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"C-NRLF *B EkB 534 31s< Edition, price Is., or with 48 pp. of Questions, U. 4<J., (JEO&RAPHY FOR BE&INNERS. By James ConNWELii, Ph.D. "It is remarkable for its simplicity, comprehensiveuess, and pecuKar adaptation to the minds of children. We know of no Geography which we consider as anything like equally appropriate to the rising generation." —Scottish Press. Just published, 48 pp., price 6d., aUESTIONS ON THE aEOGRAPHT FOR BEGINNERS. Also by the same, price Is. 8d. plain .• 2s. 6d. coloured, I. A MAP-BOOK FOR BEGIMERS, Consisting of Twelve Plates of Maps (above Seventy large and tanall), being a Companion Atlas to the " Geography fob Beginners." Separate Maps of our Colonies and Foreign Possessiona. Also for Map Drawing, price Is., n. BOOK OP BLANK MAPS. The above Twelve Maps, complete in everything except the names, which are to be filled in by the learner. Price Is., .m. BOOK OP MAP PROJECTIONS. Twelve Plates, consisting of the Lines of Latitude and Longiii.'le only to the above Maps. 49'4 Edition, price Ss. 6d., or with 30 Maps, on steel, 5s. 6d., v A SCHOOL GEOGRAPHY. By James Cornwell, Ph.D. " "Without exception, the best book of its class we have seen. We recom- mend its immediate adoption by all public and private teachers." — Atlas. " We are qualified by ample trial of the books in our own classes to speak to their great efiiciency and value. We have never known so much interest evinced, or so much progress made, in the study of geography, as since we have employed these as our school-books." — Educational Times. " We have not before met with a work so complete and original in its details, so comprehensive and carefully arranged in its plan, as this geo- graphy of Dr. Comwel', which will certainly supersede all other school abridgments aa soon a.3 it is generally known. — Simmonds's Colonial Magazine. •»* In, this Edition the statistical and other information is brougbt down to the latest period, especially as regards the United Kingdom and her colonies and dependencies. An Index is also added, comprising every name found in the work. London; SiaxKis, Mi.ssHAZ.1., & Go. ; HAUii.TOir, Asahs, St Co. Edinburgh : Olivsb & BoTS. Alto, by the same Author, price 2s. 6d. plain, 4t. eoiomvd, A SCHOOL ATLAS. THIS ATLAS CONSISTS OF THTRTYBEAITTIFULLY-EXECUTED SMALL MAPS ON STEEL, IN WHICH IS FOUND EVERY PLACE MENTIONED IN THE AUTHOR's "SCHOOL GEOGRAPHY." IT ALSO CONTAINS A LIST OF SEVERAL HUNDRED PLACES. WITH THEIB LATITUDE AND LONGITUDE. These aamee are accentuated ; and, in cases of difficulty, the inronun^iation is also given. •«• A new Map of Prussia aaid Germany. 34^A Edition, price Is. 6d., THE YOima COMPOSER; Ob, PnofiRESSivE Exercises in English Compositioit ; eompridBg Sentence-making, Variety of Expression, and Figuratiye Lmguage, with Appendices on the use of Capitals and Punctuation. By Jambs COKNWELL, Ph.D. Westminster Review. " The plan of this work is very superior. We are persuaded that this little work will be found valuable to the intelligent instructoi:." Colonial Magazine. " Dr. Comwell has furnished an admirable work in this descriptiou of- literature, a very valuable addition to ordinary, or what should be ordi- nary, school-books. He has carefully avoided the adoption of technical terms of strange and deterring sound, employing common terms in thoir nsual meanings, so that the familiar phraseology of elementary works in made accessory to the introduction of a new but necessary branch ol English education. We have no hesitation in recommending the additioL of ' The Yoimg Compoeer ' to the regular contents of every satchel." 11<A Edition, price 3»., A KEY TO THE YOUNGF COMPOSEB, Witii Hints as te the mode of using the book. London: Simpkik, Marshall, & Co, ; Hamiltok, Asamb, & Oo. Edinburgh : Olivbb & Botd. Dr. Comwell's Educational Series. Just added to the Series, 96 pp., price Is., SPELLING FOE. BEGINNEES: A METHOD OP aJBACHINa BEADING AND SPELLING AT THE SAME TIME. In this Work the words which hare i^e same vomel MOfMid are formed into groups, and each group b sub- diTided into smaller portions according as the same sound U represented hy different characters. The meaning of the words is taught by using them in simple sentences, these Bentences forming at the same time an easy course for teaching Beading. Also, 144 pp., price Is., POETRY EOR BEGINNERS: 4 BlLSCIIOir OP SHOBT AKI) BAST POEMS POB BBADIVa AKD BECITATIOir TS SCHOOLS AlTD PAMILIB8. The aim has been to form a collection of such Poems as will \i%%nt€resting to children, and which, while forming a ewrrect taster shall instU into their minds only pure and noble sentiments and right principles. With the first poem of each Poet not now living, is fiTen the date of his birth and death ; and a few Notes are toattered here and there explanatory of such words as a child might not always find in his dictionary. ig^ In the Press, I.— A SCHOOL HISTORY OF ENGLAND. II.— AN ARITHMETIC FOR BEGINNERS. LONDON : •IMPKIN, MARSHALL. & CO., STATIONERS' HALL COUBI HAMILTON, ADAMS, & CO., PATERNOSTER ROW; WHITTAKER & CO,, AVE MARIA LANE. EDINBURGH: OLIVBB & BOYD. DR. CORNWELL'S EDTJCATIQML WOEKS. ARITHMETIC FOR BEGINNERS. BEING AN ELEMEKTAKY INTRODUCTION TO COENWELL AND FITCH'S SCHOOL AEITHMETIC. SAME AUTHOES. LONDON: SIMPKIN, MARSHALL & CO., STATIONERS' HALL COURT j HAMILTON, ADAMS AND CO., PATERNOSTER ROW ; WHITTAKER AND CO., AVE MARIA LANE, EDINBURGH : OLIVER AND BOYD. 1872. ''Ifir LONDON : PBINTBD BY J. AND W. BIDEB, BAKIHOLOMEW CLOSE. PREFACE. In preparing tliis "Arithmetic for Beginners" an en- deavour has been made to keep in view two or tliree simple principles which are suggested by familiar expe- rience in teaching, but which are often overlooked : — (1) That yount? children learn the processes and mean- ing of arithmetic more readily by the help of short, easy jDroblems, than by dealing at first with numbers too large for their imagination to grasp: (2) That the diflficulties of this study should be pre- sented to the understanding of a learner one at a time. (3) That as soon as each principle or rule has been learned and illustrated, exercises are needed, calling on the scholar to put the rule or principle into practice. Accordingly, it will be found that the sums and examples in this little book are very simple, dealing for the most part with the familiar computations in use in ordinary life. They are so grouped and graduated that each step is seen to be a very natural sequel to the former. The tables of notation, addition, and multiplication are so divided, that as soon as each small portion of them is learned, a few exercises are given in the use of that portion before the next portion is attempted. The range of the book includes all the most important applications of the simple and compound rules, and a brief introduction to Fractions, but does not extend to' Proportion and Decimals. CONTENTS. TAQM SIMPLE NUMBERS AND THEIR NAMES . . . . .6 COUNTING . 6 NUMBERS COMPOSED OF TENS ....... 6 COUNTING 8 ADDING AND SUBTRACTING . . . . . . .12 HUNDREDS .......... 15 THOUSANDS 19 THE MULTIPLICATION TABLE AND ITS USES . . . .21 MILLIONS 28 LONG MULTIPLICATION 30 DIVISION .......... 34 SIGNS AND THEIR USES 40 EXERCISES IN SIGNS . . . . . . . .41 MISCELLANEOUS EXAMPLES IN SIMPLE RULES . . . .42 MONEY 44 MONEY TABLES 46 ADDITION AND SUBTRACTION OF MONEY 47 MULTIPLICATION OF MONEY 64 HOUSEHOLD ACCOUNTS AND SIMPLE BILLS . . . .68 SIMPLE REDUCTION AND OTHER USES OF MULTIPLICATION . . 60 DIVISION OF MONEY 62 REDUCTION AND OTHER USES OF DIVISION . . . .66 MISCELLANEOUS EXERCISES . . . . . , . 68 ' WEIGHT 69 LENGTH 72 SURFACE 76 CAPACITY OR BULK 79 TIME 81 INTRODUCTION TO FRACTIONS 85 MULTIPLICATION AND DIVISION BY FRACTIONAL NUMBERS . . 87 ANSWERS TO EXERCISES 90 AElTHilETIC FOR BEGINNERS. SIMPLE NUMBERS AND THEIR NAMES. NAME OF THE OBJECTS. NUMBER OF THE SPOTS SHOWN. SPOTS. IN WORDS. IN FIGURES. • One I • • Two 2 • • • Three 3 • • • • Four 4 • • • • • Eive 5 • ••••• Six 6 • •••••• Seven 7 • ••••••• Eight 8 • •••••••• Nine 9 Exercise I. ^» (i) Say what is tJie name of each figure : — 4, 7, 3» 2> 6, 5, 7, I, 9i 8. (2) Write the figure for each mimher : — Nine, three, four, seven, five, six, three, eight, two. 6 ahithmetic for beginners. Counting. [Nine counters, marbles or pebbles, should be used, and the learner may be allowed to use the fingers for finding each result.] 1. Count how many fingers you have on your hand. 2. Take two away, and how many remain ? 3. How many letters are there in the word " JSTumber " 1 4. If I have five shillings in my purse, and put three more in, how many have I 1 5. There are eight children in a class, and four go aAvay; how many are left 1 6. Begin with the number nine, and say the numbers backwards, taldng away one each time. (7) Place under each of the following pairs of figures the sum to which they amount : — 46525746 32173123 (8) Place under each of the following pairs of figures the difference between them : — 87645987 24333453 NUMBERS COMPOSED OF TENS. !• "When a figure stands in the second place to the left, it means ten times more than if it stands in the first. Thus,— II Ten and one eleven 12 Ten and two twelve n Ten and three thirteen 16 Ten and six sixteen 10 Ten and nine nineteen 24 Two tens and four twenty-four NUMBEES AND THEIR NAMES. 7 57 Five tens and seven fifty-seven 63 Six tens and three sixty-three 88 Eight tens and eight eighty-eight 14 Ten and four fourteen 47 Four tens and seven forty-seven 93 Nine tens and three ninety-three 65 Six tens and five sixty-five 72 Seven tens and two seventy-two 99 Nine tens and nine ninety-nine Exercise II. 1^ (i) Give the figures for these numhers : — Thirty-four, seventeen, sixty-five, forty-three. Eighty-seven, twenty-five, seventy-six, fifty-two. Ninety-six, eighty-four, twenty-six, thirty-nine. . (2) Give the mimhers for these figures : — 12, 34, 29, 64, 83. 25, 52, • 95, 72, 81. i3> 62, 94, 31. 24. ^* A cipher or is used to show that there is no number to fill a vacant place. Thus, — lo means ten. 20 „ two tens, or twenty. 30 ,, three tens, or thirty. 50 „ five tens, or fifty. 70 „ seven tens, or seventy. Exercise III. 1^ (i) Put into figures these numhers : — Seventy, ninety, twenty, eighty, forty, ten. (2) Fut into words the figures — 20, 50, 80, 30, 70, 90, 10. (3) Write out in order the tohole of the figures from one to ninety-nine. 8 arithmetic fou beginnees. Counting. [A box of marbles or pebbles, a bag of nuts or some counters, should be used; the abacus or ball-frame will also be useful. At first no greater number than twelve should be placed before the learner.] The following should be learned by heart Two and one are three two three four five six seven eight nine ten eleven twelve four five six seven eight nine ten eleven twelve thirteen fourteen 3 4 5 6 7 8 9 lO II 12 13 14 Three and one are four eight nine ten two „ five three „ six four „ seven five „ eight 8 six „ nine 9 seven „ ten 10 „ eleven 1 1 „ twelve 1 2 „ thirteen 13 eleven „ fourteen 14 5 twelve „ fifteen i Exercise IV. 1. Count the fingers of both hands; the panes of glass in the window ; the books on the table ; the scholars in the class. 2. If I have three nuts in one pocket, and four in the other, how many have I ? 3. Place two pebbles in one hand and five in the other, and say how many they make. 4. Add five farthings to three. 5. How many legs are there on two chairs? 6. Count out as many pebbles as you have fingers on your hand. 7. Arrange on the floor as many stones as there are panes in the window, or children in the class. 8. Make four marks on a slate ; add three more ; count them all together. SIMPLE COUNTING. 9 9. If there are ten scholars in the class, and four go away, how many are left 1 10. Out of six pence I spend four pence ; how many pence are left ? 11. How many more are eight nuts than three ? 12. One child has .ten apples, and the other seven; how many more has the first ? 13. Make twelve strokes on the slate ; rub out three, and see how many remain. 14. Place eleven marbles on the floor; take two away, and say how many remain. 15. Begin with the number twelve, and repeat back- wards to one. 16. Say how many letters are in each word of the first line on this page. 17. What is the difference between the number of letters in " Caroline " and in " Jane " 1 Exercise Y. 1. Two and four, seven and three, eight and two, nine and one, four and three, two and six, eight and three, three and five. 2. Take two from eight, from seven, from nine, from six, from five. 3. Take three from twelve, from seven, from eleven, from ten, from nine, from eight. 4. Add 6 to 3, 2 to 7, 5 to 3, 3 to 7, 8 to 2. 5. Add 7 to 2, 3 to 8, 6 to 3, 9 to 2. 6. What is the difference between 10 and 12, between II and I, between 4 and 6, between 9 and 3 '? 7. Take 2 from 11, from 9, from 7, from 6, from 3. 8. Take 3 from 12, from 4, from 9, from 5, from 8. 9. Take 7 from 9, from 10, from 8, from 12. 10. Take 5 from 10, from 12, from 9, from 7. 1 1. How many more are 1 2 than 8, than 6, than eleven, than four ? 12. How many should be added to twelve to make fifteen ? B 2 10 AEITHMETIC FOB- BEGINXEBS. Exercise YI. 1^ (i) Place underneath each of the follotoing pairs of figures the sum to which they amount: — 754756989 232323233 (2) Place underneath each of the following x>ciirs of figures the difference hetween them : — 5 7 8 9 12 8 7 6 9 10 II 23263513638 The folloicing shoidd he learned hy heart : — Four and four are eight 8 Five and five are ten 10 „ five „ nine 9 5) six „ eleven II „ six „ ten 10 )j seven „ twelve 12 „ seven „ eleven TI )> eight „ thirteen 13 „ eight „ twelve 12 » nine „ fourteen J4 „ nine „ thirteen 13 )) ten „ fifteen. 15 „ ten „ fourteen U JJ eleven „ sixteen 16 „ eleven „ fifteen 15 )} twelve „ seventeen 17 „ twelve „ sixteen 16 Six and six are twelve 12 Seven and seven are — „ seven „ thirteen 13 fourteen 14 „ eight „ fourteen 14 » eight are fifteen 15 „ nine „ fifteen 15 » . nine „ sixteen 16 „ ten „ sixteen 16 j> ten „ seventeen 17 „ eleven „ seventeen 17 J) eleven „ eighteen 18 „ twelve „ eighteen 18 j> twelve „ nineteen 19 Eight and eight are sixteen 16 ,, nine are seventeen 17 „ ten ,, eighteen 18 „ eleven „ nineteen 19 „ twelve „ twenty 20 Nine and nine are — eighteen 18 „ ten are nineteen 19 „ eleven „ twenty 20 „ twelve „ twenty-one 2 1 COUNTING. 11 Exercise VJX 1. There are two piles of books, seven in one and five in the other ; how many are there in all ? 2. Find the difference between 15 and 7. 3. Eight cows are in one field, and nine in the other; how many are there in all ] 4. There are nine lamps in one street, and five in the other ; how many are there in both ? How many more are there in one street than in the other 1 5. Take the number eighteen, and repeat the ^numbers backwards to one. 6. Suppose there were seventeen sticks in a row, and yon took away two, and then two, and then two, &c., how many would be left each time i 7. Add four apples to seven, and take away three. 8. If out of seventeen nuts I give away four, how many remain? 9. How many more are eighteen than three I 10. Of twelve eggs four were broken; how many remained ? 11. Take seven shillings out of a purse containing fifteen ; five out of twelve ; eight out of sixteen. 12. How many days are in two weeks? 13. How many hours is it from four o'clock to eleven ? Exercise Vill. I^° (i) Place underneath each of the following pairs of figures the sum to which they amxmnt : — 79864698 43859435 (2) Flace underneath each of the following pairs of figures the difference between them : — 12 16 14 8 10 15 18 II 13 579357946 12 ARITHMETIC FOR BEGINNERS. ADDING AND SUBTRACTING HIGHER NU^IBERS. 3. AVhen numbers are "written with, two or more figures, and have to be added or subtracted, the sum must be worked by steps. Example I. Add eighteen to twenty-four. 2 I 4 24 Eight and four are twelve. I I 8 18 One ten and two tens are three tens. — So 24 and 18 amount to 3 tens and 12. 3 I 1 2 42 But twelve consists of one ten and two. Therefore there are in all four tens and two. The one ten is " carried " from the right column to the left, and the answer is forty-two. Whenever the figures in a column amount to more than ten, the ten or tens are carried to the next. Example II. Take twenty-three from fifty-seven. 57 Three from seven leaves four. 23 Two tens from five tens leaveg three tens. — So twenty-three taken from fifty-seven leaves 34 thirty-four. Exercise IX. (i) Work these additions : — 24 39 68 59 38 54 63 36 13 42 24 32 16 21 12 14 (2) Place underneath each pair of numbers the differ- ence between them : — 47 84 65 69 85 48 6z 35 28 23 51 14 10 31 24 30 14 12 SUBTRACTION. 13 4. Sometimes one figure of the number to be taken away is greater than the figure above it. Thus, — 73 Twenty-eight can be taken from seventy-three, 28 but eight cannot be taken from three. — In such cases we add ten to both lines. Add ten to the three ^ \ 7 I Eight from thirteen leaves five 8 ( 18 Add ten to the two tens - ^ ' I Three tens from seven tens leaves four tens. ^ ^ Adding ten to both does not alter the difference.* So the difference between 73 and 28 is 45. o. In subtracting it is better to set down the greater number above the less. Exercise X. 1^^ Place underneath each pair of numbers the differ- ence bettceen them : — 17 20 35 71 93 85 50 33 12 9 16 16 24 26 17 16 28 7 1. Take sixteen from twenty, twenty-nine from sixty- five, forty-three from eighty-one. 2. !N'inety hurdles are wanted to make a fence, and the owner has only forty-seven; how many more must he buy ? 3. How much are twenty-four pence more than nine pence ] 4. If I have fifty books, and give away eighteen, how -many remain ] 5. How many shillings are in two purses, of which the one contains twenty-nine, and the other forty-seven ] 6. How many must be added to seventeen marbles to make forty ] 7. Take from eighty, the two numbers, forty-two and seventeen, and say what remains. * See "School Arithmetic," p. 12, and "Science of Arithmetie," Axiom YI. 14 ARITHMETIC TOR BEGIITNERS. 8. Count the letters in eacli of the two lines of this question, and find the difference. 9. If a man owes me ;£'75, and pays me only ;£'48, how much is he still in my debt ? 10. Of thirty-five children in a school eighteen go home ; how many remain 1 11. Take thirty-six pence from seventy. Exercise XT. }^ Work the following addition sz^ms : — (I.) 8 10 (2-) 9 2 36 7 26 29 12 6 35 8 53 17 12 5 19 20 12 10 6 20 4 18 20 17 20 7 20 7 15 6 3 15 3. Add together 14, 7, 30, and 6. 4. Find the sum of 28, 16, and 54. 5. How much do twenty-seven, twenty-eight, and twenty-nine make ? 6. A man has to pay four bills, of ^26, ^g, £zi9 and ;£'2o each ; to what sum do they amount ? 7. There are four paths in a garden, measuring 29 yards, 31 yards, 27 yards, and 18 yards respectively; what is their total length ? 8. Add together 46 and 36, and take 26 from the amount. 9. Out of -QS'^i I first pay a bill of ;^i7 and then another of ;£2 2 ; how much have I left ? 10. Add together 10, 11, 12, and 13, and take the amount from seventy-five. 11. Take forty-six from the sum of 22, 23, and 24. 12. How many times can eight be taken from 90 ? HinfDEEDS. 15 G. When a fignre stands in the third place from the right it. means hundreds. Thus, 731 seven HUNDRED and thirty-one. 800 eight HTINDRED. 210 two HUNDRED and ten. 305 three hundred and five. Exercise XII. ^^ (i) Read in vjords the following figures : — 902, 516, 201, 824, 753, 961. 587, 911, 340, 921, 812. Explanation. — ^The first numher is made np of nine hundred, no tens and two, and is read nine hundred and two. The second is made up of five hundred, one ten and six, and is read five hundred and sixteen. (2) Give the figures for the follomng numbers : — Seven hundred and eleven. Three hundred and six. Four hundred and fourteen. Eive hundred and nine. Eight hundred and twelve. Three hundred and seventy-four. Six hundred and nineteen. !Xine hundred and twelve. Five hundred and ten. Four hundred and fifty. Examjple of Addition of Hundreds. 3 6 5 = Three hundred and sixty-five 5 I 8 4 = Eighteen. = Five hundred and four. 3 I 9 2 = Thirty-nine. =: Twelve. 9 I 3 I 8 = iS^ine hundred and thirty-eight. Two and nine, and four, and eight, and five, make twenty-eight. Set down eight and carry two tens. Two tens, and one, and three, and one, and six, make thirteen tens, or one hundred, and three tens. Set down three tens and carry one hundred. One hundred, and five, and three, make nine hundred. Set down nine hundred. The whole sum is nine hundred and thirty-eight. 16 ARITmiETIC TOR BEGINNERS. 7. Caution. — Always put figures of the same meaning in the same column, — tens under tens, hundreds under hundreds, &c. Exercise XIII. Work the follmcing additions : — (•■) (2 .) 268 321 185 ) 231 212 610 15 250 27 28 83 19 305 18 3 540 124 124 219 302 19 79 71 63 6 65 204 6 60 115 54 4 12 3. There are in a library forty-two books in one row, twenty-eight in another, eighty in another, and sixteen in the last ; how many are there in all ? 4. A man owes ^£719 to Jones, ^£28 to Smith, ;£ioo to Brown, and ;3ji7 to Johnson; what does he owe altogether 1 5. Count the panes in four windows, having twenty-four panes in each. 6. On a farm are 14 oxen, 208 sheep, 17 horses, and 3 1 pigs ; how many animals in all 1 7. In the five classes of a school there are nineteen, twenty-seven, thirty, fifteen, and twenty four ; how many are there in all ? 8. Add together a dozen, a score, six, and eleven. 9. In four bags of marbles there are 27, 16, 39, and 20 respectively ; how many marbles are there in all 1 10. If I change half a sovereign into twenty sixpences, half a crown into five, and a florin into four, and if I have seventeen sixpences besides, how many sixpences have I in all '? 1 1. There were three candidates at an election, of whom the first had 159 votes, the second 216, and the third four hundred ; how many people voted 1 SUBTRACTION. 17 8. In subtracting, add ten to the npper line whenever the figure beneath cannot be taken from it. But when- ever ten is added to the npper line it mnst also be added as one, to the figore next to the left on the lower line. Example of working Subtraction with Hundreds. What is the difTerence between 385 and 731 1 Set down the crreater number above the other. o 731) 7 I 13 385 ', _ 4 1 9 II Since 5 cannot be taken 5 from I, add ten to the one (4). — Five from eleven leaves six. 346 ) 3 I 4 I 6 Set down six- Add one ten to eight tens in the lower line. 9 tens cannot be taken from 3 tens, so add ten ten* to the upper line. Nine from thirteen leaves four. Set down 4 tens. Add ten tens, which are one hundred, to the 3 hundred. Four hundreds from seven hundreds leaves three ^hundreds. Set down 3 hundreds. The difference is three hundred and forty-six. EXERCISB XIY. 1. Add together three hundred and four, five hundred and seventeen, and one hundred and thirty-eight. 2. Take sixty-five from one hundred j and three hun- dred and fourteen from six hundred. 3. How many more books has one gentleman who has 856 in his library than another who has 695 ? 4. What sum given to a person who has 28 pounds would make up his money to 50 pounds ? 5. How many must be put in a bag containing 163 nuts to make up the number to 350 1 6. Out of a set of 150 prints, 26 are lost : how many remain ? 7. Of two windows, containing twenty-four panes each, seventeen panes are broken : how many remain whole 1 18 ARITHMETIC TO*. BEGINNERS. 8. A person lias saved jQi^"] : how mucli more must lie save to make up ;^5oo 1 g. '\'\niat is the difference between the incomes of two persons, of whom one has ^6y^, and the other ;^85o a year ? lo. At an election one candidate has 847 votes, and the other 691 : what is the majority'^ T 1. A man owes two sums of money, ;£6^ and jQi^'y he has only £^^0 to pay : hoAV much does he still owe % 12. Out of a debt of ;£'ioo a man pays first ^^25 and afterwards jQ2)^ : how much remains unpaid ] 13. Add together three hundred and fourteen and tAvo hundred and seventy six, and take four hundred and six- teen from the result. Work the following siibtractions : — (14.) 729 512 840 (15.) 368 500 434 326 127 29 124 (16.) 287 206 597 (17.) 500 240 629 153 9 329 18 73 142 18. Take 187 and 456 from 900. 19. From 314 and 625 take 274. 20. A man drives 32 miles on Monday, 25 on Tuesday, 24 on Wednesday, rests on Thursday, drives again 20 miles on Friday, and 18 on Saturday: how far has he travelled in the week % 21. In two villages, containing 136 and 348 people respectively : what is the total population % 22. At the census of 1861 a parish had 343 inhabi- tants, and in 187 1 there were 512 ; what was the in- crease ? 23. Take the sum of 243 and 356 from nine hundred and fifty. THOUSANDS. 19 0. When a figure, stands in the fourth place from the right it means thousands. Thus, — 1340 One THOUSAND three hundred and forty. 7298 Seven thousand two hundred and ninety-eight. 2000 Two THOUSAND. 3040 Three thousand and forty. 5012 Five THOUSAND and twelve. Exercise XY. ^p° (i) Read in wfyrds these figures : — 7342, 1085, 71 12, 9026, 3720, 5102. 8721, 1963, 2018, 1702, 3960, 8541. 2165, 3094, 2708, 6130, 5291, 5012. (2) Express in figures these numbers : — Three thousand nine hundred and twelve. Two thousand and seventeen. Five thousand and nine. Six thousand eight hundred and twelve. Four thousand and fourteen. Five thousand six hundred and four. ^Nine thousand eight hundred and eighty-eight. Four thousand and fifty. Six hundred and forty-one. One thousand two hundred and eleven. Exercise XYI. 1. How many miles would a man travel in a week who went 58 miles on Monday, 126 on Tuesday, 70 on Wednesday, 119 on Thursday, 310 on Friday, and 67 on Saturday ? 2. If there are five hundred and forty-six people living in one street, two thousand seven hundred and four in another, and three hundred and eleven in the next, how many are there in all 1 3. An irregularly shaped field has four sides, of which the first is 1204 feet long, the second 395, the third 2038, and the fourth 685 ; how many feet are there in the fence surrounding the field ] 20 ARITHMETIC FOB, BEGINNERS. 4. If a man has five debtors who owe him ;^57, ;£io38, ^19, ;^2i2, and ;£"66 respectively, how mnch is owing to him 1 and if he owes ;£"2 95, what is he worth ? 5. How much longer is a road a thousand miles long than one measuring 674 miles ? 6. To what sum must I add ^£'453 to make up ;!^84o 1 7. Three boys have respectively 79 nuts, 83 nuts, and 220 nuts; how many has the last more than the two others put together 1 8. If at an election 794 voted for A, 1628 for B, and 1577 for C, what was the majority of B over C, of B over A, and of C over A "? 9. Take 372 twice from a thousand, and say what remains. 1^ In the folloiclng sums, lilace iDords by the side of each line, thus : — 17 1 2 One thousand seven hundred and twelve. 29 Twenty-nine. 4804 Eour thousand eight hundred and four. 712 Seven hundred and twelve. 16 Sixteen. 7273 Seven thousand two hundred and seventy-three. (12.) Addition. 3162 2984 1061 (11.) 127 219 845 127 2138 3069 62 17 3206 547 218 1357 209 518 1019 57 287 1630 79 67 135 4096 7 3120 125 2634 23 Suhtradion. 1270 2160 7140 (13) 51^30 2070 184 1329 2765 2271 614 _, MULTIPLICATION. 21 THE MLLTIPLICATIOX TABLE AIS^D ITS USES. 10« The following shoidd he learned hy heart: — Two twos are four . . 4 Three threes are nine . 9 „ threes „ six . . 6 „ fours are twelve . .12 „ fours „ eight . . 8 „ fives „ fifteen . .15 „ fives „ ten . . 10 „ sixes „ eighteen . 18 „ sixes „ twelve . 12 „ sevens „ twenty-one 21 „ sevens „ fourteen . 14 „ eights „ twenty-four 2 4 „ eights „ sixteen . 16 „ nines „ twenty- „ nines „ eighteen . 18 seven 27 „ tens „ twenty . 20 „ tens „ thirty . .30 „ elevens „ twenty-two 2 2 „ elevens „ thirty- three 33 „ twelves „ twenty-four 2 4 „ twelves,, thirty six . 36 These numbers are found by adding two and three at each step. Exercise XVIL 1. How many legs have three chairs ? 2. How many fingers are there on three hands ? 3. If there are eight panes of glass in each window, how many in two windows ? In three ? 4. In three purses containing eight shillings each, how many shillings are there ? 5. What is the half of 12 ? of 16 ? of 1 8 ? of 20 ? 6. What is the third part of 12 ] of 15 ? of 9 ? of 6 ? 7. Divide twelve pence among two persons. Among three. 8. Give fifteen nuts among three persons ; how many has each? 9. "What is the third part of twenty-one ? 10. How many threes are there in twelve % how many twos] 1 1. What number multiplied by five gives fifteen % 12. How many rows of twelve each could be made of twenty-four soldiers ? of eight each ? 22 ABITHMETIC FOE EEGINXEBS. 11. "When sums are worked in multiplication, a part of each answer is set doTni, and the rest carried, as in addition. See 3. Example I. Multiply 1762 by two. I 7 6 2 2 1762 2 ^ 14 12 4 3524 Twice 2 are 4. Set down 4. Twice 6 teus are 12 tens. Set down 2 tens and remove 10 tens, that is i hundred, to the hundreds. Twice 7 hundreds are 14 hundreds, and i hundred brought from the tens makes 15 hundreds. Set down 5 hundreds and remove 10 hundreds, that is, i thousand, to the thousands. Twice I thousand is 2 thousand, and i brought from the hundreds makes 3 thousand. The result is 3,524. Example II. 8 5718 3 3 '!■ 15 I 21 I 3 I 24 17154 Note. — The same should be set down as on the right. Exercise XVni. 1. Find twice eighteen ; Three times twenty-five. 2. Multiply forty-six by two; Thirty-eight by three. 3. In three fields containing 106 sheep each, how many sheep % 4. On two pages containing 453 words each, how many words? 5. How many letters are there in 245 words of three letters each ? MUXTIPLICATIOX. 23 6. In 3 rows of 169 trees each, how many trees ? 7. Find the difference between twice forty-six and three times fifty-seven. 8. In five columns of names, two contain thirty-eight each, and three contain thirty-seven each ; how many are there in all ? 1^ Wo rTc the folloioing questions : — (9.) 17 529 123 1406 (10.) 718 627 526 2323 223 sixes „ thirty . •30 sevens „ thirty-five •35 eights „ forty . . 40 nines „ forty-five •45 tens „ fifty . . •50 elevens „ fifty-five .55 twelves „ sixty . .60 Multiplication Table {continued). The following should he learned hy heaH : — Four fours are sixteen . 16 . Five fives are twenty-five 25 „ fives „ twenty . . 20 „ sixes „ twenty-four 24 „ sevens „ twenty-eight 28 „ eights „ thirty-two .32 „ nines „ thirty-six .36 „ tens „ forty . . 40 „ elevens,, forty-four .44 „ twelves,, forty-eight . 48 12. It is not necessary that all these tables shall be of the same length, and shall begin with the number two. For five times three is the same as three times five, which has been already learned. The diagram will show this : — 3 3 3 3 3 5 = In the same manner it might be shoiaiftitji^ scseendODrors are the same as four sevens, or that fif ^^IJdWrte^sft T « to eight fives. V. -■«\' 24) AKITHMETIC FOK BEGIXNEKS. Exercise XIX. 1. What are seven fours? five sixes ? four sevens? 2. Three fives 1 eight fours? five twos? four threes ? 3. How many lingers are there on four hands ? on seven ? on nine ? 4. How many pence in nine fourpenny-pieces ? in seven? in three? in six? 5. There are four farthings in a penny. Change into farthings — five pence, nine pence, fourpence. 6. Change into pence — three sixpences, four, five, two. 7. What is the eighth part of 32 ? the seventh of 28I the third of 2 1 ? the ninth of 18 ? 8. How many sixes are^ there in 30 ? how many fives in twenty ? 9. Find how many marbles are possessed by four children who have eight each. 10. How many legs have twelve chairs ? 11. If there are twelve pence in a shilling, how many are there in five shillings ? 12. Multiply eleven by five, by three, by four. (13.) 1712 5098 7121 (14.) 5060 3 24 4 (15.) 8121 1563 7096 (16.) 6127 8193 425 43 (17.) 202 1027 3162 (18.) 1964 719 354 54 MULTIPLICITIOX. The Multiplication Table Continued). The following should he learned hy heart : — Six sixes are thirty-six . 36 Seven sevens are forty- „ sevens „ forty-two . 42 „ eights ,_, forty-eight . 48 „ nines „ fifty-four . 54 „ tens „ sixty . .60 „ elevens „ sixty-six . 66 „ twelves „ seventy-two 7 2 Eight eights are sixty-four 64 „ nines „ seventy- two 72 „ tens „ eighty . . 80 „ elevens „ eighty-eight 88 „ twelves „ ninety-six , 96 nine 49 „ eights are fifty-six . .56 „ nines „ sixty-three . 6^ „ tens „ seventy . .70 „ elevens „ seventy-seven 77 „ twelves „ eighty-four . 84 Xine nines are eighty-one 8 1 „ tens „ ninety . . 90 „ elevens „ ninety -nine. 99 „ twelves „ one hundred and eiofht 108 Exercise XX. 1. What are seven eights ? three sixes 1 four nines 1 2. How many shillings must I give for five articles at seven shillings each ] For seven at nine shillings each ] 3. How many marbles are there in eight bags contain- ing nine each ? In seven containing five each ? 4. AVhat is the seventh part of forty-two 1 the ninth of seventy-two ? The third of twent^^-seven ? 5. Eind the fifth of thii-ty, the third, the sixth, the tenth. 6. Divide twenty-four cakes among four children, among six, among eight, among twelve, among two. 7. How many squares are on the carpet in four rows seven each ? in five rows of eight each 1 8. If seven boxes containing nine pence each were emptied, how many pence would there be in all ] 9. In how many rows could you arrange forty-eight soldiers, and how many would there be in each 1 10. Write out the whole of the tables, from twice two to nine times twelve, working them by addition. 26 ARITHMETIC FOR BEGINNERS. Example of Working Multiplication. 13. Ill nine villages, each containing two thousand four hundred and seventeen persons, how many persons live] 2417 Two thousand four hundred and seventeen. 9 21,753 Twenty-one thousand seven hundred and fifty- three. Nine times seven are 63. Set down 3 and carry the 6 tens. Nine times i ten are 9 tens, and 6 tens make fifteen tens. Set down 5 tens and carry i hundred. Nine times 4 hundreds are 36, and i make 37 hundreds. •Set down 7 hundreds and carry the 3 thousands. Nine times 2 thousand are 18, and 3 make 21 thousand. Set down 21. The result is. Twenty-one thousand seven hundred and fifty-three. Exercise XXI. 1. Multiply four hundred and thirteen by five and by six. 2. In a regiment of 950 men, each has eleven rounds of cartridge ; how many rounds are there in all ? 3. There are twelve pence in a shilling; how many pence are there in 1 3 shillings 1 in 2 7 shillings ? in 48 shillings 1 in 173 shillings? 4. There are 8 bushels in a quarter of corn; how many bushels are there in 17 quarters? in 39 quarters? in 217 quarters ? 5. If a town contains 16,382 houses, and on an average 7 persons in each house, what is its population ? 6. There are twelve inches in a foot ; how many inches are there in 14 feet ? In 59 feet ? In 625 feet? , MULTIPtilCA.lIOK. 27 7. What is the weight in pounds of seventy-nine parcels weighing nine pounds each 2 8. What is the di erence in number between 213 rows of trees containing 5 each, and 326 rows containing 4 each? 9. How many words are there in seven columns of a spelling-book containing eighty-nine words each 1 10. There are four quarts in a gallon ; how many quarts are there in 29 gallons 1 In 538 gallons 1 In 714 gallons 1 11. Add together the values of six houses worth £'J2^ each, and of nine houses worth ;^ii32 each. 1 2. Which is greater, and by how much 1 — seven times twenty-nine, or six times thu'ty-nine ? 13. Add together 357 and 619, and multiply the result by 8. 14. On unpacking 6 parcels containing 234 biscuits each, how many do I find in all ? Work the following sums : — (15.) 728 6139 278 (16.) 1472 963 8714 5 II 12 567 (17.) 3194 8625 2169 (18.) 8271 3192 2028 3 12 7 696 (19.) 4163 2196 5127 (20.) 1815 4137 2017 857 968 C21.) T379 51S0 6178 (22.) 5163 8041 5172 6 II 12 7 9 12 28 ARITHMETIC FOR BEGINNERS. MILLIONS. 14. Any number written mth six figures to its right means millions. A million is equal to one thousand thousands. Thus 2,000,000 means two millions, 5> Ij563;Ooo „ one million five hundred and sixty-three thousand. „ 8,045,195 „ eight millions forty-five thou- sand one hundred and ninety- five. „ 14,628,014 „ fourteen millions six hundred and twenty-eight thousand and fourteen. 15, XoTE. — It is always useful, in reading numbers consisting of many figures, to divide them into threes from the right. The group of figures mth six to the right means millions ; that with only three figures to the right means thousands. Thus, 27,416,845, is to be read twenty-seven million, four hundred and sixteen thousand, eight hundred and forty -five, and 217,013,302, is to be read 217 million, 13 thousand, 302. Exercise XXII. (a) Express in words these figures : — (i.) 171,028 6,510 17,216,370 (2.) 6,380,521 10,714,816 9,500^00 - (3.) 318,721,625 219,346,285 10,716,800 (4.) 192,005 31^060 18,851,000 (5.) 7,120,008 3,197,620 85,070,110 (6) Express in figures these numbers:- — * I. Two miUious. Eight millions five hundred thousand. 2. Three hundred and forty-two thousand five hundred and nineteen. 3. Six millions ten thousand and nineteen. Fourteen millions and eleven. MILLIONS. ' 29 4. Fourteen millions, tliree hundred and fifteen thou- sand, six hundred and nine. 5. Eleven millions and fifteen. Seven millions, tliree hundred and twelve thousand. 6. Fjorty-six millions, three hundred and nineteen thousand, six hundred and fifty-four. 7 . Three hundred and t\Yenty-two millions, seven hun- dred and twelve thousand, nine hundred and eleven. 8. Fifty- one millions, six thousand and three. Three millions and twelve. 10. We multiply a number by 10 Avhen we place a (jipher after it, or remove it one place to the left. We aiultiply by 100 when we place two ciphers; and by 1,000 when we place three ciphers, or remove it three places to the leit. Thus : — ^, 728,niultipliedby 10 is 7,280 =: seven thousand two hundred and eighty. „ „ 100 „ 72,800 = seventy- two thousand eight hundred. „ „ 1,000 „ 728,000 = seven hundred and twenty-eight thousand. „ „ 10,000 „ 7,280,000 = seven millions two hundred and eighty thousand. Exercise XXIII. 1. Multiply 17 by ten ; 28 by ten ; Three hundred and ten by ten. 2. Multiply 216 by 10; by a hundred, by a thousand. 3. How many men are their in 200 regiments contain- ing 976 men each 1 4. Take a hundred times 1384 from a thousand times the same number. 5. Add together a hundred times 117 and a thousand times 65. 6. Multiply 738 by 10 ; 21 by 100 ; and 317 by i,oooj and add the results together. 7. What are five hundred times sixty-five ? 30 ARITHMETIC FOR BEGIlfNERS. 17. 'When a multiplier consists of two or more figures, the multiplication is to be worked in two or more lines, thus : — Exam]jle (a). Multij^ly 3172 by 18; that is, by eight and by ten. 3172 18 25376 Eight times 3172 (see 13). 31720 Ten times 3172 (see lO). 57,096 Eighteen times 3172. 18. Note. — The result of multiplying numbers is called their Product. Thus 63 is the product of 7 and 9 ; TOO is the product of 10 and 10; and 57,096 is the product of 3172 and 18. Example (b). How many biscuits are there in 327 cases containing 4638 each 1 4638 327 32466 Seven times 4638 (see 13). 92760 Twenty (or ten times two) times 4638 (see\^). 139 1400 Three hundred (or 100 times 3) times 4638. 1,516,626 Three hundred and twenty-seven times 4638. Note. — The cipher (0) at the end of the second line, and the two ciphers (00) at the end of the third line are not necessary in the ■working of the snm, and are usually omitted. Exercise XXIV. 1. Find the number of houses in eighteen streets containing sixty-seven houses each. 2. Multiply four hundred and thirty-five by twenty-six. 3. How many nuts will be required for seventy-four children that they may have twenty-five apiece ? LONG 5I[JL*riPLICATI0X. 31 4. In forty-seven regiments, comprising one thousand three hundred and seventy-five men each, how many soldiers are there ? 5. What number would be produced by multiplying 6283 by 147 1 6. In twenty-eight chests of tea weighing 315 lbs. each, how many lbs. are there ? 7. There are 112 lbs. in a cwt. ; how many lbs. are there in 1 7 cwt. 1 How many in 3 1 5 cwt. ? 8. There are 28 lbs. in a quarter; how many lbs. are there in 11 quarters'? How many in 29 quarters? 9. Find the difference between twenty-seven times three hundred and sixteen, and thirty-nine times one hundred and twenty-eight. 10. There are 20 shillings in ^^i ; how many shillings are there in ;£"i2 8 "? How many in ^2163 1 11. Add together the product of 763 and 29, and the product of 2138 and 17. 12. In a church there are 85 pews, of which 47 hold seven persons each, and the rest six each. How many persons can be seated in it 1 13. There are 16 ounces in i lb.; how many ounces are there in 827 lbs. ? How many in 1236 lbs. ? 14. 21036 26 5172 19 15- 17. 19. 31062 29 17831 35 16. 813 813 215 106 37205 59 11825 37 18. 17386 37 5068 162 41380 370 21639 306 32 ARITHMETIC POR BEGINKEBS. 10« When one number is the product of two others, we may multiply by it by multiplying by those two others in succession. Examjjle (a). ^Multiply 3 1 7 2 by eighteen. !N'ow eighteen equals twice nine. There are therefore two methods of doiijg this ; first, that which is shown in 17, and second, as follows : — 3172 9 28548 nine times 3172. 2 57096 twice nine times 3172, or eighteen times 3172. (h) Multiply 7298 by 42. 'Now 42 equals 6 times 7. This sum may therefore be worked in either of these two ways : — I. 7298 42 14596 twice 7298. 291,920 forty times 7298. 306,516 forty-two times 7298, 2. 7298 7 51086 seven times 7298. 6 306,516 six times seven times 7298, or forty-two — — ■ — times 7298. LONG MrLTIPLICATIOir. \ /> 0:#^ Exercise XXV. ^^'^^gli Wo?'7c each of the foUovnng sums in ttQO ways as in the exami')lp.s just given : — 1. Multiply 729 by 24. 8643 ^J 3^- 2. Find the number of windows in 39 houses containing twenty-one 'windows each. 3. What is the product of 623 and 108? of 5163 and 96 ? 4. There are 24 grains in a pennyweight of gold ; how many grains are there in 47 dwts. ? in 318 dwts. ? 5. There are 36 inches in a yard ; how many inches are there in 17 yards? in 108 yards? in 94 yards ? 6. 2372 50861 7. 3198 21945 35 27 . 120 72 8. 51738 49 2136 44 10. 17293 45 3187 50 12. 31920 96 41785 80 9- 3702 15 81369 63 II. 71938 32 21964 56 13- 3621 108 413298 81 14. Subtract 236 from 500, and multiply the result ^756. 15. Add together sixty-three times 251, and fifty-four times 835. 16. Find the product of 28, and 56, and 40. c 2 34 ARITHitETIC FOR BEGIXNEBS. DIVISION. 20. To divide a number is to separate it into equal parts. There are ten parts in the line in the margin. When divided by five there are two parts. When divided by two there are five. Division is the reverse of multiplication. Thus, if we divide twelve shillings among six persons, each of those persons has two shillings, because six times two makes twelve. So on dividing the number 35 into seven parts, we find the — number five. Example of Division. — /. Divide 864 by 2. 2)864 The half of eight hundred is 4 hundred ; set down 4 under the hundreds. 43 2 The half of six tens is 3 tens ; set down 3 — under the tens. The half of four is 2 ; set down 2. Therefore the half of 864 is 432. Example of Division. — II. Divide 7625 by 7. 7)7625 The seventh part of 7 thousands is one thousand ; set down i in the thousands 1089-2 place. The seventh part of 6 hundreds cannot be taken. There is therefore no figure in the hundreds place in the answer. The nearest seventh part of 62 tens is 8 tens, or the seventh of 56 tens; this leaves 6 tens or 60 units un- divided ; set down 8 under the 2, and carry the 6 tens to the 5 units. Sixty-five divided by 7 give 9, and leave 2 undivided; set down 9, and place 2 as the remainder to the right. The answer to the, question is 1089, and 2 remaining. DIVISION. 35 21, The answer to a question in Division is called the QUOTIENT. The dividing number or divisor should be set down on the left side, and each figure of the quotient should be set down as it is found, and the remainder carried to the next figure to the right. Exercise XXYI. 1. What is the fourth part of 84728 ^ Of 212 ? 2. Divide ;^2oo among five persons. Among ten. 3. What number multiplied by 3 will produce 1236 1 4. There are 1 2 pence in a shilling ; how many shillings are there in 504 pence? in 1584 pence? in 3192 pence? 5. If 1000 nuts are distributed among children who are to have 8 apiece, how many children receive them ? 6. On a page of 5 columns there are 1525 words; how many are there in each column ? 7. In a regiment of 1200 men how many rows could be formed of eight each ? Of six each ? Of ten each ? Of four each ? 8. If a sum of ;£" 17,038 were left equally between seven persons, how much would each receive ? 9. In a street there are in all 1672 windows, each house having 8 ; how many houses are there ? 10. What is the diiference between the ninth part and the third part of 95,086 ? II. 2)42846 12. 3)3579 13. 8)672091 5)49028 14. 7)31685 10)71986 15- 1.1)43972 3)2176381 16. 4)359851 12)63987 17. 8)31698 12)57629 18. 7)56941 6)410847 36 AUITHlifETIC FOR BEGIN^'EBS. 22, When the divisor is greater than 12, the process is called long division. The following example shows the method of working each step in such a process : — Example of Long Division Divide 73476 Ijy 26. {a) 26)73476(2000 (*) Divide 73 thousands by twenty- six, and the nearest answer is proved by trial to be 2, or 2 thou- sands. Take 26 times 2 thousands from the dividend. This leaves 21476 undivided. Divide 214 hundreds by 26, and the nearest answer is 8, or 8 hundreds. Take 26 times 800 from the remainder. This leaves 676 undivided. In 67 tens 26 is contained 2 times, or 2 tens. Take 26 times 2 tens from 676. This leaves 156 undivided. Divide 156 by 26, and the answer is 6. There is no remainder. The answer is 2826. !N'oTB. It is usual to omit the ciphers shown in («), and to set down the figures as in {h), bringing down each new figure of the dividend as it is required. 52000 800 21476 20800 6 676 520 156 156 26)73476(2826 52 214 208 67 52 156 DIVISION. Exercise XXYII. 37 1. What is the fifteenth part of six hundred'? 2 . D ivide twelve hundred and sixty-eight by twenty-four. 3. How many packets, containing 14 lbs. each, can be made up out of a chest containing 11 34 lbs. 1 4. T^ind the forty-seventh part of two millions. 5. What number multiplied by 17 will make 5712 ? 6. Add together the fifteenth and the sixteenth part of two hundred and forty. 7. A mile contaius 63,360 inches. If a number of flagstones measuring 32 inches are laid end to end, how many will be required to extend so far as a mile 1 8. There are twenty shillings in ;,^i ; how many pounds are there in 3560 shillings? 9. How many times can I take the number 6^ out of a thousand 1 10. Two hundred and fifty-nine bushels of corn were eaten in a certain time by 37 horses : how many bushels on an average were eaten by each ? 11. What is the difference between the twenty-fourth and the twenty-fifth part of twelve thousand 1 12. Divide seventeen thousand six hundred and ninety- two by one hundred and twelve. 1^ Work the folloicing sums in division : — 13. 16)7263 31)107,821 25)31,690 14. 711)350,006 82)51,472 33)98,217 15. 3024)863,197,281 357)862,319 13)62,501 16. 713)627,812 305)1,796,831 314)816,291 17- 351)472,098 713)542,618 18)72,196 18. Take 72,638 from a million, and divide the result by 27. 19. Add together 2,163 ^^^ 5i,02 7,anddi^^dethesum of those numbers by 135. 38 ARITHMETIC FOR BEGINNERS. !S3» We divide a number by lo, by loo, by i,ooo, by 10,000, or by 100,000, when we cut off as many figures as there are ciphers in the divisor. Thus : — We divide 100 by 10 by cutting off one nought, which leaves 10 : 500 divided by to becomes 50, one nought having been removed; divided by 100 it becomes 5> two noughts having been removed. 750,000 divided by 100 gives 7,500 ,» » 1,000 „ 750 4,693,825 divided by 10,000 „ 469 and 3,825 rem'* „ „ 100,000 „ 46 „ 93,825 „ 24. Hence, when there are ciphers at the end of a divisor, we cut off as many figures from the dividend, and divide by the rest of the figures of the divisor. Example (a) Divide 726,837 by 5000. 5,000) 726,837 145-1837 remainder. We divide by 1000 by cutting off 3 figures (23). Eut 726 divided by 5 gives 145 and leaves i thousand remaining. The quotient, therefore, is 145 and 1837 remainder. Example (b) Divide 835,426 by 3700. 37,00)8354,26(225 A- 'A ^. X. ^. Here we divide by 100 by cutting off the two figures to the 95 right. 74- • We then divide the 8354 by 37 ill the usual way. jgr The answer is 225, with a re- mainder 29. 29 The quotient, therefore, is 225, with a remainder 2926. Divisioy. 39 Exercise XXVm. 1. Find the hundredth part of 3279. 2. TThat is the thousandth part of 392,185 ? 3. Divide 1,769,382 by ten, by a hundred. By a thousand. By ten thousand. 4. Find the hundredth part of 1,769; Of 38,351 ; Of 52,684; Of 479,382. 5. How many times greater are 3 2 70 than 32 7] 826,000 than 826 ? 479,300 than 4793 1 6. Divide 479 by sixty. 7. From a total of 47,963 men how many regiments could be told off containing 800 each ? 8. How many times are 170 contained in 34,823 ? 9. Divide 387,256 by 280 and by 28,000. 10. Divide 1,723.865 by 4500. 11. There are 20 shillings in a pound, how many pounds are there in 1080 shillings 1 In 2370 shillings 1 12. There are 60 fourpenny pieces in a pound, how many pounds are there in 7360 fourpenny pieces ? In 40,960 fourpenny pieces ] 13. Add together 496 and 5080, and divide the result by 320. 14. Multiply 76 by 15, and 238 by 30, and divide the sum of the two products by 30. 15. There are 1760 yards in a mile, how many miles are there in a million yards ] 16. 23o)i86752( i240o)798265( 17. 528o)32695o( 3i8oo)2763975( 18. i56oo)279638( 32o)567928( 19- 3oo)379687( i24oo)7i9876( 20. A^Tiat number multiplied by 300 would give 52,797,000? 21. Take 5,286 from two millions, and divide the result by seventeen hundred. 40 ARITHMETIC FOR BEGINNERS. SIGNS AND THEIR USES. 25. The four principal processes in arithmetic are often expressed, for convenience and shortness, by signs, as follow : — + is the sign of addition, and is called 2)^us Thus 7 + 9 is read 7 plus 9, and means 9 added to ). — is the sign of subtraction, and is called minus. Thus 9 — 7 is read 9 minus 7, and means 7 taken from 9. X is the sign of multiplication. Thus 9 X 7 is read 9 into 7, and means 9 multiplied -1- is the sign of division. Thus 20 -1- 5 is read 20 hy 5, and means 20 divided by 5 . This is sometimes expressed by placing the divisor underneath the dividend. "-^ means 20 divided by 5. zr is the sign of equality. Thus 5 + 3 = 8 means 5 with 3 added to it equals 8, or is equal to 8. ( ) means that the whole quantity within the bracket is affected by the sign before it. Thus, 18- — (6 + 3) means that the sum of 6 and 3 or 9 must be subtracted from 18. And (12 — 7) x (3 + 4) means that 12 — 7 or 5 must be multiplied by 3 + 4 or 7. Hence, — 7 + 9 = 16. Seven ^jZz^s 9 equals 16. 9 — 7 = 2. Nine minus 7 equals 2. 9 X 7 = 63. Nine multiplied by 7 equals 63. 20 -i- 5 — 4. Twenty divided by 5 equals 4. 2S. = 24d. Two shillings equals 24 pence. ;^3 = 60s. Three pounds equals 60 shillings. Expressions of this kind, showing equality between two different expressions for the same number, are called EQUATIONS. 41 EXERCISES IX SIGXS. ExsBCiaE XXIX. fg^ (a) BeadaefoUommg exprtssi&mg: — 8 + 4 12-15 <> + 7 3X6 20 + 8 l8-^2 Four nods = cne acre; Two pints = one qoait. xbree fininMBnT Mecca = two {b) Pbee tlie true lesnll afier Oie ii%n of eqmlitf in eadi of tiwee cases: — I. 20 + 16 + 3 = . 2. 18 + 17 — 5 = 3.8x2x5== . 10 — 5—3 = 4. 16 -£- 9 28 X 4 5~ — ' 4 + 3 = 5.15 + 16 + 17—28= . 6.5x8x4 = 156 + 230 + 49 + 7 = 8. (15 4^ 8 X 2) + {12 X 6 X 3) = 9l 27 — 16 + 187 — (23 + 15) = ID. (24 + 17 + 26 + 33) -^ (30— 5) = 262 -i- 18 — 7 II. = 12. 236 X 15 X 9 = . 418 + 275 — 63 =. 13- 540 + 127 + 165 - (783 - 219) = 14. (3401 X 16) + (542 X 28) =z 15- (i74<> + 5«4 - 1926) X (2347 - 1978) = . ^^4i3;x 51 4278 - 1396 (e) Make up six equations amikr to tiiose in tibe 42 ARITHMETIC FOR BEGNNERS. Exercise XXX. Miscellaneous Examples of the Simple Rules. 1. An empty jar weiglis 308 grains ; when full of water it weighs 4372 grains, what is the weight of the water ] 2. A person born in 1792 lived 75 years, in what year did he die ? 3. Milton, who was born in 1608, died in the year 1 674, how old was he when he died ] 4. A labourer earns 17 shillings a week, how many shillings does he receive in the whole year of 5 2 weeks 1 5. From a fountain 15 pints of water flow per minute, how many flow in an hour (60 minutes), and in a day (24 hours) 1 6. A man buys cloth for 585 shillings, at 13 shHlings per yard, how many yards does he buy 1 7. Add fifteen to twenty, take away five, divide the remainder by six, and multiply the result by seven. 8. There are seven days in a week, how many days are there in 176 weeks ] 9. If a railway train travels 38 miles an hour, how far will it go in 1 6 hours 1 10. In fifteen bags, containing equal numbers, there are 1980 nuts, how many are in each ? 11. A landowner sold 327 acres of land at £,1^ per acre, and 278 acres at ;£^23 per acre, what was the total purchase-money 1 12. If a person owed ^^1200, and paid back at different times ;£'298, ;£"i54, £^(>Zi ^^^ £^Si ^^^^^ P^^ of his debt remained unpaid ? 13. Multiply 628 by 156, and divide the product by 700. 14. What is the difference between 168 + 95 -f 64 and i6 X 8 x 5 2 15. If I take i860 steps in walking a mile, how many shall I take in walking 1 5 miles and a half ? MISCELLAXBOrS EXAMPLES OF THE SIMPLE RULES. 43 1 6. To what number can I add 768 to make up 1,100 1 17. How many pounds vreight are there in 7 bags of sugar containing 224 lbs. each; and in eleven bags con- taining 168 lbs. each] 18. What is the forty-fifth part of a million ? 19. A mile is equal to 1,760 yards ; how many yards are there in 2 7 miles ? How many in 1 8 miles ? 20. Take 238 from a thousand; and multiply the re- mainder by thirty-four. 21. Take the number 6, double it, double the result, and again until the sixth time ; to what will it amount ? 22. AVhat number is that which, multiplied by 64, will give 81,856 as product? 23. Multiply 154 by itself; and the result by the same number. 24- (365 + 18 + 279) - (274 + 115). 25. There are four to^vns with an average population of 11,476 persons each; how many people are there in them all ] 26. Find the difference between the twenty-fifth part and the twentieth part of one million. 27. London contained 2,680,735 persons at the census of 185 1, 3,222,720 at the census of 1861, and 3,883,092 in 187 1 ; iind the increase at each period. 28. (623 + 35 + 108) X (723^- 518). 29. Subtract 374 from 8,000, three times in succession, and find the result. 30. In a spelling-book there are 56 pages, each con- taining 2 columns of words, and in each column 64 words ; how many words are there in all 1 31. What is the difference between the sum of 1,684 and 2,132, and the product of 185 and 247 ] 32. The population of the United Kingdom in 1871 was 31,465,480 ; of these, 3,358,613 were inhabitants of Scotland, and 5,402,759 of Ireland ; how many remained in England and Wales ] 33. Find the number of soldiers in an army consisting of five divisions, each division containing eight regiments composed of 1,250 men each. 44 ABITHMETIC FOB, BEGDJlfEBS. MOXEY. SO* The coins in use in England are — Gold. The Sovereign. „ Half-sovereign. Silver. The Crown, or Five Shilling piece. „ Half-crown. „ Florin, or Two Shilling piece. „ SJiilliug. „ Sixpence. „ Fourpenny piece. „ Threepenny piece. Copper. The Penny. „ Halfpenny. „ FaHhing. But of the names of these coins only four are used in keeping accounts. » The following table must be learned by heart : — Four Farthings make One Pexny. Twelve Pence „ One Shilling. Twenty Shillings „ Oxe Sovereign, or Pound. The letters £ s. d. are commonly used to show Pounds, Shillings, and Pence.* Thus ;£i 6s. yd. is read one pound six shillings and seven pence. £1^6 I2S, 8d. is read one hundred and thirty-six pounds twelve shillings and eight pence. Farthings are not separately enumerated, but are always written as parts or fractions of pence. Thus, — \ means a fourth of a penny, or a Farthing. I means a half of a penny, or a Halfpenny. f means three-fourths of a penny, or Three Farthings. Thus 17s. 6^d. is read seventeen shillings and sixpence ferthing. £1 I2S. 3M. is read one pound twelve shillings and threepence halfpenny. * These letters are the initials of the names of Roman coins — Libri, Solidi, Denarii, — -"which were not of exactly the same value as pounds, shillings, and pence, although the names are still used. MONEY KULES. 4$ Exercise XXXI. Read the following expressions : — 1. i6s. 2d., £i I2S. 3d., £45 7s. lod. 2. ;£io 19s. 3id., £27 15s. 6id., ^239 5s. lid. 3. ;^4028 OS. 6|d., ;^3i92 12s. o|d.,;^i5oo 6s. ii^d. Write in figures the following sums of money : — 1. Eightpence, fourpence halfpenny, elevenpence three farthings. 2. One pound twelve and ninepence ; Three pounds five and sixpence halfpenny. 3. ^Nineteen pounds four and sixpence farthing ; Twenty- four pounds eleven and ninepence haKpenny. 4. Twenty-five pounds and sixpence ; Twelve pounds five shillings and three farthings. Exercise XXXII. Simple Calculations in Money. 1. How many farthings are there in twopence ? How many pence in three sixpences 1 2. Add together fourpence, fivepence, and sixpence. 3. Add together three farthings and seven farthings. 4. What change will he left on paying yd. out of is. ? 5. What is a quarter of a shilling ? A half of half-a- crown 1 6. If I buy five articles at 2d. each, and seven at 3d. each, how much will they cost 1 7. Out of a two shilling piece I spend 6d., 4d., and 5jd., how much change shall I receive 1 8. Divide sixpence among four children. 9. To how many people can I give twopence each out of half-a-crown 1 10. What is the difference between seven fourpenny pieces and five sixpences 1 11. Add together eight farthings and eight halfpence. 12. How many fourpenny pieces are worth the same as five shillings 1 46 ARITHMETIC FOR BEGINNERS. Five farthings Eight farthings Twelve farthings Sixteen farthings Twenty farthings Twenty-four farthings Forty-eight farthings MOJS^EY TABLES. To he learned by heart Farthings. make one penny farthing ... o two pence o three pence o four pence o five pence o six pence o one shilling i Twelve pence Twenty pence Twenty-four pence Thirty pence Thirty- six pence Forty pence Forty-eight pence Fifty pence Sixty pence Seventy pence Eighty pence Ninety pence A hundred pence Twenty shillings Twenty-one shillings Thirty shillings Forty shillings Fifty shillings Sixty shillings Seventy shillings Eighty shillings Ninety shillings One hundred shillinf^rs Pence. make one shilling one shilling and eight pence i two shillings 2 two shillings and six pence 2 three shillings 3 three shillings and four pence 3 four shillings 4 four shillings and two pence 4 five shillings 5 five shillings and ten pence 5 six shillings and eight pence 6 sevenshillings and six pence 7 eight shillings and four pence 8 Shillings. make one pound ^i o „ one guinea * i i ., one pound ten 1 10 two pounds 2 o two pounds ten ...... 2 10 three pounds 3 o three pounds ten ... 3 10 four pounds 4 o four pounds ten ... 4 five pounds 5 10 * Though guineas are no longer coined, this name for twenty-one shillings is frequently used. Example I. £Z 6s. 5d £ s. d. I 7 6 o i8 9 3 6 5 5 12 8 MONEY RULES. 47 ADDITIO:tT A^T) SUBTRACTION OF MOXEY. 27. When sums of money have to be added or sub- tracted, the pounds, shillings, pence, and farthings should be arranged in columns and dealt with separately. Add together jQi 7s. 6d., i8s. pd., "We first add the pence. 5 and 9 and 6 make 20. But as 12 pence make one shilling, 20 pence make i shilling and 8 pence. Set down 8 under the pence, and carry i to the shillings, i and 6 and 18 and 7 make 32 shillings. But as 20 shillings make i pound, 32 shillings make j£\ and 12 shillings. Set down 12 shillings and carry ^1 to the pounds, i, 3 and i make ^5. Set down 5 under the pounds. The answer is jQ^ 12 s. 8d. Example II. Take ;^i6 3s. 4|d. from ;;^2 7 i8s. 6Jd. Take a halfpenny from three far- things, one farthing remains. Set it jQ s. d. doAvn in the farthings place. 27 18 6 1 Take fourpence from sixpence. Two ^6 3 4-2 pence remain, and must be set down under the pence. II 15 2 J Take three shillings from eighteen, fifteen remain, and must be set down under the shillings. Sixteen pounds from twenty-seven leave eleven. The answer is eleven pounds fifteen shillings and two- pence farthing. 48 AllITUilETlC POR BEGINNERS. Exercise XXXIII. 1. Add together 2S. 6d., i8s. 4d., and ^i 13s. 9d. 2. Find the amount of ;^2 14s. yd., j£i i6s. 3d., ;z^i2 6s. 8d., and ^ij 2s. 4d. 3. Subtract ^^ los. from ^^ i8s. yd. 4. What is the difference between ;£'i23 12s. 9d. and £71 5s. 4d.? £ s. d. 27 15 8 19 6 7 324 12 4 9 5 8 ^ s. d. 18 7 10 6 12 15 9 24 13 6 TFori: the foUoicing subtractions : — 6. ^ s. d. £ s. d. 24 12 8 319 6 5 12 7 5 28 3 2 £ s. d. 234 2 9 19 18 4 123 6 7 5 10 £ i 3. d. 200 ] [8 7i 172 ] [2 6d 7. If I buy coffee for 3s. 8d., tea for 5s. 4d., sugar for I lid., and soap for is. 4d., how much shall I spend ? 8. Add together a sovereign, a half-crown, three six- pences, four shillings, and sevenpence halfpenny. 9. At a stationer's I bought 3 quires of paper for lod., some envelopes for 6d., two books, of which one cost 3s. 6d. and the other 4s. 8d., and some newspapers for pd. ; so how much did my bill amount to ? 10. To what sum will the following coins amount : — five sovereigns, six half sovereigns, three crowns, eight florins, and sixteen pence ? 11. Add together fifty guineas and seventeen pounds, and subtract forty-seven pounds five shillings from the rasult. COMPOUND ADDITTCN. 49 ADDITIOX OF 'MO:SEY—co7.lmu€d. 28, It iB roquirt-d to add together the following sums of money: — ^£1314 i6s. yd., /^zo^S 12s. g^A, ^i los., ^316 5.S. 4|d., ;£"409i6 I2S. 8^d., and ;£'ioo8 16s. 5d. Add up three farthings, one farthing, and one halfpenny. Tliey make six fartliing"s, or one penny halfpenny'. Set down a halfpenny and carry one penny. One and 5 and 8 and 4 and 9 and 7 make 34 pence. Thirty-four pence are ^ s. d. 2 shillings and 10 pence. Set down 131416 7 10 pence and carry 2 shillings. 2038 12 9.^ Two and 16 and 12 and 5 and 10 I 10 o and 12 and 16 make 73. Seventy- 316 5 4^ three shillings, 3 pounds 13 shillings, 40916 12 8J Set down 13 shillings and cariy 3 1008 16 5 pounds. Three and 8 and 6 and 6 and i and 44596 13 io| 8 and 4 make 36 pounds. Set down 6 and carry 3 to the tens. Three and i and i and 3 and i make 9 tens. Set down 9. Isine aud 3 and 3 make 15 hundreds. Set down 5 hundreds and carry i to the thousands. One and 2 and i make 4 thousands. Also set down 4 tens of thousands. The answer is 44 thousand five hundred and ninety-six Pounds thirteen Shillings and ten Pence halfpenny. Exercise XXXIV. 1. Add together £^15 12s. 3d., ;£'2096 15s. 4id., ^18 17s. 9id., and ;£4036 12s. 8|d. 2. ;^i79 14s. 9H + £206 IIS. 5d. -f £iB 3S.7id., + ;£3207 IIS. 7id. D 50 ARITUMETIC FOR BEGnc^'ERS. 3- £n^1 13s- 9i<i- + ^^6235 17s. 2d. + ^^480 I2S. A^' + ^3196 los. + £^(i 15s 3d. 4. ;£75 15s. 8H + ;Jii25 i6s. 8d + ^726 13s. 9i^- + ^£^3271 los. 6^d. 5- ;^854 7s. 2d. + ;^io6 iis. 5jd. + ^1032 15s. 8|d. + ;£6i95 14s. 7id. 6. ;^2i36 13s. 6d. + ;£732 los. 8id. + ;^3i 19s. 9|d. + ;£62 15s. 8d. + ;£3053 15s. 6d. 7. If I have in my purse three ;^5 notes, four sove- reigns, and five half-sovereigns, three half-crowns, a florin, seven shillings, five sixpences, two fourpenny pieces, and five threepenny pieces, what sum have I in all ? 8. A debtor owes to five creditors ^^189 15s., ;£"235 16s. 3d., ;^io8 17s. 4d., ^50, and;^97 los. : how much does he owe altogether % 9. Add together fifty pounds, fifty shillings, and fifty pence. £ s. 1796 3 28 17 354 12 9 10 2038 12 139 5 10. £ s. d. J 083 17 3 156 4 9^ I 10 28 12 6i 375 4 8 19 2 6 d. £ s. d. 54 19 7 6- 9 234 15 8 4 18 7f 6 65 12 4-i 2\ 5098 4 7 7i 325 16 8 II. ;£" S. d. ;^ S. d. j;^ S. d 1275 6 7 30528 II 2^ 3271 14 7 5196 14 8| 1976 6 5J 596 19 9j 20127 8 6 287 14 n 1827 15 7| 37 15 5l 4096 2 8 74 9 4* 549 7 H 17278 15 6 20756 II 2| 1726 12 2 3197 12 8 1982 7 9 9 15 8i 150 10 638 17 4 12. Add together aU the English coins in present use. (See page 44 ) I ', MONEY KrUES. SI ■ £ s. d £ s. d. £ 8. d. 28671 14 10 3165 2 Si 2167 4 9 598 7 4^ I 19 2i 31287 5 6i 1365 12 6 472 16 7 2172 19 2 209 18 2i 1096 18 6| (>^ 5 6i 4718 6 3 12718 5 7 1096 12 4l 17 12 10 3127 II II 723 8 5 SUBTEACTIOX OF SL^mYX—coittinued. S9* When, in any subtraction of money sum, the number in the upper line is less than that below it, the method of equal additions described in 4 must be used. It was there necessary to add ten to each line, because hundreds, thousands, <fcc., differ from each other by tens. But here it wOl be necessary to add a penny, a shilling, or a pound to each line, in order to work the subtraction. Example I. Subtract £^ 12s. 7d. from £1^ 16s. 3d. We can take the less sum from the greater ; but we cannot take 7 pence from 3 pence. Add a shilling or 1 2 pence to the 3 pence in the upper line. Take 7 from 15 pence; there remain 8d. Set it down. Add a shilling to the lower line. Twelve and i are 13. Take 13 from 16. Set down the 3 shillings which remain. Take 9 from 15. Set down the £6 which remain. The answer is £6 3 s. 8d. One shilling has been added to both lines ; to the upper in the form of 1 2 pence, to the lower in the form of one shilling. £ s. d. 15 16 3 9 12 7 6 3 8 £ 9 s. 16 13 d. 7 6 3 8 o2 ARITHMETIC FOR MGUfNERS. Examplell. Find the difference between ;^i 250 los. 6|d. and ;^768 12s. 9|d. We cannot take a half- penny from a farthing. Add a penny (four far- things) to the upper line. Two farthings from 5 leave three farthings to he set down. Add a penny to the 9 pence of the lower line. Ten pence from 6 pence cannot be taken. Add 12 pence to the upper line. Ten pence from 18 pence leave 8 pence, to be set down. Add a shilling to the lower line. Thirteen shil- )t be taken. So add 20 shillings to the upper line. Thirteen shillings from 30 shillings leaves 17 to be set down. Add ;!^i to the lower line. Xine pounds from o cannot be taken. Add ;£"io to the upper line. Kine pounds from 10 leaves jQi to be set down. Add ^10 to the lower line. Seven tens from 5 tens cannot be taken, so add 10 tens to the upper line. There remain 8 tens to be set down. Add 100 to the lower line. Eight hundred from 12 hundred leaves 4 hundred to be set down. The difference is ^£'481 17s. 8|d. Note. — On comparing (a), which is the sum as ordi- narily set down, with (6), the sum as actually worked, it will be seen that a penny, a shilling, a pound, ;£io, and ;^ioo have been successively added to both the upper and lower lines. (a) £ s. d. [250 10 6| 768 12 pi 481 17 8f £ (I) 12 1 15 81 7 s. d. f. io„3o„i8„5 9„i3„io„2 4l 8 I »i7»8„3 lings from 10 shillings cam COMPOinfi) ADDITION AND SrBTKACTION. 63 Exercise XXXV. 1. Add together four shillings, four half-cro"WTis, four sixpences, and four pence, and take the sum from j£i. 2. Take ^^-j^ 14s. 6d. three times from ^£^350 ios.,and say how much remains at last. 3. What profit does a tradesman gain who buys goods for ^45 I OS., and sells part of them for j^^ij 9s. 6d., and the rest for ^^33 16s. lod. ? 4. On offering to pay my tailor ;£'i9 4s. 6d. he allows me 19s. 3d. discount : what sum do I actually pay 1 5. A gentleman leaves at death ;£" 1,256 to be divided among four daughters, of whom the first is to have 200 guineas, the second 250 guineas, and the third three hun- dred : what sum remains for the fourth ] ;^ s. d. £ s. d. £ s. d. 6. 2582 15 4.^ 3287 II 5 2056 13 6 196 8 6' 1965 4 8.1 1978 12 8 £ s. d. 7. 3069 10 o 274 5 7i £ s. d. 17862 11 3^ 2974 5 6 £ s. d. 3000 287 13 6* 8. £1792 13s- 8d. -f- ;^236 14s. 7|d. — ;^io5o 1 8s. lod. 9- ;^2387 15s. 6d. + £35 MS. 2d. + ;^928 12s. 6d. — ^315475. 6d. 10. Add together ^y^ 13s. 6Jd., ^219 los. iid., and £s^^ 4s. 6d., and subtract the result from ;^iooo. 11. Add together fifty-four farthings, fifty-four shil- lings, and fifty-four pence. 12. Find the difference between forty-nine fourpenny pieces and thirty-nine sixpences. 13. "What sum of money is that which must be added to £2^ 15s. 6jd. to make ;£^ioo ] Prove the answer by adding it. 14. How much is left after taking ;£^35 7s. 6d. twice over from £120 ics. ] t-* ahithmetic ron beolkkers. MULTIPLICATION OF MOXEY. SO* When any sum of money is to be multiplied, the farthings, pence, shillings, and pounds must be separately multipHed in order, and the results set down and carried as in addition. Example 7. Multiply £26 los. 4|d. by 4. £ s. d. Four times a halfpenny are 8 farthings, 26 10 4^ or 2 pence. 4 Carry 2 to the pence. Four times four are 16 pence, and 2 make 106 I 6 18 pence, or i shilling and 6 pence, Set down 6 pence and carry i to the shillings. Four times 10 are 40 shillings, and i make 41 ; 41 shil- lings are 2 pounds i shilling. Set do^Tn i shilling and carry 2 to the pounds. Four times 6 are 24, and 2 make 26. Set down 6 pounds and carry 2 to the tens. Four times 2 tens are 8 tens, and 2 make 10 tens. Set doAyn 10. The answer is ;£^io6 is. 6d. Exercise XXXVI. 1. Multiply 2S. 6d. by 5 ; £1 12s. 4d. by 6. 2. Multiply £2 3s. Sjd. by 7 ; ^£6 2s. yd. by 3. 3. Five pairs of gloves cost is. yjd. each : what is tha price of all 1 4. Add together the cost of six books at 3s. 6d., and four at 5 s. 6d. each. 5. What sum is that which, given among eight person.% allows them to receive ;£i2 17 s. 6d. each 1 6. Find the price of 3 lbs. of sugar at 4.2d., 2 lbs. i\i coffee at is. 8d., and 4 lbs. of tea at 3s. 4d. per lb. £ s. ± £ s. d. £ s. d. 7. 10 II 8J 267 13 17 9j 452 8. C031P0UND MULTIPLICATION. 55 £ 21 S. 6 d. ;^ s. d. £ 2j i8 7 4 19 6 7 3 d. ;^ s. d. 3 18 10 4 £ s. d. 123 6 4I 9 ^ s. d. 24 12 3'J 8 10. £2 4s. 6d. X 12 ; 19s. 6|d. x 8. IT. £i^ 6s. 3d. X 9; ^2 Ss.'sld. X 6. 12. ;!^IO JOS. lod. X 10. 13. £2> i8s. 7id. X 8; ;£'i 9s. yjd. x 12. 14. ;^43 2s. 6d. X II ; jQi los. 4d. x 6. 15. A man bequeaths to seven institutions nineteen guineas each : how much is that in all ? 16. In each of nine hags of money there are twenty- four sovereigns, fifteen half-sovereigns, twenty-one half- crowns, and eighteen shillings : what sum is contained in them all % 17. What sum must he divided in order to give to eleven persons a legacy of £^() 12s. 6d. each? 18. If I pay five hills averaging £i2> 17s. 8d. each, what change will remain from ;2^ioo ? 19. What is the difference between seven times jQi 1 6s. 3d. and nine times £1 4s. 7d. ? 20. {£2 i6s. 7d. + £s i8s. 8d.) x (12 - 3). 21. (;£256 i2s. 6d. + £i2() los. - ;^i83 3s. 4d.) X (7 4- 4). ' . . 22. Add ten times £2()^ 5s. lod. to eight times £1$^ 13s. 4|d. 23. Multiply ;£'78 6s. 5|d. by seven, and the result by five. 24. What does an employer pay to 12 workmen, each of whom receives £^^ 12 s. 8d. yearly 1 25. If eight persons receive nine half-crc sum is received by them iii aU ? J^^^^oe'^^ Sj'j ARITDMETIC FOR BEGIXXEBS. LONG MULTIPLICATION. 31. When the multiplier is more than 1 2, it is 'neces- sary to proceed Ly steps, as in lO, Example \6). Example I. Multiply ^17 3 s. 6d. by 35 Here, because 35 = 5 x 7,"we multiply by 7 and by 5 in succession, and the second product is the answer req^uired. £ s. d. 17 3 6 7 120 4 6 z= £i-j 3s. 6d. X 7. 5 601 2 6 = £l^ 3s. 6d. X 7 X 5. Example II. Multiply £2^4 13s. S^d. by 58. Here the multiplier 58 is not a product of any two numbers in the tables. AYe therefore take the nearest. 56 equals 7x8; and after multiplying the number by 56, we add twice tlie upper line to make up 58. £ s. d. 254 13 Si 7 1782 15 11^ = 7 times the upper line. 8 14262 7 8 = 56 or 7 X 8 times the upper lifjt 509 7 5 — twice the upper line. 1477 1 15 I = 58 times the upper line. The nuswor is ^14771 15s. id. LONG MULTIPLICATION. n? Exercise XXXYIL 1. Multiply jQt, I OS. 4d. by thirteen. 2. Multiply ^26 15s. 3|d. by seventeen. 3. Multiply ;^54 15s. 8|d. by nineteen. 4. Add together five times £2 3s. 6d., and twenty- three times 17 s. 9d. 5. What vrill 47 pairs of boots cost at £1 is. 6d. per pair? 6. Find the price of three dozen articles at jQz 15s. pd. each. 7. What will 59 acres of land cost at ;£^2 2 los. per acre? 8. Multiply ;^37 15s. 6d. by 73, and subtract ^£"1250 63. 4d. from the product. 9. ^28 13s. 6d. X 19; ^12 14s. 7^d. X 23. 10. ;^22o los. 4|d. X 41 ; ^£^153 i6s. 8id. X 26. 11. ;^'274 los. 2d. X 30; £S^2 15s. 2id. X 23. 12. £1 i6s. 5jd. X 37; ^'1862 I2S. 4id. X 53. 13- ;£2i6 los. loid. X 17; £10 I2S. 3id. x 29. 14- £^o^ 3S. iiid. X 53; ^617 2s. 9d. x 46. £ s. d. £ s. d. 683 5 2 7294 10 4^ 31 19 16. Find the total cost of twenty- three articles at £1 9s. 6d. each, and of thirty-five articles at 17s. 8|d. each. 17. What is the value of 24 casks of wine, each worth ^i5 4s. 7d.? 18. Deduct fifteen times ;^23 4s. 6d. from ;£^iooo. 19. If a draper buys seventy-hve shawls at;^3 17 s. 6d. each, and sells them at four guineas and a half each, what proht does he gain ? 20. AVhat is the cost of 19 tons of iron at £<) 9s. 6d. per ton ? J' 2 58 AKITHiLETIC FOR BEGIXKERS. HOUSEHOLD ACCOUNTS AKD SIMPLE BILLS. S2» The most frequent use to ^liicli easy Multiplica- tion and Addition of money are put is the calculation of small accounts after making purchases at shops. Example I. If I buy at a stationer's six quires of note- paper at 4jd., three packets of envelopes at 8d. each, some drawing-paper for is. 3d., five black-lead pencils at 3id., two boxes of steel pens at is. 6d. each, and an inkstand for 4s. 6d., how much do I spend 1 It is usual to arrange such an account thus : — s. d. 6 quires of note-paper at 4 Jd. ... 2 3 3 packets, of envelopes at 8d. ... 2 Drawing-paper I 3 5 pencils at 3|d. ... ... I S\ 2 boxes steel pens at is. 6d. ••• 3 Inkstand ... 4 6 14 52 Exercise XXXYIII. Compute and finish the following accounts: — 5 lbs. of rice at 3|d. per lb. 6 lbs. of soap at 5d. 8 lbs. of Valencia raisins at 6^d. 3 packets of starch at 5|d. . . . 6 tablets of soap at 3d. 5 quires of paper at 7d. 2 quires of foolscap at 9 id. S packets of envelopes at 4d. 4 magazines at pd. . . . 7 prayer-books at 2s. 3d. ... BILLS AND ACCOUNTS. 5*) S. d. 4 lbs. of tea at 3s. 6d. 5 lbs. of coffee at is. Sd. 7 lbs. of loaf sugar at 6^,d. ... 6 lbs. of moist sugar at 4.UI. ... 3 pairs of gloves at 3s. 9d. 2 neckties at is. 6d. ... 4 pairs of stockings at 2s. 2d. . . . 3 silk handkerchiefs at 3s. 6d. . , . 3. i3.yardslongclothat 3Jd., 25 yards shirting at 8.^d., 2 dozen napkins at is. 4d. each, 3 tablecovers at 8s. od. each, 4. 19 yards black silk at 5s. 2d. per yard, 5 yards crape at 6s. 6d., 12 yards black alpaca at is. yd., and 3 pairs kid gloves at 2s. 8d. 5. 2 bottles of pickle at lojd., 3 of fruit at gd., i bottle of blackini^ at is. 2d., 9 lbs. of candles at 6|d. per lb. 6. 5 pairs cotton hose at is. gd., 6 pairs worsted at 2S. 3jd., 4 pairs merino at 3s. 2d. per i^air, and 2 dozen children's socks at yld. per pair. 7. 27 1 yards of carpet at 4s. 9d. per yard, 27!- of felt at 9|d., making the same 27^ yards at 4d. per yard ; stair carpet, 27 yards at 3s. 9d. ; two dozen stair rods at 2hd. each. 8. Two dozen port at 48s. per dozen, 2 dozen pale sherry at 46s., 3 dozen Sauterne at 24s., 4 dozen pints of claret at 13s. 9. 3 pairs lace curtains at 23s. 9d. per pair; tapes, rings, &c., for the same, 6s. 6d. ; making up and fixing same, i8s. 6d. 18 yards grey silk at 6s. gd.; 14 yards of muslin at 8Jd. 10. Making and fixing 3 window-blinds for drawing- room (2 at i8s. 4d. each, i at 12s. rod.); 7 blinds for bedrooms (viz., 2 at iis. 8d. each, i at 7s. 6d., and 4 at 6s. 2d. each) ; rods, screws, lines, &c., for fixing, 6s. 6d. Altering spring rollers, 4s. 6d., cleaning and repairing outside blinds, ;!^i 3 s. GO ARITHMETIC FOR BEGIXXERS. SIMPLE REDUCTION, AXD OTHER USES OF MULTIPLICATION. Jl»$, Example I, How many pence are tlieire in £2^ ? ;^23 Because there are 20 shil- 20 - liners in jQi : There are in ^£^23 20 times 460 = shillings in ;^ 2 3. 23 shillings, or ^60 shillings. 12 And because there are 12 pence in a shilling, there are 5520 = pence in £27,. in 460 shillings 12 times 460, or 5520 pence. Hence there are 5520 pence in ^£^23. Example II. Reduce ^59 i6s. 2|d. to farthings. ;^59 i6s. 2\^. AVe multiply ^59 20 by 20, and add in the 16 sliillings. 1196 zz shillings in ^59 i6s. There are thus 12 .1196 shillings in £S9 i6s. 14354 = pence in ;^59 i6s. 2d. We multiply 11 96 4 I>y 12, and add in the 2 pence. 57417 farthings in ;£"59 i6s. 2|d. There are thus 14354 pence in ;^59 1 6s. 2d. We multiply 14354 by 4, and add in the i farthing. There are thus 57417 farthings in ^£"59 i6s. 2jd. ExamjjU III. How many fourpenny pieces are there in '139 15s- ^ jQ s. d. We multiply ;£"i39 by 20, and add ^39 150 ^^ ^^^^ 15 shillings. There are 2795 20 shillings in ;^i 39 15s. But there are three fourpenny pieces 2795 in a shilling. Therefore we multiply 3 2795 shillings by 3. There are thus 8385 fourpenny pieces S385 in ^139 15s- SIMPLE KEDTTCTIOy. 61 Exercise XXXTX. 1. Eednce ;£i769 to sMUmgs; jCiS los. to pence. 2. How many sixpences are there in ^1385 5s. ? 3. If there were a coin worth two pence, how many could I have in change for two guineas ] 4. Eeduce £^ 19s. 6jd. to farthings. 5. Find the price of 17 articles at 2|d. each. 6. How many things worth three halfpence each can I buy for 5 s. ? 7. Find the difference between the number of four- penny pieces and the number of threepenny pieces in £2 15s. 8. In seventeen half-crowns how many pence f 9. If I changed a five-pound note into threepenny pieces, how many should I have ? 10. How many more shillings are there than half- crowns in twenty guineas ] 11. Reduce the two sums ^12 i6s 3 id. and ^£^24 7s. 9d. to farthings. 12. Find the difference in pence between ^£36 14s. 8d. and^5o. 13. Divide ^£^175 i6s. 9d. by 3, and give the answer in farthings. 14. How many halfpence are equal in value to twelve bags of money containing j£i i6s. 3d. each ? 15. Multiply ^£"763 i8s. 4d. by 15, and reduce the 'answer to pence. 16. How many halfpence are there in seventeen guineas ? 17. How many farthings are there in seven times ^i8 6s. 4d? 18. Find the total number of farthings in nine guineas, three half-sovereigns, and fifteen half-crowns and seven sixpences. 19. How many articles worth three halfpence each coidd I buy for j^^y los. ? 20. Add the number of farthings in seven hundred and fifty founds to the number of shillings in the same sum. 62 AETTHMETIC FOR BEGDTNEES. Divisio:Nr OF money. 34, In dividing a sum of money, pounds, shillings, pence, and fartliings must be separately divided in succes- sion, and when there is any remainder, it must be reduced to the term next below it. Example I. Divide £^^ 6s. 3d. by three. £ s. d. We find one-third of £2^'^ by the 2,)^T, 6 3 method of sunple division, lO. ■ The answer is ;j^i i. 1 1 2 I A third of 6s. is 2s. The third of 3d. is i penny. The answer is jQii 2s. 3d : Example II. Divide ;^i64 iis. 4M. by 7. £ s. d. ^^e divide 164 by 7 )164 II 4i 7^ and find the quo- 23 10 2J : f remainder. tient to be ;£23 with a remainder, jQ^. Xow £^ and iis. reduced to shillings make 71 shil- lings. The seventh of 71 is 10, with a remainder of i shilling. One shilling and fourpence make 1 6 pence. The seventh of 16 is 2, with a remainder of 2 pence. 2 pence and Jd. reduced to farthings make i o farthings. The seventh of 10 is i, with 3 farthings remainder. The nearest answer therefore is ^£^23 los. 24d., with three farthings remaining undivided. Exercise XL. 1. What is the fourth part of ;£"i los. I 2. Divide ;£26 by five. 3. Add the half of ;£"io los. to the third part of the same sum. 4. If ;£'25o I OS. are left to be divided among 6 persons, how much will each receive ? 5. ;£"i8 have to be divided among 10 persons : how much will each receive ? coMPOTUfD Dinsioy. 63 6. From the half of five guineas take the third of five guineas. ^ s. d. £ s. d. 7. 8)7 2 6 7)23 10 4 ;^ S. d. £ S. d. 8. 10)123 16 8 11)25 2 9 9. ^18 I2S. 6d.-Mo; ;^24 5s. 7d.-f 7. 10- ^38 17s. 3<i-^ii j ;^i9 6s. 5d. --I2. 11- £37 15s- 3^.-5; £^^4 10S.-8. 12. ;£'207 15s. 6d.-6; ^£'327 14s. 8d.^9. 13. Add together the eighth and the tenth parts of ^53 I 28. 6d. 14. Take the twelfth part of ^126 33. from the whole of that sum. 15. A gentleman bequeaths ^2^1250, of which one-half is given to his eldest son, one-third to his second son, and the remainder in charities ; how much money is given to each purpose ? 16. ^213 17s. 6d. + ^519 I2S. 8d. 12 17. ^504 IPS. -^196 13s. 4d. 8 18. ^27 15s. 6^d. + £196 i8s. 7d. - ^59 IPS. 4ld. 7 + 4 19. ;^325 163. 7d. X 10 7 20. Find the difference between the eighth and the twelfth parts of ;£i25o. 21. K the sum of ^1827 193. 6d. be divided into nine parts, of which A receives five, and B four, what is the share of each % 22. Divide a legacy of ;£^8757 2s. among three persons, so that the first shall have five parts, the second four parts, and the third two parts . 61? AUITHMETIC FOR BEGIKNEES. DIYISOX OF MOXEY {continued). So* When the divisor is greater than 12, each remain- der must be set down separately, and the work done as in Long Division (22). Example. Divide £713$ i6s. 4d. by 27. We first divid e;^7i35by27, as in 2'£. The quotient is ;^2 64, and ^j are left undivided. We next reduce these ^j and the i6s. to shillings. They make 156 shillings. On dividing 156 by 27, the nearest answer is 5 s., and 21 shillings remain undivided. We next reduce these 21 shillings and 4d. to pence. They make 256 pence. On dividing 256 by 27 we find the quotient to be 9 pence, and 13 pence remain undivided. We next reduce the 13 pence to 52 farthings. On dividing these 52 by 27 we find the quotient i, and a remainder of 25 farthings - which cannot be divided by 27. 25 farthings remain undivided. The answer is, therefore, ;£"2 64 5s. 9^d., and 25 re- mainder. £ s. 7)7135 i6 54 4(264 173 162 115 108 7 20 27)156(5 135 shillings. 21 12 27)256(9 243 pence. 13 4 27)52(1 •27 farthing. compound division. 1 ' ' 65 Exercise XLT. 1. Find the thirteen tli part of ;£"3co. 2. Divide ^£^2^ los. by sixteen, and by eighteen. 3. Add together £ti6 ios, and;^i38 4.S. yd., and divide the snm by nineteen. 4. Find the difference between the fifteenth and the sixteenth of ;^ 1 000. 5. A gentleman leaves ^^10,000, of Avhich one-half is to be paid to his widow, one-third to be equally divided among his six children, and the rest among his four nephews : how much is received by each child and by ecch nephew ^ 6. ^834 ics. 4-^17 i6s. -t-pfi47 i2s. 8d.-M7. 7. ;^i25o -J- 24 ; ^£638 IOS. 6d. -f- 27. 8. ;£"i39 2S. 4d.--i5; ;£"3i68 i6s. 2d. ~ 2>Z- 9. ^274 r2s. od. -^ 29; ^835755.-52. 10. ^^7265 14s. 6d. -f- 37 ; ^1273 4s. 6d. -f- 45. 11. ^^2198 14s. 6d. -4- 18; ;^3i25 I2S. 6d.-4- 29. 12. ;£3i86 i2s. lod. -- 65 ; ;£"2 5oo -f- 73. 13. Add together ^^568 13?. 7d.; £2/^6 los. 5d. ; and ;;^i20o ; and divide the sum by 24. 14. If a prize equal in value to ^^1728 is captured at sea, and one-third is distributed among the officers, and the remainder among 68 men, what is each seaman's share ? 15. Divide the sum of ;^583 into 960 equal parts. 16. ;^i38 i6s. 7d. -f ;^i53 14s. 10 29 17. ^1347 5s. 6^d. - ^216 5s. 8 d. 47 18. Add together the thirty-second and forty-eighth parts of ^1625. ' 19. Divide ^2^3147 15s. by forty-seven, and reduce the quotient to farthings. 20. Part ;^iooo between two persons in such a way that fifteen parts shall be received by one for every seven- teen parts received by the other. 66 ARITHMETIC TOE BEGmNERS. , EEDUCTION, A:N'D OTHER USES OF DIVISION^. 30. When it is required to reduce any number of farthings into pence, or any sum of money into another of higher value, the sum must be worked by Division. Example I. What is the value of 10,000 farthings % 4)10,000 farthings. 12)2,500 pence. 20)208 shillings, and 4 pence remaining. 10 pounds, and 8 shillings remaining. Because 4 farthings are i penny ; Therefore we divide 10,000 farthings by 4. There are 2,500 pence in 4 farthings. But because 1 2 pence make one shilling ; We divide 2500 pence by 12 to reduce it to shillings. There are 208 shillings and 4 pence in 2500 pence. But because there are 20 shillings in ;^i, AYe divide 208 shillings by 20. There are ;£"io and 8 shillings in 208 shillings. Therefore ten thousand farthings are found to equal ;^io 8s. 4d. •JY. When it is required to find how many sums of one value are contained in another, both sums must be reduced to the same name before the division is worked. ExamjjU II. How many times can I take 4s. 3d. out of £S los. 1 By 33 we find that ;£"5 los. contains 1320 pence ; and 4s. 3d. contains 51 pence. The question is, therefore, how many times are 51 pence contained in 1320 pence? We divide 1320 by 51. 1320 -^ 51 z=: 25 times and 49 remainder. The answer is therefore 25 times, leaving a remainder of 49 pence. EEDTJCTION BY DIVISION. 67 Exercise XLIL 1. How many pence are there in ^^ los. ? 2. How many pounds are there in 1683 farthings ? 3. Eeduce 22,840 pence to shillings and pounds. 4. How many coins worth five farthings each could I have in change for ^£4 1 5. What is the difference between 5000 halfpence and 7350 farthings 1 6. Eeduce to pounds, shillings, and pence, the following sums : — (a) 18,364 farthings; 23,086 halfpence; 4196 pence. (h) 27,463 fourpenny pieces; 8165 sixpences; 12,796 farthings. 7. How many articles worth 3^d. each can I buy for ^20] 8. To how many persons can I give 3s. 6d. out of 9. In 1728 sixpences how many guineas ] 10. 25 francs are worth an English sovereign : what is the value in English money of 17,287 francs? 11. What is the difference between the number of farthings in five guineas and the number of pence in the same sum ? 12. How many articles worth 33. 4d. each can I buy for y^79 I OS. ? 13. A prize fund of ^£"500 is so distributed that one- fourth of it falls to the share of the officers, and the rest is given in sums of ^£2 los. each to the seamen ; how many seamen share it I 14. In 12,350 farthings how many sixpences? How many half-crowns? 15. If there were a coin worth 2|d., how many could I obtain in change for ^^50 ? 16. If a million farthings were divided into 12 parts, of which one person received 7 and another 5, what would be the share of each ? 63 ARITHMETIC FOIl BEGIXNERS. MISCELLANEOUS EXERCISES.— XLIIL 1. Eind the price of 12 articles at 3^d. each, and of five at 7 J-d. each, and add them together. 2. Add together five half-crowns, seven sliilKngs, nine sixpences, and fifteen pence. 3. If I have in my purse a ^£"5 note, four sovereigns, seven half-sovereigns, a crown, five florins, seven shillings, three fourpenny pieces, and nine threepenny pieces, what sum have I in all ] 4. What is the difiference between 172 sixpences and 1720 pence? 5. Make out a bill for 4 pairs of shoes at 12s. 6d. each pair, 2 of boots at 19s. 6d. each, 3 pairs of slippers at 3s. 9d., and repairs amounting to 12s. lod. 6. A man earns 27s. per week, his wife 30s. per calendar month, and three children 3s. Qd. per week each : what is the income of the whole family per annum 1 7. When the income tax is at 5d. in the pound, what amount of tax does a gentleman pay whose income is ;2fi2 5o per annum? 8. At a church offertory j^zS los. were collected, and it was calculated that on an average 4d. had been given by each person : how many were there in the congregation 1 9. What is the difference between the number of far- things in ;£"53, and the number in ;^24 7s. 6d. 1 TO. Out of an income of ;£^8oo per annum a man saves ;j{^i2 every quarter : what does he spend per week 1 11. Find the sum of three guineas and ^£6 14s. 8Jd., and reduce the whole to farthings. 12. If I pay for 56 yards of cloth at 2s. 8Jd. per yard, wliat sum will remain out of a ;^20 note 1 13. Eind the total cost of a score of articles at 3s. gd. each, and of a gross at 5s. 2d. each. 14. If an equal number of men, women, and children recpive each a gift, the men of 5s., the women of 2s. 6d., and the children of is. each, and if the whole sum dis- tributed amounts to ;£6^ os. 6d., how many persons in all are relieved. EXERCISES I2f '.rElGHT. 6D WEIGHT. 38. The common table in use in England, for weighincj all articles of ordinary sale, is as follows : — It is called Acoiiflupois weight; other weights, such as Troy, and Apothecaries*, being only used in special trades. The fottmcinff should he learned by heart : — 1 6 Drams make one Ocxce. i6 Ounces make one Pound. 28 Pounds make one Quarter. 4 Quarters (or 112 lbs.) make one Hundredweight. 20 Hundredweights make one Ton.* Multiply 7 cwt. 3 qrs. 13 lbs. 6 oz. by 5, or Five times 6 oz. are 30 oz. But because 16 oz. make i lb., 30 oz. ^ I lb. 14 oz. Set down 14 oz. and carry i lb. Eive times 13 lbs. are 65 lbs., which added to i lb. make 66 lbs. But as 28 lbs. = I qr., 66 lbs. 518 o 410 are 2 qrs. and 10 lbs. Set down 10 lbs. and carry 2 qrs. Five times 3 qrs. :ii= 15 qrs., T^hich with 2 makes 17 qrs. But since 4 qrs. = i cwt., 17 qrs. ziz 4 cwt. i qr. Set down the i qr. and cany 4 cwt. Five times 7 cwt. are 35 cwt, which added to 4 make 39 cwt. But 39 cwt. equal i ton 19 cwt. In like manner on multiplying i ton 19 cwt. i qr. 10 lbs. 14 oz. by 3, we find the answer to be 5 tons 18 cwt. o qr. 4 lbs. 10 oz. * The full tables of weight and measure, for purpose? of reference, will be found on p. 70 of the " School Arithmetic," and an explana- tion showing the rise and history of our system of weighing on p. 332 of the " Science of Arithmetic." Example I. Mu Itip Y 5 and 3. cwt. qrs. lbs. oz. 7 3 13 6 5 119 I 10 14 3 70 AKITHMETIC TOR BEGINNERS. Example II. Find tlie difference between one ton, and 17 cwt. 3 qrs. 12 lbs. 9 oz. ton. cwt. qrs. lbs. oz. Add 16 oz. to the npper -10 000 line. 9 from 16 leaves 7 oz. 17 312 9 Set down 7. ^dj 4 lbs. to the low^er line, 2 015 7 and 28 lbs. to the upper. 13 from 28 leaves 15 lbs. Set do^vn 15. Add I qr. to the lower line, and 4 qrs. to the upper. 4 qrs. from 4 leaves nothing. Set down o. Add I cwt. to the lower line, and 20 cwt. to the upper. I 8 cwt. from 20 leaves 2 cwt. Set down 2. Add I ton to the lower line, i from i leaves o. The difference is 2 cwt. 15 lbs. 7 oz. Exercise XLIY. 1. Add together 2 lbs. 6 oz., 14 oz., and 12 lbs. 2. Find the difference between the weight of one parcel of 5 lbs., and that of two weighing j lb. 9 oz. each. 3. What will three pounds of tea cost at 3 jd. per oz. % 4. Add together 7 cwt. 3 qrs., 2 tons 5 cwt., and 3 cwt. I qr. 19 lbs. 5. Find the total weight of five parcels, weighing respectively 5 J lbs., 2 lbs. 4 oz., 15 lbs., 3 lbs. 12 oz., and 29 oz. 6. Reduce 3 cwt. 2 qrs. 1 9 lbs. to pounds and ounces. 7. How many ounces are there in 3 qrs. 1 1 lbs. ? 8. Eeduce 1000 ounces to pounds. 9. How much butter at lod. per lb. can I buy for £a ios. % 10. How many parcels of sugar weighing 4 lbs. 4 oz. each can be made up out of a hogshead weighing 3 cwt. 2 qrs. 1 5 lbs. "? 11. Find the price of 7 cwt. 3 qrs. 16 lbs. at five farthings per lb. 12. What is the difference between 1000 lbs. and 1000 ounces % EXERCISES IN WEIGHT. /i 13. Find the price of 7 cwt. 3 qrs. of sugar at 4.Jd. per lb. 14. How many three-ounce packets can be filled up from a box of lozenges weighing 3 qrs. of a hundred- weight 1 tons. cwt. qrs. lbs. oz. tons. cwt. qrs. lbs. oz. 15. 7 I 19 6 35290 3 18 5 8 I 15 II 5 10 o o o 10 3 19 o 3140 I 20 7 6 o 18 5 16. 7 tons 3 cwt. 18 lbs. + 19 lbs. 12 oz. + 3 qrs. 18 lbs. 7 oz. + 19 cwt. 19 lljs. 17. 2 cwt. 14 lbs. 7 oz. + 25 lbs. II oz. + I cwt. 1 qr. I lb. + 3 qrs. 12 lbs. 18. 5 tons 7 cwt. + 6 cwt. I qr. 23 lbs. — 17 cwt. 2 qrs. 18 lbs. 19. 18 c^vt. 2 qrs. 9 lbs. X 6 ; 5 tons 3 cwt. 2 qrs. 9 lbs. XII. 20. From four tons take thirty-nine cwt. three qrs. seventeen lbs. 21. How many j)arcels weighing 2 J lbs. each can be made up out of 1 7 cwt. 3 qrs. ? 22. At 8|d. per lb. what quantity can I buy for ^79 6s. 8d.'? 23. At ^£^224 per ton what is the price of coffee per oz. 1 24. Find how many times a pound and a half is con- tained in 3 1 cwt. 25. What is the difference between 32 lbs. and 132 ounces ? 26. Find the price of one hundred and thirty-seven lbs. at fourpence farthing per oz. 27. Eeduce 11,100 oz. to hundredweights and tons. 28. Eeduce 5^ tons to ounces and drams. 29. What is the difference in ounces between 3I tons and 39I cwt. 72 AllITUMETIC FOR BEGINNERS, LEXGTH. 39. The me^ures of length in use in England are chiefly the Inch, Foot, Yard, and ]\Iile. Other denomina- tions are only occasionally used. To he leanied hy heart : — Twelve Inches make one Foot. Three Feet make one Yard. Five and a half Yards make one Polf. Forty Poles make one Furlong. Eight Furlongs make one Mile. It is also useful to remember that — Two hundred and twenty Yards make one Furlong.* Seventeen hundred and sixty Yards make one Mile. Example I. Add together the lengths of 5 roads, of which the first is f of a mile long; the second i mile 3 furlongs ; the third, 2 \ miles ; the fourth, 7 furlongs 20 poles; and the fifth, i mile i furlong 30 pole^ 4 yards. miles, furlongs, poles, yards. There are only 4 yards in the right-hand column. Set down 4 yards. 30 and 20 make 50 poles. But as 40 poles make i furlong, 50 poles are i furlong 10 poles. Set do^vn 10 poles. I and I and 7 and 4 and 3 and 6 are 22 fur- js make i mile, 22 furlongs 2 and I and 2 and i make 6 The answer is 6 miles 6 furlongs 10 poles 4 yards. * Unless poles are expressly mentioned in the sum, always use the number 220 as multiplier or divisor, and proceed at one step from furlongs to yards. 5^ is an inconvenient number ; and " poles " are every day less and less used in practice as measures of lengtb. I 2 I 6 3 4 7 I 20 30 4 6 6 10 4 longs, make miles. But since 8 furloi 2 miles 6 furlongs. Set do\\Ti 6 miles. EXAMPLES IN LENGTH. 73 Example II. How many feet are there in 7 J miles ] miles, furlongs. 1 6 8 62 furlongs. 220 1240 124 13640 yards. 3 40920 feet. Since 8 furlongs are i mile, j of a mile equals 6 furlongs. 8 X 7 +6 = 62 furlongs, the number of furlongs in 7 miles 6 furlongs. Since 220 yards make one furlong we multiply 62 by 220, and find that there are 13,640 yards in 62 furlongs, or in 7 miles 6 furlongs. Since 3 feet make one yard, we multiply 13,640 yards by 3, and thus hnd that 40,920 feet = 13,640 yards = 62 furlongs = 7 miles 6 furlongs. Example III. AYhat will be the cost of a wall 2 miles and a half long, at 2s. 9d. per yard i 2)1760 4 3520 880 z= yards in 2 miles. Sz „ half a mile. 4400 1=. a 2 1 miles. zz 12)145200 = cost of the wall in pence. 20)12100 = „ ghillings. 605 = „ pounds. Since there are 1760 yards in a mile, there are 4400 yards in 2 J miles. In 2S. gd. there are 33 pence. The whole cost must therefore be 4400 x 33 pence. And this product is (by 3«J) equal to jC^^S' -UlITmrETIC FOR BEGIXXISRS. Exercise XLV. 1. How many inches are there in 3 yards 2 feet ? 2. Eeduce 7 furlongs to feet and inches. 3. In 100,000 feet how many miles 1 4. Add together 29 yards, 17 j^ards 8 inches, 15 yards 3 feet 4 inches, and 2 feet 1 1 inches. 5. What is the dift'erence between 27 yards and 2 7 inches ? 6. How many lengths measuring 5 inches each can be cut off two balls of string, of which the one measures 178 3'ards and the other 256 feet? 7. What is the cost of 17^^ yards of gold thread at a halfpenny an inch ? 8. There are three roads, of which the first measures I mile 870 yards ; the second, 1260 yards; and the third is as long as the other two put together. Express their united lengths in miles, furlongs, and yards. 9. Suppose it cost 6d. per foot to pave the three roads in the last sum : what will be the total cost of the paving 1 10. How many hurdles measuring 3 feet 4 inches each will be required to surround an oblong patch of ground, of which the two long sides measure 360 yards each, and the two short ones 270 yards 2 feet each? 11. From a road two miles and a half long, two por- tions are paved measuring 1500 yards and 7 furlongs 120 yards respectively : what length remains unpaved ? 12. Find how many lengths of 3 feet 6 inches each can be cut off from a wirei mile 6 furlongs long. 13. If the telegraphic wire be supported by poles at in- tervals of TOO yards, how many such poles will there be along a railroad 67^ miles long ? 14. What Avill it cost to put up a fence on each side of a path three-quarters of a mile long at g^d. per foot. 15. How many times Avill a wheel which is 5 feet 6 inches in circumference revolve in a journej^ of 7 J miles 1 SURFACE 3iEASlIRE3fEXt. 75 SUEFACE. 40. ^Vlien square or oblong surfaces are measured, it is usual to multiply the length by the number representing the breadth. The reason of this will be seen from the diagram. ^ B If A B were three feet long, and B G 2 feet long, the whole space would be divided into six spaces (3x2), each being one foot square. The units of surface chosen for *^ measurement are always squares formed upon the units of length. To he learned hy liexui : — 144 SQUMiE INCHES make one square foot. isine SQUARE feet make one square yard. Example I. How many square yards of carpet will be required to cover a floor measuring i8 feet long and J5 feet mde ? 18 X 15=1270 square feet. But because 9 square feet make i square yard, 270 _;. 9 :r:: 30 square yards. Example II. How many yards of paper J a yard wide will be required to cover the walls of a room 12 feet high, which measures 21 feet by i8 feet? and what will it cost at 7 ^d. per yard ? There are four walls in the room. The dimensions of each of the longer walls are 2 1 feet by 12, or 21 X 12 = 252 square feet. The dimensions of each of the shorter walls are 18 feet by 12, or 18 X 12 zr 216 square feet. The total dimensions of ihe four walls therefore are 252 + 252 + 216 -f 216 zz: 936 square feet. But 936 square feet =936-^9== 104 square yards. And if the paper is half a yard wide, twice this number of yards will be required, or 104 x 2 or 208 yards of paper. But 208 x 7jd. zi i56od. z=l ^6 los., which is the cost of papering the room. 76 ABITHlEEtlC FOR BEGDTSfEBS. Exercise XLYL* 1. How many square feet are there in the floor of a room 9 yards long and 4 yards wide ? 2. Find the dimensions of the ceiling, and of each of the four walls of a room 65 feet long, 34 feet broad, and 16 feet high. 3. How many square inches are there in a sheet of paper I foot 3 inches long and 7 inches broad ? 4. If floorcloth costs 4d. per square foot, what will it cost to cover a passage fifteen yards long and 7 feet wide ? 5. If 8 square feet of space be allowed for each child in a schoolroom, how many children can be accommodated in a room 90 feet long and 40 broad ? 6. How much space wiU be enclosed if 40 hurdles mea- suring 3 feet long are arranged so as to include an oblong space, 1 4 hurdles being on each of the longer, and 6 on each of the shorter sides 1 7. A man buys a plot of building ground at is. 3d. per square foot; the frontage is 27 yards, and the depth 13 yards : what does he pay for the land ? 8. How many square inches are contaiaed in a floor 14 feet long and 9 feet wide ? 9. What will be the cost of laying down encaustic tiles along a gaUery measuring 35 feet long and 16 feet broad, at the rate of i penny per square inctu 10. 'VVTiat will it cost to paper a room 28 feet long, by 18 broad, and 13 feet high, if the paper is two feet wide, at lod. per yard? 11. How many spaces containing 20 square feet each are equal in area to a space measuring 60 yards by 18 ? 12. HoAv many paving-stones, measuring 3 feet by 2, will be required for a footpath half a mile long and 18 feet broad, and what will it cost to lay it down at 3d. per square foot. * Throughout this exercise no questions involving fractions or the technical use of duodecimals are used. For a full explanation and advanced exercises in this rule, see " School Aiithmetic," p. 58, and ** Science of Arithmetic," p. 275. SUKPACE MEASUB^3LEXT. 77 SVBFACE— (continued). 41. When large surfaces, such as fields, gardens, and roads are measured, the following table is used : — To be learned by heart : — Thirty and a quarter (30 J) square yards make one perch. Forty (40) PERCHES make one rood. Four (4) ROODS make one acre. Six hundred and forty (640) acres make one square mile. Example I. How many square feet are there in 17 acres 3 roods ? 17 acres 3 roods. 4 7 1 roods in 1 7 acres 3 roods. 40 2840 perches in 17 acres 3 roods. ' 3oi >52oo = 30 times 2840. 710 = a quarter of 2840. 85910 — 30 and a quarter times 2840. 9 7 73 1 9Q = number of square feet in 1 7 acres 3 roods. AVe multiply the acres by 4, and add in the 3 roods. There are 71 roods in 17 acres 3 roods. We multiply 71 by 40 because 40 perches make i rood. There are 2840 perches in 17 acres 3 roods.. We multiply 2840 by 30^ because 30 j square yards make i perch. We multiply 85910, the number of square yards in 17 acres 3 roods by 9 in order to reduce to square feet. The answer is 773190, the number of square feet in 17 acres 3 roods, 78 ABJTHMETIC TOR BEGINNERS. Example II. What are the dimensions of three fieldsj measuring respectively 29 acres 3 roods 27 poles; 15 acres 2 roods 18 poles; and 31 acres 3 roods 39 poles. acres, roods, perches. On adding 39, 18, and 27 toge- 29 3 27 tlier, we find they make 84. 15 2 18 But because 40 perches make i 31 3 39 rood, 84 perches = 2 roods 4 per- dies. Set down 4 perches and 77 2 4 caiTy 2 roods. • 2 and 3 and 2 and 3 make 10. roods, liut because 4 roods make i acre, 10 roods make 2 acres 2 roods. Set down 2 roods and carry 2 acres. 2 and 31 and 15 and 29 make 77. The answer is 77 acres 2 roods 4 perches. Exercise XL VII. I. Find the difference in size between a field measuring 100 acres, and one measuring 79 acres 2 roods 18 perches. .. 2. What is the total area covered by five garden plots measuring i rood 1 9 perches each ? 3. How much should I give for a square mile of waste ground at j£t, ios. per acrel 4. How many plots of land measuring 1 1 yards square* can be taken out of 15 acres % 5. If a plot of ground measures one mile long and a quarter of a mile broad, how many acres does it contain 1 6. A man buys a piece of land for a house, measuring 15 yards in frontage and 14 yards in depth, at 2s. 6d. per square foot : what does the land cost ? 7. Find the rent of five fields, measuring respectively 17 acres 2 roods; 14 acres 20 perches; 7I acres; 12 acres 8 poles; and 19 acres 2 roods 12 poles; at 15 shil- lings an acre. * Obsei-ve the difference between 11 square yards and 11 yards square. The first means 11 spaces measuring I square yard each; the second means one square space having 1 1 yards as the length of its side, or 11 x 11, or 121 square yards. -y^—^ Hi \/ CAPACITY OR BULK. 79 CAPACITY OR BULK. 42. Wlien a solid mass has to be measured, its length, breadth, and thickness have to be separately calculated. If a cube measures three inches each way, it would, if cut into pieces of one inch each wa}^, be found to contain th'ree times three times three such pieces, or twenty- seven cubic inches; i. e., nine in each of three layers, as shown in the diagram. For this reason twenty- seven is often called the cube of three. And lo X lo X lo, or looo, is the cube of lo. Hence, to find the cubic units in any solid mass we measure the length by the breadth and by the height. To be learned hy heart : — 1728 CUBIC INCHES (i 2 X 12 X 1 2) make one CUBIC FOOT. 27 cubic feet (or 3 x 3 X 3) make one cubic yard. Example. How many cubic inches are there in a block of stone measuring 14 feet long, 7 feet wide, and 10 feet deep 1 14x7X10 = 980 = the number of cubic feet in the block of stone. Therefore 1728 x 980= 1,693,440 or the number of cubic inches in the block. Exercise XLYIII. 1. How many cubic feet of air are contained in a room measuring 21 feet long, 18 feet wide, and 11 feet high? 2. How many bricks containing 108 cubic inches each can be cut out of a mass of clay measuring 20 feet long, 16 wide, and 8 deep 1 3. A reservoir of water is 36 feet long, 30 feet wide, and 5 feet deep : how many cubic feet does it contain ? 4. What will a block of marble cost which measures I foot and a half long, 7 inches wide, and 1 1, inches deep at lid. per cubic inch ? b'O ARITHMETIC FOR BEGINNERS. CAPACITY OR BVI.K~(cantinued). 4*$. AVlien the bulk of liquids, of seeds or of corn, has to be measured it is more convenient to employ the names of vessels which are in common use. To he learned hy heart : — Two pints make one quart. Four quarts make one gallon. Two gallons make one peck. Four pecks make one bushel. Eight bushels make one quarter (of com). Exanqyle. What will ly-J gallons of wine cost at 3s. 6d. per pint ? 17 gallons 2 quarts. Eeduce the gallons to 4 pints. — There are 140 pints in 70 quarts in 17^ gallons. 17!^ gallons. 2 Because 3s. 6d. equal — 42 pence, 140 pints in 17 J gallons. Therefore 140 x 42 m 42 5880 pence = price of 17^ gallons in pence. 12 )5880 20) 49.0 5880 pence = £2^ los. 24.10 Exercise XLIX. 1. Add together 3 pints, 13 quarts, and 12 gallons. 2. How many pints are contained in 17 quarters of wheat ? 3. How many bottles containing a pint and a half can be filled from 3 casks containing 4J gallons, 6 gallons, and 8 gallons respectively 1 4. Find the difference between the contents of a vessel of 28 gallons I peck, and one of 19 gallons 3 quarts. 5. AVhat will be the total capacity of 15 casks contain- ing 5 gallons 3 quarts i pint each ? 6. In 23^ bushels how many pints ] 7. Eeduoe 10,000 half-pints to gallons. 8. Divide 17 quarters 7 bushtls 3 pecks by seven. LONG IIULTIPLICATIOX. 57 Exercise XXXVII. I. Multiply £^ los. 4d. by thirteen. 2- Multiply ;;^2 6 15s. 3^d. by seventeen. 3. Multiply £S4 15s. 8id. by nineteen. 4. Add together live times ^2 3s. 6d., and twenty- three times 17 s. 9d. 5. What will 47 paire of boots cost at ^i is. 6d. per pair? 6. Find the price of three dozen articles at ^£2 15 s. gd. each. 7. What will 59 acres of land cost at ;£^2 2 los. per acre ? 8. ]Srultiply ^37 15s. 6d. by 73, and subtract ^1250 65. 4d. from the product. 9. £28 13s. 6d. X 19; ^12 14s. 7^d. X 23. 10. ;£"22o los. 4|d. X 41; £tS3 i6s. 8id. x 26. II- ;^274 los. 2d. X 30; ,^832 15s. 2-|d. x 23. 12. £1 i6s. 5jd. X 37 ; ^1862 I2S. 4id. X 53. 13- ^'216 los. io|d. X 17; ^10 12s. aid. X 29. 14- ;^io7 3S. iiid. X 53; ^617 2S. gd. x 46. ;f s. d. (>^3 5 2 31 £ «. d. 7294 10 4-1- 19 16. Find the total cost of twenty-three articles at £1 9s. 6d. each, and of thirty-five articles at 17s. 8 Ad. each. 17. What is the value of 24 casks of wine, each worth .£1545. 7d.? 18. Deduct fifteen times ;^23 4s. 6d. from ^£^1000. 19. If a draper buys seventy-live shawls at;^3 17s. 6d. each, and sells them at four guineas and a half each, what profit does he gain 1 20. AVhat is the cost of 19 tons of iron at £g gs. 6d. per ton ? ]. 2 58 AKITH3IETIC TOR BZGIXXEBS. HOUSEHOLD ACCOUNTS AXD SIMPLE BILLS. 3S. The most fireqnent use to Trhicli easy Multiplica- tion and Addition of money are put is the calculation of small accounts after making purchases at shops. Example I. If I buy at a stationer's six quires of note- paper at 4jd., three packets of envelopes at 8d. each, some drawing-paper for is. 3d-, five black-lead pencils at 3id., two boxes of steel pens at is. 6d. each, and an inkstand for 4s, 6d., how much do I spend % It is usual to arrange such an account thus : — s. d. 6 quires of note-paper at 4jd. .. 2 3 3 packets of envelopes at 8d. 2 Drawing-paper I 3 5 pencils at 3 Jd. . I 5l 2 boxes steel pens at is. 6d. . 3 Inkstand .... .. 4 6 14 5^ Exercise XXXYin. Compute and finish the following accounts: — s. 5 lbs. of rice at 3|d. per lb. 6 lbs. of soap at 5d. 8 lbs. of Valencia raisins at 6 id. 3 packets of starch at 5|d 6 tablets of soap at 3d. 5 quires of paper at 7d. 2 quires of foolscap at 9|d. 8 packets of envelopes at 4d. 4 magazines at pd. .. . 7 prayer-books at 2s. 3d. ... BILLS AND ACCOUNTS. 59 4 lbs. of tea at 3s. 6d. 5 lbs. of coffee at is. 8l1. 7 lbs. of loaf sugar at 6 Ad. 6 lbs. of moist sugar at 4.^d. .. 3 pairs of gloves at 3s. Qd'. 2 neckties at is. 6d. ... .. 4 pairs of stockings at 2s. 2d... 3 silk handkerchiefs at 3s.- 6d. . , 3. 13 yards longcloth at 3|d., 25 yards shirting at 8.^d., 2 dozen napkins at is. 4d. each, 3 tablecovers at 8s. od. each. 4. 19 yards black silk at 5s. 2d. per yard, 5 yards crape at 6s. 6d,, 12 yards black alpaca at is. yd., and 3 pairs kid gloves at 2s. 8d. 5. 2 bottles of pickle at lojd.. 3 of fruit at Qd., i bottle of blacking; at is. 2d., 9 lbs. of candles at 6^d. per lb. 6. 5 pairs cotton hose at is, 9d., 6 pairs worsted at 2S. 3|d., 4 pairs merino at 3s. 2d. per pair, and 2 dozen children's socks at 7|d. per pair. 7. 27^ yards of carpet at 4s. 9d. per yard, 27^ of felt at 9|d., making the same 27 1 yards at 4d. per yard; stair carpet, 27 yards at 3s. 9d. ; two dozen stair rods at 2|cL each. 8. Two dozen port at 48s. per dozen, 2 dozen pale sherry at 46s., 3 dozen Sauterne at 24s., 4 dozen pints of claret at 13s. 9. 3 pairs lace curtains at 23s. 9d. j^er pair; tapes, rings, &c., for the same, 6s. 6d. ; making up and fixing same, i8s. 6d. 18 yards grey silk at 6s. gd.; 14 yards of muslin at 8Jd. 10. Making and fixing 3 window-blinds for drawing- room (2 at i8s. 4d. each, i at 12s. lod.); 7 blinds for bedrooms (viz., 2 at iis. 8d. each, i at 7s. 6d., and 4 at 6s. 2d. each) ; rods, screws, lines, &c., for fixing, 6s. 6d. Altering spring rollers, 4s. 6d., cleaning and repairing outside blinds, £1 3s. CO ARITHMETIC FOR BEGINNERS. Si:srPLE EEDCCTIOX, AND OTHER USES OF MULTIPLICATION. i%Sm Example I. How many pence are there in £2t, 1 20 shil- 460 = shillings in ;!^ 2 3. 12 5520 = pence in jQ2t,. Because there are lings in ;£i: There arein ;£"2 3 20 times 23 shillings, or ^6o shillings. And because there are 12 pence in a shilling, there are in 460 shillings 1 2 times 460, or 5520 pence. Hence there are 5520 pence in ^23. £xainplG II. Eeduce ^^59 i6s. 2|d. to farthings. 1196 12 14354 4 shillings in £$() i6s. pence in ^59 i6s. 2d. 57417 farthings in £^g i6s. 2\<1. £S9 i6s. 2|d. We multiply y;59 20 by 20, and add in the 16 shillings. There are thus II 96 shillings in ^59 i6s. We multiply 11 96 by 12, and add in the 2 pence. There are thus 14354 pence in ;£"59 16s. 2d. We multiply 14354 by 4, and add in the i farthing. There are thus 57417 farthings in £^<) i6s. 2jd. Example III. How many fourpenny pieces are there in -^'139. 15s- ^ We multiply £i^g by 20, and add in the 15 shillings. There J\re 2795 shillings in ;£"i 3 9 15s. Eut there are three fourpenny pieces ill a shilling. Therefore we multiply 2795 shillings by 3. There are thus 8385 fourpenny pieces S3S5 in £139 15s- £ s. d, 139 15 20 2795 3 SIMPLE REDUCTION. 61 Exercise XXXIX. 1. Eeduce ^i']^^ to shillings; ;^i8 los. to pence: 2. How many sixpences are there in jQi2)^S 5^- ^ 3. If there were a coin worth two pence, how many could I have in change for two guineas ] 4. Eeduce £2> ^9S- 6|d. to farthings. 5. Find the price of 17 articles at 2|d. each. 6. How many things worth three halfpence each can I buy for 5s. 1 7. Find the difference between the number of four- penny jDieces and the number of threepenny pieces in £^ 15s. 8. In seventeen half-crowns how many pence 1 9. If I changed a five-pound note into threepenny jneces, how many should I have? 10. How many more shillings are there than half- crowns in twenty guineas % 11. Eeduce the two sums ;!^i 2 1 6s 3 ^d. and £2^ 7s. gd. to farthings. 12. Find the difference in pence between ;£^6 14s. 8d. and;£'5o. 13. Divide ;^i75 i6s. Qd. by 3, and give the answer in farthings, 14. How many halfpence are equal in value to twelve bags of money containing jQi i6s. 3d. each 1 15. Multiply ;£^763 i8s. 4d. by 15, and reduce the answer to pence. 16. How many halfpence are there in seventeen guineas '? 17. How many farthings are there in seven times ^i8 6s. 4id? 18. Find the total number of farthings in nine guineas, three half-sovereigns, and fifteen half-crowns and seven sixpences. 19. How many articles worth three halfpence each could I buy for ;^57 los. ? 20. Add the number of farthings in seven hundred and fifty I'ounds to the number of shillings in the same sum. 62 - AKITHilETIC FOR BEGrN'>T:RS. divisio:n^ of money. 34:. In dividing a sum of money, pounds, skillings, pence, and farthings must be separately divided in succes- sion, and when there is any remainder, it must be reduced to the term next below it. Example I. Divide £^^ 6s. 3d. by three. jQ s. d. AYe find one-third of £2)2> ^7 *^^® 2,)^2> 6 3 method of simple division, lO. • The answer is ;£i i. 1 1 2 I A third of 6s. is 2s. The third of 3d. is i penny. The answer is jQi i 2s. 3d : Example II. Divide jQi6^ iis. 4M. by 7. ;^ s. d, ^Ye divide 164 by 7 )164 II 4i 7^ and find the quo- 23 10 2J : I remainder. tient to be ^£"23 with a remainder, jQt^ J^ow jQ^ and us. reduced to shillings make 71 shil- lings. The seventh of 71 is 10, with a remainder of i shilling. One shilling and fourpence make 1 6 pence. The seventh, of 16 is 2, with a remainder of 2 pence. 2 pence and Jd. reduced to farthings make 10 farthings. The seventh of 10 is i, with 3 farthings remainder. The nearest answer therefore is ;£22, los. 24d., with three farthings remaining undivided. Exercise XL. 1. "Wliat is the fourth part of ;?^i los. ? 2. Divide ;£'26 by five. 3. Add the half of ;£"io los. to the third part of the same sum. 4. If ;£^25o I OS. are left to be divided among 6 persons, how much will each receive ? 5. ;£i8 have to be divided among 10 persons: how much will each receive % COMPOUND DIVISION. 63 6. From the half of five guineas take the third of five guineas. ;£■ s. d. . ^ s. d. 7. 8)7 2 6 7)23 10 4 8. 10)123 16 £ s. 11)25 2 9. ;^i8 I2S. 6d.-f-io; ^2453. 7d. 47. 10. £3^ lys- 3^.-11; £19 6s. 5d.-f-i2. II- ;^f37 15s. 3^.-5; £^H 10S.-8. 12. ;£"207 15s. 6d. -6; ;£"327 14s. Sd.^g. 13. Add together the eighth and the tenth parts of £S3 I2S. 6d. 14. Take the twelfth part of ^126 3s. from the whole of that sum. 15. A gentleman bequeaths ^1250, of which one-half is given to his eldest son, one-third to his second son, and the remainder in charities ; how much money is given to each purpose 1 16. ;^2i3 17s. 6d. + ^519 I2S- 8d. 12 17. ; ^5o4 108.-^196 13s. 4d. 8 18. ;^27 15s. 6id. + ^^196 i8s. 7d. - £s9 los. 4$^- 19- ;£"325 i6s. 7d. x 10 7 +4 20. Find the difference between the eighth and the twelfth parts of ^£1250. 21. If the sum of ^1827 19s. 6d. be divided into nine parts, of which A receives five, and B four, what is the share of each 1 22. Divide a legacy of ^8757 2s. among three persons, so that the first shall have five parts, the second four parts, and the third two parts . 64 ARITHMETIC FOR BEGINNERS. DIVISON OF MONEY {contmmd). 3o« Wlien the divisor is greater than 12, each remain- der must be set down separately, and the work done as in Long Division (2S). Example. Divide ;£7i35 i6s. 4d. by 27. AVe first divide ;£"7 1 3 5 by 2 7, asin2?. The quotient is ^£"264, and ;£'] are left undivided. AVe next reduce these ^£'7 and tlie i6s. to shillings. They make 156 shillings. On dividing 156 by 27, the nearest answer is 5 s., and 21 shillings remain undivided. "We next reduce these 21 shillings and 4d. to pence. They make 256 pence. On dividing 256 by 27 we find the quotient to be 9 pence, and 13 pence remain undivided. We next reduce the 13 pence to 52 farthings. On dividing these 52 by 27 we find the quotient i, and a remainder of 25 farthings which cannot be divided by 27. 25 farthings remain undivided. The answer is, therefore, ;£264 5s. 9|d., and 25 re- mainder. £ s. 7)7135 16 54 d. £ 4(264 173 162 115 108 7 20 27)156(5 135 shillings. 21 12 27)256(9 243 pence. 13 4 27)52(1 27 farthing. MISCELULSTEOrS EXEKCISES. 89 3. To how many persons can I give 5Jd. out of ;^46ol 4. How many lengths of 8§^ inches can be cut from a piece 172 yards long? 5. There are 30 J square yards in a perch : how mauy perches are there in 5289 yards 1 6. 32067 -^ 6f; 5183-1. I li. 7. 41682 -i. i5|; 31625 -f- 8^. 8. 2 196 + 578; 516382 - 29547. i5§ 172I 9. Find the total number of shillings in 28 half-crowns, twelve half-sovereigns, and 17 ^£"5 notes. 10. What is the worth of a 17 lb. bag of tea at ^{d. per oz. ? 1 1. How many persons can receive 4jd. each out of a sum of ;£"i2 i8s. ] 12. Multiply the product of 712 and 518 by the differ- ence between these numbers. 13. Add together 45 pence, 45 farthings, and 45 shil- lings. 1 4. Take seventeen thousand four hundred and nineteen jwunds fourteen shillings and fourpence three farthings from a million pounds. 15. How many halfpence are there in fifteen guineas? 16. How many packages weighing 2^ oz. each can be made up out of two chests of tea weighing i cwt. 3 qrs. 17 lbs. each? 1 7. Add together f of is., ^ of ;£"i, 4 of a crown, and A of ^5- 18. What would it cost to put up a fence a mile and three-quarters long at is. 7|d. per yard? 19. If I draw off from a vessel successively a third, a fourth, and a sixth of its contents, what portion of the whole remains ? 20. How many yards of velvet trimming j^ of a yard wide can be cut from a piece 31!^ yards long and f of a yard wide ? 2 1. How often does a clock which chimes every quarter of an hour chime in 17 weeks 3 days ? 90 ANSWERS TO EXEECISES. VII.-(i) 12. (2) 8. (3) 17. (4) 14. 4. (7) 8 (8) 13. (9) 15. (10) 8. (11) 8. 7. 8. (12) 14. (13) 7 VIII. — (i) II. 12. 16. II. 13. 10. 12. 13 (2) 7- 9- 5- 5- 5- 8. 9. 7- 7- IX.-(i) 37. 81. 92. 91. 54. 75. 75. 50 (2) 24. 3y 51- 59- 54- 24. ss- 21. 16. X.— 8. 4. 19. 47. 67. 68. 34. 5. 5. (i) 4 36. 38. (2) 43. (3) 15 pence. (4) 32. (5) 76 (6) 23. (7) 21. (8) 12. (9) 27. (10) 17. (11) 34. XL— (i) 94. 86. 53. (2) 87. 99. 95. (3) 57 (4) 98. (5) 84- (6) 92. (7) 95 yards. (8) 56 (9) £ii- (10) 29. XII.— (i) 884. 550- 931. (2) 867. 870. 450 (3) 166. (4) ;^8o4. (5) 96. (6) 270. (7) 115- (8 49- (9) 102. (10) 46. (11) 775. XIV.-959. (2) 35. 286. (3) 161. (4) 22. (5) 187. (6) 124. (7) 31. (8) 313- (9) ;£i75. (10) 156. (11) ^39. (12) £39' (13) 174. (14) 295. 186. 713. (15) 339. 376. (16) 134. 197- 268. (17) 482. 167. 487. (18) 257. (19) 665. (20) 119. (21) 484. (22) 169. XVL— (i) 750. (2) 3561. (3) 4322. (4) ^1392- ;^io97. (5) 326 mUes. (6) ^387. (7^ 58. (8) B. over C 51. B over A 834. C over A 783. (9) 5870. 'o>034. 4957. (10) 6240. 6044. (11) 1086. 831. 4375. (12) 2859. 1456. XVII.- (i) 12. (2) 15. (3) 16. 24. (4) 24. (5) 6. 8. 9- 10. (6) 4. 5- 3- 2. (7) 6. 4. (8) 5- (9) 7- (10) 4- 6. (11) 3. (12) 2. 3. XVIII.-(i) 36. 75- (2) 92. 114. (3) 318. (4). 906. (5) 735- (6) 507- (7) 79- (8) 187. (9) 34- 1587. 246. 4218. (10) 1436. 1254. 1578. XIX.— (i) 28. 36. 28. (2) 15. 32. 10. 12. (3) 20. 25. 45. (4) 36. 28. 12. 24. (5) 20. 36. 16. (6) 18. 24. 30. 12. (7) 4. 4. 7. 2. (8) 5. AXSWEBS TO EXERCISES. 91 4- (9) 32. (10) 48. (11) 60. (12) 55. 33. 44. (13) 5136. 10,196. 28,484. (14) 20,240. 6355. (15) 32,484- 3126. 35,480. (16) 24,508. 24,579. (17) 606. 5135. 12,648. (18) 9820. 2876. XX.-(i) 56- 18. 36. (2) 35- (>Z' (3) 72. 35- (4) 6. 8. 9. (5) 6. 10. 5. 3. (6) 6. 4. 3. 2. 12. (7) 28. 40. (8) 6:^. (9) 4. 12. 2. 24. 3. 16. 8. 6. XXI.— (i) 2065. 2473. (2) 10,450. (3) 156. 324. 567. 2076. (4) 136. 312. 1736. (5) 114. 674. (6) 168. 708. 7500. (7) 711 pounds. (8) 239. (9) 623. (10) 116. 2152. 2856. (ii) £i^,SZ^. (12) The latter by 31. (13) 7808. (14) 1404. (15) 3640. 67,529- 3336. (16) 7360. 5778. 62,998. (17) 9582. 103,500. 15,183. (18) 49,626. 28,728. 12,168. (19) 33.304- 10,980. 35,889. (20) 16,335. 24,822. 16,136. (21). 8274. 56,980. 74,136. (22) 36,141. 72,369 62.064. XXIII. — ii) 170. 280. 3100. (2) 2160. 2i,6oo- 216,000. (3) 195,200. (4) 1,245,600. (5) 76,700. (6) 326,480. (7) 32,500. XXIV.-(i) 1206. (2) 11,310. (3) 1850. (4) 64,625. (5) 923,601. (6) 8820. (7) 1904. 35,280. (8) 308. 812. (9) 3540. (10) 2560. 43>26o. (11) 58,473. (12) 557. (13) 13,232. 19,776. (14) 546,936. 98,268. (15) 900,798. 624,085. (16) 660,969. 22,790. (17) 2,195,095. 437,525- (18) 643,282. 821,016. (19) 15,310,600. 6,621,534. XXV.~(i) 17,496. 311,148. (2) 819. (3) 67,284. 495,648. (4) 1 128. 7632. (5) 612. 3888. 3384. (6) 83,020. 1,373,247. (7) 383,760. 1,580,040. (8) 2,535,162. 93,984. (9) 55,530. 5,126,247. (10) 778,185. 159,350. (11) 2,302,016. 1,229,984. (12) 3,064,320. 3,342,800. (13) 391,068. 33,477,138. (14) 14,784. (15) 60,903. (16) 62,720. XXVI.-(i) 21,182. 53. (2) ^40. ^20. (3) 412. (4) 42. 132. 266. (5) 125. (6) 305. (7) 150. 200. 120. 300. (8) ;£2,434. (9) 209. (lo) 92 AIUTIIMETIC rOR BEGIXNEIIS. 21,130. (11) 21,423. (12) IT93. (13) 84,011-3. 9805-3. (14)4526-3.7198-6. (15)3997-5- 725.460-1. (16) 89..962-3. 5332-3. (17) 3962-2. 4802-5. (18) 8134-3. 68,474-3. XXVII.-(i) 40. (2) 52-20.(3) 81. (4) 42,533-9- (5) 33^- (6) 31- (7) 1980. (8) 178. (9) 15 and 55 remainder. (10) 7. (11) 20. (12) 157-108. (13) 453-15- 3478-3- 1267-15. (14) 492-194. 627-58. 2976-9. (15) 285,448-2529. 2415-164. 4807-10. (16) 880-372. 5891-76. 2599-205. (17) 1345-3- 761-25. 4010-16. (18) 34,346-20. (19) 394. XXVII [.-(1)32-79. (2)392-185. (3)176,938-2; 17,693-82 ; 1769-382; 176-9382. (4) 17-69; 3^3-5^ y 526-84; 4793-82. (5) 10; 1000; 100. (6) 7-59. (7) 59, ^ith 763 remaining. (8) 204-143. (9) 1383- 16; 13-23,256. (10) 383-365. (11) ;^54; ;£"ii8 10 shillings. (12) ^^122 and 4c foiirpences ; ^^682 and 40 fourpences. (13) 17-136. (14) 276. (15) 568-320. (16) 811-222; 64-4665. (17) 61-4870; 86-29,175. (18) 17-14,438; 1774-248. (19) 1265-187; 58-676. (20) 175,990. (21) 1173—614. xxix.-(i) 39. (2) 30. (3) 80; 2. (4) 5; 16. (5) 20. (6) 160. (7) 442. (8) 262. (9) 160. (10) 4. (it) 13; 73-246. (12) 31,860; 630. (13) 268. (14) 69,592, (15) 149,076. XXX.— (i) 4064 grs. (2) 1867. (3) 66 yrs. (4) 884 shillings. (5) 900 ; 21,600. (6) 45 yds. (7)35- (8) 1232. (9) 608. (10) 132. (11) ^12,280. (12) ;£2oo. (13) 139-668. (14) 313. (15) 28,830. (16) 332. (17) 1568; 1848. (18)22,222—2. (19)47,520; 31,680. (20) 25,908. (21) 384. (22) 1279. (23) 3,652,264. (24) 273. (25) 45j904. (26) 10,000. (27) 541,985; 660,372. (28) 157,030. (29) 6878. (30) 7168. (31) 41,879. (32) 22,704,108. (33) 50,000. XXXIL— (i) 8—18. (2) 15 pence. (3) 2^,d. (4) 5d. (5) 3d.; IS. 3d. (6)2s. 7d. (7) 8|d. (8) I Id. (9) 15- (10) 2d. (II) 6d. (12) 15. Ai»S\rERS TO EXERCISES. 93 XXXlII.-(i) £2 14s. 7d. (2) £zz 19s. lod. (3) £'2 8s. 7d. (4) ;^52 75. 5d. (5) ^50 9s. id.; ^,^381 OS. 3d.; £-7^%2 17s. 8d. (6) ;£i2 5s. 3d.; ^£'291 3s. 3d.; ^28 6s. i|d. (7) iis. 3^d. (8) ;^i 8s. 7jd. (9) los. 3d. (lo) £^ i2s. 4d. (11) ^22 5s. XXXIV.— (I) ^6327 i8s. iid. (2) 7:3612 IS. 5id. (3) ;^i2,3i7 8s. 4id. (4) ^5199 i6s. 8ld. (5) 7:8189 8s. I lid. (6) ^4017 15s. 2d. (7) ^22 103. I id. (8) ;£'68i 1 8s. 7d. (9) £^2 14s. 2d. (10) ^2664 IIS. 8|d. ; ;£4367 is. lod. ; ;£"5744 15s. 5id. (11)^28,923 OS. io|d.;;£'57,5i5 12s. 8id.; ^29,148 15s. 8id. (12) £2 IS. 8|d. (13) ;^35,58i IIS. ii|d. ; ^20,582 14s. 6d. ; ;£"37,5i3 ^Ss- 9^. XXXV.-(i) 3S. 8d. (2) ^123 6.. 6d. (3) £s i6s. 4d. (4; ^18 5s. 3d. (5) ^518 los. (6) ^^2386 6s. lo^d. ; ^£"1322 6s. 8M. ; ^^78 os. lod. (7) ^2795 4S. 43d.; ^14,888 5s. 9|d.; ^2712 6s. 5id. (8) ^978 9s. 5id. (9) ^'197 14s. 8d. (10) ;^i86 los. o.^d. (11) £2 19s. 7|d. (12) 3s. 2d. (13) ^74 4S.'55d. (14) £a9 15s. XXXVI.— (i) I2S. 6d. ; fy 14s. (2) ^^15 5s. 9£d. ; £yZ 7s. 9d. (3) 8s. ijd. (4) £2 3S. (5) ;£io3- (6) 17s. 9.|d. (7) ^42 6s. lod. ; £\\ 12s. iid. ; ;^27 15s. 7id. (8) ^127 17s. 4|d.;^i28 iis. 4d. ; ;^i53 8s. lod. (9) ;^iio9 17s. 4id.;^i5 15s. 4d. ; ^196 i8s. 4d. (10) £26 14s.; £1 i6s. 4d. (11) ^155 i6s. 3d.; ;^i4 los. 7id. (12) ;^io5 8s. 4d. (13) ^31 8s. lod.; ^17 15s. 9d. (14) ^474 7s. 6d.; £c) 2s. (15) ^139 13s. (16) ;£"3i5 4s. 6d. (17) ;£545 I7S- 6d. (18) ^5 iis. 8d. (19) £^ i2s. 6d. (20) £']% 17s. 3d. (21) ;£"223<2 los. lod. (22) ^£4190 5S. 4d- (23) 2741 5s. Zl^' (24) ^655 i2s. (25) £^, XXXVII.-(i) ^45 14s. 4d. (2) ;£454 19s. njd. (3) ;£io4o i8s. ofd. (4) £z^ 5S- 9^. (5) ^5° los. 6d. (6) ^100 7s. (7) ^1327 los. (8) ^1507 5s. 2d. (9) ;^544 i6s. 6d. ; ;£292 i6s. 4jd. (10) 94 AWTHMETIC POR BEGIKNEBS. ;£904i 5s. 4jd. ; £3999 i3S- lo^d. {n) £^23$ 5S-; ;f 19,153 9S. 3|d. (12) £67 9s. Sjd.; ^98,718 15s. io|d. (13) ^3681 4S. 6id. j £soj i6s. 5|d. (14) ;^568i 8s. 8id.; ^28,388 6s. 6d. (15) ;^2i,i8i OS. 2d.; ^£138,595 17s. i^d. (16) ;£64 i8s. 3|d. (17) ^365 los. (18) ^£651 i2s. 6d. (19) ^63 15s. (20) ;£"l8o OS. 6d. XXXVIII.-fi) £1 17s. i|d. (2) ;^3 IS. 9|d. (3) ;£3 17s. 9id- (4) ^7 17s. 3d. (5) 10s. ojd. (6) £ 210s. 2d. (7) £13 7s. 9|d. (8) ^15 12s. (9) ^11 7S. 8d. (10) ^6 19s. XXXIX.— (i) 35.380 shillings 4430 pence. (2) 55,410. (3) 252. (4) 3819. (5) 3s. 6Jd. (6) 40. (7) 55. (8) 510. (9) 400. • (10) 252. (11) 12,302; 23,41?. (12)3184. (13)56,268. (14)10,440. (15)2,750,100. (16) 8568. (17) 123,095. (18) 12,480. (19) 9200. (20) 735>ooo- XL.-(i) 7s. 6d. (2) £s AS- (3) £S 15s. (4) £41 T5S- (5) £^ i6s. (6) 17s. 6d. (7) 17s. 9|d.; £3 7s. 2ld.-i. (8) ^12 7s. 8d.: £2 5s. 8|d.-9. (9) £1 17s. 3d.; £3 9s- 4id.-5. (10) £3 los. 7|d.-7; £1 i2s. 2id.-8. (11) p^7 IIS. oid.-2; £23 is. 3d. (12) £34 i2s. 7d.; ^36 8s. 3id.-2. (13) ;^i2 is. 3id. (14) £i^S i2S. 9d. (15) ;£625; ;£4i6 13s. 4^. ; ^208 6s. 8d. (16) ;f6i i2s. 6d. (17) ^38 9s. 7d. (18) £^5 OS. 4d. (19) ^465 9S- 4|d.-3. (20) £z2 IS. 8d. (21) ;£'ioi5 los. lod. A; ;£^8i2 8s. 8d. I (22) The first has ^£^3980 los. ; the second, ^^3184 8s. the third, ;;^i592 4s. XLL— (i) ;^23 IS. 6id.-ii. (2) ^45 4S. 4|d. ;^40 3S. ioid.-i2. (3) ^44 19s. 8|d.-6. (4) £4 3s. 4d. (5) Each child ^555 us. i^d. ; each nephew ;^4i6 13s. 4d. (6) £58 i6s. 4|d. (7) ^^52 is. 8d. ; ^23 I2S. iifd.-3. (8) £9 5s. 5ld.-7; £9^ os. 5|d. -17- (9) £9 9S- 4-3^.-6; ^160 14s. 3jd.-36. (10) ^196 7s. 5id.-4; £28 5s. ioid.-6. (11) ^122 3s. o4d.-6 ; ;£^i07 15s. 7d- 28. (12) ^49 os. 6d.-i6; ;£34 4S. iid-52. (13) ;^83 19s. 4d. (14) £16 18s. ANSWERS TO EXERCISES. 95 9ld.-36. (15) I2S. i|d. (16) £10 IS. 9i(l.-3. (17) £2^ IS. 3id.-7. (18) ^84 I2S. 8id. (19) 64,294. (20) The one receives ;£468 15s. 3 and the other ;^53i 5s. XLIL— (i) 1320. (2) £1 15s. o|d. (3) ^^95 3S- 4d. (4) 768. (5) £2 15s. 2jd. {6)a £ig 2s. 7d. £^2> IS. I id., ^17 9s. 8d. ; h ^457 14s. 4d., ;£204 2S. 6d., ^13 6s. 7d. (7) 1280. (8) 522. (9) 4igs. 3s. (10) 691-12. (11) 4780. (12) 477. (13) 150. (14) 514 sixpences and 3|d. ; 102 h.-c. 2s. 5.^d. (15) 4800. (16) ^607 i2s. 8|d.; ^"434 OS. 7|d. XLIIL-(i) 6s. 7 id. (2) £1 5s. 3d. (3) ^13 l5s- 3d. (4) £2 17s. 4d. (5) £s 13s. id. (6) ^117 9s. (7) ^26 OS. lod. (8) 17 10 persons. (9) 27,480. (10) ^14 9s. 2|d. (11) 9491. (12) ;^i2 8s. 4d. (13) £"1 IS. (14) 153 of each, or 459 persons in all. XLIV.— (i) 15 lbs. 4 oz. (2) I lb. 14 oz. (3) 15s. (4) 2 tons 16 cwt. 19 lbs. (5) I qr. 5 oz. (6) 411 lbs. 6576 ozs. (7) 1520. (8) 62 f lbs. (9) 108 lbs. (10) 95- 52. (11) £^ i2s. id. (12) 8 cwt. I qr. 1 3 lbs. 8 oz. (13) ^16 5s. 6d. (14) 448. (15) 6 tons I cwt. 2 qrs. 13 lbs. II ozs. ; 4 tons 11 cwt. i qr. 26 lbs. 7 ozs. (16) 8 tons 3 cwt. I qr. 19 lbs. 3 oz. (17) 4 cwt. i qr. 25 lbs. 2 oz. (18) 4 tons 15 cwt. 3 qrs. 5 lbs. (19) 5 tons 11 cwt. i qr. 26 lbs. ; 56 tons 19 cwt. i qr. 15 lbs. (20) 2 tons 11 lbs. (21) 883—5. (22) 2240. (23) ijd. (24) 261-1. (25) 23 lbs. 12 ozs. (26) ;^38 i6s. 4d. (27) 6 cwt. 21 bs. 12 oz. (28) 197,120 ozs. 3,153,920 drs. (29) 5,4656. XLV. — (i) 132. (2) 4620 ft. 55,440 ins. (3) 18 miles 7 furs. 113 yds. i foot. (4) 6^ yds. 11 ins. (5) 26 yds. 9 ins, (6) 1896. (7) ;^i 6s. 3d. (8) 4 miles 2 furs. 100 yds. (9) ^568 los. (10). 1135-8. (11) 5 furs. 140yds. (12)^2640. (13)1188. (14) ;^3i3 los. (15) 7200. XLVI.— (i) 324. (2) Ceiling 245 sq. yds. 5 ft. ; 2 long walls 115 sq. yds. 5 ft. each ; 2 short walls 60 sq. yds. 4 ft. each. (3) 105. (4) £^ 5s. (5) 450. (6) 84 sq. yds. (7) £i()'j 8s. 9d. (8) 18,144. (9) ^336. (10) ^8 i6s. lid. (11) 486. (12) 7920; ;^594. 7) 1 OG ARITHMETIC FOR BEGINNERS. XLVII. — (i) 20 a. I r. 22 p. (2) i a. 3 r. 15 p. (3) ^/:224o. (4) 600. (5) 160 a. (6) ;^236 5s. (7) \xLVliL-(i) 4158. (2) 41,960. (3) 5400. (4) £8 13s. 3d. XLIX.— (i) 15 gal. 29 qt. i pt. (2) 8704. (3) 95— 2< (4) 10 gal. I qt. (5) 88 gal. i pt. (6) 1504. (7) 621 gal. (8) 2 grs. 4 bus. 2 pks. L.— (1)8760. (2)2976. (3)9,936,000. (4);£"26i5s.6d- (5) 3406. (6) ^35 15s. od. (7) 300,960. (8) 10,950. LI.-(i) £6 i6s. 6d. (2) 2346. (3) ;^47 i8s. 6d. (4) £9 8s. 4d. (5) £3 13s. ijd. (6) ^276 2S. lojd. (7)284. (8)248. (9)676. (10) ;£83 2s. 8id. (11) 6080 yds. ; ;£'i596. (12) 1800 cub. ft. ; 3,110,406 c. in (13)3520. (14) 448; 1792; 35,840. LII.-(i) 10; 9. (2) 4; 8. (3) 2; 5. (4) 2. (5) 4- (6) 20; 10; 6; 15. (7) 12; 12. (8) 5d.j 15s. (9) 2jd. (10)9; 4; 15. (11)15. (12)21. (13)20. (14) I; TO-; T- (15) t- (16) 2 feet; 6 furs, j 7 ins. (17) 6s. 3d. ; IIS. 8d. ; 8s. 4d. (19) 4 ; 8 ; .10. (20) 6 furs. ; 1232 yds. ; 550 yds. (21) 14 lb. ; 8 cwt., 2 qrs.^ (22) 2 ft. 6 ins. ^Hj LIII.-(i)4. (2) J. (3)4. (4)Aor|. (5)8s.4d. (6) ^ lb. or 14 oz. (7) 8. (8) 7 ins. (9) 35 minutes. (10) 3 qts., ij gills. (11) ^. (12) IS. 8d.; £1 8s. LIV.— (i) 621. (2) 66,674. (3) 9570; 14,432; 2854^. (4)8i6|; 3751; 13,8244. (5) 997J. (6) 9180. (7)143,6561. (8) 8858i ; 299,559i. I,V.— (i) 1953I. (2)5940; 960 p., 5 yds. (3)19,200. (4) 714 and 4 ins. remain. (5) 174; 25^ yds. remain. (6)4858-^^; 465-' ^ (7) 2725-^2 ; 3614-2. (8) 177—3; 2826— 1215. (9) 1890. (lo)' ;^3 13s. 8d. (11) 688. (12) 71.550,304. (13) £2 9S. 84d. (14) ^^982,580 5s. 7|d. (15) 7560. (16) 2478—6. (17) £2 IS. iijd. (18) £2So 5s. (19) J. (20) 378. (21) II;7I2. J. AKD W. BIDBB, FBIKTBBS, LONBOH'. FOB, lB'JtEgtlmm,rna4t^ XBJXfr SIGLQS fOEISS, 17SK C9 SCHOOLS ASB YOUSG FESSON:^ E£iad by tke Ue Sx: Al£«K. rh^ vcKk coBtaiaB exknets final the Poons of AdfiHB, Dr. AxMBtnafe Hcbcr. Mb. HewM^ fi«Me^ Be. . KcUb; La^lt, lESimm, Mmrv Jna MimImiij, IBekk; Mn. H. THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO 50 CENTS ON THE FOURTH DAY AND TO $!.00 ON THE SEVENTH DAY OVERDUE. kno fo), Em of tl gen A tha T rul. the mei an' 3Ii an VA Q2402 I 5th EdUumy price 3*. doth, DIL ALLEarS EDTROPIUSi With a comtmt* Dicnoif aky for Schoois. iS:i Edition, prux 2s. red leather,- Is. 9d. dofk, ALLEN & (XmirWELL'S SCHOOL OBAHKAB. Wiih Teiy copiooa Exerdaes, and a Systematic Yiew <A the Foniatiosi and Derintion of WoatdB, owinriaiB g Anglo-Saxon, Latin, and Qw e k 7.0OO English WordiL (5^ UNIVERSITY OF CALIFORNU LIBRARY " This simple Inirodaction » as good a bocA as (an be nasd. Court jommal "We hare nera-secasniaR desirable donaitaryiraik.' London : SncPEcy, Mabshaix, & Co.; Haviltok, At*am«, & Co. Edinburgh : Omtbb k, Born.