Essentials of Business Arithmetic

141 Pages·2010·26.27 MB·English

by  Van Tuyl

ESSENT;IALS OF
BUSINESS ARITHMETIC
BY
GEORGE H. VAN TUYL
1
TEACHER OF BUSINESS ARITHMETIC
I mGH SCHOOL OF COMMERCE, NEW YORK
FORMERLY TEACHER OF ARITHMETIC IN THE ALBANY
BUSINESS COLLEGE, ALBANY, N.Y. AND IN THE
PACKARD COMMERCIAL SCHOOL
NEWYORK
I
AMERICAN BOOK COMPANY
I
j- NEW YORK CINCINNATI cmCAGO
I
1
I
.I-
--J....
PREFAOE
THISbook has been preparedto meet theneeds of businessschools
and academic high schools where an intensive study of the most im
portant topics of arithmetic is required, with a view to developing
. skill in the fundamental operations. This requirement is met by
C9PYRlGHT, 791:1, 1913,BY
GEORGEH. VAN TUYL. the omission of some of the more advanced topics found in the
author's"Complete ArithmeJic" and by the inclusion of a number
CoPYRIGHT, 191:3, IN GREATBRITAIN.
of new features; such as problems in Domestic Parcel Post, farm
ESSEbl. BUS. ARITH. problems, problems in estimating, and a comparisonof commonfood
w, P. 9 products,accompanied by aseries of exercises to determine the value
ofgiven foods as tissue builders and as energy producers.
The book is adapted also for use in the upper grades of ele
mentary schools where a business training in arithmetic is desired.
The clear and full explanations, the practical problems, the short
methods of solution,and the numerous exercises for drills and
reviews render this book available for such courses in grammar
schools.
Many suggestions have been made for rapid calculation. The
Speed and Written Tests ofthe larger volume have been retained
with sucli changes in the problems as have been necessary to meet
the requirements of the smaller text.
r Attentionis directed also to the following features:
The chapter on aliquot parts, as applied to billing, ·trade dis
count, and simple interest, is placed early in the text.
Commonand decimal fractions are treated together,'asis the case
in business.
·:f..
.. 3
,.
4 PREFACE
A great many problems are provided for mental work.
Many of the problems are takenfrom the business affairs of cor
porations, cities, states, and nations ofthe world.
Many calculation tables are illustrated and applied to the solntion
CONTENTS
of problems.
There are fivesets of examinations (each set consisting of a speed
test and a written test) to determine the student's mastery of the PAGE
READING AND WRITING NmfBERS 7
subject at various stages of the work. UNITED STATES }'lONEY 10
The author gratefully acknowledges his indebtedness to his many ALIQUOT PARTS 12
.
friends who, by their advice and suggestions, have aided him in ADDITION , 33
preparing this volume. SUBTRACTION 42
11'.!:ULTIPLICATION • 48
DIVISION 56
FACTORING 60
GREATEST CmI~IONDIYISOR 62
LEAST COMMON MULTIPLE 63
CANCELLATION 64
FRACTIONS • 67
FUNDAlIlENTAL PRINCIPLES OF ARlTH~lETIC 100
DOlllESTIC PARCEL POST 110
EXAlIllNATIONS 112
PRACTICAL },lEASURElIlENTS 116
GRAPHS 140
ELUIINATlONS 143
PERCENTAGE 145
TradeDiscount 166
ProfitandLoss 174
MarkingGoods 188
Commission andBrokerage 191
EXAlIlINATIONS 198
INTEREST 202
Accurate 211
BankDiscount 214
TAXES AI>""D INSURANCE 222
Taxes 222
Fire Insurance 227
5
6 CONTENTS
PAGE
234
POSTAL SAVINGS BANKS
235
EXAMINATIONS
238
STOOKS
BONDS, 247 .ESSENTIALS
253
EXOHANGE
258 OF
EXAMINATIONS
261
INvOLUTION AND E'I"OLUTION BUSINESS ARITHMETIO
265
PARTIAL PAYMENTS
267
DENOMINATE NUMBER TABLES
271
hmEX •
READING AND WRITlL'{G NUMBERS
1. Numbers are expressed in three ways: (1) by written words,
(2) by letters (Roman system), and (3) by figures (Arabic system).
ROMAN NOTATION
2. In the Roman systemof writing numbers sevenlettersare used.
They are:
I V X L C D M
1 5 10 50 100 500 1000
3. Writing numbers by the Roman system is based on the follow
ing principles:
PRINCIPLES: 1, Repeating a letterrepeat»its value.
2. The value ofa letterw?'itten after a letterofgreatervalue is to be
added tothe larqeroalue.
3. Thevalue ofa letterumiiten. before a letter ofqreater value is to
besubtractedfrom theqreateroalue.
4. .A horizontal. bor ove)'a letter inm'eases its value one thousand
times,
NOTES. (1) Only whole numbers can be written in the Roman system of
notation.
(2) Roman notation is of little practical value, being nsed only to'record
dates andchaptersinbooks, datesonbuildings, numbersonawatchface, etc.
7
0.\~t~
READING AND WRITING NUMBERS ARABIC NOTATION 9
8
~ 4. ROllIAN NOTATION ILLUSTRATED TABLE SHOWING HOW TO READ NUMBERS
= '"
"J IIIIVVXIIIIorIIII*=====23964 XXXXXIVIXXVXIXIIIIV, =====1121369344 LLLXCXXIXCXXX·IXVIX=====19758140990" DCMMMCCCCCCXMMnLCXXXVVII===-=613119961,069611090,000 ~..<<<..'I"..J..::) ~.s<..J.:): :§.""<<<:s~:00I1a:J::::)J: §:.''<s.aI1".":.:: :§<<a1J:) §.'""E.<<<:<':I00.1":J:.:::)J §".'<s<.EI1".J:.::) §'E<<1J:) .""s".<<<::~C0<.C::,00::.J:::.:::JJ)Il ."..<'<<:C0<<.C.:I":..JJ::..J::))Il s".<:oCC<<.::.JJ::.J:))Il· ""s.'':s:00.":"::.:J: .'s<.".J:.:) ".:<.c::.J:.J)
5. 1. Writein Roman notation: 8 9, 7 2 4, 5 6 3, 9 0 0, 1 0 6.
12 85 336 598 10,000
The number is read, "eighty-nine trillion, seven hundred twenty
18 94 472 1077 15,000 four billion, five hundred sixty-three million, nine hundred thou
21 111 505 1384 100,000
sand, one hundred six."
47 128 666 1527 150,000
63 247 872 1898 1,000,000 9. In like manner readthe following,numbers:
1. 21,460 7. 962,024 13. 27,250,820
2. Read the following:
2. 34,829 8. 872,463 14. 20,300,600
XVIII LXIX CDLIX MC
3. 127,724 9. 900,047 15. 65,897,249.
XXIX XCIX DCD MDCCCXCIX.
XXXI CIX ,DCCCLXXXIX MDCCXXVIII 4. 306,200 10. 1,456,789 16. 185,496,728
XLIV CLXXII CM VCCLXXX 5. 425,002 11. 3,248,764 17. 593,972,847
XLIX CCCLX MC:1IiIX L (f(O6.. 800,005 12. 5,002,005 18. 15,647,989,721
Write the following numbers, using the Arabic system:
ARABIC NOTATION
1. Seven hundredforty-three.
6. The Arabic system of notation makes use of ten characters or
figures, and a period or decimal point. They are 0,1, 2,3, 4, 5, 6, 2. Nine thousandfourteen.
7,8,9, and. 3. Eleventhousand one hundredfour.
7. With these figures and the decimal point any required num 4. Fifteenthousand twenty.
ber can be written.
5. Seventy-sixthousand ninety-nine.
8. For convenience in reading numbers, the figures are some
6. Fourteen hundred eighty-eight.
times divided into groups of three, in this way:
7. Onehundred sixty thousandfour hundred.
2,564,879,598.
8. Eight hundred thousand nine hundred ninety.
The.reason for this grouping is best understood by observing
9. Two million sixteen thousand seventeen.
the following table:
*' 10; Six hundred elevenmillionfourteen thousand eighty-six.
IIIIisusedontimepieces.
10 READING AND WRITING NUMBERS UNITED STATES MONEY 11
pennies, gold certificates, silver certificates, Treasury notes, United
UNITED STATES MONEY
States notes (greenbacks), and national banknotes.
11. Any number of cents less than one hundred is read as cents:
18. The gold dollar, containing 25.8 grains of standard gold .9
thus, $.45or 45jfis read "forty-five cents," butanyvalue equal to
fine,is the unit of value.
or greaterthanone hundred centsis readasdollars,or as dollars and
cents: thus, :$8.75 or 875~ would be read "eight dollars, seventy 19. The silver dollar weighs 15.988 times as much as the gold.
five cents." .Aperiod,or point,separatesthenumber of dollarsfrom dollar; That is, the ratio of gold to silver is 15.988 to 1 (commonly.
the number of cents. called16 to 1).
12. Read the following: 20. DENOMINATIONS, WEIGHT, AXD FDIENESS OF THE COINS OF THE
:$3.17 $12.40 $826.52 $1476.83 UNITED STATES
$4.28 $16.50 $1624.43* $1982.76
$9.15 $85.90 $1837.16 $14,728.41 GOLD
$10.20 $104.26 $2487.49 $146,789.09
, FmE GOLD ALLOY WRIGIlT
13. Write thefollowing infigures: DENOMIN1I.TION CONTAn'ED CONTAI:'~D (GRAINS)
(GRAINS) (GRAINS)
3.. One hundred sixteendollars, fifty-nine cents,
Onedollar (notcoined since 1890) 23.22 2.58 25.80
2. Three hundredniue dollars, seventy cents.
Quartereagle ($2.50) 58.05 6.45 64.5
3. Twelvehundred twenty-one dollars, eighty-eightcents. Halfeagle ($5.00) llG·10 12.90 129.
4. 'I'wenty-fourhundred fo~ty-threedollars, nine cents. Eagle ($10.00) 232.20 25.80 258.
Doubleeagle ($20.00) 464.40 51.60 516.
5. Fifty-seven hundred six dollars, thirty-three cents.
14. Money is the generally accepted measure of value. SILVER
15. Each nationbas its own system of money or coinage. PURE SILVER
CONTAThr:n
The principal nations of theworld haveadopted gold as thestand-
ard of monetary value. . Onedollar 371.25 41.25 412.5
Halfdollar 173.61 19.29 192.9
16. UnitedStatesmoneyconsistsofthecoins,notes,and certificates Quarterdollar 86.705 9.645 96.45
authorizedby Congress to be used asmoney. Itisadecimalsystem. Dime 34.722 3.858 38.58
TABLE MINOR
=
10mills 1cent, f!
=
lOcents 1dime, d. PURE COPPER
10dimes =1dollar, $ CONTAI:N"ED
=
10dollars 1eagle Fivecents* (nickel) 57.87 19.29 77.16
(Themillisnota coin.) Onecentt (copper) 45.60 . 2.40 48.
17. There are ten different kinds of money in circulation in the
United States: gold coins, silver dollars, subsidiary silver, nickels, NOTE. Thealloy ingoldand silvercoins neither adds to nordetractsfrom
.thevalueofthe coins. Itspurposeisto hardenthe coin, thusreducingthe loss
6'In reading $1624.43 say "sixteen hundred twenty-four dollars, forty-three by abrasion.
cents," not"onethousandsixhundred twenty-fourdollars,forty-threecents." One
reasonfo; sayingit andwritingitassuggestedisthatittakeslesstimeandspace. *'75%copperand25%nickel. t95%copperand5%tin andzinc:<J7J
ALIQUOT PARTS 13
4. 5. 6.
13 yd. @25fl. 3486 lb. @25P. 128lb. @75fl.
21 yd. @50P. 1984 lb. @ 50I. 324lb. @50P.
39 yd. @2556. 482~ lb. @ 25P. 233lb. @ 25P.
31 yd. @751 8448ib. @ 75I. 199lb. @75I.
48 yd. @75P. 1331 lb. @50I. 247lb. @25I.
, ALIQUOT PARTS ,t
, Make np andfind the total value ofeach of two or more groups of
quantities like the above as directedby the teacher. ,
21. An aliquot part of anumber is anumber-that is contained in
itan integral number of times.
ar~ -to J\ f$)'j/ ,EIGHTHS /
Thus, 2,4,5,10,20,25,and50 aliquotpartsof100; thatis,2 of100,
=t 24. 1. 12tI 'is what part of 2556? { 2. toft is how mnch?
25 of100,etc.
NOTE. Other fractional parts of 100 are called aliquant parts of 100. For 3. 12t56is what part of $1?
convenience, allfractionalpartsof100will betreatedasaliquotparts.
4. 25Pis how manyeighths ofadollar?
ARTER~
fuLYES AND Qu 5. 25¢+12t56= how many cents?
3
22. 1. What part of100 cents, or $1.00, is 2556? 50¢? 7556? 6. 37t56is what part of a dollar? i
2. At 2556 a yard, how ma~y yards can be boughtfor $1.00? 7. Whatis the sum of t and t? 5056+ 12t56=?
3. If4 yd. cost $1.00, howmuchwill8yd. cost? 12 yd. ?,16 yd.? 8. 62t56is what part of a dollar? 9. 75¢+12t56=?
4. How much will 20 yd. cost at 2556a yard? at 5056 a yard? at 10. :$t = how many cents? 5 7.
75 56 a yard? ' ./. .Y'
5. Compare 2556with 5056; with 75}6. 501with751; with 251. n. What part of adollar is 12._}¢? 37-_}I? 6~-}fi? ~.}-56?
75¢ with 2556; with 50I. 12. What is the cost of 16 lb. of raasms at 12t¢ a pound?
6. Compare the number of yards that can be bought for 501 and of 16 baskets of potatoes at 37t¢ a basket? of 16 yd. of cloth at
for 25fi; for 25¢ andfor 7556;'for 7556 and for 50fi. 62t¢ peryard? of16 bu. of apples at 87tla bushel?
7. State arule for finding the cost of any number of articles at 25. Using the aliquot-part method, find the total value of each of
25¢each; at 50fieach; at 75Peach. thefollowing: '
23. Make all extensions mentally, and find the total valueof each 1. 2. 3.
of the following: 24lb. @37t¢. 48 lb. @12t¢. 120 yd. @12t¢.
1. 2. 3. 32lb. @12tI. 64lb. @2556. i64yd. @12t¢.
16 yd. @ 25P. 32 yd. @50P. 120 yd. @25p. 40u, @ 62tI. 72 lb. @ 37t¢. 200yd. @37tl.
24yd. @25P. 48 yd. @251. 140 yd. @ 50I. 56lb. @37t¢. 88 lb. @87t56. 240 yd. @12t¢.
30yd. @ 501. 54yd. @50P. 150 yd. @25p.
p. Make two or more groups like the'above aud find the total value
16 yd. @751. 60yd. @75P. 160 yd. @75
of each.
40yd. @50P. 80 yd. @75P. 126 yd. @ 25p.
12
14 ALIQUOT PARTS ALIQUOT PARTS 15~
b(".!. NOTE. In the second item,in No.3, 53yd.@I2l'¢=$6~=$6.62!; write
SIXTEENTHS I the extensionas $6.63. "
26. 1. 6~/ is what part of12t¢? of 25¢? of 50;? of $1?
Write two or more groups like the above and find the total value
2. 3 times 6!¢ is how many cents? of each.
3. 18!¢is what part of a dollar? THIRDS AND SIXTHS
4. 25;or $t is how many sixteenths of a dollar? 29. 1. What part of a dollar is 33t¢? 66t1'?
5. 25¢+6!; are,how many cents? .2. Whatis t oft? t of 33t¢is how manycents'?
3. 16i¢=what partof a dollar?
6. 31!¢is what part of a dollar?
4. 3times 16t56= how many cents? ,whatpart of a dollar?
7. t - l6 = ? 43i¢ is what part of a dollar? 5. 4 times 16i56= how many cents ?b~what part of a dollar?
8. t +l6 =? 56!¢=what part of a dollar? 6. $1-16i¢ = how many centsr>twhat part ofa dollar?
9. In like manner find how many cents there are in $i~, $i~, . 30. Complete the following table. Statethe relation of eachpart
and si~ by comparing 6!¢ ($1\) with 75¢ and $1. to the parts thatfollow and precede it.
31. Find total value of each
27. Complete thefollowing table of sixteenths, eighths, quarters,
TUIRDS HALVES CENTS group:
and halves. f
1. 48lb. @ 16i¢.
Compare onepartwithanother. 6t I6}
H H 33! 54lb. @66i 56. ,
" H $,1 50 30lb. @ 83t¢.~
---EIG-HTI-IB -QUA-RT-ER'S HA1.VES CENTS -EIG-HTH-S -QUA-RTE-RS-HALV-ES -CE1-\TS H 2. 66yd. @ 33t¢.
H
sr1: 6l 8ft $t 76yd. @25¢.
$ft ~t I2~ 8M 76yd. @ 12t¢.
$ft 18t 8H
3. 4. 5.
$r'. $f H 25 $H 64lb. @ 6t¢. 48 qt. @ 33t56. 120yd. @ 37t¢.
$ft Ht
$Ts• SH 96lb. @ 33t¢. 72 qt. @ 16!¢. 126yd. @ 16t¢.
Sf,; $ri 88lb. @ 37tf<1. 96 qt. @12t¢. 132yd. @ 83t¢.
h\ $:1l.~" 91lb. @ 66!1'. 60qt. @ 6!¢. 144 yd. @ 33t1'.
Writeandfindthetotalvalueof twoormore groups likethe above.
28. Make the extensions mentally, and find the total value of
-IS gi
each of the following: 1) TWELFTHS
1. 2. 3. 32. 1. t of2556= how many cents?
32 yd. @6!¢. 80yd. @31!rI. 47yd. @25¢. 2. t of!=? 8t¢= what part of a dollar?
48yd. @12t¢. 128yd. @ 37t¢. 53yd. @ 12t¢. 3. 50¢n- 8t¢=how many cents?
64yd. @ 18l¢. 144yd. @ 56!¢. 58yd. @6t¢. 4. t- =? $41!¢= whatpart of a dollar? ~-z..
96 yd. @6!¢. 96yd. @ 93!¢. 63yd. @ 50¢. 5. 50¢+8i¢=how manycents? what part of a dollar?1z-
6. $1- 8t¢= how many cents? .whatpart of a dollar?
160yd. @43l¢· 72yd. @ 37t¢. 75yd. @37tf!.