than the third, which weighed 2 lbs. less tha
the fourth. Find the weight of each.
AVERAGES
2 men was 1896 lbs.
,'ere : Monday, $200 ;
4.75 ; Thursday, $325 ;
7. Find the average
in 480 steps. What
?
at $17 each ; 2 at $23
and I for $22. I sold
fe gain.
, C, 1), E and F is 31
;, U and E is 28 years.
her cost $2566. T
average cost of each
• lb. of the following :
bs. at 25 cents ; 24 lbs.
?r lb. of the following :,
lbs. @ 31C., and 17 lbs,
lbs. tea worth 32 cent
I. worih 56c. Find thi
coffee Of 27c., 3 lbs. f)
two and a-half pound
^e of three farms, th^
)nd measuring 200 rod;
hird measuring 20 rod:
ilf the length ?
)rses was 1 287 pounds
;'e than the second, h\i
veighed 2 lbs. less thai
ch.
@ 17c. ^^•' ^^ ^t)s. @ lie, and 13
41
ng:
lbs.
->
ExercUe XXV.-APPLICATION OF SQUARE
MEASURE. «"«RE
squir^e fiSl;^^:.Ce%;der^;:;!e^^^^^ ^''^'^ ^"'lowing
yds., 37 yds., 59 yds. """ ^espect.vely are : ,5 yds., .4
(3) find the area in so yds 7„fr ■
lowing square fields, whose sido^t^" ' ''^' I"" "^ ^^'^ ^ol-
2 ft. 5 m.; 7 yds. 2 ft. 8 in o vr ^'f'J'^'^^V'^''^ = 4 vds.
2 ft. 10 in. '"•' 9 yds. I ft. 9 i„. j^y^^^
(4) Find the area in t:r. ff «r
I'X'oycis.aft.; .3yds.ift b;.^\,r'^' 3>*- I ft.
2 ft. by 24 yds. 2 ft >^ - >''^- ' f'-; aiHl 26 yds
U'rlC^'oV'"-^>-3.is:2't^.'/'y^Il?;:'^,-'-,3
5 y..rdl\vider °""' ■•'"'= '^ " fi*' '^o yards 1„„,, a„d
"i"te;\f's;,';::irJ'„?rdT'ir,h''. °' ■■' ""'"^ '™« ^ ""^ -he
■"til sides. ' ^ '""' '" "«= P--»eme„ts 3 fcct ,nde on
ilii
42
ARITHMETIC
^To^ Each window of a house is 4 ft. 2 in. by 2 ft. 5 in.,
find thl nmnber of panes of glass in each, a pane measur-
inir 1 1 inches by 8 niches.
"'(n) Howmanysodseach i6in by 12 n. w,ll be re-
quired for a plot of ground 24 ft. by 18 It. ?
(12) Find how many bricks "^f,f l-'^^^^-^^^-.^,,"^ '"•'
will be required to cover a space 18 ft. by 12 ft. b in.
B.
(I) Find how many planks ^^^ %Y^l'l '^ ''" '"'^^
will be required to floor a room 24 ft. by ib t.
\') Find how many persons .can stand ma room
measuring 18 ft. by 15 ft., supposmg each pcr.on to
q^ire a space of 27 m. by 18 ni.
(A Find how many trees there are m a ^^oocl halt a
mil ing and^^ quarter of a n.ile wide, supposn.g on an
^° T.rH~y rails 1 1 ft. long would be required to
end^L a ectanladar.field 30 rods by 48 rods, wuh a
straight fence 5 rails high ? j ,^,-
6) Find the rent at $3 an acre of a piece of land 423.
yds. long and 280 yds. wide.
C'7\ A rectangular court measures 18 ft. 6 in. b> i- n^
3 ii'; find the expense of paving it at 8 cents per squaie
^°°^rR^ Find the cost of the wire at 6 cents for 5 'A yards
for ila^-bed-wfre fence six wires high, to enclose a rec
tangular field 36 rods by 45 rods.
(Q) Th. celling of a room is 20 ft. by 15 ft., find th
length in inches around the walls.
/to\ At a cent and a half a square yard, how muc
will !t cott to sod a lawn half a mile long and 63 feet wide
1
[ ft. 2 in. by 2 ft. 5 in.,
each, a pane measur-
by 12 in. will be re-
18 ft.?
isuring 9 i"- ^^V 4 ""'•>
ft. by 12 ft. 8 in.
CARPETING
Exercise XXVI.-CARPETING.
41
Urn}'-
icle
by 9 in. \vi
Ft.'by°i8ft.
an stand in a room
ig each peibon to re-
arc in a wood half a
A.
() sT' h -'Vr'"' ^^^'^" following dimensicm"
yj . r ^ ,^ ?■' ^'^'P^'' ''1 y-'i^'d wide.
-a ?• '^ '^ ^'•' '^'^''Pet a yard wide.
I 3 18 ft. by I2ft., carpet 27 in. wide.
I (4) 21 f^. by 9 ft. , r in., carpet 27 in. wide
? i^ind the expense of carpeting the fbllowini^ foin-
rooms, the duiiensions and cost being • ^
y.ud ""^ ^^' ^^ "' ^'•' ''^'P'^^ ^ ■^'^''^^ ^'^^^ ^"^l 90 cents a
|arc? ^°^'' ^'^' '^ ^'•' "''"'■P^' ''' y^^^ ^^''^e and $1.20 a
.IsV^fd^ '"•' ''^' '^ ^'- ^ ^"•' "''^'■P"* '7 in. wide and 75'
;ide, supposing on an ^^J J^
luare chaui. /o\ , -, f,. , • 1
Sards, and a path 2 yds. «^nls a^^Jd ^ '"' ^ '^ ^^ ^ ^"•' "^"P"' '^ in. wide and 99
. of a piece ofUn.^.s/n "JS^rr "^"^ -' -" « - P" -^^-SS
^ _'i).How many yards of carpeting, i yard wide will
.-es 18 ft. 6 in. by 12 ^"^ ^n' ir<:tht,?: oVtHo'" '^- '^^, ^' '^^ ^^ "'' ''thrs'tn, s
it at 8 cents per square '^^'^l^-j^^^^^^ «f the room, and 9 m. per strip be wastid
(12) Find the cost of carpet for a room 22 ft. 7 in hv
ft., If the carpet be 27 in. wide and cost $1.20 a yard
d 6 m. per str.p be wasted in matching the string
mmg crosswise of the room. '^^^"ini,, tne strips
It 6 cents for 5 'A y
high, to enclose a
ards
rec
20 ft. by 15 ft., find th(
3.
sauare yard, how muc (i) How many vards of thirW mn^r -.^ • -j
Se long and 63 feet wide .er a floor 20 ft. long and , 8 ft rd'^? ^° '"' ^''^^' ^^'^^
>-i**'
■•'
' I
iil'll I
ill
III
ll'ii
iiiiii
m
44
ARITHMETIC
(2) How many yards of Stair carpet will be required
for a flight of stairs of 16 steps, 12 in. wide and 5 in. rise,
allowing i ft. 4 inches f(;r a turn in the stairs .-*
(3) What will it tost to crapet a room 24 ft. long and
16 ft. wide with carpet 32 in. wide and costing 80 cents a
yard, the carpet running lengthwise of the room.''
(4) Find the cost of carpeting, with carpet at 85 cents
n. square yard, a room 2,3 ft- hy - - ft.
(5) Find the cost of carpeting a room 18 ft. long and
16 ft. 6 in. wide with carpet 27 in. wide, at 96 cents a
yard, the carpet being cut into strips 16 ft. 6 in. long.
(6) What will it cost to carpet a room 25' 6" long and
14' 5" wide with carpet 27 in. wide and costing $1.44 a
yard ; first carpet laid crosswise, second lengthwise?
(7) How many yards of carpet will be required for a
hall 18 ft. long and ii ft. wide, the carpet being 27 in.
wide and running lengthwise? How much would it cost
at 87 '/^ cents a yard ?
(8) Which will cost more, to use, lengthwise, carpet 32
in. wide at 96 cents a yard, or carpet a /ard wide at $1 a
yard, for a room 18 ft. by 1 5 ft., and how much more ?
(9) How long must a strip of carpet 27 in. wide be, to
contain 24 sq. yds., and find its cost at 89c. a yd.?
(10) A room 17'x 13' is to be ^arpeted with carpet 27
in. wide and costing 87 cent? a yard. Which is the
cheaper, and how much, to lay the carpet lengthwise o.
crosswise of the room, no allowance for matching ?
(11) A room 15' 8" x 14' 8" is to be carpeted with car-
pet a yard wide and costing $1.08 a yard. If I2''per|
strip be wasted in matching, which is the cheaper, j
to lay the carpet lengthwise or crosswise, and how much ?j
How much is wasted in turning under and matching inj
each case ?
Exercise XXVII.-PAPERING.
liin
The method on which this exercise is worked is asj
follows : The sum of the widths of doors and windows is
PAPERING
45
jCt will be required
I. wide and 5 in. rise,
le stairs?
oom 24 ft. long and
id costinjr 80 cents a
[)f tlic room .''
th carpet at 85 cents
■oom 18 ft. lonf( and
1. wide, at 96 cents a
16 ft. 6 in. loi'ig.
room 25' 6" lon,t( and
and costing $1.44 a
ond leng til wise.''
/ill be required for a
carpet being 27 in.
V muc:h would it cost
lengthwise, carpet 32
t a /ard wide at $1 a
how much more .''
pet 27 in. wide be, to
at 89c. a yd.?
peted with carpet 27
yard. Which is the
carpet lengthwise o.
for matching?
>e carpeted with car-
l a yard. If 12" per
lich is the cheaper,
wise, and how much ?
ler and matching inj
>ERING.
'cise is worked is as'
loors and windows is|
deducted from the perimeter of the room, and tlie number
of s r.ps .s obtamed by finding how often the en i ler
contains ,8 mches (The width of Canadian and \ c can
h.lfthJ r;'''''"^'"''' '^'^^'^ "" ^P^^'i'^1 rule: Deduct
ha f the area ot the openmgs (in square feet) from the area
of the walls, and d.vule the remainder by 30. This gives
the aDproxnnate number of rolls "'s ^ives
-oom\8"frT.v?"r''''''Y,"^P*''P^'"^"'"'^^ ••^^"■■•■^^ ^or a
.com 18 ft. by ,5 ft., no allowance for do<,rs and windows?
24 ft .? "'"""^ ''"^' '"" ^'° "^""'^ ^ ^°«'" 19 *"t- by
1 2 , ff^^/!h"' "'''"^' '^"P". ^'^ '■^'1"''"^^ ^o'- a room 31 ft. by
24 ft if there are 4 windows and 2 doors each 3 ft. wide?
-'i';'^^bv??."'''"rh'°i' ^''" ^" ^^^"'^^d fo? a room
/r\ w ^ ^ ' '''^^ " '^^'"''''^ ^"'^ 2 windows each 3' wide?
i inrl i ft '• 1"'''"^ '''-'P' ''";^ required for a hall 26 ft. long
and 6 ft. wide, papenng the sides only, on which there
! '^'■e 4 doors, each 3 f 3 in. in width ? ^
(6) How many rolls will paper a ceiling 24' x r8' ?
(7) How many rolls of paper are required for the wilU
%?r '^ ^'- ^°"^^' ^7 ft^v^cle and 9 ft. high ? '
i-^ft h^,TfJ"^"X«"J''j'u P^P^^ -^^ ^^a"s of a room-
112 ft. by 16 ft. and 8 ft. high, allowing for i door and ->
[windows each 3 ft. 4 in. in width ?
B.
K^'^fi-"'^^^^^?^^'' paper for the walls of a room 17
1. Yi ^ ^^^""^.9 ft. high, with 3 openings, at 36 cents per
louble roll (each opening 2 ft. 11 in. wide). ^ ^
room ,- ft K ^"^^f PaP,^^ 21 in. wide for the walls of
DerTuble rnll ^ '"^ '^^ ^"^^ ^^^X ft. at 65 cents
latrh^nSi ll \ ^""^^ ^" ^^^^ ^t^'P 's allowed for
latchings and the border costs 8 cents a yard
\m 8 cental paper-hanger charges $2.50, the border cost-
Kf is?of^".^Ll!'l^4^_iP?-/5 cents per roll, find
B f"t"-'-"6 'I »o<J»" 22 ft. by 14 It. and 12 ft hiVh
mh^paper 30 ,„. wide, allowing ', /ft. for doors a^^j
i !
i Hit it
1 : ::::ill
if
I liiij^ii^'^
46
AklTHMKTlC
• (4) Find the cost of the wallpaper 21 in. wide, at 25
cents a roll, required for a room 20 ft. 8 in. by 15 ft. 4 >"•
by 10 ft., with 2 doors each 3 ft. 8 in. wide and 3 windows
each 4, ft. wide. . ., ^ ^_
(0 Find the cost of the wall paper, 21 m. wide at 20
cents a roll and bordering worth 10 cents -^ V'^rd, for a
room 27 ft. by 17 ft. and 12 ft. high, allowing for 2 doors
each 4 ft. 3 in. wide, and 4 windows each 3 ft. 10 in. wide.
(6) If a double roll make only 4 strips, and 8 strips be
deducted for doors and windows, find the total cost ot
papering a hall 30 ft. long and 8 ft wide, with P^M^er worth
62 cents a roll and bordering worth 12 cents a yard , the
hanging of the paper costing 8 cents per roll, and putting
on the border i cent a yard.
(7^ What will it cost to paper the walls and ceiling ot
a room 27 ft. by 33 ft. and 18 ft. high, at 35 cents per
square yard ?
k
Exercise XXVIII.-PLASTERING AND PAINTING.
A.
NOTE~It is customary in plastering or painting the
walls of a room to deduct half the area of all openings, 1
etc., and take for the required area the number of square
yards nearest the remainder.
(i) Find the cost, at 20 cents per square yard, ot
plastering the walls and ceiling of a loom 27 ft. long, 16
ft. wide and 10 ft. high, allowing for 2 doors, each 7 ".
by 3 ft., and 3 windows, each 6 fl. by 3 ft.
h) Find ihe cost of plasterin^ the walls and ceilin;.;
of a room i6x 12 xg feet, allowing for 2 doors, each 7 ft.
by 3 ft. 6 in., and 2 windows, each 6 ft. by 4 it., and a
skirting board i ft. high, at 1 5 cents per square yard.
(3) How much will it cost to paint the ceiling of a
church 1 20 ft. long, 70 ft. wide, at 1 5 cents a square yard r
(4) r mu use luvui v^Osv Oi {^a!..^i!,j5 — 1-
box, with lid, 4 ft- by 3 ft- by 4 ft. deep, at ib cents per
square yard.
a 111!
PLASTERING AND PAINTING
47
2r 21 in. wide, at 2;
ft. 8 in. by 15 ft. 4 i«^-
I. wide and 3 windows
)er, 21 in. wide, at 20
» cents a yard, for a
allowing for 2 doors
, each 3 ft. 10 in. wide,
strips, and 8 strips be
ind the total cost of
A'idc, with paper worth
1 2 cents a yard ; the
s per roll, and putting
le walls and ceiling of
ligh, at 35 cents per
G AND PAINTING.
itering or painting the
e area of all openings,
. the number of square
5 per square yard, of
■ a room 27 ft. long, 16
)r 2 doors, each 7 ft.
))' 3 ft.
the walls and ceiling
r for 2 doors, each 7 ft.
:h 6 ft. by 4 ft., and a
Ls per square yard,
paint the ceiling of a
5 cents a square yard ?
<->t'in>f tViA o'lf'^ide of a
. deep, at 18 cents per
(5) Find the cost, at 10 cent
ing both sides of a close board ft
s a square yard, of paint
cc 4 ft. high, round a
rectangular lot 132 ft. by 66 ft., allowing S3 for painting
posts ar.d scantlings.
(6) How much would it cost, at 20 cents per square
yard, to panit the walls of a room 20 ft. by 17 ft. and 9 ft
higli, deducting for 2 doors, each 7 ft. Ijy 4 ft., and 3
wmdows, each 6 ft. l)y 3 ft., and also paint the ceiling at
30 cents per square yard ?
(7) Fmd the cost of plastering the walls and ceilin*'
of a room 24 ft. long, 18 ft. wide and 15 ft. high, the
skirtmg board bemg 18 in. high, at 22 cents a square
yard, three coats bemg put on the walls and two on the
ceihng.
(8) Find the cost of painting the walls and ceiling of
a room 26 ft. 6 m. long, 18 ft. wide and 14 ft. high, a^ 34
cents per square yard, allowing for 2 doors 7 ft. 6 in. by
4 ft., 2 wmdows 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 paintings the > ills and ceiling of
a room 15 ft. 6 m. long, 14 ft. uiue and 10 ft. high, at 36
cents per square yard, alkn- Mig So square feet for doors
and wmdows.
(i I ) 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. lon^ 18
ft. wide and 13 ft. high, at 12 cents a square yard, allowing
200 square feet for doors and windows ?
(2) Find the cost of painting the walls and ceiling of
a roun-i 18 6" long, 14' wide and 10' high, at 21 cents^er
square yard, allowing for 2 doors 7' x 4', and 3 windows
o X3X-
:ili:t:
1 11'
! !
!i nil
■ Ml i
"II
i i
! m\\\}
ililMlM
i:';
48
ARITHMETIC
(3) Allowing for an 18-inch baseboard find the number
of yards of plastering in a room 33 x 27 x 12 ft.
(4) P'ind the cost of plastering a wall 56 ft. long and
18 ft. high, at 21 ;^ cents per square yard.
(5) Find the cost of plastenng the walls and ceilmgof
a room 20 ft. long, 12 ft. wide and 9 ft. high, with four
openings, each 8x4 ft., at 16 cents per square yard.
(6) Find the cost of cementing the sides and bouom
of a cistern 8 ft. by 12 ft. and 8 ft. high, at 9 cents per
square foot. . • 1 ^
(7) How much white lead paint is required for one
coat on a fence 187 yards long and 6 ft. high, if a pound
covers 4 X square yards? r . u
(8) What will it cost to paint a double roof 40 leet by
27 feet, at 12^ cents a yard ? o r ^ r
(9) What will it cost to kalsomine a room 28 tt. by 10
ft. and 9>^ ft. high, at 7 cents a yard ?
(10) What will it cost to paint a close board fence 5
ft. high around a lot 45 yards by 35 yards, at 8 cents per
sc^uare yard ?
J
i '1 :
! ■ ;
V .1
1
i
1
1
'i'-!^
il ; ri;;;:;j
iiii
ard find the number
7 X 1 2 ft.
■all 56 ft. long and
ard.
walls and ceiling of
ft. high, with four
;r square yard.
; sides and bouom
gh, at 9 cents per
is required for one
ft. high, if a pound
ubie roof 40 feet by
a room 28 ft. by 16
?
:lose board fence 5
ards, at 8 cents per
MECHANICAL WORK.
(I)
76894
68317
34567
89123
45678
91234
56789
1234s
67891
23456
78912
34567
Exercise XXIX.-ADDITION.
(2)
31467
28913
45678
91234
56789
12345
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)
4SI28
81476
45678
91234
56789
12345
67891
23456
78912
34567
8gi23
45678
"(49)"
(4)
98621
94628
67891
23456
78912
34567
89123
45678
91234
56789
12345
67891
(9)
12689
82649
56789
12345
67891
23456
78912
34567
89123
45678
56789
(5)
73409
37645
78912
34567
89123
45678
91234
56789
12345
6789;
23456
78912
(10)
90437
54673
67891
23456
78912
34567
89123
45678
91234
56789
^2345
67891
ARITHMETIC
Exercise XXX. -SUBTRACTION. ^
^.rh of the following subtract 444444 ten times
From each of the toumv u ^^^^^ ;
in succession: (i) 5oi2j3i » V-; 4S a-o
<,o) 5664.69; <'\L5g£4 ; ( )^S'53^6^^^ ,„,,:
From each ot tne IOllo^^lug ^5 _. .„oc7. ^11:^7207272;!
in succession: 03) 7'7M5' ^ <'4>//o^f "g' ^
(16)7076173; ■7)71456";. <'f,Z~c? 777777 ten times!
".T8ir57BT; ('^3^^^^^^^^^ ten timesi
i,s ccLssl^nnl|96^1S7T^^
• 037679:f0"i .ii;U°:lf .osilS. :°^6)ToS9788,J
Exercise XXXI-MULTIPLICATION.
(2^) 49392- , r,y following : (24) 14 *
Jr;^/; V6TSf(S)'35'o- (i8) 43.3 ; (39) 7.: •
(30) 8424.
m i
RACTION.
MECHANICAL WORK
Exercise XXXII.-DIVISION.
51
tract 444444 ten times
4519063; (3) 4490612.
S"555555ten time^
6032441 ; (9) 6068767 ;
6015369.
)tract 666666 ten timc>
7249857; (15)7207272-.
7006738-
btract mill ten time
8474893; (21) 84901 1 5 ••
8102918.
btract 888888 ten tmies
9678492; (27)9567792.
19455983-
ibtract 999999 ten tniie.
• (32) 10278908; (33
0503071 ; (36) 10897889
TIPLICATION.
Divide each of the following numbers bv -^8^ • ^.N
, 36261 12: (2) 4070^76- (■XS iS:»TS,A /\ ^ ,i' '')
., Divide each of the following numbers by q ten con
I (.5)4371202965504 '' <''*>^'"4'35.3io336;
* Divide each of the followlne- numh^i-^ 1,,, , .
Divide each o^ ^h following numbers bv 6 t^n .
Using factors, find the result of each nf th*. f^ii^ •
2I 'i&^'i • <r>^749847i7f '(2^) 8967° ° I"! i
(29) 98764024-84 ; (30) 45296787 -f 72. ^^ • ^ '
ng numbers by 427 : (j
4) 18432 ; (5) 27648 ; (<|
9) 55296. . .1
ig numbers by 560 . Uj
(13) 19152; (14) 2553^
!o72; (18)57456.
ing by 9 ten consecutnl
; (21)24696; (22) 3292^'
fl-,A fnllowine- : (24) Moj
o; (28) 4212; (29) 70^0
Exercise XXXill.-GENERAL REVIEW
PROBLEMS.
lucl'Jh^;;Se'„t "'feh^ -'^' '- y'^- •=>' '3, and re-
gie nuniijer of ounces in ;j7 tr^r xri,- u u ^"""t^d
.e greater number, ^ndVolv much grlai:?? '"'>' ^'""^^
1)1!
\V'''"i
:i' l!
111
liil
ItlHiii i
iiniii
■.\\\\
ARITHMETIC
U) John and James started '» »-'k feTclIrTohn
noo^n; Jnd walked u„.,l ao -- f ^^VTdVesl^^oyHs.
^'.Jw'to^^rArel^tLe'fa/terand how far apart were
'•''^.f HtTta^wmSea man walking at the rate
of lii" s an hour, to walk round a farm uo chams long
and 80 chains w^e^ find the cost of the 2-inch plank
• yl 8 ftlonee ft wide, the water bemg 5 ft. deep?
:£S^r'-&ow„s^--^"-
"liEb:':^trj?;^^?ir"^anr»^;;ni
Sfv L ya?d':if Sfstrips run fengthwise and 6 m. of each
strip be turned under for matchmif.
fio^ Reduce 7 miles 4 rods to mches.
In) What is the value of 1200 lbs. of hay at $8 per
'""(,2) How many pickets, each 3 in. wide, placed 3 in.
apak Will be required for "^°f^,^f,,6859 inches!
(irt) How many miles, etc., aretnereiu /4 jv
I'll An oblong field is 30 rods long ^}f?°^'^^'Z
What > all it cost to put a fence around it at 15 cents a,
^^'05^ How many bags each holding 2 bus. i pk. 4 qts-,
will cintain in bus. 2 pk. 4 qts. of gram?
hour does the tram go ?
(17) How many minutes are there from 10.15
Monday to 6.30 p.m. Wednesday?
(18) Kit cost $1.75 to make 20 feet of road. What
will be the cost of makmg a mile.'' , , „,„
(iq) Find the difference in square mches between
square rods, and one million and ten square inches.
a.m.
GENERAL REVIEW PROBLEMS. 53
bus? TpksT °'^'™ '™ ' ^"''- ' 'l'- ^^ '"btracted from 36
«4o an acre «„d ,he lent.h '„^ fuZtJ^Tl^?"' '™""
yard, allowing- 6 in. for niMtrh;r,/r .k ' ^ ^^^ a
lengthwise. niatchmg-the carpet running
'lo„l??it1 '""^ " * ■■"''^ "■"'-= -d ""'-"S '^'a^res, how
(25) How high must wood be piled upon a rack i. ft
poJIsT ' ""'' '" '""' "''^'= '"">' be'o- ."S'a'haff
er^l the yard bei„t°'8^,^ol™!e'"'"* °"' ^"=' ^' *'^
;nts a busliel '^ '■ ' ""'' 5 ' t"'s, 30 lbs., at 60
S/X ''dfep'VC? 1''"' r "*«/-•' °f one ace, and
=ep wiilTtTravelV •'' '""'•'"■ "^ ''™'' '"t f' "'''<= and 9 in.
(30) Divide 275, acres, ,39 rods, 26 yds., 3 sq. in., by
yds^ fy:*' !'"=.'''«■<"■';"« b^ron 99 miles, 3.9 rods,
>"s., 2 n., II in., and loo miles. '
. u,^i/'"^ the cost at 13 cents per sq. yd. of njasterine-
r "^ ""f. ^,^'^'"« »f a room 2 r^ft. loV^ , 2 ft.^ndl and
' • -6". U has 4 openings, each « ft. by 4 ft
lired tr!!°''' T"^ ^'""'^^ of carpet 30 in. wide will be re-
1 i.''c':st79l ceTs-: J.^rl/™''' ^"'' '' ''• "■^'"=- ^^hat
1 ii
1
1'! I
1 '.
WB
\ %
ARITHMETIC
1 .ft nt 1 steo ; how many miles, etc.»
(34) A boy takes 2 ft. at a sicp ,
^^^'(!::)^A 'lolll S 8377 sq, ft. in one cut ; how many
acrei^sq.nxls,etc^,arethe^^^^^^^^ ^^,^ ^ ,
(36) A farmer had 89 tons ot Y^ ^^ ^ ^^ ^j^^,
1 146 lbs. to A., aid ?^°"|'-;jtl portions. How many
divided the remamder mto 8 equal po
tons and lbs. m eachj ^ ^ ^.us. i gal. 3
(37) Subtract ^ ^ bus^^^ P^. P "J^^ ^^^^
qt., and divide the difference imo denominations.
^ 38) Reduce 7563J -ch- to h.,her ^^^^^^ ^^ ^^_
(39) How much will it cost vu , j ^ce for a
andfift. wide at 7 cents a scj^ yd. df^u^^^^^^
gravel walk 3 ft- ^;^^i7,er tei^^ ^ «^-' ^"^ ^ ^^'"^°"
(40) If a cub. ft. of water ^e^^n ^ rectangular
^^^^'^^"8T\t"6ft vidTIanTS'ft^leepcont.^
cistern 8 ft. long, ° "• " , ■ ,11^5 and rods.
(4,) Express >83997 yards mm ^^ ^^^ g^y^ ^
(4-) How many acres aie uieic 1
side of which is 726° ft- ■ person's step is 2' h'
(43) Assummg ''>"; l™f'"°',iiiin„ , miles, 720 yds.
1 J',4ny. steps ^o" he '^^^ ' at SS an'e\ghA .:
^'^(fsrWh-'t is the length of «he -T^^'^J'i^^ h^h? '
stairs of 24 steps, each .0;^ m- ;'^'^<= f„' ^^ /ml 6 ft' dec
,J^ ;!SoV;a*JhV4e ived' How w,de ..
"^t;; What is the surface area of a block of stone 4
,on^' 28 in. wide and ,8 ,n. cteep ? ^^^ ^^^^
(48) What is the value at S(8 per acre,
ar^y4om,leslong 8ro_ds.v,de ^^
0^^ A farmer sold 223O ms. 01 ^ h„shel :
bushel and ■ '9° jbs. ot cats a pC- c<;m^.^-^^-^^^j ^^
^r- T^r'nZt manytn'Sfd'he buy ? \
" ;o)™ fanncontatni'ng 50 acres is 40 rods w,de. V
IC
p ; how many miles, etc.*
:. in one cut ; how many
AQ cuts ? , , ^
f hay. He sold 7 tons
;48 lbs. to B. He then
ial portions. How many
nt. from 23 bus. i gal. 3
o seven equal parts.
higher denommations.
to sod a lawn 42 ft- lo"^^^
vd., deducting space tor a
Entire length of the lawn.'
Mirh 1000 oz., and a gallon
any gal. wiU a rectangular
1 8 ft. deep contani ?
in miles and rods.
there in a square field, a
of a person's step is 2' 6".^
,n walking 3 miles, 720 y^l^ J
ing a sidewalk an eighth 0! I
,ith planks i;^ in. thick, a
r the carpet for a flight ol
,.wideand7^it^hig^M
orods long and 6 it. cieef
e removed. How wiae wa
area of a block of stone 4 f|
eep? .1
c $68 per acre, of the land i|
wide ?
lbs. of wheat at 96 cents
ts at 36 cents a^ bushel ;
remainder bought coal al
ns did he buy ?
o acres is 40 rods wide. Hn
GENERAL REVIEW PROBLEMS. 55
many miles of straight fence are required to go around it
and what will the fence cost at , K cents a foot .P ^ '''
(51) A stick of squared timber is 18 in. by i = in ind
4lasureT^' '^'^' '^ '' ^^^^^^ ^' ^- P-' M-l Wd
Ifencels puI'mundTt ^° h' '° '"^'^i ^°"^^' ^^ 5-strand wire
icuceis put round It. How much wire, at ; cents t Ih
Will be required if 2 yards coot 3 cents .^ ' ^ ^ ^^"
hilic /r \ ^P^''^' ^^'^^'^'ht in llJs. of: 3 bbls flour-
ran Jt\^K";e?„v„ra5V:r!^-.er' ^ -■ ^^-^ -"'
LnhK ."'''"'-'^"yf'^^^t of lumber are required for a i"
nch baseboard around a field 40 rods by 30 rod T
'einorier^th'?.'?;^' 12 ft square, what' must its height
^^^(58) Find the value of a field 50x32 rods, at $95.50 an
(59) Allowing 90 cubic feet of air for each punil how
Zntfr'^'f '^ ---"^^^^^^^ ^" - schoK;,m°"
• iong, IS ft. wide and 10 ft. high ?
kr bofh^hi^/^"^' a square yard, find the cost of paint-
l^alut'^^^^^^^^^ room 27 feet^ong
(61) A bag of grain weighs i cwt. 45 lbs t, oz how
u h less than 45 tons would 18 bags ofsuch grlirwetd"
rli I . '''"''''f ^''^'''^^ ^'f^' "f 13 rods I ft. 6 in on each
^le, has trees planted all around it. There is a tree in
Jch side thel^'^ "^^' '-^"^ '-^'""^ ^'- '"-'" ^eng h "f
l^hovtfer^^^^^^^^^^^^ Howmany trees are ^here, ,
, (63) To pay his rent on 7c q^res if *-> -- -,^
.ant h ja 2350 lbs -of baHey't^^c-en^s'l" ?a?k' o'f
h^ hen..Z ''"''7 ^"'^^f^' ^^^^-^^^^^ '-^t «8 cents abushe
11 he need to sell to make up the balance ?
i (
■
!
i
ill
III > i
111! ; I I
li 1
i
i
1 1
ifl^Hiii 1
iiU 1
li !
mil .
m,
I :;
56
ARITHMETIC
a bushel and found ^w m^b s1.elfper 1 had he?
he had $335-95 left. Ho\n "?' "> ''' X^ day:
(66) Make out the follow mg pay sheet, 10 m ^ ^
C .
D.
M.
9
10
8
10
T.
7
8
9
9
W.
10
9
10
10
T.
10
10
10
10
F.
8
10
10
8
S
6
5
4
5
$2.00$
$1.90;$
$1.80'$
$1.60;$
Exerci e XXXIV.—
BUSINESS TRANSACTIONS^
Find the total value of the articles in each of the fo
corn at 77c. . , _, . q, u,,c]-. b^pt"^ at 7;f
(i) 76 bush, turnips at4-<-' ^4 1^" l- "— '; ^^..:.
K.f} /^ '^"■''" . ,..0.,^ . 1 •37 bush, onions at b2c., -
112 bush, parsnips at 87c., ^7 ' 'f V^^^^^-es at 53c.
BUSINKSS TRANSACTIONS.
57
>oy walk round a play-
;, in order to walk seven
Ac\ containing lo acres,
iold the peas at 85 cents
ing expenses of hilior.
)ushels per acre had he?
ly sheet, iohrs. = i day.
-*
S
8
6
$2.00
$
5
$1.90,$
4
$1.80'$
8
5
$1.60
%
$
iS TRANSACTIONS!
irticles in each of the fol
03 lbs. cheese at 14c.; '■•.
,,t 6c.; 125 bush, potatoe
58c. , '
• 67 bush, barley at 631
peas at 57c., and 73 1^^'^'
, . Q, k.icIt hep\9. at 7^c«et?
'bush, onions at 82c.;: ^■
doz. cabbages at 53c. .
3 ; 64 bush, plums at $1 oj
Infl 8^"lir''''''''' ""'J' ^7 ; 93 bush, cherries at $,.40,
and Sj, bush, pears at $1.95 ^ '
saeo^L'f^c^'-'.MV'S^' i ^^ ^^'- '^P'°^^ ^' '3c.; 42 lbs
8r^ nnrl ., ihc^ ^'''''"^^ ^^ ^c; 39 Ibs. dried apples at
oc, and 22 lbs. prunes at 9c.
(6) 25 bbls. flour at $5 50 ; 36 bags florr at $2 80 • 18
bags bran at 85c.; ,5 stone oatmeal at 37c.: ,7 stone
cornmeal at 36c., and 29 lbs. wheat meal at 5c
n.„ni"^. f • P^'n ""^ '4c.; 35 lbs. beefat I2C.; 19 lbs
mutton at i6c ; 14 lbs. veal at 12c.; 17 lbs lamb -it , -
and 24 lbs. ham at 13c. ^ ^^^ '
(8) 13 tons hard coal at $6.25 ; 17 tons soft roil nt
$4 50 ; 19 cords maple at $3. 75 ; 2^ cords oak at $^60
10 cords pme at $4 25, and 23 tons coke at $3 70 ^ '
:,o v^i ^fl ^ , ''"^^"" ""^ '^^- 41 yds. cashmere 'at 57c •
39 yds. flannel at 35c ; 56 yds. muslin at 17c • 67 vds'
prmt at i8c., and 52 yds. lace at 99c ' ^ ^
h.Hi°^ ^ "'''" exchanges 14 bush, wheat for 24 bush of
barley, when 12 bush wheat are worth $11.52. Fi d the
Sarley.''""'" ^'" ^^"^^ "^ ^ bush. Iheat and'7
•ents'atra^nH^rn''T'l' f ^^'- °^ "^^^ '"'"< ^t 16
ents a gal. and 60 gal. of skimmed nnik at ^ cents i
4" nts a'T-llir^K^l together, he sold th;"„™ru"?.«
.4 ccnis a gallon, t ind his gam.
J at\7 cenK ' T M^^ ^^'r^ ^^ ^'"^^5, and 287 bush.
'ats at 37 cents. I sold the wheat at a loss of a rpnt^ -.
'ush and 34 bush, oats at a gain of ircentsabush
nd the remamder at a gain of 13 cents a bush V^at'
^•as my gam on these transactions ?
B.
L .1.-3 a yd ; }i doz. ties at $4.12 a doz • i7 vrl^; of
'?n fw^ """^^ '"^ >'^^ ' '-^"^l 3 collars at $?.4o'a dol He
anded h.m m payment ^25. How much dmnge did he
(2) A merchant bought 13 doz. orantres for $^ 7c H*.
ve away nine, and sold the'remainder a d e^rit'e of^^
angcs for 10 cents. Find his gain. ^
iililll!
i
i
58 '
ARITHMETIC
(3) A dealer bought 8,946,7 5opoun;;^^J-y.^^ $- ^
ton!i^.d sold it for 68 -^ ^^^ J ^^^ ;^.ainin, .5
(4) How many 1"^^^^ ^^r^.fiu 'nv for 12 rolls of car-
bush.! worth 43.cents a bush. . U pa>^fo.
pet, each conta.mng 56>^s.,at 75 .merchant,
(5) Make pt.t t- fol^-74^^^^,;on at S/^-'- 7 V^-
sold Hubert ^^n^v^^^-'^.^^; 'Iv ^ 75 ; 14 lbs. tea at 35c.>
tweed at $1.23 ; t^'";"Xf,/7or a' dollar. You took m
and 90 lbs. sugar at 18 lbs J ^^^^ ^^ ^^^ ^ n,.
exchange a tub of butter ^^ u^ ^ J ^^ ^^^^^ .
(6) Fin^lthetotalcostof 84o^nsaJ^^ ^^/^^^^^^^ ^^
,080 pencils at$-ooa grosS'^3^^^^^,7^eentsascore.
$2.20 a ream, and 720 excic weighing i734
^7) A fonner exctenRcd a Wad of oa^;; ^ 5; ^ of
bush.? ^fcvruD and mixed it with
,„fi tX"i?r fl^^'-HetSTe.Ho. a. .5 cen.
a quart. Find his gam. _^j g^_
J?; Stts.ta"I t. 17^^.°^ bush,, and 47.90 lbs. of
wheat at $1.00 a bushel. ^ ^ ^^^
(,o) John Adams ^-^^^^^37 S^^^baK 75 "-• each.
HepaidSi atonf^orFCS m^^^^ ^^^^, as to gam
How much must he ^^^'^^^^ V^^^.^e bales sold ?
the cost of one bale on e^ e^^^ th ^^ ^ ^^^^^^^^^^ ^^
(ii) Farmer Frank Hamilton ^ account of
following articles ^o ^PP ^^ ,^,\ ton, 3 3^ cords wood at^
$34-45 -.1680 lbs. of hay at $'5 a ton 3^ ^^^^_ ^^^^^
S si'a cord, 4 bbls. app es at $^-7^^J f^^at 16 cents pe^
Ul.6423lbs-u.at hcu^^^^^^^^
^hi
of wheat!" How much per
BUSINESS TRANSACTIONS
59
kIs of hay at $io a
iiul h'.s gain,
each containing 15
y for 1 2 rolls of car-
its a yard ?
• You, a merchant,
'ton at5>^^--. 7y^^s.
• 14 lbs. tea at 35c.,
lollar. You took ui
J lbs. at 19c- a ^^^
nsatyfora^^cents;
3 sheets of paper at
s at7>4 cents a score.
,f oats weighing i734
pair, and iSSl^^- «♦
re the oats worth a
Lip, and mixed it with
the whole at 25 cents
an overdue account (
;34 cords wood i
Dbl., 350 lbs. floi
Hitter at 16 cents pt.
ng the balance, and to
H
12.24 for his gram. -'^
,er bushel, and 6600 lbs
:1 did he get for his wheal
(i) Bruce Duguid bought 7 qts. coal oil at i6r. a ..a!
lb 8 oz. tea at 40c. a lb., 10 lbs. flour at $2.50 per cw "
ey, bs. hsh at IOC. a lb., 48 oz. of butter a 17c. a lb'
Find the amount of his bill. ^
(2) Make out in proper form, supplying dates : Mrs
Walter Jessop took to Chas. G. Fmser's store 6 Ib^'
^:inli^U ' "?•' "^' '^ ''"'- ^'^^ ''^t^'3c a do. ' it
for ? r \^ , "''""'^ '''' '^'- ''^ "^•' 6 "^^- biscuits at 3 lbs.
for23C., 14 yds. print at 11 c. a yd., 10 lbs. tea at ^cc alb
Tern? " '""""'^ °^ '"^'"'- ^^"^^ "^"^1^ -'•' ^^^ttie
(3) Make out a bill of the following : You sold Frank
Dickson 146 yds. cotton at 7c a yd., T56 eggs u ilcl
doz , ,7 pairs boots at $3.50 a pair, and 98 11^ of salt' at
(4) A grocer mixed 15 lbs. of tea worth 40c. a lb 8
s/.o ° find ?,"' ^",r ' ' ""• ^"'■^^ 30c. He stld it to giin
:t>7.3o ; find the selling price per pound. ^
Jit $,7 P^rh'^'T- ^T^' '7 ^r^ ^^ ^29 each, and 39 cows
"&t ont^Xore:"^''^'""^^^ ^^^^^ '- ^-
bs of be-ns at 60c. a lu ^am q)4oo on tne whole.
ush., and 47190 lbs. of • (6) Bou^t 75 cows fbr $38.25 a head, fed them 9 tons
of hay at $16.25 a ton, and sold them at $60.20 a head
.ns of hay at $9 a ton. j ^ md mv ^am n.r W..^ . '^^ad.
to bales of 75 lbs. each. I
ch bale so as to gaui|
3 bales sold ?
sold to a merchant the
overdue account (>t|
cf3/ cords wood at
lt*^ .rr. Ih^. flour
ind my gain per head.
(7) Find the total cost of the following : 19 lbs i- oz
iu hMfb" Pf '•' ^'^' ""• "^ ^^'^^y ^^ ^^5 per tonl 49
fc MO a pair ^^ ""^ ^°'' ^'^ '^"^h., and 65 geese 1?
(8) Find the total cost of: 26 yds. silk at $1.45 ; 4 yds
men at 15c ; 2% yds. lining at 20c.; 4 yds. muslin at
;Vo hhl ^;o lbs. flour 'f;5 2 doz. buttons at 25c.; 12 yds. flannel at 38c.: ; yds
JA f 1" ^^'^ ^""^^ °^- 560 lbs. hay at $9 a ton •
.320 !bs. of wheat at 650. n biwh ..^.a .,/ r. -ri ,. V '
t $11 per M..? ' ^"^ "• "' lU"iber
bldklt^rf" ^°"^^' 4750 lbs. hay at $20 a ton, and
Did it at $1 15 per cwt. W hat did he gain .?
I
ARITHMETIC
.u. the ,o,al cost of ■. jSSolbs. «*eat a.
(y,2 lbs. «)ats at
28c. a bush.; 435° lbs. peas
and 518 lbs. corn at 44c
a
bush.
A farmer .old 4oyl»^^J><;-X;5oc^S.r
bush.; 86^, bush. ',f^^; ,f„»hr,,ol ;'susar'-u the rat
at $9.50 P" ton. '1'^ .""'*>" ', .j( n-c. a vt\., and 47
on May ^7, '897, f™m W^lham f r * "^,;; ,3
^,?,:i'far'r5o a'paiV.^'oav^ hS 4 ha^n,s, ea.h we,«h,n,
r--^ Tom Loudon bought trom ^^''"^ > ,,
,nd^,^\alt, as f""--,3P\hn^e at J3^ccn.s,_^ ^^^^
handles at 25C. each, 6 lbs. n.uj^ ^^3/ ^. ^^^^ .
w re nails at 4<^- ^ ^'-'•' '^ „ r. ,,f chain at yc aft.; lo
.vhiteleadat$2.45acan; H ft.^f c^^^^^^^^ ^7^ ^.^^ ^^^^
curtain nngs at I/2C. eacn,
receipt it. bottles of wine at 70 cents
Jfi ^.;^^^r^l^^ he sold the remauuler
at$io.'75adozen. ^md Uie g^^^^ ^^^ following
(5) Make out l^^/l^^''^',^ "er cwt.; 3 ladders at
^^7S^rM?at of 13-^^^^
20c per lb., and i . 10 eggs at 14 cents pe ^^^^^ ^^^^.,
(7) A g^««\,^;f,hr$i perp-^ndfortea?
^^""^"l'fT' '%ri^lUor ?he following : 4 lbs. 4 o..
(8) Make out a bill or ^^^^^^ ^.^ ^^ ^^^^ ,^ ^^ .
butter at 20c. per lb , 3 "f' K^ ^f thread at 5 for 20c.
yds. cloth at 49^, a yd 4 ^P^^'-'^' ^^ j ^^^^h, and
b^^^ t. Sr^o'eS' H^wtS will he gain or lose by
^Stl-m^^lUt $4.40 each? I
WAGES.
6t
(ro) A grorer bought 3 bbls. vinegar, each containing
f^n^r'his ptfiY'' ^^ ^"- '' '^'^ ^"'^ ^"'^ '^ ^' ^- '^ Muai
Exercise XXXV.-WAGES.
Alan Taylor on Jan.
3 at 13 cents; 2 axe
t3>^c. a lb.; S'A ^'^^•
It $1.05 each ; 3 cans
chain at yc '\ft-' »°
ike out the bill and
A.
(i) A man earns $2.15 a. day. l\"y much will he
TuTsda r'"" of ^"Kust, the mst d: y of which i!
Iwii/'^ ^ r""" '^"'■[^'"^^ 9 hours a dr v ., 2/ a Us an hour
Iwill earn how much m 3 weeks ?
I (3) How much will a boy"earn u fortnight, who
learns 1 5 cents an hour and works ten hours a day ?
(4) A carpenter worked a certain number of days and
rece.ved $41 25 ;. if he had worked 22 days mo'; he
tork I? ^e^eived $68 75. How many days did he
.omhl^ "i^" "^"^^'r^ ^ r^''^' .'''''^'■y '^f ^700, paid
lonthly. How much does he receive each month ?
(6) A man earning $2.50 a day— ten hours— lost ir
►ours m one week. What were his wages for that week?
iJi^/'^J?''" receives a yearly salary of $,,96, paid
[reekly. How much does he receive each week ?
(8) At the rate of $2.61 a day of nine hours, how much
lould a machmist receive for 143 hours' work ?
(9) If a man receives $1.95 a day, how much will he
im m the month of June, the first day being Sunday.?
Lil'f ^ P''^P^*'-^«y buys 3 papers for 2 cents, and sells
|em for a cent each. On Mon. he sold 64 papers, on
aes^^,onWed.69 on Thur. 74, on Fri.%Vand on
It. 112. How much did he clear during the week ?
B.
(I) If. 20 men can do a work in 12 days, and 40 boys
1 do It m 8 days ; which will be the cheaper, to get
l!hi
.^ , ARITHMETIC
boys to do the work at 40 ce"ts each per day, or men at
7f cents each per day, and how much ?
^t^^Ut!^^^^ wages for .3
4)^«r^^ "A^BrlT^g.^ to^ethe.^ -
a^s;a5^¥^E5^S&^^^r
<^°7;r,raTnr„7arl"$r8o a day and spends $4 a week,
^ritt^Ltn^eX^dT;-^^^^^^^^^^^^
4)*^ W%TS:o'^e^t5Y3 HnT-'*'^^^-
^ilVtrekl^Tva-^"^^^^^^^^
much a day does each man earn ?
^^-^o? , , ^^^,. Ct 7c a dav. How much
shoas"r="££B''"^"^''"
first day of the month v .s " d;>';^„^y , „rtain
^f ^f'Savs'trhrSaS "rLf." day? more he
™ u d ha/e rec'eiCei $.67.5°. r.M his dady wages,
t) A -y hires with a f-er f;^v„ years^npon^tK
r*^ 'if her'cei:er$'..5o'tiiefirst month, what wm
his entire wages amount to r
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 him 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 boys to do a
piece of work, giving a man 60 cents a day more than r;
boy. They are engaged nine days at the work, and
all together receive $70.20. Find their daily wages.
(8) A boss carpenter agreed to build a woodshed for
$96. He employed two men for $1.25 a day each, and
they finished the job in 15 days. How much per day id
the carpenter make ?
(9) A man engaged with a farmer from the ist
May to the 29th Nov., inclusive, at $1.25 for every day
worked. Allowing 33 days for Sundays
during this time, find how much he earned
(10) Make out the following pay sheet
hours.
of
he
and holidays
a day =10
M.
T.
W.
T.
F.
A....
10
6
10
9
10
B. . . .
10
10
10
9
9
C. . . .
8
7
s
10
10
D. ..
9
10
9
ID
8
K. ..
10
5
10
7
10
5
4
5
5
3
$2.50
$
$2.00$
$1.80$
fi.6o$
$1.50
$
$
64
Exercise
ARITHMETIC
XXXVI.-PROFIT AND LOSS.
(0 1 buy 3048 bus. potatoes at 88c. a bus., and sell
^^if\Sl^^^^-o?SS\ic.andsoiaUati^^^
^^^"^n^oseby buying 307 cords of wood at
sell it at $1.31; y{^^ l°uir""vch weighing V7 H-- net.
(5) Bought 13 ^^ t^l/whole for $500. Find my gam.
at 7c. per lb., -^"^ '"^ «^ wnr h of su-ar and sells it aia
pifeo^e^v^^^l^rr HOW mucU aoc. Ue
profit on every $100 ot cost.
"^ ';; A grocer mUes together 45 ms.co«ee . on>;;-.c.
^ "- V ^^U^S hTgSnt^ioseld how much ?
34c. a lb. Dots ne gel at 7;c a peck, and
(9) Aboybought .epecfeo nut-at 75^^^^
.oldthemfor '°'^- %''""'• """"cents a bus., a grahr
"^To At™er bought 30 cows for SS4o;.>;efe.^
rSleSforiiVTear^^^^^^^^^^^^^^
how much ? , ^ j2 75 each, his
(,.) Abook agent bough 90 books^at^^ 7,^^^^ ^
Srnna\^:faL,>nWweresoMf.^^^^^
,i' fln^d foKr . S ?- a^dcen; How much end
he lose ?
i
PROFIT AND LOSS.
B.
(i) A fruit dealer bought 243 dozen of oranges at
13c, 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 destroyed 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 1 5 bush for waste, would
he gam 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 cents. How muc h did he clear ?
(5) A farmer bought a horse for $i2q cash ; he traded
hun for a yoke of oxen, and gave $13 into the bargain.
One of the oxen died, and he sold the other for $7^.
How much did he lose .''
(6) A man bought 123 head of voung cattle for $27.50
a head. He paid $11.35 -i head for fattening them, and
then sold the entire lot for $6150. Hov/ much did he
gain or lose ?
(7) A drover bought 247 sheep for S5 each. It cost
$149 to get them to market, and 8 sheep died on the way.
He sold the remainder at $6.7; a head. How much did
he gain .-'
(8) A butcher pays $119.25 for 159 turkeys. At how
much a pair 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
he gain or lose, and how much ?
(10) A grocer bought 12 bbls. of pork at $14 a bbl.,
and letailed it at loc. a lb. Find his gain.
(i i) A farmer bought a 20-acre field of ripe wheat for
$250. Hepaid^$i.45 an acre for cutting and saving, j.
cents a bushel for threshing and cleaning, and $2 a load
(46 bushels) for teaming. The wheat yielded 23 bus. to
^1
66
ARITHMETIC
the acre, and was sold for $i.37 a bushel. How much
did the fanner clear ? ^^i.or -,
(1-2) A merchant buys at 65 cents on the dohar a
bankrupt stock which cost, per invoices, $5250. He sold
half of t clearing 5c. on the $., a third of. he sold at a
gain of 7.. on the i,and the balance at a loss of 12c. on
the $ Did he g-in or lose on the whole, and how much ?
d'^) A man buys a bankrupt stock at 57c. on the *.,
which cost $2500 per invoices, and sells it at an average
of 75c. on the $. How much does he pay for the goods,
and how much does he gain ?
Exercise XXXVII. -ANALYSIS.
A.
(i) If b yards of cloth cost $8.40, what will 24 yards
^^^2) If 10 yards of cloth cost $14.50. ^^1^^^ will iQ yds.
(3) How many apples can be bought for 11.36, if 23
apples cost 8 cents. .1 u
(4) If 72 men do a piece of work m t/^ days, hr long
will it take 288 men to do the same work ?
(5) How long will it take 9 men to do the same amount
of work that 6 men can do in 1 5 days ?
(6) If 5 bbls. of flour cost $60, how many cords oi
wood at 59 a cord will pay for 3 bbls. of flour ?
(7) If 8 horses plough 12 acres in a day, how much
will 20 horses plough in 2 days ? , . ,, , . :ii
(8) A bankrupt pays 59 cents on the dollar ; what will
a man lose to whom he owes $13675 ?
(9) A dealer bought 468 turkeys at $7.50 a dozen, and
sold them at $1.50 a pair ; find his gam or loss.
do) A newsboy made $100 in a year, by buying papei s
at 20 cents a dozen and selling them for 45 cents a dozen.
How manv papers did he sell ?
(11) If a train moves 48 leet m a second, wnac
rate in miles per hour ?
ANALYSIS.
67
th^.^'f^ ^ '''°'''^" '^^"^ ^^^'^ ^^ ^° cents a dozen, irainine
thereby 2 cents on each dozen. How much did 6^ egg!
B.
}r.S^ ■u'^'' "'^" "^'1" '^"^ ''' P'^c^ o'' ^vork in 60 days how
long will 1 5 men take to do half as much ? ^ '
(2) Three turkeys cost $2.25, and three g-eese cost as
much as two turkeys. Find th^ price of 5 turkeys and 4
(3) If 6 men dig a trench 34 yards long in 10 davs
how long a trench can 20 men dig in 15 da/s ." ^''
^rrM^ , ^^^^^^ ^^''"s f6 while his son eirns •K-. -r
When^they both have earned $,05, how much wUl belo;!;
as \^LuJ ^l?''5^s cost $192, and 2 horses cost as much
sheep. ^^' ""^ '^' '""^'^'"^^ ^°^^ °f 5 horses anS 6
wil/f?t![ '^,"l^",^^,u'ld a wall in 18 days, how many men
the time?' ''"'''' ' """ '^'''' times L' long in ha'lf ^he
momhs^fo,"^? T ^u^ "" '"^'J^ '^^^ ^"^'^^ ^'" ^ast him 4
months for $1.76. He can buy a black hat which (1
last h,m 9 months for $5.67. How much w II be saved
'" ^l^'')? '7 ^"y^"^ '^'^ ^^'^^P^' kind of hat ;
?..n , 1 I -Tf^''^ \^''^ °^ ^ ^^™ «f '87K acres be
m^^hs? '' '"'^ ^' ^'^ ^"^' "^ ^ squar/i;.ile for 20
day?? ^ftpr.'l°^ ''°'^ ^' '° '^^ ^°"^ ^'y 25 men in 16
<ia>s after 4 days 15 men go awav. How lontr will it
take the rest of the men to ffnish the work ? ^
. (10) A clock which loses 4 min. in i^ hours is rn
mm. fast at midnight on- SundV What o'clock w 11 i?
mdicate at 6 o'clock on Wednesday evening^ " ''
$;8 -'o ul '"''^^^^ ''^^'^' °^ 4 men and c boys are
tt'£ilypeTof e" h .. ^^'"^^ ^^ "^"^^^ '' ^ '->'' ^^-^-^ --
for «l"L" ^' j'^ -/oranges containing 36 dozen was bought
?ol£ F^nd fh'"^ '"' ''^^''^^ °^ ''^^'^ q'^^"cr of a
<ioiiai. i<md the gam on it.
'%
\mM^
I i'i
RITHMETIC
(i) A drover bought .< number of cattle for $4050. He
sold 34 of them for I1836, gaining $306 on thosi sold..
Find how many he bcught and the cost of each.
(2) Dividvi $87.50 among three boys A, B, and C, sc
that for every $1 A gets, B may gt i $2 and C 'I4.
(3) A man exchanges 48 sheep lov 192 himiis, when iz
sheep are worth $48. Find the difference betweoi the
cost of 9 sheep and 9 lambs.
(4) A boy buys 30 oranges at the rate of 3 for 8 cerus,,
and yells them at the rate of 5 for 14 cents. How much,
does he gain ?
(5) A purse and i;he a>oney in it were worth $21.63 ;
the amount of monev was six tunes the cost of the purse ;.
find the value of the pu se.
(6) Divide S28;':i; betv/een two men, giving one three-
fourths of what the other receives.
(7) A railway chi'.rges a cent a mile for the first 50'
miles for carrying a cord of wood and then 3 cents for
every 4 miles beyond the fifty. What will it cost to carry
250 cords 90 miles ?
(8) If a bushel of wheat makes 40 lbs. of flour, how
many barrels of flour can be made from 4263 bushels of
vvjieat ?
(9) If a boy walking at the rate of 4 miles an hour,
takes 18 minutes to get to school, how long will he take if
he walks 3 miles an hour ?
(10) Goods are bought for $5000 and sold to make $30-
profit on every $100 cost. What were the goods sold for?
(i i) A man bought a fanii for $3600 and sold it clear-
ing $25 on every $100 purchase money. Find the selling
price.
( 1 2) An agent sold a house and lot for .f 6000, and for
his services received $5 on every $100. How much did.
the owner receive
D.
(i) I buy groceries to the amount of $475, and by-
paying cash I get $5 allowed off every $100 worth. How
much do I pay ?
SHARING. 6g
(2) If the tax on every dollar's worth of property is -»
cents find the taxes on a house and lot valu( i 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
tax<-s on property worth $3500 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; 3^475 ; for one year?
(8) If the money lender received 5 cents for the loan
ot 3)1 for one year, what would he get for the loan of S^so
for 2 years ? for the loan of ^300 for 4 years ? for the loan
ot 31425 for 3 years?
(9) If he received $5 for loaning Si 00 for one year
Avhat would he receive for the loan of J630 for 2 years '
.t74i for 3 years? $500 for six months? $224 for ili
years ? and 5360 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 J4 for $100
How much money did he withdraw at the end of the
year ?
I
«
Exercise XXXVIII SHARING.
(i) Divide 16 apples between John and James, tjiving-
John 4 more than lam.es. ' & &
(2) Divide 60 marbles between Thomas and Henry
giving Henry 10 more than Thomas.
(3) Robert has 6 pigeons more than William ; together
they have 22. How many has each ?
70
ARITH.METIC
(4) A man walked 52 miles in two days. The first
day he walked 6 miles more than he did the second day.
How far did he go each day ?
(5) Divide $1000 between two men, giving one I120
more than the other.
(6) If $2845 be divided between A and B, so that A
receives S265 more than li, find A's share.
(7) If $1631 be divided between A and 15, so that 1>
receives $161 less than A, find A's share.
(8) If J80 be divided between A and B, so as to give
A $7.40 more than B, how much will B receive.'*
(9) Divide Si among Frank, Harry and Tom, giving
Frank 6 cents more than Harry, and Tom 4 cents more
than Frank.
(10) Divide 50 apples among John, Annie and Mary»
giving to John 2 more than to Annie or Mary.
(11) Divide $127 among three men, giving the first
$3 more than the second, but $7 less than the third.
(12) A man sold 3 sheep for $34. f^or the first he
received $4 less than for the second, but $3 more than for
the third. What did he get for each ?
B.
(i) Divide $541 among A, B and C, giving A twice
as much as B, and C $25 more than three times as much
as B.
(2) Divide $1500 among A, B and C, so that A may
have $60 more than B and twice as much as C.
(3) If $3973 be divided among A, B and C, so that R
gets $23 more than A and $27 less than C, find the share
of each.
(4) If %:^y7 be divided among A, B, and C, so that A's
share is $7 more than B's share, and B's share $5 more
than C's share ; find A's share.
(5) Divide J82.60 among 27 men and 37 boys, so that
each m.'>.n may have three times as much as a boy.
(6) Divide $89.16 among three boys, Lyle, Bert and
Robbie, so that the first boy may have J2.18 more than
the second, but 80 cents less than the third.
SHARING.
71
(7) A mixture of green and black teas is made, 3 ounces
of green to every 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 J398 among A, B and C, giving l\ three
times as much as A, and C $6 more than IJ.
(10) Ernest has $1000, Warren has as much as Ernest
less $82, John has as much as Ernest and Warren and
S694 besides. If the whole of their money were divided
equally among them, how much would Warren have more
than he has now }
(n) 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 S840 among A, li 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) Divide 27 bushels potatoes between A and B,
givuig A 2 bus. 3 pks. more than B.
(5) Divide $500 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 $r 10. The
colt brought $15 less than the cow, and the calf $25 less
than the colt. What did they each bring 1
(7) A woman sold two tubs of butter 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 r..« nuts, oranges and apples,
135 in all. There are 3c .5 pies and oranges, and no
oranges and nuts. How 1 .any are there of each >
f::f
;
72
ART, ',
to each ? ^y-'-j-j iun\ .ituch Vi in oelon""
Exercise XXXIX. -CANCELLATION.
What is the quotient of:
' fx""-. 'r,' ; V ^^"^^^^ 4x6x7x13 ?
y A:^^^j;^£i^st;^x^:^'^^^^-^
55x20x84x39x14x44x96
(6) 36x 38^<^4ox4^. ^ 44 x 43 x 49 x , so
3ox3ox57x78x75inn^^^^l^^
(7) ^^2111^154x^6x^x58x60x63x64x4
40x40x85x27x48x88^29x84-^
(8) il>03_xi4_x r5_x_^6 x 3^,0 x 21 x 2 x .4
39x56x40x3. 7ox3j^^ —
(9)31x20x22x24x25x26x27x28x30x32x33x35
^ro^ /r'''''-''''^^^^'-^~'5'^'^^^Sx6^
conli^ii^' ^2 pL?:":/^ ?:!::^ -" !,5 bales of cloth, .ach
carpet of '75 y.^ds'elchl; '^^^^^ ''' ^^ '^"^ ^^
B.
ft. ide and
CANCELLATION.
u-n and 8
n's share,
I. When
iU helon.r
< 22 ?
X9?
73
wn/fh\^'"'' ^r'^' "^ ^'°''^ containing 30 yards each
worth per yard? ^ '^''^ '"'''' ^'^^' ^^^O"^' '-'oth
bus^tr'cb£';;?^^"!f^-V""'^'^ ^^'^^ ^^ ^-« -
^et? ^ '^ ^''•' '^""^ ^"a"y yds. does he
22 i£ ^wmh?.'">'';' h'^ P'S^" °^^^"^^^' ^^'-^ch containing
iong 10 ft 8 in. wide and 6 ft. 9 in. high ?
V7; /v pile of bricks is 4oy')7v7r f»^* u
bnck. 8x4x2 inches are tU°1n1ire'^i,?r' '^^^ "^"^
(each^i3^<^'i, t^"x r i:^;^;/^^;!' \< ^t^ -^ ^5' -de
$12.50 a thou., q p"" ^ ^ 2-^ ^; ^hat is.the pile worth at
(9) Find by cancelHng the simplest value of_ 69^0
45 X 25 xy
■ each
)lls of
i and
4, 36
.t -'
1 1f
MECHANICAL WORK.
Exercise XL. -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
75698
56987
69875
98756
87569
75698
56987
6987::
98756
(3)
65847
58476
84765
47658
76584
65847
58476
84765
47658
76584
65847
58476
(8)
98756
87569
75698
56987
69875
98756
87569
75698
56987
69875
9S7=;6
87569
(74)
(4)
58476
84765
47658
76584
65847
58476
84765
47658
76584
65847
58476
84765
(9)
87569
75698
56987
69875
9S756
87569
75698
56987
69875
98756
87569
75698
(S)
84765
47658
76584
65847
58476
84765
47658
76584
65847
58476
84765
47658
(10)
7569;
56987
69875
98756
87569
75698
56987
69875
98756
87569
75698
56987
SUBTRACTION.
Exercise XLI. -SUBTRACTION.
75
the ^::^-i^'75^?l^V^^'^ -session n-om each of
(4) 5554035; (5/5659.-46 ' ^"^ ^^^^'^^y^(3) 5443534;
(9) ^^59i.o8r(.o) 67^3^31?^-' ^^^ ^^'56564; (8) 6377886;
Exercise XLII.- MULTIPLICATION.
;;;si<spsisH;::::
%\^u'V ^'^ f-«54; (14) 3428. ; (,5) 45708^ '^-7
Exercise XLIII.-DIVISION.
(3) 1960192493568 0,jy;74978,6 ; (2) 9Soc»,62467S4 ;
(3)^;!;^;;^-r;:^--^-w,794S4;73.96,
Divide by 9 ten times in succession- ^lo^ -.7-7 .^s-^
694356; (1036987808925808; (iT=;u8;7 /•SS7^f ^
Divide each of the fol o^vin^- 1 wV.'Ce fimf/ n
cess.on : (13)278424834; (,4)4' 76'.7l,6"f/;"^^^^^
•,,16)035274472. -^ • ,- J/ j3'5^hvo4o
succ^ss'lon'^r7^°n '^' ^'"^^;'"^: '^>' 347 three times in
i8^^8^7^2^^ ^^fX^i^^^, 13544863798.4 ; (.9)
rf ■
FACTORS AND MULTIPLES.
Exercise XLIV.-Pr.me AND COMPOSITE
NUMBERS.
■- W!
45, Sr, 57, 63 and 75 ? ■^' '' ' '' "' ''• =7, 3i, 39, 41, 43,
3 Fmluhe";™,,";?™- ""■"''"^ '«s than 30.
■ind 50. "'" °' "'= P'"'« numbers between 30
35 .-.ml 55"' "' "" °f "- ™'"Po-te numbers between
nu,£rs ',^lt„™<S r,K,r '"^ P"- -''i <'- composite
,„, (6) Write do™ an the integers, ess .ban 35 and pritne
.ha,'l''Xe'',o"^r'"'^'"'^»"^ between 80 and ,00
.0 if ^ '^"'^ ''°"'" "- '"«^-- less than ., and pri^e
^«/lr|:i;::t-:^---™r<.e.te,e. between
3 aidi ' "' """"^"^ "=^^ •"-> '50 .-.re divisible by both
5 aid i ?"'■■" """''^^-^ '-^ '"» '75 are divisible by both
3 aid's ?'^""' ""'"'-- '- *a„ .00 are divisible by both
zS.
>SITE
■ime and
h 41, 43,
30.
«een 30
':)et\veen
mposite
;1 prime
ncl 100
prime
'tween
y both
i both
■ both
PRIME FACTORS.
Exercise XLV.-PRime FACTORS.
?T
210 ; (7) V4 ■ rS^ rof V V °^ ' ^^^ ^'- ' (5) 128 ; (6)
and(22)4s'6456.^^^' ^ ^^"'^^^' (-^0)32320,; (21)3453^3:
(32) 64, 96, 112, i36T(33f7r\^.l'/;.'^ ;-^'^: ^8°' 2,6;
510. ' ^ ' ^^^^ 75, 12:,, 163 ; (34)306, 408,
Find'?Lm^' P'"''"'-^^ °' ^ consecutive numbers is 756.
Find'them' ^'"^"'^ ^U consecutive numbers is ,680.
Fimf ?Lm' P'^'"'^ °^" ^ -"^ecutive numbers is 2730
-. ^'^n^^Z^T'' °' ^ "-^- - ^> 3, 5, 7 and
^3S^J^^^^^it::!?,f--berare3,2,,^
nun^^sb^^^';.^;^-^^^^^^^
Exercise XLVI.-GREATEST COMMON
MEASURE.
770; uf^<2llfd^V^};.%3''A,T''^^'!S''' 735 and
4141 : (7\ >■,-,,, „-j .^'._*5-' -3* and i6o ; (6) t628 and
«VIooand-,io, (4 SarU^^j;^',';' -■' ■35«3 r(9)
7S
ARITHMETIC
it
I
I"
M--
B.
W33a'nd$85^t) 'Vs^llfa'nS'^;;' ?34 rods ; (^3)
ft. and 2788 rods •C6ro''r?i 1^^^ ^''^^•'' ^5 12341
$1463 and 1T175' Jems- 8^60^'? "^ '^fl "^^""^^^ 5 (')
^narbles- (c) liL^h' ^^> ^P^9 marbles and 23023
(13) 2769 Ss and 3195 tU^^^^^^ ""^^ 2057 thirds;
C.
'exa^ll^'^asL^'rhe'Sth' ^'wM"^^^^^ ^^^^ ^^at will
land 3^2 rodsTo;jt^T8^'ror^^^^^ ^' ^ P-- of
ft. ind 2'o'ft^:::e" cSto th^r"-^ ^^'^P^^^'^^^y - ^^-^ '6
e,ual length. . VV^arv;a"s"ti;i^l^nXVrpTe^^^^^
.allSs.'^Tind'thTlaSt If^T'^'^'^ ,'^" ^^^ 5o88
both cisterns ^ ^ ''^^''^' ^^P''^'^^^ «f measuring
vjy VA nat is the ereatesf Ipnrrti-. ^f ./-'"'"'>•
used, wiihoue ciittin., ,„ nm' f"^ °^ ™' "''" "'"n 1«
feetby2S8ofee" tirnvmlf, T'^'rV'' " f'"™ 3588
it if tfe fence te six mi;: S^"//"'^ "'" ""' "''>""-'' '"^
893 2u 96rre'spectelv'llv"r"'"" f '^''' '*™ f™"
a measure? '^'='P^"''='>'' '^a^e remainders of which 7 is
.o/^fr'b'r;jt rd^n;^rr,t?f ^^^^ ''v^/^
"::irTh:d''st erch-'i;'"-"-- ^^°«n^^ ' lie
anio*f '^^l!^^::^^ "-' - a factor of 54,80,
98;|^a|j^:;Sst»?r^tS;--
s.ii'thar„^itf ,:Li'^L 's7r\°vti™fr? ■"--^^"^'
GREATEST COMMON MEASURE.
79
(11) Find the length of the longest chain that will
fn feet^ ""^""'"'^ ^^°^ '"• """"^ ^"^"^ '"• ^'''^ ''^"^^^er
(12) Three drovers, A, B and C, bought sheep at the
cTLT^?^^'}?'"'^' ^'' ^^^^'^ ^"^^ ^'°2' I^'^ $138, and
C s :|)99. t ind how many each bought.
Exercise XLVII.-MULTIPLES AND COMMON
iVIULTIPLES.
Fomi a table of the first nine multiples of : (i) i v
35 ini ]o'f (T4 ;^ Ui^:' '""'"■' <^°> ■' ^"^ '■°-' <="
Of w-liat two integers are the following common
tiples : 23) 30 ; (24) 35 ; (25) 4- ,
96; (29)121 ; (30) 132; (3,) 187
(34)289; (35)631 ; (36)221.
(26) 56 ; (27) <S4
(32) 119; (33)
mul-
(28)
169;
Exercise XLVIII.-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, 12, 15, 18 and 20.
(8) 4, 5.9, 12, 15 and 20.
(9) 10, 16, 24, 40 and 64.
(ro) 36, 4c, 60. 7c anf] h^
(n) 25,40, 75, i^and "
120.
8o
ARITHMETIC
('2) 13, 23, 26, 39, 46 and 78.
(13) 4, 6, 8, 9, 12 and 15.
(14) 42, 52, 36 and 156.
('5) 3) 5> 6, 8, 15, 20 and 24.
B.
(I)
(2)
(3)
(4)
(5)
5040, 7770 and 1848.
24, 108, 180, 84, 96, 12 and 48.
i«; 35,. 54, 64, 70, j-^, 84, 90 and 96.
5 It. 6 ni. and 7 ft. 4 in.
5 lbs. 4 oz. and 4 lbs. 8 02.
(6) 6 rods and 66 ft.
(7) 12 yal. 2 qts. and 10 gal.
(8) $6061 and %-j^Xj.
(9) I acre and 1728 sq. yards.
(10) I pound Avoir, and i pound Trov
(11) 320 rods and 880 yds.
(12) 16 days, 18 hours, and 21 minutes.
C.
(i) 112 sixteenths and 133 sixteenths.
(2) 78 twentieths and 102 twentieths.
(3) 105 fourths and 126 twelfths.
(4) 144 fifteenths and 108 thirds
;1( i^^T'''' 9 fif^'is and 15 sixths.
or ,. T ^^''^ ^"-^'^'^ """'^^^^ '^^^'ch, divided by 3, 7 I,
A^l ^"-^ a remainder of i in each case. ' ^' '
.midin\?hm'r <tf?^n''' sum of money that can be
paicl m .-^4 bills, in $5 bills, or m $10 bills .?
(6; What IS the smallest sum of money that ran h^.
counted out .n 5 cent, in 10 cent, or in 25 cent pieces"
^9; vVhat is the least weit-ht of yrain th-^f ,,nii „," 1
(11) \yhat is the least number by which 217 must In
multiplied to yield a multiple of 279? ^ ^^
(12) What IS the least sum of money with which von
01 sJatc3 UL 13 cents each, a.^.d have no change left ?
LEAST COMMON MULTIPLE.
8i
D.
(i) What is the smallest sum of money that can be
$Tohms'? ^^ '^'"'' '" ^4 '^'"^' '" ^5 bills, in $6 Mis or in
(2) Find the least number which, divided bv 6 bv 8
by 15 or by 21, leaves in each case the remainder 3. ^ '
hv S . 1 '^^ "" ^^^'' number which, divided by 16,
by 18 or by 24, leaves m each case the remainder 7 ?
th.= V 1" ^S^.P'?"'? ^''''^^^'■' °f ^26 and i960; usinff
the e fac ors, find the L. C. M. of the numbers. ^
TArA^' vVhatisthe least number from which 1224 and
1656 may each be taken an exact number of times ?
(6) Fmd the L. C. M. of 7, 9, 11, m ic and 2r •
She's' ^- "fVf'- '^ ^^^^ «^ the'give'n^il^bers" and
hnd the sum of the several quotients.
..V^j^^!^^' '^ ^^^ smallest sum of money with which 1
cattle dealer can buy sheep at $4.50 each, or p gsT$7 co
each, or cous at $45 each, or horses at $13? eacl , anS
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 exS
7 x^'i.'^f ^°""^'- "°^^ "^^"y dozen hkd she ?
(9; VVhat is the smallest quantity of wheat that can
"(To)"wr' '" "^'-^^ ^°' t' ' 3°' 35 or4obushe"arts?
rr.l\A K I" "" ''^'l^"' ""•''*'^'' ^f dozeus 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 ofifinto companies of 60, of 7'
ot 80, or of 90 men. Find the number in the battalion
MISCELLANEOUS.
Exercise XLIX.-ON THE SIMPLE RULES.
A.
(i) Find the value of 9087064 x 89706 -i- 336.
(2) The product of two numbers is 1270374, and half
of one of them is 3 1 29. What is the other ?
(3) One-third of the divisor is 1226, and one-fourth of
the quotient is 676, and one-fifth of the remainder is 343.
Find the dividend.
(4) How many times must 133 be added to 70 times
^7 to give twenty-six thousand, one hundred and seventy-
three? '
(5) By what number must 1999 be divided, that the
quotient and the remainder may be the same as the
quotient and the remainder in the division of 109 by j i ?
(6) The sum of 27 equal addends is 98642880. If one
of the addends be divided by 10, 8 and 4 in succession,
the result is 7 times what number ?
(7) Multiply 7648 by 687. Divide 6897996 by the
factors of 63. Give the sum of these two results.
(8) From seven hundred millions, six thousand and
seventy-five, take six hundred and seventy-three millions,
one hundred thousand and ninety-seven. Multiply the
remainder by 97, and then divide the result by 897.
(9) If five times the minuend is 3784875, and seven
times the remainder is 356335. Find the product of the
subtrahend and the remainder.
(10) Multiply, using factors 766485 by 63.
B.
(i) Multiply 83102254 by 7090.
(3) i' ind 78 times the sum of 894967, 38739, 69297
83
ON THE SIMPLE RULES.
83
than one million " °" '""''' '" "«= °*e,- less
ma^f iSc'.r;s^rsi,ri';r4'?"""'^'' ^™'" ^^'^34 .»
m.lS.f^eli'T"'' ""^^ »"=' ?^° be added ,o 5.4 to
duc'tV'slj^ ''"'''' ">' "^''^"^ ^""^ 'he pro-
.ho^'^L'^rnfse'vS^^V^^.PTSV^
C.
by iaU'""*'^' '^^''^'^fi by 7869 and divide the product
(2) Multiply 97653, by 999, short method.
thei'i^d'eM-'ires°ul'."byP,T'"" "' ^«7 and eight, and
8903^ ^'""^ '"' ™'"'= °f (363S0250-,35)-(4034,56^
738i?^ and'' sS'^Talfe^^lSo, '/'''■.. ''39, 667586,
the d,fl-erencer98, Jnl'^di^i^t'^h^TotctlTir"''''''^
(7) Divide one billion by 256
.JoV^'v^r.o!<i;ii;r',i^-;-t^.*'^=''^"'' ^^ '-
- ^ - -•'•••n5_ij-..t.
(9) Multiply 456789s by 192648 by short process.
(10) Square 6384 and divide the product by 3192.
84
ARITHMETIC
BHS
'■'U
D.
b I'L^"^^'^'^ 4786926 by 7869, and divide the product
(2) Divide 72983000742 by 904307 and prove the result
by multiplying the divisor by the quotient.
(3) Multiply 428009700 by 908600, and prove the
correctness of your result by division.
iS^lilf'"^*]'^ ^""u' difference, product and quotient of
1863675 and 825 ; then add the four results.
}ll li''?-^Y ''.^^o^ of (68379 X i4739)H-987.
(6) Multiply 1698732 by 9998, short process.
(7) 1 he quotient is 908 times 987, which is 227 times
the remainder. If the remainder is 5 less than the
divisor, find the dividend.
and^S^ 16'"*^ ^^^ difference between the squares of 7684
(9) The quotient is 6987, the remainder 219, and the
dividend thirty-two millions, five hundred and fifty-two
thousand, six hundred and fifty-two. Find the divisor
18 ? ^'^^ ^3^7S8, by what number must I multiply
E.
(i) Divide 108419716001 by 18748005.
(2) Multiply 9876543 by 216546, short process.
y( 2. ^''t^i number is 7006 both divisor and quotient ^
(4) The difference between 83372 and the product of
the two numbers is 70300000. One of the numbers is
9402 ; find the other.
(5) If the remainder is 68849 and the subtrahend
25703. find one-seventh of the minuend.
(6) The divisor is 761, the quotient 1439, and the
remainder 27. If 9. be added to each of these three, by
how much is the dividend increased ?
(7) Multiply the sum of 59404 and 47675 by their
difference, and divide the product by 7 x 13 x 19
(8) What is the least number from which "1987 and
297^1 may^eachJDe taken an exact number of times ?
v9/ vTiiat inuliipic of 595 divided by 1591: mves as
quotient 595 ? ^ ^^^ ^ ^
I
ON THE SIMPLE RULES.
85
th/'°\?^''^'^''V "^456789 from 987654321 and prove
the result by addition. ^tJ"-' ^1111 pio\e
F.
^;,-9^ The divisor is 54321, the quotient 1234s and the
^'^',dent 670605090 ; find the remainder. ^^
(4) Multiply 507308 by 4620, and verify the result bv
(5) Multiply 2468642 by 29 in one line.
2jS^dTar'!T^'^U ^"'r^'^^ '^>' *^" difference between
rT^FinH^H ''^" make the sum of 20948 and 45021 ?
(7; i* ind the remainder in subtracting- 6631 as manv
times as possible from twenty millions. ^ ^^ "^
(8) If 217 be added to a certain number it will contain
231 JUS 129610 times. Find the number.
(9; VVhat number divided by 537 will sWe 120 for n
quotient and leave 76 as a remainder.? ^ ^ '^
(10) I- ind the quotient obtained by dividinjr the pro-
duct of the seven whole numbers next in orderWe^ 3^ by
the product of the first seven whole numbers. ^ ^
G.
cess.'^ ^'""^ '^^ P"'"'^''''^ 0^897643 and 999998, short pro-
(2) Find the product of 11 88 132 12 and 2 34;678oi
hav-ing s.x lines of figures when the'sokuion is c'c:}nS
the riU nder''Tl'' '^ '""!f '^-^ ^"^^'^^^ '^"^^ 34 times
(A\Tul 1 ^ J^"^ainder is 358, find the dividend.
JA) The product of two numbers is 760069388 and one
milhin.""""''''' ^'^^'^ "'"^ ^''"''' '" succession from one
(6) The sum of the quotient and divisor is 143715.
>
86
ARITHMETIC
and
and
ti^'cSildl"' ''*'^^' '' ''^""' '" '^'''' ^''^^'•'^"^e. Find
"0.7^^ KH "'"';'P''.^^"'l i^ 7869 and the multiplier is
hvf hv I "^"'^IP^'^.y/^^l multiplicand be each increased
^ ^«N \r V'' '."'''' ''■■'' ^'^^ product be increased?
wot Id 1 e 6uSr''T/''r ^'f ?^- ^'^^''^^ '^ ■^' ^'^^ ^"^tient
wouia 1)664184. J he dividend is 789482? and the re
mainder 193. Find the divisor. ^ *^
(9) Seven times the minuend is 163912, and one-
seventh of the subtrahend is 2643. How much is the
remamder less than ten thousand?
th^i- ^^^^*^^'^'f/>r 's 2034 and the quotient 5901. If
the divisor were 843, what would the quotient be ?
H.
(i) Find the difference between the laivest
smallest numbers ending in 33? between 39867
(2) The divisor and quotic V nre each 7641, and the
Send!' ''""' "^^"^' "' '■"■' ■ P°^"^'^ ^^'"^ the
(3) The remainder is 56 r and the divisor the smallest
whole number possible. If the ouutient is as large agaTn
as the divisor, find the dividend. " ^ ^
(4) The product of two numbers is 11211- What
would the product have been if both multiplier and multi-
phcand had been nine times as large ?
^,-^IL^q"''^'''''^ ^^J ^.'"'^ ^''"'^^ °^tl^^^ following numbers :
add th/r;n?^^596, 834, 10238, 4300, 539, and 1000, and
aad the lemainders ; short process.
(6) The product of the divisor and quotient is iq;oS^
and the remainderi 6758. Find the dividend.
(7) The sum of five addends is 243029 ; the first three
addends are 18963, 26876 and 6i589rihe fourth addend
Js 17173 larger than the fifth. Find the fourth addend.
(8) The sum of the remainder and subtrahend is
'^o..43, and the sum of the minuend and subtrahend is
103810. P ind the remainder.
GENERAL REVIEW.
Find
il"soT;""">' ''■"" '""^' 347 be acMcd t„
make 98895 ?
itself to
23 J
(10) Hou' many times must 127 be added to -n
I to give 24170/ "Jt. auaeci to 59
times
Exercise L.-GENERAL REVIEW.
need to complete the full number ? ^''^ ''^^ "^"^^ ^^
(3) A farmer bouL-^ht 20 stPfMx nt «^^ 1
keeping- them 4 weeks •t?ro.rnf-^^ '''"'^'' '"''^ ''^^t^'-
two of them diid. At how m ch J*-.;,'""' ''^^^'' ^'''' ''■'''^^
resttog..in$56onthctn;nsaSo,r' """^ ^" ^^" ^^-
How much did she get for each ? ^ ''" '"'' '' ^'""^^•
(6) A grocer mixes 12 lbs. coffop nf oQ . . , .
lbs. at 23 cents, with lolbs. of chfcon' fi TT f"^ f
what price per lb musf ho =nii fi ' ^ ^ ^^"^^- ^t
oil the whole ? ^ ''" ^'^'^ "^'-'^^"^■^^ t" iiain $4.50
HeSld^4oTd:emSlo,rr""'"^ "^ "^^"^^ ^^ ^405a
(9) A butcher sold 8 turkevs nnrl 9 r r ^
getting 30 cents apiece more fm-t i^'^'^'f ^"^^ ^'^'
goose. XMku did lie g^t fo?".d". " ^"'^'^^ ^^^" *"-• ^^
(r.) A farmer bough, 75 ,o„. on,ay a, $,6 a ,-„„, and
IMAGE EVALUATION
TEST TARGET {MT-3)
/.f
\.\J 150
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1.8
IL25 III 1.4
1.6
Sciences
Corporation
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23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 872-4503
^p
If^V^^
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i/.A
88
ARITHMEnc
Snde/hTpSTn bu,f "'"'<' ''' ^^'^S each. The re
of the form for w ,Tch he p'id r ^f i^^S^S. The ,„' c
;■;■; ac,e, and the other $87 ak acre Hn"' "™ ""'" »''4
"oth farms ? ' ''*^'^'^- "ow many acres ■11
ibs/;i'^;:L?;r\tV".»'=*ir''i'; " ""■•,°'"^ '«■"'-' 3
weigh ? ' - ^"^^r. How much does cmcIi
wai;,t^;f,^3',i:nran'cor';T ^^'^ ^^^ ^^•-- -hich
. ('5) A man paid out t.no'"'^ ^^V^^^^ i"aves.
g'vng two fewef ;\^slan fives '"^^^^ ^^ ^5 bills,
, 06) On the first of Apr i T T? Tf'""' °^ «^'^«
for $37 50 ; he sold her orf the i s^ s''^"^ ^«"^^^^^ ''^ ^<>w
her milk during- th-^t tfm^ ^^t September for $^0.
Bland's gain wi' V. /rfi'ndle'f ^f f.^'"' '^ ^^ •'
month. ^^ ' ""'^ t"e cost of her keep per
, (17) Find the dailv wncr^c ^r
hours per day, and ?ZSL/i'' ^^'^^ ^-^o works 10
a cluch 3 ft. vVide and 4 f? 'deep f r'h^ ^''^ '? '^^"^^"^ '>f
per cubic foot. ^ ^P' ^* "^ charges half a cent
-h-e'p.4etr.,;^ S fAs'TU" l'™'^,"' "- -' """
second, but 3 yards lonu-prfi ^.P''f' ^^^o'*tcr than the
length of the^^e^ond ? ^^"^ ''^^" '^^" ^^^'^d- ^hat was the
anc/s^dlt S^t^rf?!^:?--^;^ /-c, f.r 5^5.00,
(20) A and B had "E-'ovS I ^ ^>a'" o"" loss.
«^3i5. Then A had wice as mucKR^'^i ""^ ^^ ^P-"t
each at first ? "^""^'^ '^^ ^' How much had
J4o!;;,'d1ii;r"I.';™i:;;/p^^--e-f a ,„n of s„,ar for
gain ? • ^ "-"'^ P^^ pound. How much did he
^r ^r^H^^^tT^^^^J^y;^ spends 55 a week
expenses. How long an" 1 it tal',?"'^,^' "" ^'^^^ ^or other
2^) A farmer miH f. ^^'"' ^"^ ^'^^e $072 ?
- -armor paid for a cow and a sheep with the
GENERAL REVIEW.
89
Vn\?.f ^ '?"' ^ ^"^^^ °^ ^^y ^' 60 cents a cwt. The cow
cosj^scven t,mes as much as the sheep. Find tie pr^c:
66o^?t'Ul/an5'/64t:id";^'"' ^^" ^° ^^^ ^ «^^^
buif ^C^ 1;^:^- -;!r,^:;| -:^3^^- J^^e^js . be
:i^SjwXon''^"h^' °r ^^"'"^^ $6sTo,"?he':th:f /,6^^ ;
po ?s at ?,^n T'k "'''^- ?'''"^ ^4 a rod ; and 16 lamp-
posts at $3.50 each, n the cost of grading- and viv\mr]L
^10 a sq. rod, what will the total coft of tl^e streS bef
;n.K r ^°'^^a"y feet of lumber are required for a i->-
mch baseboard for a fence around a field of "o acr s
iiavmg a frontage of 40 rods ? ^^'^'''
yds^?ft^onr/LTT^"'';°^''\" ^^^'■^f '-^ ^•««"^' 60
yus. in. long, and 5 -ds. 2 ft. wide, a 2; -cent oiere i^
placed. How much money is on the floor ? ^
(28) A clock strikes all the hours in Februarv Mirrh
whit .^ri-auJ^frjreSS I'^^^r'^ ■'
(30) A cellar is 18 by 20 feet, how many bricks 8 hv .
by 2 inches, laid on their sides, will cover Ue floor and
what IS their value at $,4 per thousand bricks ?'
fi 1 i^i-^ Find tbe cost of building a six-rail fence round 1
field 65 rods long and 40 rods Nvdde, the rails beim^ if?
long and costing 8 cents each. " ■^•
(32) What would it cost for stone to m^'A o „.^n
rotind the outside of a yard 40 roH. g a^fc 66 v'^t
wide, If the walk be 5 feel wide and the Vvenen^^ °^^^
10 cents per square foot of surface covered ?
lot 6n ft •5^"^'T''" '/^'.' ""^ ^3-6o a square foot a town
get for ; Tr^XZV"'' ^' '" ^'^'^'- ^'"^ ^^'^^-^ ^^^ ^houkl
gei lor 3 acres at the same price.
of tvvu-inch plank
quare block 360 feet to the side has a side^
arou
t md the value of the plank at $15 per thous
nd it. The sidewalk is 4 ft. wid
alk
and.
90
ARITHiMETIC
for each pupil ? ^tuuvving lo sq. it. of floor space
ference, has midp -? i^ T, ' ^"''^'^ '^ ^ "• m circum-
which is .6f..rdrc^;!nfe™?e'r'= *"" "^' '™'' "-'
ft. w^l and'e fdeep'at'sf S''' " "","? ^ "^ "'"'>'• '«
(''.RN w^ "eep, at 65 cents per cubic yard
of the Inmh!; f P^' ^'?°"^'?"d, how much will be the cost
ft high r '' ' '^"'^ '^^'-^^^ ^^"^^ So rods long and 6
is 2^1 lonTaS ft"wid^%™^ ^^ ^^''^ '■" - --^ which
( . .\ A f ', f '^^' ^° contain 14 cords ?
(44) A fanner sold a horse for ^r-^S co ,V r
-ds s„,d ,he shee*!, for^irercV'^t'o^l^^clT-did'he
. (45) The wood contained in a box cj ft , ;„ i„ r
l^iZf' 7t I ''■ ' •"■ "^ >">• !<- "aMV runZ^Vo;
i*he X e .iingT -"""^ ^^^^ '"" ^S cords of woofkeep
to4tid\;:,^h''pi'vL's;c„lr?fr"''if h"- '^ '"••"'"=• ■•'
the cost at 55 cents a stone ' ' ^^ ' "' ^ '"• ^"""^
(47) If 12 cords of wood equal 1!/ fnn« n' ^„,i u
oTcoXt;e^a;r''"™'''' '--'''"^^''-^"-^
doif Lit?' ""'"'' "'' ^ ""'^' "'«' will a barrel of ,47
GENERAL REVIKW.
91
(49) If 50 men do a piece of n-ork in 12 days, workino"
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 dav, liowmuch
should 19 men and 27 women earn in 15 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 arc 5000 miles apart, and
approach each other, the one at the rale of 19 miles an
hour, the other 24 -.niles an hour. How far will they be
apart in two days i '
(53) If a boy waste on the average 2 minutes every
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 746^ ? ' ^^' ^
640 by the G. C. M. of 32^2 and 1952.
(57) If the area of a field is 326700 square feet, and
the length 540 rods, what is the width ?
(58) Find the value of iie rails in a straight fence 40
rods long, each rail being 11 ft. long, and the fenced
rails high, at $22.50 per M.
(59) In eight equal loads there were 9 tons, 10 cw^
^^ /A \ A '\'''"y ^''"^' ^^'^•' '^'^'■''' tl>erc in 5 loads.?
(60) 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 seUing at $6 a ton, and oats at ^o
cents a bushel, It costs a man $9 for hay and $6.7.; 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 m. wide and 3 m. thick.?
(63) A garden is 48 yds. long and 29 yds. wide. There
are two paths, each 6 ft. wide, running across each other
92
ARITHMETIC
5 -{'° -^"''Hl'lfHt^;5- side .„ .Me and
Ztrif"" "f--" house wtcl,° ?n°"r "'^ '/"^ i"
S; ^'"= '™-'-- wans an ^: ,X"|;' -f ;/.f;.
.he Xt,!?:;?,^f;;*-Vif 8^x6^x4'. ho. ™„eh .„.,„
(66) A field 60 chains lorn' . ?f ^"'-wl l^ushel ?
<luce 2,600 bushels o potatoes H° "''^ "■''''= «i" Pro-
per acre ? Potaloes. Ho>v many bush, is il,"t
"^iTiS-^-^oj.-ijjf-. -d.o ,
anc^ ii. de"p^."'Tha wm Te'^f "' '""f' ^ «• ^ i". wide
, (69) Find th6 cost- of ^. ,
^n. wide and i^ in. th ck at Srl'°''''''; ^^"^^ ^4 ft. long, S
(72) A schoolboy J^ts ,?. I ^^ ^*- ^^«^P?
quarter, and he attends srhn.^ street-car tickets for a
r;- --^ his annut, ^^ ^^ tj^*-^ 'he
for?dJk'(Su";;i';;r^',Srfi^ f P'- ^ v. . p.. a day
v/:); It ten wordt; r>,- i„
-nts, and each M-ord ov^r' e" ^Jl'/ ^^'^^'"^P^^ ^^^ ^5
l^r^^'T ^"^ ^^^^"Jate the cost of .'^'""^^' ^^'^^ «"t
(76) A man's money 1 n.""^'^"^'"^" 't.
^ '' "'^^^^ "P of 5-dollar bills
GIJNERAL REVIEW.
95
4-clollar bills and 50-cent pieces. There are five times as
many 5 s as 4's, and twice as many 50-cent p e?es as c^s
Altogether he has $10.. How JJy of eacT kfnd h\s
^"^^^J^v^ "'""^^^ "'"^^ ^^ a^l^^ed to the product of the
.1, '■j** I purchase loooo lbs. hard coal. What must be
ohord''i'ti.°Ar '''"' '■'''"^ '" " <■'• '""if and 5 Hide!
tonolclitf A ton measures 33 cubic feet
inched ^"""^""^ ^"^ ^''■^'' y"^'-' ^^^^ '"-^767 square
(80) What is a bin of wheat worth, if its length bo u
a bishd .?''' ^ ^'•' '^' ^"^^' 5;^ ^^•' ^"^ '^^ -^t 64 cents
(81) A house is 44 ft. long and 21 ft. wide, outside
measurement. What will it cl^st to put two floors n it
of iK mch lumber, the walls being 18 in. thick, and lumber
bemg worth $1 5 per thousand ft. ? iumoer
sidi^^'^i^ '"^'T '^lo^^^ of land is I mile 80 rods on each
Ift ' • fu "" uf °,""'i '^ '" 4 rods wide. Find the number
/A' a" ^^l '''?"^ °^ ^^"^' ^"d also in the road.
, {03) A school-room is 40x28x14 feet there nr«- (^
eTntX""1,'^°r "1^^ ^'^ ^^- ^'fnScorof pTast'
^i\ T^"""' a"d ceding at 12 cents per square yard.
(84) There are 6 ft. m a fathom, how many fathoms
deep could a cable 12 rods long reach ? ^ latnoms
nf thr^'^^''^/'^ ^^'r. P'""^ numbers. The product
?L, ^''Z.?'^ '^'°"3 '^ '537, of the first and third is
2««i, and of the second and third is 3953. Find them.
• ^^^\P'}y''^^ sixty thousand and sixty-nine by 4-^0
using all the factors of the divisor, and find true remainde^'
Find its treafn'L^^^'* '"'5'' '°''^^ ^"^ 7314 inches wide,
r ma its area m acres, yards, etc.
c f/?L\'"'n" ^9"^ajJis 2500 gallons. If it measures
5 ft. 4 in. by 6 ft. 3 in., find its depth.
(89) A plate of copper ^ ft. wide. 7 ft. 2 in !"n^ inH
iiaif-an-inch thick is rolled" into a sheet '2 inches thick knd
I ft. 7 m. wide. Find its length.
94
ARITHMETIC
(90) In a field 649 ft. long and 597 ft. wide, how many
acres, yards, etc., in it ?
ii5^*^ A grocer mixes together 7 lbs. tea worth 54 cents
a lb., II lbs. worth 47 cents, and 13 lbs. worth 43 cents.
t md the value of one pound of the mixture.
(92) A dealer bought 248 geese at $6.24 a dozen, and
sold them for $1.25 a pair. Find his gain.
(93) From April 8th at 9 a.m. to November i8th 5
p.m., how many minutes ?
(94) How many boards 14 ft. long and 10 inches wide
will be required to build a sidewalk 40 rods long and 4 ft
8 m. wide ? o t •
(95) Out of a cistern containing 1 14 gallons, 28 pail-
fuls were taken. If the pail held 2 gal. 3 qt., bow much
water still remained in the cistern ?
(96) The wheel of a carriage is 9 feet in circumterence.
How many times will it turn in going over 5 miles, 178
rods, 4 yards ? o ^ y /
(97) A farmer sold 147 lbs. of butter at 18 cents a
pound, and 2456 lbs. of cheese at 9 cents a pound. How
many lbs. of tea at 36 cents a pound can he buy with his
money after redeeming a note for $230 and paying $5.26
interest thereon ? -j f } & ^0
(98) Divide $309 among Mary, Jane and Annie, giving
Mary $9 more than Annie, and Annie $6 less than Jane.
(99) Find the total area of the walls an^ ceiling of a
room 18 ft. 8 in. long, 15 ft. wide, and 12 ft. high.
(100) At 22 cents a square yard, what will it cost to
plaster the walls and ceiling of a room 27 x 18 x 10 feet
deducting 90 square feet for openings ?
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