IMAGE EVALUATION TEST TARGET (MT-3) // ^/ ^ >. .** .« fe ^0 1.25 Bi|21 121 mm U22 Sf U£ |2.0 1.4 1.6 Hiotographic Sciences Corporation \ iV •^ \\ ^^V 6^ 23 WfST MAIN STMiT WnSTIR.N.Y. 14SS0 (716) S72-4S03 '^ , signifie "A SUIVRE ', le symbols V signifie "FIN". Les cartes, planches, tableaux, etc., peuvent Atre filmto A das taux de riduction diff«rents. Lorsque le document est trop grand pour Atre reproduit en un seul ciich*. il est film* A partir de I'angia auptriaur gauche, de gauche i droite, et de haut an bas, an pranant le nombre d'imagea ntcaaaaira. Lea diagrammea suivants illustrent la mtthoda. 1 2 3 1 2 3 4 5 6 >*v^. *>* '■ i' Uw-t CAi J ^f* t^^- ,v - ''i" PIILH ^-f- ^ ■'"•) ■5' -i n '):tp*s^' i^^l^^ '?.?:. / J FIRST CANADIAN ARITHMETIC, INTENDED FOR TUK PIILHARY DEPAKTHE^T OP COMMN SCHOOLS. BY ,. . ^' - :i H. L. WHITCOMB. ►-•-< v/ ,' -^'^, ■■*♦ I PRINTED roll THE AUTHOR BY JOHN LOVELL, AND FOR SALE BY ALL B00KSELLEB8. J860. . 1 M,':3 Entered according to the Act of the Provincial Parliament in the year one thousand eight hundred and sixty-six, by H. L. Whitoomb, in the office of the Registrar of the Pro* viuce of Canada. The the foil PREFACE. 'arliament in sixty-six, by r of the Pro- The distinctivo character of this little work will appear from I the following: Instead of a short introduction to all the rules of arithmetic, leading principles only are introduced, and those are thoroughly elucidated both in theory and practice, while all vulumiuous explanations are avoided. - Mental exercises are combined with the written exercises throughout, and thus applied to tlie illustration of the same principles. The important department of the simple rules is arranged in lessons according to the pages, a table forming the head of each lesson, and more copiously illustrated by examples than in any other arithmetic known to the author. Analysis takes the place of proportion, it being really what the latter long pretended to, a key to most of the processes of arithmetic. How much soever of reliance is to bo placed on the teacher in giving life and interest to the recitation, books prepared on the model he pursues will best assist him in thefe respects, and will tend to produce uniformity in methods of teaching. No written system of numbers can by any means supersede the use of numerous oral exercises, both mental and written, and illustrations on the blackboard. For the use of the inexperienced teacher notes are interspersed throughout the book, and the autliur would respecttully oll'er the following SU««ESTI<)NH TO TKACIIE15S. The mental exercises form the heads of lessons to be prepared by the pupils, but which should be extended and diversiHed by the teachers till the principle they embody is fully compre- hended. No one principle can be passed superiicially without loss to the luture arithmetician. In order to form habits of correctness and self-reliance the pupils should be instructed to prove their vfork ; and for this purpose the answers to many of the exercises are not' given. And if the teacher keep by him a book with the answers tilled out in it, and accustom the pupils to number on their slates tlie exercises they work out, he can see at a glance, or by occasion- ally calling for their answers, whether they are working cor- rectly. Recitations in written arithmetic should generally be con- ducted by the use of the blackboard. A usual method is for the class to go up together, and work ont the exercises appointed by the teacher in the order of their numbers, and afterwards in succession to give the demonstration, the most expert taking the precedence, liy giving these demonstrations and the solutions of mental exercises in a clear and distinct tone, keeping before the mind the subject, and not words or rules, the pupils will acquire not only clear ideas of the principles of numDers, but also the power of expressing their i4caB, and g natural and graceful elocution, CONTENTS. PAGB Definitions and Notation 5 Addition 6 Subtraction 30 Multiplication 45 Division 61 General principles^. 74 Miscellaneous exercises in preceding rules 81 Bills of Parcels 83 Analysis 84 Tables of weights and measures 91 Reduction of compound numbers 100 Addition " « . 108 Subtraction " " Ill Multiplication " " 113 Division " " 115 Analysis " " 119 Miscellaneous exercises 121 • Answers to exercises 124 1. Aritj 2. A nui 3. A un 4. Anal 5. A sii one denon 6. Nota 7. Num( pressed, figures or 8. Thee their posi second te being equ 9. Thr following Ob P O at & 9 n 7 9 s 4, 18 17 16 The 81 lions, O Note nection ARITHMETIC. PAGB 5 6 -. 30 . 45 . 61 . 74 . 81 . 83 . 84 . 91 100 108 111 113 115 119 121 124 1. Arithmetic is the science of numbers. 2. A number consists of one or more units. 3. A unit is a single thing of any kind, as 1 book. 4. An abstract number is of no denomination, as 2, 4, 9. 6. A single number is an abstract number, or of but one denomination, as 3, 6 shillings. 6. Notation is the expression of numbers by characters . 7. Numeration ie the reading of numbers thus ex- pressed. The characters used in notation are the ten figures or digits, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. 8. These figures have different values according to their position, the right hand figure being units, the second tens, the third hundreds ; each order on the left being equal to ten of the order next it on the right. 9. Three orders make one period, according to tlie following, NUMERATION TABLE. P o at OB n Q t3 a s « 5 "S « j2 K H hJ n E^ p i ^ w -2 w .« ^5 n H D •mm n H P 79 4, 36 7. 83 6, 847 18 17 16 15 14 18 12 11 10 9 8 7, iH I W H P 3 6 8 6 6 4, a n 9 8 J2 a ED a 1 2 6 1 Orders. The succeedine periods are QuintilUons, Sextillions, Septil* lions, Octillions, Nonillious, Decillions. Note.— Notation and numeration should be taught in con- nection with the simple rules. 6 ARITHMETIC. 10. The four fundamental rules of arithmetic are! Addition, Subtraction, Multiplication, and Division. A D D I T I X . 11. Addition is the process of finding the sum of two or more numbers. The numbers to be added are called addends, and the result of the addition, the sum. 12. The sign +, signifies addition. Thus 5+2 denotes that 2 is to be added to 5. The sign = denotes equality ; 5 + 2 = 7 is read 5 plr.s 2 equal 7. MFiNTAL EXERCISES. 1. Count 100. 2. How many windows in the school room ? 3. How many panes of glass in 1 window ? in 2 windows? 4. How many boys are in the cla8s ? How many girls? How many boys and girls? 1 2 3 4 • 1. 2. J| how 3. and 3 TABLE. 1 + 1 = 2 2 + 1 = 3 3+1 = 4 4+1 = 5 B + 1 — 6 6+1 = 7 7+1 = 8 8+1 = 9 9 + 1 = 10 + 1 = 11+1 = 12 4- 1 = 10 11 12 13 # X WRITTEN EXERCISES. in ad addc (I) (2) (3) (4) (5) (6) (7) (8) Th bytl 1232 1324 3210 3232 1234 5424 1024 2132 1653 1436 2451 3210 1445 4206 3210 4628 1 Th 1 H® 1 seen ADDITION. ritliraetic are Division. TABLE. - sum of two nds, and the liiia 5 -f 2 1 = (lenotea 7. Ij I = 10 I = 11 . ^: 12 — 13 (8) 10 3210 >6 4628 1 + 2 2 4-2 3 4-2 4 + 2 = 3 = 4 = 5 = 6 6 + « + 7 + 8 + = 7 = 8 = 9 = 10 9 + 2 10 + 2 11 + 2 12 + 2 11 12 13 14 • 1. Add two successively to 50 ; thus, 2, 4, 0, 8, 10, &c. 2. John had 3 apples, and his sister gave him 2 more ; how many had he then? 3. A man gave 1 cent to Harry, 2 cents to Emma, and 3 cents to Kate ; how many did he give to all ? (9) 24113 34123 (10) 22222 58764 (H) 34212 12634 (12) 24321 41264 (13) 23214 63412 (14) 14321 83414 (18) 32142 64253 (15) 14213 10142 (16) 31248 83701 (17) 12314 42344 (19) 21021 76235 (20) 32100 61964 * These exercises with the tables are intended to give rapidity Id adding. Tlie pupil shun! 1 be practised in them till able to add each figure successively to 100 without the least, hesitation. The written exercises will be distinguished iVom the mental by their numbers which are continuea from page to page. The mental exercises are intended rather as the heads of a lessou to be prepared by the pupil than a guide to the teacher. He should modify and enlarge them as circumstauoes shall seem to dictate. 6 ADDITION. • M 42S a 345 25 •o < 34 Sum. 827 Proof. 827 18. The addition of siuple numbers is called simple addition. 14. To add siiuplu numbers, * Rule with example : Find the sum of 423, 345, 'iC) and 34. We write tlie addends units under units, tens under tens, hundreds under hundreds, &c. Then, commencing at the units we add (without naming the figures) thus 4, 9 — 14 — 17 units equal to 1 ten and 7 units ; set down the 7 units under the column added and carry the 1 ten to the next column. Add the remaining columns in the same manner, setting down the units and carrying the tens ; because 10 of each order is equal to 1 of the next order on the left. NoTB.— The pupilfl should onrly be made familiar with the names of the onderti, their increaHe lowards the left, and decrease towards the right in a tenfold ratio, and with tht^ eflbct of removing a flguro in either dUrootion. 15. Proof 1. Commence at the top and add the columns downwards. If the two results are alike the work is supposed to be correct. Ah this process reverses the order of the figures, any mistake made in the lirst operation is likely to be detected in the second. Proof 2. Cut off the first addend ; add the others, and to their sura, add the first addend, The result should be the same as the first sum. (33 714 714 (3 \V 12 14 (21) 32414 18365 (22) 14320 42834 (23) 31034 18264 (24) 63214 63296 ADDITION. 9 •ailed simple f l. Add 2 gucceggively to 100. 2. Add 2*8 to lOO commencing with 1. 8. How many are 7 -f 2 + 2 + 2 + 2 ? ^23, 345, 25 f 4- Kitty paid 2 cents for cakes, and 3 cents for andy, Ijow much did slie pay for both? 2 -f- 3 = how "nder „nlts, »"'"^' '^ »r hundreds, »e units we 1*08) thus 4, tnd 7 units ; he column o the next the same g the tens ; next order »»• with the le Jett, and ^d with th« I add the 5 alike the "y mistake the second. hers, and t should 24) 1214 296 (26)^ (26) (27) (28) 21632 32142 10233 40204 •22032 64764 34123 14523 (29) (30) (31) (32) 32404 21042 31610 32147 03721 61459 4&62R 92864 (33) (34) (35) (30) 71468 32187 69789 32168 71464 32187 60789 78679 (37) (38) (39) (40) 11021 32114 21102 31213 12324 12342 14212 21042 14213 13214 13121 33425 (41) (42) (43) (44) 23241 40021 32102 44221 41234 11234 12324 22334 12351 42321 21423 44300 10 ADDITION. 1 TABLE. 1 + 3 = 4 2 + 3 = 5 3 + 3 = 6 4 + 3 = 7 5+3=8 6+3=9 7+ 3= 10 8 + 3 = 11 9 + 3 = 12 10 + 3 = 13 11 + 3 = 14 12 + 3 = 15 3. Ad 4. Ad 5. Ad 6. Ai DW mai 1. How many are 8+3?6+3? 12 + 374 + 3' 9 + 3? 2. Harry paid 5 cents for a top, and 3 cents for al cord ; how many cents did he expend ? 2] 31 Al h a' (45) (46) (47) (48) 1 22133 21421 10032 33232 ■ 23022 32130 12431 23123 1 32134 21142 43213 13321 1 1 (49) (50) (51) (52) 1 31023 31021 10213 31023 1 32103 43210 31043 31323 ■ 62313 33634 21031 41433 I (53) (54) (55) (56) 1 13210 32341 34343 10431 f 13426 33123 43432 34234 1 13436 43243 34343 18476 1 • Note.— The pujiils should be taught to add without naming I the figures ; thua, in 41st example instead of saying 4 and 2 mal(e I 6and3malce9,(merely toucliiug the figures wita his pencil) name the sum thus, 4—6—9. ADDITION. 11 + 3 = 12 + 3 = l;^ + 3 = 14 + 3 = 15 13. Add 3's to 50 ; to 100. '4. Add 3's to 50; commencing with 2, 1. 5. Add 3*8 to 100 ; commencing with 1,— — 2. 6. A man gave 3 peaches to each of his four children, >w many peaches did he give to all? + 3? 4 + 31 3 cents for (48) 33232 23123 13321 (52) 31023 31323 41433 (56) 10431 34234 18476 thout naminff ? 4 and 2 make 3 pencil) nam* (57) (58) (59) (60) 21023 23323 21324 21343 31203 33333 41233 33333 32313 34313 . 43343 31033 45300 50261 12510 41504 (61) (62) (63) (64) 13432 22212 21032 312102 42324 24343 34341 231230 23213 30234 32432 321433 36340 46341 64204 330975 (65) (66) (67) (68) 10210 21034 43213 23433 06123 34123 23433 36133 14332 32433 64333 43633 6354 34234 86343 12367 (69) (70) (71) (72) 21010 32610 52433 23333 42632 02321 62004 32433 23436 14333 23031 23044 89796 76389 97889 87682 12 ADDITION. • TABLE. 1 + 4 = 5 2 + 4 = 6 3 + 4=7 4+4 = 8 5 + 4=9 6 + 4= 10 7 + 4=11 8 + 4= 12 9 + 4 = 13 10 + 4 = 14 11 + 4= 15 12 + 4= 16 1. What is a unit? a simple number? 2. What does addition teach ? 3. 7 + 4+4 + 4 + 4 = how many ? (•73) (74) (75) (76) 24341 32102 20343 13102 43241 12341 20343 41234 43221 43214 * 20343 32146 14432 41234 28746 33240 (77) (78) (79) (80) 16214 10410 31030 14342 32432 44236 43444 54342 43462 34340 41234 23463 (81) (82) (83) (84) 10321 25043 21034 42103 46321 24342 86426 26436 21423 14324 36243 14442 60372 56344 (86) 16883 16628 (85) (87) (88) 34431 14334 3244 23441 10444 14344 1024 44140 32544 43434 4034 23444 14324 34334 3543 44845 ADDITION. 13 abers to be added called ? tit of the addition called ? to 100. -commencing with 2, 1, 3. Hattie paid 5 cents for pens, 4 cents for paper, Id 2 cents for pencils ; what did she pay for all ? What are the What is the vf>.- Add 4's to 50 ;- Add 4's to 100 ;- (89) 21043 12342 43244 43423 (90) 13240 34344 43143 43144 (91) 32104 34343 34344 62343 (92) 32210. 4362 1621 4432 (93) 72103 12144 10123 21072 (94) 14213 44342 34521 42341 (95) 14121 21021 23126 10436 (96) 10321 10321 4632 2601 (97) 11241 43262 12303 46384 (98) 32104 43624 40123 32106 (99) 10321 46302 61236 10206 (100) 34321 44304 24342 43414 (102) 3244 4324 3323 4345 (104) 3214 4345 4324 4345 14 ADDITION. 9 4- 5 = 14 10 -f 5 = 15 11 4- 5 = 16 12 + 5= 17 TABLE. 14-5 = 6 54-5 = 10 24-5 = 7 64-5 = 11 34-5 = 8 74-5= 12 44-5 = 9 84-5 = 13 1 . What does addition teach ? 2. What are the given terms of addition? 3. What is the required term ? 4. How are the addends written to be added ? 5. Why do you carry for ten ? (105) Find the sum of 5542455 and 863494. (106) How many are 2268340 4- 45687098 ? (107) How many are 170 4- 360 4- 28 4- 312? (108) Find the sum of 154 4- 3265 4" 54. (109) (110) (HI) (112) 43256 32141 41230 16032 13246 14345 32440 14334 13^45 54354 32144 36755 43214 45544 54610 10054 32143 55324 54081 11246 (113) (114) (115) (116) 326012 14321 63245 5250 143241 45144 41234 5434 325543 35434 43244 5355 432434 14341 54234 5434 121434 43214 55435 5355 - 5 = - 6 = - 6 = 14 15 16 17 n? dded? 494. 098? ■f 312? i. (112) 16032 14334 36755 10054 11246 (116) 5250 5434 5355 5434 5355 TABLE. 1 + 6=7 2 H- 6= 8 3-1-6=9 4 -f 6= 10 5-1- 6= 11 6 -1- 6 = 12 7 4- 6 = 13 8 -f 6 = 14 9-1-8 = 15 10-1-6 = 16 11-1-6 = 17 12-1-6= 18 15 A man bought 2 sheep at 6 dollars a head, and a at 20 dollars ; what did the whole cost ? John Mills bought a waggon for 20 dollars, he re 6 dollars to have it repaired, and 5 dollars for |nting ; what did the waggon cost in all 7 (117) 17 -f 36 -h 75 = how many? ! (118) gentleman planted on his property 478 oaks, 784 beeches, 64027 firs, 690 apple trees, 160 pear trees, md 300 other trees ; how many trees did he plant? (119) (120) (121) (122) 63543 36466 31023 33264 25644 26533 14624 46354 30556 26520 32635 46366 66546 36426 74335 21046 64848 36426 76216 (125) 36781 (123) (124) (126) 61002 32475 21006 712106 43263 42364 32056 146305 14326 46364 30556 165346 23216 46734 70256 616564 12789 16734 19866 364656 16 ADDITION. 1. Adcl6'stoY2 ; commencing with 3, 1, 1 2. How many are 19 + 6+64-6-1-64-64-6^^ 3. How many are 16 + 6 = 6 + 16 ? 4. Emma is 7 years old, Kate is 2 years older, ani Colin is 2 years older than Kate ; what is his age, an| the sum of their ages ? (127) Find the value of 2632 + 365 + 4300 + 66321. (128) 739 + 32 + 46 + 3654 + 30 + 66 = how many ? (129) Harry King had 19 geese, 45 turkeys, 150 hens, an| 25 ducks, what is the number of his poultry ? (130) 145 + twice 145 = how many? (131) 24356 43562 34566 43562 34566 43562 (132) 26463 23654 26463 43654 66463 63654 (133) 54663 64356 56436 46644 12665 10665 (134) 31021 46063 35466 46563 45466 36563 (135) 36210 63463 34646 63463 34646 63463 (136) 16036 15465 46546 45436 45646 53346 (137) 31064 63545 63466 63566 56345 10066 (138) 36102 46104 66506 46506 4564 536 <^ + 6 4- 6 ?| jars older, ad |is bis age, ani I6632I. many ? 50 hens, anj ultry ? ADDITION. TABLB. • 14-7^8 2 4-7=9 3 4- 7 = 10 4 4- 7= U 54- 7= 12 6 4- 7 = 13 7 4. 7 = 14 8 4- 7 = 15 94- 7= 16 104-7 = 17 114-7= 18 12 4- ■? = 19 17 [1. If I pay 60 dollars for a horse, and twice as much a waggon-; what is the cost of both? 12. 6-1-74-74-74-74-7 = how many? (139) Ichard gave 1 7 marbles to each of his 4 brothers ; how [many did he give to all ? (140) man has three farms, one containing 600 acres [another 243 acres, and another 176 acres ; how many I acres in the three farms? (134) (141) (142) (143) (144) 31021 72463 37104 32576 21043 46063 21463 46707 43747 72664 35466 72767 47663 34576 10550 46563 01264 36746 32747 32660 45466 72106 77637 63576 47660 36563 32147 26717 36747 74068 (138) (145) (146) (147) (148) 36102 32136 36775 32603 72107 46104 42367 77456 72362 64736 66506 63676 36775 76324 86378 46506 37653 77466 47634 73647 4564 64673 36775 76047 37436 636 46876 77456 56754 63476 9 18 ADDITION. p. 1. Add Tb to 10 ; commencing with 3. 2. In 1 week there are 1 days ; how many days there in 3 weeks ? 3. James has twice as many marbles as John, aij John has 6 ; how many have they both ? (149) A box contains 215 grammars, 327 reading books, ^ arithmetics, and 79 geographies; how many boo^ are there in the box? (160) A man bought 7 horses at 75 dollars each ; how mui did he pay for the whole ? (151) A man left 2766 dollars to each of his four ohildres what amount did he leave them 7 (152) There are four numbers, the first 12776, the secou| 3769, the third 17847, and the fourth 128 more thaj the first ; what is the sum of the numbers ? (153) 6789 + 5832 + 4671 + 8907 = how many ? (154) (155) (156) (157) 762736 675476 763675 706345 716213 126714 712132 706345 216132 361236 237647 706346 177641 210473 167367 706345 146732 173472 234072 706345 412761 623162 147766 706346 123712 413214 417617 706345 ADDITION. 19 a. lanjr days as John, a^ TABLE. 1 + 8=9 64-8 = 13 94-8 = It 24-8 = 10 6+8 = U 10 + 8= 18 3 + 8=11 7 + 8 = 16 11 + 8 = 19 4+8 = 12 8+8=16 12 + 8 = 20 |ng books 4^1- ^ ^^^ borrowed $8 at one timej and 3 times as many boolj"^^ ** another time ; how much did he borrow in all ? j2. 8 + 3 times itself = how much? •h ; how muc 'our ohildrej B, the Beconl 28 more tha^ irs? (157) 706345 706345 706346 706345 706345 706345 706345 (158) irry King distributed a number of nuts among four of I his companions, giving to each 27 nuts, and kept 27 I himself ; how many nuts had he at first 7 (159) 82328 41686 88278 46876 88318 43726 83268 (160) 32107 14706 43807 47806 87387 47686 14787 (161) 32438 14767 34873 48747 16873 21687 38078 (162) 10710 18763 268 732 168 7687 3687 (163) (164) (165) (166) 34681 71634 87645 67146 37600 34216 87645 36478 87630 88274 87645 374074 46784 48648 87645 736488 43867 18027 87645 874688 36847 18776 87645 836488 66728 18767 87645 884674 77i84 38168 87845 798716 20 ADDITION. I : It 1. Add S's to 80 ; — commencing with 4, 2, 6. 2. A boy bought a fish hook for 4 cents, a line foi cents, a pole for 8 cents, and had 8 cents remainin how many cents had he at first? (167) A farmer owned 11 horses, 57 cows, 210 sheep, and pigs ; what is the number of his live stock? ^'i (168) A man paid $86 for a horse, twice as much for a carriH^ and $79 for a harness ; what did the whole cost ? (169) (170) (171) (172) 72683 71063 36872 91076 1G776 14862 63789 36871 10376 16873 37867 . 6877 62438 34836 68476 6877 37268 67836 62378 6877 36726 67878 87368 9867 71683 36878 86786 1837 62738 84878 76878 837 7608 7896 7698 1890 9698 9986 9898 (175) 6258 (173) (174) (176) 46732 12788 46767 8767 71072 37168 18324 8710 45378 8674 14768 7710 45387 2687 76873 8768 62736 7867 68736 18768 87368 2687 86748 78768 16877 7786 73687 78768 87268 1687 61786 96877 74407 8678 63876 42877 6879 6879 6899 8909 7689 1298 1887 1869 2 + 9 3-1-9 4 + »f the an ADDITION. 21 4, 2, 6. fnts, a line for Hits remaininl |0 sheep, andj Istock ? h for a carrias whole cost ? (172) 91076 36871 6877 6877 6877 9867 1837 837 1890 6258 (176) ■ 8767 8710 7710 ^ 8768 18768 78768 78768 96877 42877 8909 1869 TABLE. 1 4- 9 = 10 5 + 9= 14 2 + 9=11 6-1-9= 15 3-1-9=12 74-9= 16 4-1-9=13 84-9=17 9 4-9 10 4. 9 114-9 12 + 9 18 19 20 21 Bought 3 cows at $20 a head, 2 calves for $7, and leep at $9 a head ; what did the whole cost? 94-3 times 9 = how many ? Eddie is now 2 years old ; in what year will he be lears old ? (177) gentleman left to each of his three daughters $1900, ^o each of his two younger sons $2500, and to bis eldest son $4000 , how much did he leave. to all ? (178) [man sold 3 loads of hay, the first weighing 1670 lbs., [the second 890 lbs., the third 1720 lbs. ; what was hhe amount sold ? (179) 7S879 + 9 times itself = how many ? (180) 369878 463786 167362 686746 276386 147368 483769 19867 14789 68796 86378 (181) 867964 789687 710974 270867 168734 687368 178697 896879 876897 786786 368789 (182) 878996 819796 109368 8697 7687 7867 6873 786 689 798 689 (183) 108796 108796 108796 8796 8796 8796 8796 8796 8796 8796 8796 22 ADDITION. 1. Add 9'8 to 100; commencing with 11. 2. What is tho cost of 9 pairs of shoes at $2 a paij 3. Find by addition the number of peas in 6 poii each containing 9 peas. 4. How many are 19 + 9-|-9-|-9-|-9+9 4-9 + (184) Bought a farm for $2368, and sold it again so as to gn $400 ; what did I sell the farm for ? (186) Find the sum of 48763 + 86270 + 4687 + 578 4 4r + 18709+ 70471. (186) Find the sum of 46C37 + 54263 + 4^986 + 5060 + 8l + 641 + 98076 + 7362 + 689 + 1907. (187) Add together 587, 9658, 67, 431, 28670, 100000, 63O0,| 851, 8796, and 389476 + 7198 + 87968978. . (188) s ^:*>^ Find tho value of $8635 + $2194 + $7421 + $93 + $5063 + $135 + $2196 + $89 + $1225 + $16. * (189) Borrowed from A. $735, from B. $634, and from C. as much as from the other two, how much did I borrow in all 7 (190) A man distributed money am< i » li'S rhildren as follows ; | $700 to '^pch of his three :1au,';'i'e , and 1 :.t8 son a sum equal to that of all ij ;ntjtera ; how much did he give to all? ADDITION. 23 With II. ^068 at $2 a pni] f peas in 6 pod gf^ln 80 AS to ga. 10 10 10 10 10 10 10 10 11 12 13 14 15 16 17 18 TAILR. 9-f 10 = 10 4- 11 = 11 -f 11 = 12+11 — 11 + 11 + 11 + 11 + 1 2 3 4 lU 21 22 23 12 13 14 15 11+5 11 + e 11-1-7 M + 8 11+9 11 + 10 11 + 11 11 + 12 16 17 18 19 20 22 23 ^ + B78-f 40 '6 + C060 + gj 7. ^ 100000, 63O0 1 58978. ■ •', ,ifr >,■'. •■■ $7421 + $93 1225 + $16. id from C. as did I borrow 3n as follow? * "^ "' -''»[ -■. 4. How many are 70 + 80 + 9? 35 + 61? — 20 + 48 + 32? 79+ 79? ■h (195) id the Find the value of 82893 + 45 + 817526 + 456 + 4268: + 7676 + 96734 + 124735869 + 3749286. -. : . . . (196) . ^ . ' • Find the value of 9482 + 39867 + 29479 + 4892; + 9276 + 850 + 5273 + 98 + 7000 + 80072 + 19 1 + 8467. .• (197) Find the value of 978 + 749 + 4764 + 8967 + 94622 + 45237 + 77592 + 59286 + 89294 + 3789 + 2936 + 5700 + 619 + 378 + 9168 + 79 + 6899. (198) The fore quarters of an ox weigh 108 pounds each, the hind quarters 124 pounds each, the hide 76 pounds, and the tallow 60 pounds ; what is the weight of the whole ox? :-; ^^^- <199) ' - A man paid 95 dollars for a horse, the same sum for a harness, and for a carriage as miich as for both; what did the whole cost ? :> c , ,; * 1014 Sif I a m ADDITION. 25 ,^+12 = 21 ^+^2 = 22 |2+12 = 24 Nh 6. ,. . The number of one order that mukes one of the higher, is called a ratio. '^hen the same ratio applies to all the orders it is led a common ratio. Thus, 10 is the common ratio pimple numbers. . i ->> r > •" ,;. ■•he system of numbers of which ten is the common Pennjr each^lilBo is called the decimal system. ;re add the tec, f— 95-100, i^ -36 + 617 ] + 456 + 4268 286. -- ; ^4^9 -f- 4892: 80072 + IS 9967+94623 3^89 + 2936 '899. ^^ each, the » ^6 pounds, eight of the sfore leaving addition, the pupil should be able to add ^mns of figures without any nesitation, and give the order period of the sum of each column. ''": " (200) ' • ''"' id the value of 6379 + 6947 + 8476 + 8476 + 4736. OPERATION. — We write the numbers units under units, |379 tens under tens, &c., (because units of diflFerent orders can not be added together, e. g. 6 units nnd 5 tens would neither be 1 ] units nor 1 1 tens); commencing at the right hand, 6 — 12 — 18 — 25 — 34 units = 3 tens and 4 units; set down the 4 units under the units, and carry the 3 tens to ^e column of tens ; 3 — 6 — 13 — 20 — 24 — 31 tens = 3 mdreds and 1 ten, set down the 1 ten and carry the 3 mdreds to their proper column ; 3 — 10 — 14—18 — 27 — hundreds = 3 thousand and no hundreds ; set down and carry 3 thousand to the thousands' column ; 3, f, 15, 23, 29, 35 thousand =: 3 tens of thousands and thousand, both of which we set down ; the sura is j^hirty-five thousand and fourteen. 'M% sum for a for both ; (201) 'ind the value of 36850 + 4347b + 18964 + 62840 + 71 500 4- 68400 4- 1 760 + 716^^0 -f 376809 + 16890 + 7689 + 3796 + 19736 -f 468 + 1678 + .3800 -f 76890 + 768. 26 t ADDITION. . . 3- How many units of 1/ "."'' P'"''"'' ? higher 7 ^ """'» of o-e order make one of the „ J T'-«arefo„rn™hors:rL.l« „ I "Ofe than the first- ,h7,u.r^' ""^socond, li '-"-"i; the fourt ;,tn h ' T ""^ •'"'° 'J "dded together; whl^Lr? "V'"' *'^' "■"» "■« .wfi»t.8thesumofthefournumber, ^'"^thevalneoflaJ^'i,,,;,,, + 92503 + 684, ^ +_f''2" + 3834 + w, + 7934 + 2C8 + 6?^ + 39487'" ^ '' + "'^' Find the sum of ^^"^^ ' i --J eight, and ^.^0^ """ '■■"■='^' "^ """'-o.' The population of Ou.J^*^^ - •' ' '"""' ^ f-«00, Montreal , too" ot?'""' "'^"-Rivers 1^.884, Toronto 44 425 H»!w'"' '"■''*' Kingston '/'=«' ; What is ihe L^rjT" ''''^»<'' «■"» I-ondon eight cities 7 'Kgi-egate population of these Knd the sum of tenths ^'^T '"ousand and se.e 'trS T"'' "■""<'- --"tr h-nOred thousand, tt'entf;* "' """"'"' '"^^'^en fi;e, thirty thousand, fiftr mm """^ *'"' "'enty. thousand and ten, e'fn^ "'T;"" '""'"^' "'enty and six. • 'e'^enteen bill.ons, fo„r minions SW" notation ? iod? ^eoneofthenej ^ensonebnndred '00 i-njts = hoi the second, il ^ore than tlil ' fi^st and ml e four numbers I 3834 ^. 9275;! 34935 4- 267i ADDITION OP THE DECIMAL CTTRRENCY. 27 The decimal currency diflfers from simple numbers ^ving two denominations, viz. dollars and cents, las the same common ratio, and may be taught in [ection with simple numbers. add dollars and cents, JLE. — Write the numbers with the decimal points le same vertical column, and add as in simple jers, observing to place the decimal point in the j directly beneath those above. $2.25 -I- $3. 5C = how much? 30 cts. + 40 cts, -f 19 cts. + 99 cts. + 18 cts. cts. := how much ? A lady paid for a mantle $12.00, a dress $10.50, It $2.50, gaiters $3.00, gloves $1.50 ; what was the- »unt of her bill? ^y, one million Three Rivers ^4, Kingston! > and London '^'on of these (1) $72.37 t8.99 47.36 79.90 46.37 25.80 87.68 99.77 19.78 88.73 68.47 90.70 (2) $128.97 54.73 165.94 75638 418.99 718.55 867.66 479.90 89.78 66.89 977.90 689.00 (3) $287.91 416.38 478.45 732.61 419.80 968.78 368.90 87.66 76.88 19.72 9.87 .01 (4) $184.72 37.94 76.48 73.92 16.78 98.76 17.98 54.77 167.90 716.87 748.76 870.99 (5) pnd the amount of $76.30 + $768 + $8649 + $783.83 4- $987.40 + $8767.94 + $3849.39 -f $9878.44 + $876.80 4- $799.36 + $376.88. 28 ADDITION OP THE DECIMAL CURRENCY. ADDI' 11 m ii 1. How does the decimal currency resemble sira| numbers ? 2. How does it differ from simple numbers ? 3. What is the common ratio of simple numbers a| dollars and cents ? 4. Why must the addends be written with units the same order under each other ? 5. How are dollars and cents added ? 6. 70 cts. -f 35 cts. 4- 42 cts. + 5 cts. + 85 c^ + 95 cts. + 10 dollars = how much?* (6) Find the sum of $58.75, $11.27, $71.43, $91, $41.8P $77.58, $0.64, $30.72, $95.60. $189.12, $198.15. O) A man sold 350 bushels of wheat for $490, 720 busliei of oats for $129-50, 75 bushels of beans for $93.7; 130 bushels of peas for $95.50, 50 bushels of barle | for $42.75 ; how many bushels of grains did he sel and how much did he receive for the whole ? (8) A man left $1250 to each of his three daughters, to hi son, a sum equal to two of his daughters ; how muci did he leave them ? • ■' (9) A merchant's cash sales in one week amounted one day with another to $231.16 per day; what was tlic week's receipts ? (10) A farmer paid $75.41 for a horse, $54.04 for a yoke of oxen, $21.00 a piece for two cows, $7.41 each for three sheep, and $10.21 for three pigs ; what did they all amount to ? 1 'M CURRENCY, fesemble aim ibers ? ^ fe numbers « with units ADDITION OF THE DECIMAL CURRENCY. 29 A lady paid 50 cents for cambric, 35 cents for )n, and 16 cents for thread ; what did she pay for all ? 17 + 25 = how many? 45 + 75? 84 ^ 32? 72 + 32 + 14? REVIEW. , cts. -f- 85 ^91, $41.8.^ $198.15. >0, 720 bnslieil ns for $93,7; 3hel3 of barle ns did he sel hole ? % What is arithmetic? 1. f. What is a number ? 2. |. What is a unit? 3. What is an abstract number? iber? 4. 5. , , What is Notation ? — Numeration ? a simple 6. 'ghters, to hi ^ ') how muci nounted one ^hat Was the for a yoke 41 each for lat did thej What are the characters used in expressing num- ? 7. How does the position of a figure affect its value ? 8. , In what ratio do the orders in crease and diminish? 8. . What is the effect of removing a figure one place he right or left ? ^0. What are the orders of each period ? 9. - *.» ^1. Name the first six periods; backwards. ^2. What are the four fundamental rules of arith- itic? 10. ip3. What is addition? simple addition ? 11. 13. ii^4. What are the numbers to be added, and the result Hthe addition called? . -. 15. How are the addends written to be added ? — Why ? 16. Why do you carry for ten? 8. 17. How do you prove addition? 15. 18. How do dollars and cents resemble simple imbers? 17. 19. What is the Decimal system of numbers ? 16. 20. How are dollars and cents added? 17. 30 SUBTRACTION. To 81^ fill I V - ■ h " SUBTRACTION. BATIOII Example 1. — James bad 2 marbles and be gave John; bow many bad be left? I from 2 leaves many? Ul|. 2091 2. Emma had 4 roses and she gave 1 to Jane, a^^' to Julia; how many bad she left? .| 3. Charles bad 5 cents, and be paid 2 cents for a i bow many cents had he left? Solution. — He had the diflFerence between 5 cents !(<| 2 cents ; 2 cents from 5 cents leave 3 cents. There! be bad 3 cents left. NoTK.— The teacher should illustrate by means of visible jects the process of taking one number from another. 18. The process of finding the difference between t a»bi0ve it, numbers is called subtraction. bQ^^^^^^^ The greater number is called the minuend^ the 1( ^thftn ^^® the subtrahend^ and the number found the difference of the n remainder. to the ^ \fi carr; gilbtrali of tbei 19. The sign — , called minusj denotes subtractiot thus, 8 — 3 = 5, denotes that 3 is to be subtracted froi 8, and is read 8 minus 3 equal 5. 1. Count from 50 backwards to 1 from 100. 2. Take two successively from 50 : thus, 50, 48, 46, &c .21. ||esu 3 — 2 4—2 5 — 2 6 — 2 1 2 3 4 1 8 9 10 TABLE. -2 = 5 -2 = 6 -2 = 7 -2 = 8 11 12 13 14 2 2 2 2 9 10 11 12 BUBTRACTION. 81 and he gay, r 2 leaves ^ to Jane. cents for a t''^* 'een 5 cents To subtract simple numbers, lAMPLE. — Find the difference between 2091 and 147. taATioN. — Commencing at the right hand, we cannot „-_- take 7 units from 1 unit, we borrow from 147 1944 CS?i,°J,««* „, ce between 9 lens 1 = 10 units, 10 + 1 = 11, 7 from 11 leave 4, which we set down beneath the figures subtracted ; then 4+1 (the I wed) from 9 leave 4 ; 1 from we cannot ; borrow 2, 1 = 10 of that order, 1 from 10 leaves 9 ; 1 led) from 2 leaves 1. lULE. — Write the subtrahend under the minuend so units of the same order may stand under each other, in addition. Commence at the right hand, and Sttlitract each figure of the subtrahend from the one ''''^nd, the ]e^^ 3 difference * ve it, setting down the reraftinder under the figure tracted. If any figure of the subtrahend be greater the corresponding figure of the minuend, borrow 1 Cthe next higher order of the minuend, add it as 10 *the upper figure and subtract as before, observing carry the 1 C'orrowed to the next figure of the ^tracted froi liiS)trahend ; (which is thus subtracted from the figure ^the minuend from which it was taken). subtract lor >m 100. ^' 48, 46, &c m rf21. Proof, — Add the difftrence to the subtrahend ; le sum should be equal to the minuend. : 9 ; 10 11 12 (1) 726384 312162 (2) 371680 240120 (3) 328768 121232 (4) 468926 125612 rr 32 SUBTRACTION. 1 ^Hr 1. Count 2's to 100 and backwards ;• —comment] ■ with 1. n I 2. A class in arithmetic contained 12 girls anfl ■4_3 = boys ; how many • more gifls than boys in the class 1 KZ3 = 3. Charles had 10 marbles and he gave 2 to C(J and 2 to Frank ; how many had he left? ] :; >~''"-^ • . .vs, ! BCount 1 (5) (6) 0) - (8) I B^^B^^^ ^ Min. 376210 143214 132103 310890 1 Ka ball Sub. 221032 37824 24322 102629 J Wn'^ Dif. 155178 (10) 646723 (11) 183264 i - (1?) 632 J69 Suowm Proof. 376210 1 (29) . - ". ■:„- 222222 22222 1*;2836 |128914 (14) (15) (16) J|61232 (13) w " 3210362 3462046 102144 142110 .wKL (33) 1123141 1217822 23124 101232 ftp ; 1 ' ' ' (17) - (18) (19) ' (20) 7105198 7149902 316913 321896 2123126 432129 186412 161833 ^2843 (21) (22) (23) (24) i (*^" 6131021 102132 100211 63210 4714214 14321 20423 14341 (25) (26) (27) (28) 1 ("1 2921023 321021 102110 448200 ''^m ATQ^ 2311224 41234 12312 12325 •commcDji 1 2 girls anJ In the class frtve 2 to C(| (8) 310890 102629 (1?) 632^69 l':2836 (16) 142110 101232 (20) 321896 161833 (24) 63210 14341 (28) U8200 12325 — 3 — 3 — 3 [7—3 1 2 3 A BUBtRAOTION. TABLB. 8—3 = 6 9 — 3 = 6 10 — 3 = 7 11 — 3 = 8 33 12 13 14 15 3 3 3 3 9 10 12 /ount threes to 100 and backwards. icslie bought a whistle for 3 cents, and exchanged [a ball which he sold for 6 cents ; how much did jin? |How many are 8 — 3 ? ? 15 — 3? 7 — 3? 12 — 3? 6 — 3? (29) 28914 61232 (41) T310376 193436 (45) [479326 1176243 (30) 219786 191623 (34) 406372 133323 (38) 639686 364663 (42) 187265 123923 (46) 109371 81933 (31) 468907 208663 (35) 210321 112323 (39) 290398 87288 (43) 910714 616283 (47) 519231 153823 (32) 910261 123486 (36) 672104 436343 (40) 310769 245433 (44) 194567 163246 (48) 410213 144126 84 • SUBTRACTION. « TABLI. ^ 5 — 4=1 9 — 4 = 5 13 — 4= 9 6 — 4 = 2 10 — 4 = 6 14 — 4 = 10 7 — 4 = 3 11—4—7 15 — 4 — 11 8 — 4 = 4 12 — 4 = 8 16 — 4 = 12 1. What does subtraction teach ? 2. Emma is 9 years old and Charles 12, what is the difference in their ages ? 3. Count 4*3 to 50 and backwards ; to 100. • 4. 27 — 4 — 4 — 4 — 4 — 4 — 4 = how many ? m W (49) 114126 32142 (50) 721043 • 164212 (61) 371021 112634 -(B2) 471021 101234 (53) 612149 144324 (54) 710982 144341 102103 41424 (56) 310214 . 13^34 (57). 371021 123414 (58) 347191- 116234 (59) 372104 141423 (60) 321072 21441 (61) 241327 42341 (62) 362192 142341 (63) 707268 42642 (64) 102134 42345 (65) 768278 654245 (66) 360792 146540 (67) 807368 436434 ' (68) 8910726 4163451 L ' StTBTRACTION. TABLE. 6 — 5=1 7 — 5 = 2 8 — 5 = 3 9 — 5 = 4 10 — 5 = 6 11 — 5 = G i2 — 5 = 7 13 — 5 = 8 14—5= 9 15 — 5 = 10 IG — 5 = 11 17— 5 = 12 M 1. What ig subtraction ? 2. In example 59, which is the subtrahend ? minuend ?—— difference ? 3. Count 5's to 100 and backwards; commencing with 3. L (69) 673678 147634 (70) 368791 143645 (71) 768709 745637 (t2) 710876 555564 (73) 371072 157346 (74) 632637 555414 (75) 916809 601236 ^6) 309072 134465 (77) 671073 365586 (78) 680736 836458 (79) ' 607368 46345 ' (80) 621073 146704 (81) 687369 645326 (82) ^ 710767 136452 (83) 102632 ■ 45361 (84) 7102109 126354 « (85) 132104 43645 (86) 687001 ' 166524 (87) . 367204 3645G (88) 109456 64364 i ii • SttBTEAOTiON. TABLI. 7 — 6 = 1 8 — 6=2 9 — 6 = 3 10 — 6 = 4 i: — 6 = 5 12 — 6 = 6 13 — 6 = 7 14 — 6 = 8 15 — 6= 9 16 — 6 = 10 17 — 6 = 11 18 — = 12 1. Count 6'fl to 72 and backwards. 2. 37 — 6 — 6 — 6 — 6 — 6 = how many ? 3. Charles had 9 cents, and he paid 4 cents for paper, and 5 cents for a slate ; how much had he left 7 (89) 710423 . 66455 (90) 360210 156456 (91) 402916 132465 (92) 410072 140201 (93) 302641 103265 (94) 703260 86346 (95) 106200 61203 (96) 403621 117654 ' (97) 1321072 1421326 (98) " 329073 42674 (99) 182032 40274 (100) 706327 23764 (101) 107210 62774 (102) 810710 107670 (103) 43f672 56C74 (104) 100200 90290 (105) 7210'2 101296 (106) 360721 70864 (107) 360721 101764 • (108) 320101 120102 -^ 8UDTEACTI0N. TARLI. 8 — 7=1 12 — 7 =.5 16 — 7 = 9 9 — 7=2 13 — 7 = 6 17 — 7 = 10 10— 7 = 3 14— 7= 7 18 — 7= 11 11 — 7= 4 15 — 7 = 8 19 — 7 = 12 37 er. 1. What is Bubtraotion? 2. What is the minuend? — subtrahend? — difference? 3. Count sevens to 70 and backwards. 4. 60 — 7— 7 — 7 — 7 — 7 — 7 — 7 = how many? '^"' (109) Find the difference between 1890 and 809. .. 4- (110) From 1690021, take 190166. • (111) (112) (113) (114) 730726 709261 710736 109256 416724 12634 • 76376 54674 (115) (116) (117) (118) 327107 3210213 3010321 103210 147648 487648 777778 18881 (119) (120) (121) (222) 3721021 100001 301809 371021 761764 10002 18877 9887 (123) (124) (125) (126) 3121032 3121881 310214 146000 147718 861788 136784 86908 38 SUBTRACTION. 9 10 11 12 8 8 8 8 1 2 3 4 13 14 15 16 TABLE. — 8 = — 8 = — 8 = — 8 5 6 1 8 It 18 19 20 8 8 8 8 9 10 11 12 1. How do you prove subtraction ? 2. What number added to the subtrahend will give the minuend ? 3. What number added to 16 will make 24 ? Solution. — The diflference between two numbers added to the less will give the greater ; 24 — 16 = 8; therefore 8 added to 16 will make 24. 4. What number added to 8 will give 16 ? 18 ? 20? 30? 40? 100? . ^ * -■ 5. Count S's to 72 and backwards. f (127) A man had 215 sheep, and sold 57 of them ; how many had he left ? (128) Find the value of 76897 — 687 — 6937. (129) i-^W *,?.;/. What number added to 1673012 will make 371020243 ? (130) Find the value of 7638 + 376 — 172 -^400 + 7321 — 372 — 18. (131) A merchant had 2068 yards of cloth ; he sold on Monday 129 yards, on Tuesday 97 yards, on Wednesday 308 yards, on Thursday 92 yards, on Friday 78 yards, on Saturday 120 yards ; how many yards had he remaining? r_ ■"< ^- 10 — 9 = 1 11 — 9 = 2 12 — 9 =3 13 — 9 = 4 SUBTRACTION. TABLB. 14 — 9 = 5 15 — 9 = 6 16 — 9= 7 17 — 9 = 8 39 18 — 9 = 9 19 — 9 = 10 20 — 9 = 11 21 — 9 = 12 1. Count 9'8 to 100, and backwards. 2. 58 — 9—9 — 9 — 9 — 9 ;— how many ? 3. Emma is 9 years old ; ia what year was she bora? ^r (132) * , From 70080093000 take 1630032004. • - ' . • How much does 784000 exceed, twice 193049? m' M ■-'!':•: (134) From 1 billion, take 1 million, (135) .,.. . From twice 7063879, take 806767 — 7600. (136) A house and lot are yalued at $1850 ; the house is worth $960 ; what is the value of the lot? (137) 4 loads of oats weighed together 6673 pounds ; the two first loads weighed 1190 pounds each, the third 2350 pounds ; what did the fourth load weigh ? (138) (139) (140) (141) 167261 872109 9021631 1247683 — 17264 — 4763 612786 — 186176 — 46324 — 2164 — 417268 472168 — 71062 — 1472 — 7689 — 3614 — 147 — 16821 — 7167 18710 1" 40 « SUBTBAOTION. _ ■■ ' '■ • . • f * TABLE. ■ . 11 — 10 = 1 19—10= 9 16 — 11 — 5 12 — 10 = 2 20 — 10 = 10 17 — 11 = 6 13 — 10 = 3 21 — 10 = 11 18 — 11 = 7 1 14 — 10 = 4 22 — 10= 12 19 — 11 = 8 •15—10 = 5 12 — 11= 1 20 — 11 = 9 — ' ' 16—10 — 6 13—11= 2 21 — 11 = 10 17— 10 = 7 14— 11 = 3 22 — 11 = U 18 — 10 = 8 15— 11 = 4 23 — 11 = 12 1. A man bought a horse foe $100, and 3 cows at $20 a head ; how much more did the horse cost than the cows? 2. How many are 75 — 22 — 30 — 9 7 3. Count lO's and ll's to 100 and backwards ;——> commencing with 5. (142) If 1708 be minuend and 968 the subtrahend, what is the difference 7 (143) If the difference between two numbers be 740, and the subtrahend 968, what is the minuend 7 (144) ^ A merchant was owing $5000; he paid at different times the sums of $350, $970^ and $2008 ; how much is yet owing ? (145) A man sold a farm for $2000, which was $910 more than he paid for ib < how much did he pay for it ? (146) A man paid $85 for a horse, $150 for a harness, and for carriage as much as for horse and harness lacking $25 ; he then sold the whole for $415, did he lose Of gain bjr tiie bftrgaioj aud how m^cl^ ^ . .»^i,- -?- 12( nu Th Th If If W r--^ --'►- *^ -"*'»-«• r t 13 14 15 16 12 12 12 12 1 2 3 4 SUBTRA' TIOW. i TABLE. 17— 12 = 5 21 — 12 = 9 18 — 12 = 6 22 — 12 — 10 19— 12 = 7 23 — 12 = 11 20— 12 = 8 24 — 12= 12 41 1. Count 12's to 100 and backwards. 2. The sum of two numbers is 300, the less number is 120, what is the greater number ? 3. The sum of two numbers is 300, and the greater number 180, what is the less number ? (147) The sum of two numbers is 19768^ and the greater number 12769 ; what is the less number ? (148) The less of two numbers is 6999, and their sum 19768 ; what is the greater number ? (149) If 879687 be subtrahend, and 4687 the difference, what is the minuend ? (150) If 884374 be minuend, and 4687 the difference, what is the subtrahend ? (151) What number together with these three, viz. 125, 34, and 970, will make 1800? ^ (152) A xa&n sold 3 beeves at $35 each, pork to the amount of $125, and flour for $84. He received in pay, salt at $15, sugar at $21, tea at $19, cloth to the amount of $80, and the balance in cash ; how much cash di(| ]xe receive ? 42 SUBTRACTION. 1. The minuend — the subtrahend = what? 2. The subtrahend -f- the diflference = what? 3. 800 is the subtrahend, and 200 the difference ; what is the minuend? 4. loco is the minuend, and 200 the difference; what is the subtrahend ? 5. 1000 is the minuend, and 800 the subtrahend ; what is the diflference ? (153) • How long since America was discovered in 1492 ? '^ (154) Sir Isaac Newton was born in the year 1642 ; hOw long is it since? (155) '• Mont Blanc, the highest mountain in Europe, is 15680 feet above the level of the ocean, and Chimborazo in America is 21000 feet; what is the difference in the height of these two mountains? , . , , , (156) ^^:r-- ■ ^:- The area of the earth's surface is about 200 millions square miles ; of this nearly 60 millions are land, how much is water? (157) The subtrahend is 1090, the difference 1690; what is the minuend? (158) ■' ^--A^-^--' •■^■— i ^...t;.-' British America contains about 2,525,994 square miles, of which Upper Canada contains 180,000, Lower Canada 210,000, New Brunswick 27,710, Nova Scotia 19,650, Prince Edward Island 2,134, Newfoundland 57,000, British Columbia 213,500, Vancouver Island 16,000 square miles, and the Hudson Bay Territory the remainder ; what is its arejv? ^. v^*,.,- .-,,1 - '»• e; . . i ^ SUBTRACTION OP THE DECIMAL CURRENCY. 43 22. Rule. — Write the numbers with the decimal points under each other, and subtract as in simple numbers. Place the point in the answer directly beneath those above. 1. A man bought a horse for $75, and sold him again for $89.50 ; what did he gain by the transaction? 2. A lady purchased a parasol at $2, a pair of gloves at $1.20 ; she paid a $5 bill ; how much change did she receive back? 3. $5 — 5 cents = how much? - '• Opbhation.— $5.00 .05 m «.Vts;;; 'jv.: !-«' ~^' $4.95 difference. (1) Find the value of $167.01 — $68.09. What sum added to $15.09 will make $20? - ■ ■ •■ ■ (3) . -■^■•/■":^-'"^ How much does $8767.08 exceed $6298.20 ? ' (4) Find the value of $17894.37 — $123.71 — $298.67 — ^143.71 —$31.98. (5) Find the value of $3142.67 — $2.67 + $4171 — $0.66. (6) A man borrowed $767, and paid at different times $125.25, and $356.80 ; how much does he yet owe? (7) A man sold a load of grain for $40 ; he took in pay a plough at $14.90, 3 hoes at 60 cents each, 4 rakes at 22 cents, a pitchfork at $1.19, and a spade at 95 cents; how much was yet coming to him? ■* 44 SUBTRACTION OP THE DECIMAL CURRENCY. 1. How arc dollars and cents subtracted? 2. John bought a sled for 75 cents, and gave 24 cents to have it repaired; he then sold it for $1, how much did be make by the bargain ? 3. William Mills bought a colt at $25, and sold it a year after for twice what it cost him, lacking $6; what did he make by the bargain, allowing $10 for his keeping? (8) A man sold a farm for $769Y, which was $1761.50 more than h'd paid for it ; what did he give for the farm? (9) A merchant has $2760 in the bank, $16773 in stock, $17694 due him, and owes $7693.50; what is he worth? (10) A young lady went a shopping taking with her a $20 bill. She purchased a dress at $8.16, a muff at $3.19, a bonnet at $3.08, a pair of gloves at $1.12, a pair of shoes for $1.90, and a fan at 19 cents; how much money did she bring home ? ' REVIEW OF SUBTRACTION. 1. Wh&t ia subtraction? 18. - .:. 2. What are the given terms of cubtraction? 3. What is the term to be found? 4. What is the minuend ? — subtrahend ? 5. What is the difference or remainder? J 6. The minuend — the subtrahend = what? 7. The subtrahend + the difference i= what? 8. The minuend — the difference = what? 9. The sum of two numbers — the greater = what? 10. The sum of two numbers — the less = what? 11. How is subtraction proved? 21. 12. How are dollars and ceAts subtracted? 22, MULTiPLICATIOHr. ■-'»' > f -;.. Ji,v: MULTIPLICATION. »^ V - -A * 23. ExAMPLR. — Harry paid 1 cent for an apple ; what will two apples cost at the same rate 7 2 times 1 cent are how many cents ? 2. What will 4 pencils cost at 1 cent each? •* ^ 3. What cost 2 yards of cloth at $3 a yard? 4. If 1 orange cost 5 cents, what will 3 oranges cost? Solution. — If 1 orange cost 5 o^nts, 3 oranges will cost 3 times 5 cents ; 3 times 6 cents are 15 cents. Therefore three oranges will cost 15 cents. In this example, 5 cents is added together three times; 5 cts. + 5 cts. + 5 cts. = 15 cts. Hence, 24. Multiplication is a short method of performing addition. Or, Multiplication is the process of taking one number as many times as there are units in another. The number to be multiplied is called the multiplicandj the numbei' we multiply by is called the multiplier, and the result of the multiplication, the product. 25. In multiplication the multiplicand is added as many times as there are units in the multiplier. 1. Count 2 successively to 100 ;• with 1. •commencing 2 times 1 are 2 2 " 2 " 4 2 " 3 " 6 2 " 4 " 8 TABLE. 2 times 5 are 10 2 " 6 " 12 2 " 7 " 14 2 " 8 " 16 2 tir'^s 9 are 18 2 " 10 " 20 2 « 11 " 22 2 " 12 " 24 46 MtTLTTt>LICATiON. , * 26. To multiply by a number not exceeding" 12, ExAMPLE.—Multiply 6098 by 2. Operation. — 2 times 8 are 16, set down the 6 unit^ Multiplicand 6098 ^"^ ^^'""^^ *^^ ^ ^^"> *' ^" ^^^^^'°" 5 Multiplier 2 twice 9 are 18 and 1 carried are 19, set down 9 and carry 1 ; twice Product 12196 is nothing, set down the 1 carried ; twice 6 are 12, which set down in full. Rdlk. — Write the multiplier beneath the multiplicand, and commencing at the right hand multiply each figure of the multiplicand by the multiplier, setting down the units, and carrying the tens, as in addition. 27. The sign X, denotes multiplication, V X 2 = 14, is read 7 multiplied by 2 equal 14. * 3 fo ] th( m (1) 12132 2 (2) 21022 2 (3) 62102 2 (4) 43202 . 2 (5) 31032 2 (6) 62148 2 36504 2 (8) 71079 2 TABLE. 3 times 1 3 " 2 3 " 3 3 " 4 3 6 9 12 3 times 5 3 " 6 3 " 7 3 " 8 15 18 21 24 3X9 3 X 10 3 X 11 3 X 12 27 30 33 36 i;. (•• MtTLTi:tLICAT10i^. 47 1. What i? the cost of 3 books at 6 cents each? ■ Solution.^ — Tf 1 book cost 6 cents, 2 books will cost 3 times 6 cents; 3 times 6 cents are 18 cents. There- fore, 3 books will cost 18 ceiits. Note.— The solution of Himilar questious Rhould be given till the pupil is periiectly familiar with the principle involved. 2. What will 3 yards of cloth cost at 11 cts. a yard ? 3. Add threes to 100.; commencing with 5 ; 7. 4. How many are 3 x 10? 10 X 3; 30 = how many 3's? how many lO's? (9) •786133 3 (10) 768736 3 (11) 610079 3 (12) 196789 3 W . . A (13) 760763 3 (14) 160736 3 (15) .760973 3 (16) 928760 3 (17) 689764 3 (18) 690077 3 (19) 80768 3 (20) 148902 3 I (21) (22) (23) (24) 103274 642009 104725 873256 3 2 3 2 4 times 1 are 4 4 " 2 " 8 4 " 3 " 12 4 " 4 "16 TABLE. 4 times 5 are 20 4 " 6 " 24 4 " 7 " 28 4 ^' 8 " 32 4X9 4 X 10 4 X 11 4 X 12 36 40 44 48 48 MULTIPLICATION. 28. To prove multiplication, cast the nines from the multiplicand, and from the multiplier ; multiply the two remainders together and cast the nines from their product. Lastly, cast out the nines of the product, and the two last remainders, if the work is correct, will be equal. Example.— Multiply 48124 by 3. Commencing at the right of the multiplicand 4 and 2 are 6 and 1 are 7 and 2 (fiom 8) are 9, which cast away. 6 and 3 (from 4) make 9 and 1 left, which write at the left of the sign. 3 being less than 9 is written at the right then 3 times 1 = 3, which we write above the sign. Of the product 2 and 7 are 9 ; 3 and 4 and 2 (from 4) are 9; leaving 3 which is written below the sign, and being equal to the last reuiainder, the work is supposed to be correct. 48124 3 144372 (25) 730260 4 (29) 376843 4 (33) 763871 4 (26) 212340 4 (30) 168736 4 (34) 600873 (27) 167216 4 (31) 716091 4 (35) 807076 4 (28) 721093 4 (32) 768916 4 (36) 281600 4 1. 2. in e 3. he y 4. 5. 6, 5 times 1 5 *• 2 5 " 3 6 « 4 5 10 15 20 TAfiLB. 6 times 5 5 " 6 5 " 7 5 " J8 25 30 35 40 9X5 10 X 5 11 X 5 12 X 5 45 50 55 60 6 ti 6 6 6 MULTIPLICATION* 49 1. What does multiplication teach? 2. Point out the multiplicand, multiplier, and product in ex. 37. 3. If a man can walk 4 miles an hour, how far can he walk in 6 hours? 4. Add 4*8 to 100 ;—— commencing with 2, 1, 3. 5. Add 5'g to 100 ; commencing with 3, 2. 6. 4 times 8 = how many? How many 4*8? S's? V rf (37) 206721 4 (38) 637210 4 (39) 110723 4 (40) 823465 4 (41) 673789 5 (42) 365076 5 (43) 767908 5 (44) 736554 6 (45) 671099 5 ; (46) 710877 6 (47) 807836 5 (48) 896708 5 (49) 760734 5 (50) 671076 5 (51) 897687 5 (62) 946589 5 (53) 136276 6 (54) 760736 4 (55) 807326 6 (56) 910731 6 TABLE. 45 50 55 60 6 times 1—6 6 times 5 = 30 ex 9 = 54 6 " 2 = 12 6 " 6 — 36 6 X 10 = 60 6 " 3 = 18 6 " 7 = 42 6 X 11 = 66 6 " 4 = 24 6 " 8 = 48 6 X 12 = 72 50 MtLTlPLlOATlON* 1. A man ] for a cow ; w paid $6 for a sheep, and 4 times as much hat did ho pay for both? 1. duct 2. Add 6'8 to 100 and baclt wards ;— — commencing 2. with 3. poun 3. 6X8 + 6X5 = how many ? 1 whal 29. rerform before addition multiplication or tubtraotion or division indicated by signs 1 3. 4. (67) 710736 6 (58) 873684 6 (59) 766439 6 (60) 871078 6 5. (61) 876934 5 (62) 897681 4 (03) 807638 6 (64) 87096 6 77. ( 78. i 79. : 80. ( ,;';/, /:=-i- (65) 236489 6 (66) 973672 6 (67) 367268 6 (68) 876791 6 (69) 786321 5 (70) 190260 4 (Tl) 716921 6 (72) 3171091 5 (T3) 710687 3 (74) 369217 6 (•75) 369214 6 (76) 791896 e TABLE. 7 times 1=7 7 times 5 = 35 7 X 9 = 63 7 " 2 = 14 7 " 6 = 42 7 X 10 = 70 7 " 3 = 21 7 " 7 = 49 7X11 = 77 7 " 4 = 28 7 " 8 = 56 7 X 12 = 84 (I as much nmencing (1 by signH (60) ^71078 6 (64) 87096 6 (68) 876791 6 (72) 171091 5 (76) 791896 9 MtJLTIPLIOATION* u 1. What ia the multiplicand ? multiplier ? pro- duct? -* 2. Emma bought 6 pounds of soap at 7 cents a pound, and 6 pounds of starch at 10 cents a pound ] what did she pay for all ? 3. 7 -}- 6 times itself = how many 1 4. 7X6+7X6 = how many ? 5. Add 7*8 to 100 ; commencing With 4,*— i, — 6, 3. 77. 6873768 X 7. 78. 87600976 X 7. 79. 32109671 X 7. 80. 69678981 X 7. 81. 67199676 X 7. 82. 6980779 X 7. Find the value of, 83. 37102 X 6 X 6 X 2. 84. 71986 X 7 X 6 X 6. 86. 89106 X X 6 X 7. 86. 8103 X2X3X4X6. 87. 189 X 4 X 5 X 6 X 7. 88. 89 X 7 + 180 X 7. 89. What cost 128 barrels of flour at $7 a barrel ? 90. How many yards of cloth in 6 pieces containing 67 yards each, and 7 pieces each containing 64 yards ? :91. A house has 8 windows in front each containing 6 panes of glass, and 6 windows in the back con- taining 12 panes e«ch ; how many panes of glass docs the house contain? TiiBLB. 9 10 11 12 63 70 77 84 8 times 1=8 8 times 5 = 40 8 X 9 ^ 72 8 " 2 — 16 8 " 6 = 48 8 X 10 = 80 8 "3 — 24 8 " 7 = 66 8 X 11 =88 8 " 4 = 32 8 " 8 = 64 8 X 12 = 96 52 MULTIPLICATION. 30. The multiplicand and multiplier are called the factors (i.e. producers) of the product. 1. 8 and 4 are the factors of what number ? 2. 2, 3, and 5, are the factors of what number ? 3. What are the factors of 24, 56, and 40 ? 4. Add 8's to 100 ; commencing with 5, 2, 1. that : So] man 3 me: I work 2. 92. 809263T X 8. 93. 7254368 X 8. 94. Y462344 X 8. 95. 7169779 X 8. Find the value of, 96. 91026 X 2 X 6 X 8. 97. 987 X 3 X 4 X 5 X 8. 98. 98 X 7 X 8 + 389. 99. 8X8 + 6X8+7X8. 100. Sold 769 bushels of flaxseed at $4 a bushel, and received in pay 300 barrels of flour at $8 a barrel, and the balance in cash ; how much cash did I receive ? 101. What cost 350 barrels of herrings at $5 a barrel ? 102. A man bought 150 acres of land at $5 an acre and sold it again at $8 an acre ; how much did he gain by his bargain ? "^'^ ** ^ " 103. 17638 + 8 times itself = how many ? 104. 20, 8, and 7, are the factors of what number? 105. A farmer sold 5 cows at $24 a head, 7 young cattle at $16 each, 45 sheep at $3 a head, and 10 pigs at $2 each ; what did the whole amount to ? 106. 107. 108. 109. 110. 116. I 117. 118. 9 times 1=9 9 " 2 = 18 TABLD. 9 times 5 = 45 9 " 6 = 54 X 9 X 9 = 10 — 81 90 9 9 "3 = (( A — 27 4 = 36 9 9 7 = 63 8 = 72 9 X 11 = 99 9 X 12 = 108 1 10 ti 10 10 10 10 10 10 10 e called the 3r? mber? ? ith 5, 2, X C X 8. : 4 X 5 X 8. 8 + 389. X84-7X8. k bushel, and |8 a barrel, ch cash did I $5 a barrel ? I an acre and much did he f ''^: . umber ? young cattle , and 10 pigs ount to ? MULTIPLICATION. X 9 X 10 X 11 X 12 81 90 99 108 53 1. How long will 1 man take to do a piece of work that 3 men can perform in 9 days ? Solution. — If 3 men take 9 days to do the work, 1 man will take 3 times 9 days = 27 days. Therefore, if 3 men take 9 days, 1 man will t::ke 27 days to do the work. 2. Add 9's to 100; commencing with 2,— 5, 106. 6897684 X 9. 107. 38726347 X 9. 108. 38769984 X 9. 109. 71689768 X 9. 110. 76987684 X 9. Find the value of, 111. 76 X 9 X 7 X 8. 112. 80 X 8 + 178 X 9. 113. 787s X 9 — 768. 114. 91768 — 9 X 87. 115. 1716 X 7 X 8 X 9. 316. How long will a quantity of hay suflBce 1 horse, that 9 horses would eat in 29 days? 117. If a man earn $3 a day, how much will he earn in a year ? 118. If a man drink 3 glasses of spirits a day, how much will he drink in a year ; how many cents would it cost at 5 cents a glass? 10 times 1 10 " 2 10 10 10 10 10 10 a 3 4 5 6 7 10 20 30 40 50 60 70 TABLB. 10 times 9 8 = 80 10 10 10 11 11 11 11 10 11 12 1 2 3 90 100 110 120 11 22 33 11 11 11 11 11 11 11 5 = 6 = 8 = 9 = 10= 110 11 = 121 55 66 77 88 99 4= 44 11 X 12 = 133 h! I 54 MULTIPLIOATION. 81. To multiply by 10, 100, 1000, ftc, annex as many ciphers to the multiplicand as the multiplier contains ciphers. Thus, 3 X 100 = 300. 1. What cost 100 yards of cloth at $3 a yard? 2. At $5 a barrel, what cost 1000 barrels of flour? 3. 1000 X 10 = how many ? 10 X 1000 ? 100 x 100 ? 4. Gount lO's and ll's to 100 and backwards; commencing with 5. 119. 9, 10, 19, and 100, are the factors of what number ? 120. If 68 men can do a piece of work in 11 days, how long will it take 1 man to do the same ? 121. What sum must be distributed among 100 men, to give each one $590? 122. How many pins will a boy point in 9 weeks, if he work 8 hours a day, and point 10,000 pins in an hour? 123. In 1 year are 365 days ; how many days in 10 years ? 124. 716937 X H + 8763809 X U — 39864 X H := how many ? 125. In 1 pound are 20 shillings, and in 1 dollar, 5 shil- lings ; how many shillings are there in 746 ~ pounds, and 600 dollars ? 126. A gentleman's yearly income is $1000, and his expenses $3 a day; how does he stand at the ilV end of the year ? t ■ - .3»X^ TABLE. 12 times 1 = 12 12 times 5 = 60 12 X 9= 108 12 " 2 = 24 12 " 6 = 72 12 X 10= 120 12 " 3 = 36 12 " 7 = 84 12 X 11 = 132 12 " 4 = 48 12 " 8 = 96 12 X 12 = 144 1 I f MULTIPLICATION. 55 lez as many er contains ard? of flour ? 100 X 100? wards ; - at number ? I days, how | le? 100 men, to ^eeks, if he ) pins in an |] days in 10 9864 X 11 liar, 5 shil- )re in 746 0, and his md at the 9 10 11 12; 32. A composite number is oso that is the product of two or more factors. Thus, 21 is a composite number, being the product of 3 and 1. 33. A prime number is one that is not the product of two factors ; as 3, 5. 34. To multiply by a composite number, RuLB. — Multiply successively by the factors. The last product is the answer. Ciphers at the right hand of the multiplier or multiplicand may be omitted and annexed to the product. 1. What are the factors of 8, 20, 24, 36, and 200 ? 2. Add 12'g to 144;— —commencing at 6. 3. What is the value of 45 ac. of land at $128 per acre ? Operation. The pupil should name 1128 price of 1 acre, only the figures of the _____ product in multiplying. ?;40 " 5 acres. Thus,' in the example, 9 multiplying by 5 we say, "- — 40 — 14 — 6 at the same $5760 " 45 acres. , units and carrying the tens. time setting down the Find the value of. 1. 720 X 11 X 10 X 100. 2. 678 X 12 X 11 X 12. 3. 768 X 24 X 33. 4. 378549 X 27. 5. 357928 X 35. 6. 707584 X 22. 7. 580726 X 44. 8. 428571 X 540. 9. 405719 X 960. 10. 64839 X 1200. 11. 6974 X 144 -f 28. 12. 4567 X 132 + 129. 13. 6, 11, 18, and 24 are the factors of what number? 14. If 250 acres of land worth $25 per acre be exchanged for 300 acres valued at $24 per acre, what is ; gained by the transaction? •- - - 56 MULTIPLICATION. 1. What is a composite number 7 ' 2. What is a prime number ? 3. What are all the composite numbers below 100 V— the prime nunibers ? 4. How do you multiply by a composite number? 5. What cost 4 do^en chairs at $3 a piece ? 35. To multiply by a number exceeding 12 that is not a composite number, Bulk. — Write the multiplier under the multiplicand and multiply the multiplicand by each figure of the multiplier separately, taking care to place the first figure of each parti.J product directly beneath the figure multiplied by ; then add the products. ExAMPLE.—Multiply 3*71 by 47. j* 3ll 47 .2597 1484 Here 4 = 4 tens ; 1 unit X 4 tens = 4 t<^ns; hence we set the 4 in the «ens' place. In the Proof, same way units multiplied by — — hundreds would give hundreds, 17437 Prodn<;t. ^^jts ^y thousands would give thousands, &c. Hence, we set down the first figure of each partial product directly beneath the figure we multiply by. Find the value of. 1. 47963852 X 23. 2. 25836974 X 45. 3. 59826473 X 67. 4. 52007498 X 405. 6. 7964280 X 337. 6. 607 X 356 -f- 349. 7. 498857 X 4967. 8. 390867 X 50989. 9. 862479 X 537089. 10. 378600 X 75000. 11. 687900 X 87400 + 90. 12. 93000 X 97000 + 79. MULTIPLICATION. 57 low 100 ?— umber? ? that is not altiplicand ure of the * the first 1 the figure 1 unit X 4 ce we set 56. In the tiplied by hundreds, ould give figure of figure we 7. 89. 089. 30. )0 + 90. ) + 79. 1. What is the weight of 25 bushels of wheat, 60 pounds being allowed to a bushel ? 2. What is the cost 01*45 barrels of pork, at $18 a brl. ? 3. What cost 1000 barrels of flour at $7 a barrel ? 4. 40, 20, and 100, are the factors of what number? 6. How many are 7x5 + 7x6+7x8 ? 9 X 4 + 9X5 + 9 X 6? 7 X8 + 6x8 + 6x9^ 112 X 11 — 11 X 1J2? 13. How many are six hundred and forty one chousand four hundred and forty times four hundred and ninety seven thousand three hundred and sixteen ? 14. Two trains leave Toronto at the same time, going in opposite directions, one at ibe rate of 25 miles '!'' an hour, and the other at 37 miles an hour ; how far apart will they be at the end of 2 / hours ? 15. What time will one man require to dig a trench, that 37 men can dig in 9 days? 16. 36, 78, 99, and 1000, are the factors of what number ? 17. What sum must be distributed among 25 men and 19 boys, to give each man twice a boy's share, and each boy $15 ? 18. What is the number of the strokes of the hammer of t clock in a day ? year ? 19. Plow many seeds were produced by a bean which had 14 stems, each stem, 19 pods, and each pod, 6 beans? 20. How much does one thousand thousand exceed fifty times twenty thousand ? 21. A man left to his son $19536, and lO each of his six daughters $9768 ; how much did he leave them ? 22. How many bushels of oats will fill 500 of each of three kinds of bags, which contain respectively 3 bushels, 3 bushels, and 4 bushels ? 58 MULTIPLICATION OF THE DECIMAL OUBRENCY. 86. To multiply dollars and cents. Rule. — Multiply as in simple numbers, and point off the two right hand figures for c^ts. Example. — What cost 5 yards of cloth at $1.75 a yard ? Operation. $1.75 5 $8.75 If 1 yard cost $1.75 5 yards would cost 5 limes $1.75 = $8.75. 1. A lady purchased 6 yards of satin at $2.50 a yard, 4 yards of muslin at 75 cents a yard, and a pair of gloves at $ 1 . 10 ; what is the amount of her purchase ? 2. A man bought 4 rakes at 25 cents a piece, 3 pitch- forks at $1.50 each, 5 hoes at 70 cents each, and a grin istokie at $2.50 ; what did he pay for the whole ? 3. What cost 2 dozen brooms at 20 cents each? Find the value of, .■:?' 1. $9609.30 X 72. 2. $874.03 X 611. 3. $172.01 X 1000. 4. $497 X 2600 + $0.01. 5. $0.06 X 15950. ' 6. $1.89 X 279 + $1.44. 7. $9.46 X 103260 + $2.40. 8. $15.07 + $41.07 X 700. 9. What is the cost of 95 ploughs at $15.25 each, and 78 harrows at $9 each ? 10. At 12 cents a pound, what must be paid for three boxes of sugar each containing 125 pounds ? 11. Bought 11 yards of French merino at $1.05 a yard, « 14 yards of cambric at 12 cts. a yard, 25 yards % ' of cotton at 15 cts., 1 dozen setD of cufiFs and . collars at 15 cts. per set, a hat at $2.30, and gaiters for $3.25 ; What did the whole cost ? IRENCY, MULTIPLICATION OP THE DECIMAL CURRENCY. 59 point off a yard ? )st $1.75 Id cost t= $8.75. $2.50 a id a pair irchase ? , 3 pitch- , and a ^hole ? :h? .. $1.44. ■f$2.40. 1 X 700. ich, and or tliree ds? a yard, 5 yards iffs and JO, and iSt? 1. How do you multiply dollars and cents? 2. What cost 100 nails at 1 cent each ? — at 3 cents ? 3. What cost 300 oranges at 7 cents a piece ? Solution. — 100 oranges at 1 ct. = 100 ct. = $1. ^ 100 " " 7 cts. = 700 ct3. = $7. ;' w-^- 300 " " 7 cts. = 3 times $7= $21. 87. To r .ultiply by 10, 100, 1000, &c., remove the decimal point as ir < ly places to the right as the multiplier oontaina ciphers, annfA.ing ciphers if necessary. The decimal point is under* stood when not expressed at the right ot dollars. 4. What cost 400 shad at 5 cents a piece ? 5. What cost a barrel of pork (200 lbs.), at 8 cts. a pound? , , ,^,; .-'■"■'..-v „...,., /. ";: ./X--^:. 12. What is the difference in the value of two pieces of cloth, the first containing 57 yards at $3.85 a yard, the second, 47 v- -ds at $4.75 per yard ? 13. What cost 1000 barrels oi apples at $2.35 a barrel? 14. What cost 1000 bricks at 2 cents each ? 15. At 5 cents a pound, what would 15 barrels of beef amount to ? 16. A man bought a horse at $97.50, and to p. for him gave 6 tons of hay at $9.25 per ton, and the balance in wheat at $1 a bushel ; how many bushels of wheat must he give ? 17. A lumber merchant bought 95 thousand feet of white pine at 10 cts. a foot, IIS thousand feet of red pine at 22 cts., 16897 feet of oak at 32 cts. and 69768 feet of elm for $1567 ; if he sell the whole v.>n an average of 25 cents per foot, what will be his net gain ? 60 MULTIPLICATION OF THE DECIMAL CURRENCY. 1. How do you multiply by 10, 100, Ac. ? 2. What will 8 barrels of beef amount to at 9 cents per pound ? 3. Wliat cost 20 barrels of pork at 2 cents a pound, and 15 hundredweight of cheese at 11 cents a pound? 18. What will the wages of 16 men amount to in a year, at $1.25 a day to each men I 19. A man killed an ox which he sold as follows ; the hind quarters weighing 129 pounds each at 6 cents a pounds ; the fore quarters 125 pounds each at 5 cents a pound, and the hide and tallow weighing 163 pounds at 1 cents per pound ; what did the whole amount to ? REVIEW OP MULTIPLICATION. : 1. What is multiplication ? 24. "' 2. What are the multiplicand, multiplier, and pro- duct ? 3. How many times do you repeat a number by m'ultiplying it ? 25. 4. How is multiplication proved ? 28. 5. What is a composite number ? 32. "^ 6. What are the factors of a number ? 30. 7. What are all the composite numbers below 100 ? the prime numbers ? 8. How do you multiply by a composite number ? 34. 9. How do you multiply by 10, 100, &c. ? 31. 37. ' 10. How do you multiply by a number exceeding 12, that is not a composite number? 35. 11. Why do you place the first figure of each partial product directly beneath the figure multiplied by? :^2. How do vou multiply dollars and cents? 36. DIVISION. 61 DIVISION. 38. division teaches us to find how often one number is contained in another. The number to be divided is called the dividend, the number we divide by is called the divisor, and the number that shows how often the divisor is contained in the dividend is called the quotient. If anything remains after dividing it is called the remainder. Example 1. How uany pens at 1 cent, can you buy for 2 cents ? 2. How many penc'^s at 2 cts. can you buy for 6 cts. ? Solution. — For 6 cents, I shall have as many pencils at 2 cents, as the number of times I can take 2 cent^ from 6 cents, which is 3 times. Therefore for 6 cents I shall have 3 pencila. 3. If a man can earn $2 a day, how long will it take him to earn $8 ? Solution. — At $2 a day, it will take him as many days to earn $8, as the number of times %2 is contained in $8 ; $2 in $8, 4 times. Therefore at $2 a day, he must work 4 days to earn $8. The following tables should be learnt thoroughly, and the relation they sustain to the others clearly explained. ■";■,, ■'-'(''..- , TABLE. 2 in 2 =: 1 2 in 10 = 5 2 in 18 = 9 2 "4—2 2 " 12 = 6 2 " 20 = 10 2 "6—3 2 " 14 = 7 2 " 22 = 11 2 " 8 = 4 2 " 16 z= 8 2 a 24= 12 62 DIVISION* 30. Example 1. Divide 8G754 by 2. 2J8076G Having written the divisor on the loft of ~" the dividend we commence at the highest order to divide. 2 is contained 4 times in 8 ; set down the 4 under 8 ; 2 in 6, 3 times ; 2 in 7, 3 times and 1 over ; 1 = 10 of next lower order, added to 5 make 16 ; 2 in 15, 7 times and 1 over; 1 = 10, -f 6 = 16 ; 2 in 16, 8 times. Rule. — Begin at the left hand and divide each figure of the dividend by the divisor, setting down the quotient figure directly beneath the figure divided. If there bo a remainder join it as so many tens to the next figure of the dividend, and divide as before. 40. Proof. — Multiply the quotient by the divisor adding in the remainder if any ; the product should be the same as the dividend. 41. The sign -f- denotes division. 8 -r 2 = 4 is read 8 divided by 2 oqual 4. Division is also denoted by a horizontal line separat- ing the terms ; as | = 4. 2. Divide 736827 by 2. t Divisor 2 ) 736027 Dividend. 1. 2)86021848 Quotient 368013 — 1 rem. 2. 2)40267342 }-)h 736027 I 'roof. TABLE. 3 in 15 = 5 3 " 18 = 6 3 " 21 = 7 3 " 24 = 8 3. 2)9462 3 in 3=1 3 " 6 = 2 3 " 9 = 3 8 " 1-2 = 4 3 in 27= 9 3 " 30 = 10 3 " 33 = 11 3 " 36 = 12 i xnel mvisioN. 63 Jn the left of t the highest 4 times in 8 • s ; 2 in 7, 3 der, added to ^ = 10, + 6 each figore the quotient If there bo ' next figure the divisor t should be = 4 is read ae separat- ) 86021848 1. At $2 a bushel, how many bushels of wheat can we buy for $10? 2. Charles distributed 21 apples among a number of this companions, giving each one 3 apples ; how many f boys were there ? t 3. HowmanythreesinlO? 36? 24? 9? 27? 21? 18? g| 4. Count threes to 100 and backwards; com- lencing with 8, 4. (4) (5) (0) [2)699318621 2^687073638 * 2)l87368768 (7) (8) 2)132675672 2)710703360 (10) (11) 3)821607362 3)814674368 (13) ' (14) 3)876873684 3)l7l073687 (9) 2)876836822 (12) 3)973687368 (15) 3)871025546 (16) 3)189074687 (17) 3)187209671 (18) 3)72099878 TABLE. 4 in 4=1 4 in 20 := 5 4 in 36 — 9 4 " 8 — 2 4 '< 24 = 6 4 " 40 — 10 4 " 12 = 3 4 " 28 = 7 4 " 44= 11 4 " 16 = 4 4 " 32 =8 4 " 48 = 12 I 64 DIVISION. 1. What does diyision teach ? 2. Which are the dividend, divisor, and quotient, in the 19th exercise ? 3. Seven times 4 = how many? how many 4*8? 7's? 4. 40 = how many 4's? lO'a? 6. Count 4's to 100 and backwards ; commencing with 3, 1, 2. 6. How many coats each containing 4 yards, can be made from 18 yards of cloth? What remnant is left? (19) 4)897689124 (22) 4)8321096725 (25) 3)7137689142 (28) 4)68732854 (31) 4)9175387690 5 in 5, 1 (once) 5 " 10, 2 times 5 " 15, 3 " 5 " 20, 4 « (20) 4)8710768734 (23) 4)932768737 (26) 4)127143685 (29) 3)671321099 (32) 4)7435491073 TABLE. 5 in 26, 5 times 5 « 30, 6 " 5 " 35, 7 " 5 " 40, 8 " (21) 4)6710216325 (24) 4)832710237 ^ 5 (27) 4)83210973 (30) 4)3871073211 (33) 4^)6531269057 | 5 in 45, 9 times 5 « 50. 10 " 5 " 55', 11 " 5 " 60, 12 " DIVISION, 66 quotient, ia ly many 4*8? ■commencing rards, can be ant it} left ? (21) )671021G325 (24) 1)832710237 (27) 4)83210973 >• (30) 4)3871073211 (33) ■ 4)6531269057 1. If5burrels offish cost $20, what is that per barrel ? Solution. — If 5 barrels cost $20, 1 barrel will cost 5 times less or 1 fifth of $20 ; 1 fifth of $20 = $4 ; much therefore 1 barrel would cost $4. 2. Emma paid 45 cents for 5 Second readers ; how is that for each book ? 3. 13 times 5 = how many? how many 12'8? 5 '8? 4. Count 5'8 to 100 and backwards; commencing [with 3, 1, 4. (34) 5)876930024 (37) 5)710736809 (40) '5)l87l02G32 (43) 5)912691438 (46) 5)567100263 (35) 5)312072691 (38) 5)483607268 (41) 5)710736891 (44) 3)144671832 (47) 3)417168973 TABLE. (?>) 6)871687068 (39) 4)312007303 (42) 4)402073689 (45) 6)371689073 (48) 6)891683732 in 45, 9 times " 50. 10 " '' 55', 11 " " 60, 12 " 6 in 6—1 6 in 30 — 5 54 -^- 6 = 9 6 " 12 — 2 6 " 36 = 6 60 -^ 6 = 10 6 " 18 = 3 6 " 42 — 7 66-^6 = 11 " 24 — 4 6 " 48 — 8 72 -^ 6 = 12 *•■':'■.; 66 DIVISION. 1. What does division teach ? 2. What are the given terms of division ? 3. What is the required term ? 4. Count 6's to 100 and backwards; commenciDg with 4, 2, 11, 9. V^ ^*w^ (49) (54) (59) '721073689 -f 6 1 673268 T40 -f- 6 107326889-^4 (50) (55) (60) 610726478 — 6 1710932674-^5 109768769 -j- 6 (51) (56) 847687367 -r 6 4007326871 -r 5 (61) 1473G8766 -^ 6 (52) (57) 8109265543 -f 6 8107268718 -i- 5 (53) 732609368 -f 6 (58) 710736879 -i- 6 (62) 447891870 -^ 6 (63) ^ 876807681 -^ 3 C4. A man paid $1974 for 6 village lots ; what is the cost of each lot ? 65. If 1000 acres of land be divided equally among six; persons ; what is each share ? «rty» TABLE. 6 in 6=1 6 in 30 = 5 54 -f- 6 = 9 6 " 12 = 2 6 ♦' 36 = 6 60 -^ 6 = 10 6 " 18 = 3 6 « 42 = 7 66-^6= 11 6 " ^4 i_ 4 6 « 48 = 8 72-^6 = 12 DIVISION. 67 ng r4 re v-3 the six 1. If 3 books cost $13 what cost 1 book ? Solution. — If 3 books cost $13, 1 book will cost 3 times less or 1 third of $13 ; 1 third of $13 =■ $4, and $1 over which must be divided into 3 equal parts ; $1 -~ 3 = $^ (39). I book will cost $4 + J of a dollar = $4^, Note.— I is read 1 third; f, two thirds; |, three fifths, &c. These nttmbera being parts of a unit are called fractions. 2. How much is } of 20 ? of 75? 3. 7 X 12 = how many times 7? 12? 6? 4. Count 7's to 100 and backwards ; commencing with 3, 5, 9, 4. 66. 9107368732 -7- T- 67. 10721036871 -r T. 68. $9870073847 -J- 7. 69. $8167367284 -^ 7. 70. Harry King divided 108 marbles equally among 4 of his companions ; how many did each receive? 71. A man paid $127 for 7 cows; what is the price of 1 cow at that rate ? 72. How many 5 bushel bags can be filled from a bin containing 3870 bushels of oats ? 73. j of 6789768 dollars = how much ? 74. ^^ ^s-i- = how many ? 75. A man had 81 sheep, and sold 1 third of them; how many had he left? T ^ ^^ 76. How many coats each containing 4 yards, can be made from 2 pieces of cloth, each containing 47 yards? TABLE. , : : '-1 8 in 8=1 8 in 40 — 5 72 -i- 8 = 9 8 " 16 = 2 8 " 48 — 6 80 ~ 8 = 10 8 " 24 = 3 8 " 56 — 7 88-i-8 = 11 8 " 32 = 4 8 " 64 = 8 96 H- 8 = 12 es DIVISION. Division is the reverse of multiplication. Division diminishes a number as many times as multiplication increases it ; hence, 42. Multiplying and dividing any quantity by the same number does not change it. 12 X 8 1. How much is 8 X 10 -7- 10? ? 8 ' 2. 68Y X 8 = how many times 8 ? 3. How do you prove division ? Why ? 41. 4. Reckon 8's to 100 and backwards ; commencing with 5, 2, 6, 4. (n) 8)8t2637246 08) 8)38t632645 (t9) 8)8Tl64T68t (80) 8)683268716 > (81) 8)137168732 (82) 7)193729687 (83) 8)839837988 (84) 8)507302938 (85) 8)68976878 (86) 6)176873678 (87) 8)47694369 (88) 8)987387689 8768 67325 • 89. X 8 ^ X 7 = how much? 8 7 90. If 1958 tree? be planted in 8 rows, how many trees will there be in each row? ., > , 1 ^* TABLE. 9 in 9 = 1 (once) 9 in 45 =1 5 times 9 " 18 = 2 times 9 " 54 = 6 " 9 " 27 = 3 " 9 " 63 = 7 " 9 " 36 = 4 " 9 " 72 = 8 " 81 -^9 = 9 90 -r- 9 = 10 99-7-9 = 11 108 -7-9 = 12 i i ■ DIVISION. 69 911 on he ?8 5Y8 69 689 rees rC^v 9 10 11 12 1. If 6 cows sell for $126, and 3 pigs for $21 ; how many pigs are equal in value to one cow ? 2. A man invested $360 in flour, paying $9 a barrel ; if he sell at $11, how much will he gain on the trans- action? 3. If 63 be the dividend, and 9 the divisor; what is the quotient? 4. Reckon 9'3 to 100 and backwards ; commencing with 3, 6, 1, 7, 5, 8. Find the value of, 91. 7207389 -^ 9. 92. 8173610354 -f- 9. 93. 71548954736-^9. 94. 38907687314 — 9. 2107689768987 95. . 9 96. 3876847 —7-7-9. 97. 8716878 4- 9 -r 8. 98. 8716876 -r 6 -r 8. 99. 71096789799-7-9. 1476871819 100. 7689. 9 101. It is required to put 216 Iiats into 8 boxes; how many hats will there be in each box ? 102. $28970, is the dividend, and 8 the divisor; what is the quotient? 103. How many sheep at $5 a head, can be bought with the avails of 25 cords of wood, sold at the rate of $3 a cord ? ^ TABLE. ^11 = 1 11-f 99= 9 12 H '- 60= 5 - 22 = 2 11 -J- 110 = 10 12 H ^ 72= 6 -33 = 3 11-M21 = 11 12 H ^ 84= 7 r 44 — 4 11 -J- 132 = 12 12-: - 96= 8 r55 = 5 12 -i- 12= 1 12-; 1- 108 = 9 r66_6 12 -^ 24= 2 12- 'r 120 = 10 f-77 = 7 12 -^ 36 = 3 12-: 'r 132 = 11 f-88 = 8 12 -f- 48= 4 12 H - 144 = 12 70 DIVISION. ill' I'M. M m IS; If 1 1 1 1. How many oranges at 5 cents, and lemons at 6 cents ; and of each an equal number, can be bought for 33 cents? 2. How many cows at $12, must be exchanged for 120 sheep at $5 each ? 3. Reckon ll's and 12's to 100 and backwards ; commencing witL 8. 9, 8, 1, 2, 5, 10. Find the value of, 104. 1170'7368V2 105. 4710736891 106. 7109736891 107. 8107356432 108. 8710736878 •^ 11. T" !!• T- 11' r* ll- r- 11' 109. 9107687681 -^ 12. 110. 71321076871 -^ 12. 111. 81473687368^ 12. 112. 91210736871 -r 12. 113. 1072163872 -r 12. tii-n 117. 114. A teacher's salary is $300 per annum ; how much may he spend monthly, and save $100 in one year ? 115. Divide 100 cents among Emma, Kate, and Colin, so that Colin may have twice as much as his sisters ? 116. How many canisters each holding 12 pounds, can be filled from 1584 pounds of tea ? , , 7689 X 12 7689 Find the amount of X H. 12 11 118. How many bags holding respectively 2 bushels, and 3 bushels, and of each kind an equal number, can be filled from a bin containing 5876 bushels ? 119. 12 times one thousand is how many times 12 ? 6710978897896 ;/ , i, ...-. 120. ■■ =z how many? " , 12 121. A gentleman possessing an estate of $68000, be" queathed 1 fourth to his wife and the remainder to his four children : what was the share of each ? N »?'<' h-^ DIVISION. 71 6 or br 43. To divide by a compoaite number exceeding 12. Rule. — Divide successively by the factors. To obtain the true remainder, multiply the last remainder by the first divisor, adding in the first remainder if any. To divide by 10, 100, &c., cutoff as many figures from the right of the dividend as the divisor contains ciphers. Thus, 198 -r- 10 = 19.8, (19 times and 8 over). 1. If 2 dozen chairs cost $72, what is the price of 1 chair ? Solution.— 1 chair = $72 -f- 12 ~ 2 = $3. 2. Divide 5771 by 45. Operation. — 5 I 1 Quotient. 5771 1154 — 1 128 — 2 9 1154 X 5 45 = 5 X 9. 2x5+1 = true rem. 128H. Ans. Proof. 5771 7920000 1. 2. 11 X 10 X 100 1073952 -r 12 Find the value of, 5. 12527480 + 35. 6. 19966848 + 22. 7. 25551944 + 44. 8. 231428340 + 540. 9. 389490240 + 960. 10. 77806800 + 1200. 11. 1004284 + 144. 12. 602973 + 132. 11 X 12 3. 608256 + 24 + 33. 4. 10220823 + 27. 13. 28512 = how many times 66 X 18 ? 14. Bought 250 acres of land for $6250, and excbjingod it for 300 acres valued at $7200 ; what is the ■ difference in the cost of 1 acre of each kind? *» ' "t)'*^'* 72 i/IVISION. 1|: I J' 1. How do you divide by a composite number? 2. How much is 720 -'- 10 ? 100 ? Ji! i' I BM i t 44. To divide by a number exceeding 12, that is not a composite number. Rule. — Find how oft<' •. the divisor is contained. In V'Mi least number of figures at the left of the divideiiil that. will contain it, and place the niimbtr in the qi u'icnt, at the right of the dividend. Ma]ti[>ly the divisfr by quotient figure, subtract ilie product from the figures divided, and to the remaini]()r anno: be next figure of the dividend ; divide thid number as before, and eon- titvue the operation till the whole of the diviuend is When thory are cipliOrs at tlip right of the divisor cut them off, uldo as »-.'>viy figures at the right of the dividend, which muht be annexed i (ho vf'nuiinder 43. 49. Example.— 05 vido G6040 by 31. 3l)660'.l9(2K-iG}^ quot. i>3 31 40 91 93 Here 66 is the least num- ber of figures that will contain the divisor; 31 is 66049 Proof. contained in 66, 2 times ; 2 times 31 = 62 ; 62 from 66, leave 4. Annexing to 4 we leave 40 the next number to be divided ; 31 in 40 goes 1 time, once 31 sub- tracted from 40 leaves 9 ; to this we bring down the next figure of the dividend, and divide as before. — 31 is con- tained in 66049, 2130^^] times. 19 Find the value of, 1. 2. 3. 4. 5. 1103168596 -r 23. 1162663830 -7-45. 4008373691 -^ 67. 21063036690-^405. 3082176360 -f- 387. 6. 216441 -f- 607. 7. 2467902719 -^ 4967. 8. 19929917463-^50989. 9. 463227983631 -f 537089. 10. 28395000000-^-75000. 11. 60122460900-^87400. 12. 8924000079 -f 97000. uA-f^' — IMVISIOK. ii V«- ,'™' 1. What three factors will produce 240? 2. The product of two or more factors divided by one factor gives what ? 3. What number multiplied by 50 will give 1000? 4. What number divided by 20 will give 50? 5. If 864 be dividend, and 72 quotient j what is the divisor? - ■'/ "■ 13 .^^ 14 15 16 What number multiplied by 497316 will give 318998375040? Two trains leave Toronto at the same time, going in opposite directions, one at the rate of 25 miles an hour, and the other at 37 miles an hour; in what time will they be 1426 miles apart? In what time should 37 men dig a trench that one man can dig in 333 days? What factor together with these three, viz. 36, 78, and 1000, will produce 277992000? 17. Divide $1035 among 25 men and 19 boys, and give each man twicp a boy's share. 18. The strokes of th . hammer of a clock are 5b340 in a year ; how many is that per day ? 19. 1596 beans were produced by a bean which had 4 stems, and each stem 19 pods ; how many beans each pod? 20. One million is how many times one thousand? 21. A man's eflFects amounted to $78144; of this, his son was to have ^, and the remainder was to be divided equally among his six daughters ; what was each one's share? 22. How many bags containing respectively 2, 3, and 4 bushels, and an equal number of each, can be filled from a bin containing 4500 bushels of oats ? d 74 GENERAL PRINCIPLES AND APPLICATIONS. 45. The product of two factors, divided by one factor, gives the other ; 108(9 X 12) -M2 = 9 ; and 108 -r9= 12. Note.— Tho dividend corresponds to tlie product, tlie divisor and quotient are its factors. 46. The product of any number of factors, divided by one or more of the factors, gives the product of the remaining factors. Thus, 3X4X 5-r3-^5=:4. 47. Multiriying the dividend, or dividing the divisor, multiplies ^ne quotient. 40 X 2 40 Thus, ^^- = 10, while or = 20 (or twice 10). ^ 4 4-^2 r 48. Dividing th3 dividend, or multiplying the divisor, divides the quotient. 28 -r 2 28 Thus, ^7^ = 4, and or = but 2. 7 7X2 ^,,. ,, . 49. Multiplying or dividing both dividend and divisor by the same number, does not affect the value of the 12 X 2 12^4 quotient. Thus, ^4^. — ■ = = 3. 4X2 4-4-4 ^^j',^ 1. 3 X 4 X 5 -7-3 -^ 4 = how many? 45. 2. 900 is the product of three factors, two of which are 4, and 25 ; what is the third factor? 3. 270 is the product, and 90 the multiplicand ; what is the multiplier ? 4. What is V multiplied by 6? > . [ 5. How much is %^ X 3 ? \l X 6 ? 46. 6. How much is Y "r 3 ? ^ -7- 4 ? 47. , GENERAL PRINCIPLES AND APPLICATIONS. 75 1. Give examples of Art. 44 and 45. 2. Give examples of Art. 46, 47, and 48. I. Find the value of 4 x 6 X 20 divided by 10 x 5 X 4. Operation. — Here the operation may be shortened 4 X 6 X 20 by cancelling any factor common to the dividend and divisor ; for this only divides both dividend and divisor by the same number, which does not change the value of the quotient (48.) 4 cancels 4 and 4, and 10 cancels 10, and 6X2 =\2 — 2)^ Ans. reduces 20 to 2, leaving = i«^ = 2?. 5 10 X 5 X 4 2 ^ X 6 X ^IS) iq X 5 6X2 X 4 60. When multiplication and division occur in the same ques- tion, the terms should be first connected by signs and cancelled ; to facilitate which the following ahould be borne in mind : Any even number is divisible by 2. If the two last figures di- vide by 4, the whole will divide by 4. If the three last figures divide by 8, the whole will divide by 8. A number ending in 0, is divisible by 10 and 2. .... J . Find the value of, ^ \ 2. 40 X 12 X 8^(5 X 8\ 3. 87 X 9 X 8 -r 8 -j- 7. 70 X 6 X 4 X 18 ^' 9X3X4 • 5. 6. 12 X 50 X 72 9 X 24 X 25" 88 X 20 -i- 36 X 100 4000 ' 7. If 15 be multipled by 7, 27, and 40, and the product divided by 54 multiplied by 40, 10, and 2 ; what will be the result? 8. How many pounds of butter at 15 cents, will be required to pay for 60 pounds of sugar, at 9 cents per pound ? 9. A man exchanged 28 boxes of soap, each containing 24 pounds, at 9 cents a pound, for 126 barrels of ashes each containing 3 bushels ; what was allowed a bushel for the ashes ? t6 GENERAL PRINCIPLES AND APPLICA1*I0N8. 51. When the multiplicand or multiplier contains a fraction : ExAMi'LE 1. What cost Al yards of cloth at 25 cents a yard ? Operation.— 4 yards at 25 cents will cost 4 timts 25 cents = 100 cents =$1. ? of a yard will cost 3 of 25 cents. But § denotes 2 -J- .3, hence, to multi- ply by §, we must multiply by 2, and divide the product by 3 ; 25 cts. X 2 =: 1G3 cents, which 25 cts. 4 100 165 $1,165 25 cts. 2 '50 • 16? added to 100 cents = 1165 cents = $1,165. Ans. Note.— The flffnre below the line, which corresponds to tlie divisor, is callea the denominator; and the figure above the line, whicli corresponds to the dividend, is called tlie numerator. Rule. — To multiply the fraction, multiply the numera- tor, and divide I'le product by the denominator ; multiply the whole number separately,and add the products. 52. Proof. — The best method of proving multipli- cation is by division. 2. What cost 2i yards of cloth .at 20 cents a yard? .- 3. Multiply 6 by 4i, i, G}. : 4. What cost 8 sheep at $5^ a head? 1. What cost 35 books at $25 each ? 2. What will 1224f bushels of oats weigh at 34 pounds to the bushel ? 3. How much is ? of 143 bushels of corn? 4 In 254 dress patterns, each containing lOJ yards; how many yards? 5. What cost 15.? yards at $2.50 a yard? ' 6. If a man travel 2-^ij miles in an hour, how far will he travel in 3 days at 12 hours a day ? )N8. itains a J5 cents time a 25 § of a ts. But o multi- )ly by 2, by 3; I, which n3. lis to the the line, ator. nuroera- ^ultiply Ct3. in u Hi pi i- yard ? i pounds ^ \ yards; far will 86 t8 8 CJENERAL PRINCIl'LES AND APPLICATIONB. 77 53. When the divisor or dividend ontains a fraction : ExvMPLB 1. Divide 12 by 4,J|. OPERATION.—We first multiply both divisor and 4i 72 dividend bv the denominator of the _^ ^ fraction, which does not change the 13) 216 (l6H^T^^°^^®^^ (48)» ^n order to get rid of the \ W fraction, and then divide as in whoh* numbers. 3 times J = § = 1 (46 and 50) ; 3 times 4 are 12, iind I carried are 13 ; 3 times 12 are 216 ; then 216 -J- 13 = 16-i'*j^. Ans. Rule. — Multiply both divisor and dividend by the denominator of the fraction, and divide as in whole numbers. 2. If 2| yards cost 45 cents, what is that per yard? 3. Divide 3 by U ; by 2i. 4. 4g bushels of buckwheat weigh 180 pounds ; what is the weight of 1 bushel ? 5. If the ploughing of 3 acres of land cost $7^ ; how is that per acre ? 1. If 35 books cost $93J, what is the price of 1 book? 2. 1224f bushels of oats weigh 41620f pounds ; what is the weight of 1 bushel? 3. How much is 61^ -f- ? ? 4. In 2667 yards of silk how many dress patterns of lOJ yards each ? 5. 15| yards of cloth cost $39 ; what is it per yard? 6. At $17 a ton how many tons of hay can be bout^hr, for $164^? ' .♦ v^:.,.- V V 7. If a man travel 11} miles in 3 days, travelling 1? hours a day, how much is that per hour? 78 DIVISION OF THE DECIMAL CURRENCY. 64. To divide dollars and cents by a simple numbci* : Rule. — Divide as in simple numbers, and point off the two right hand figures fur cents. The quotient is of the same denomination as the dividend. ' 55. To divide by dollars and cents : Rule. — Reduce both terms to cents by taking away the decimal points, and divide as in simple numbers. The quotient will be a simple number. Taking away the decimal point multiplies by 100, tho number of cents in 1 dollar; and since both terms are ir.v.Itiplied by the same nnmber the quotient is not changed. 48> Example 1. Divide $3 into 4 equal parts. 4N$3.00 i $3 = 3 X 100 c. = 300 c. ; 300 c. -r-4 =75c. $0.75 2. How many cents in $5 ? $2 ? $10 ? $9? 3. How many pens at 3 cents, can you buy for $1 ? ' Find the value of, ' 1. $6918G9.G0 -~ 72. 2. $534032.33-7-611. 3. $172010 -r 1000. 4. 1292200.01 -r 2600. 5. $9574- $0.06; -r$0.15. 6. $528.75 -^ $1.89. 7. $976842 -J- $9.46. 8. $28764.07 -J- $41.07. 9. A man paid $1448.75 for 95 ploughs, and $702 for 78 harrows ; what is the price of 1 plough, and 1 harrow? - < 10. Paid $45 for three boxes of sugar, each containing 125 pounds; what is the price per pound? ■ 11. A lady purchased 11 yards of French merino for $11.55, 14 yards of cambric for $1.48, 25 yards of cotton at 15 cents a yard, a hat at $2.30, a ■' - pair of gaiters at $3.25, and a number of sets of cuflFs and collars dt 15 cents per set, which amounted in all to $25.53 ; I demand the number of sets of «. iflfs and collars ? DIVISION OF THE DECIMAL CUREENCY. 79 ^ 66. To divide by 10, 100, &c., romore the decimal points 1, 2-, &c. places to the left. 1. How do you divide dollars and cents by a simple number? Of what name is the quotient? 2. How do you divide by dollars and cents? 3. What is the price of 1 pencil, at $1 per hundred? 4. At $11 per hundred weight, what is the price of 1 pound of clieeso? . , , ... Solution. — 1 lb. at $1 per cwt., would cost ^^^ of $1 = 1 cent. 1 lb. at$ll per cwt., " " 11 times I ct.= 11 cts. 5. At $2 per hundred, what would 15 herrings cost? 12. Bought 57 yards of cloth for $219.45, and 47 yards for $223.25 : what is the difference iu the price of 1 yard of each? 13. Paid $2350 for 1000 barrels of apples ; what is the price per barrel ? 14. How many bricks at 2 cents, will amount to $20 ? 15. 15 barrels of beef cost $150 ; what is the price per pound? 16. A man sold a horse at $97.50, and took in pay 42 . bushels of wheat at $1 a bushel, and 6 tons of hay ; what was the hay valued at per ton? 17. A lumber merchant purchased 95 thousand feet of white pine, which amounted to $9500; 113 thousand feet of red pine for $24860 ; 16897 feet of oak for $5407.04 ; 69768 feet of elm for $1567 : what is the cost of each kind per foot, and at what average price should it be sold, to gain $32332.21 on the whole ? 18. The wages of 16 men amounted to $6260 in 1 year ; what is the price of 1 day's work? '** '' " 80 DIVISION OF THE DECIMAL CURRENCY. — quotient? not exceed- 1. $T per hundred is how much per unit? , «pt 2. Whatistbepriceof 1 poundofpork, at$9abarrel? 19. A man sold an ox as follows : the hind quarter at 6 cents a pound, which amounted to $15.48 ; the fore quarters at 5 cents, which amounted to $12.50 ; the hide and tallow at 7 cents, amounted to $11.41 ; what was the weight of the ox? REVIEW OF DIVISION. 1. What does division teach ? 38. 2. What are the given terms of division? the required term ? 3. What is the dividend? divisor?— 4. How do you divide by a number ingl2? 38. 5. He *v do you prove division ? Why? 40. 42. 52. 6. How do you divide by a composite number? 43. I. How do you divide by 10, 100, &c.? 43. 66. 8. How is long division performed ? 44. 9. Describe the relation division bears to multiplica- tion. 42. 10. What is the eflfect of multipl^'ing andr40 bushels? 13. What cost 40 bushels, at $125 for 625 bushels ? 14. If 5 hogs cost $32.50, how many will $201.50 buy ? 15. If 15 pounds of wool make 13 yards of cloth, how many yards will 240 pounds make ? 16. If 18 bags of salt cost $l7.20,what will 171 bags cost ? 17. Paid $45 for 18 pairs of boots ; how many pairs can be obtained for $187.50 ? 18. If 4 cows make 26J pounds of butter a week, how much should be expected from 25 cows in the same time? 19. If 385 yards of linen cost $252, how much will 110 yards cost ? 20. How many pounds of wool will make 208 yards of cloth, at 15 pounds to 13 yards ? 21. If three yards of broad cloth cost $13.20, what will 24^ yards cost? 22. If 90 yards of shalloon cost $72, how many yards can be bought for $390 ? 31. 32. atttti M ANALYSIS. 87 lany yards pay for J ds $1 will $3 pay for? ght for $8 ? lays' works )ushels can how many :0 bushels? ishels ? )1.50buy? cloth, how bags cost ? nany pairs week, how )ws in the chwill 110 '8 yards of , what will any yards i 1. What cfM a barrel of beef at 7 cents a pound? SoLUTioM. — 100 lbs. at 1 cent = 100 cents = $1. 100 lbs. at 7 cents = 7 times $1 = $7. 200 lbs. at 7 cents = 2 times $7 = $14. 2. What cost 5 cwt. of cheese at 10 cents a pound? 3. At 5 cents a pound, what cost 3 barrels of beef? 4. What cost 4 pounds of beef at $7 per cwt.? Solution. — 1 lb. at $1 per cwt, = j,',V of $1 = 1 cent. 1 lb. at $7 per cwt, = 7 times 1 cent = 7 cents. 4 lbs. at $7 " " =4 times 7 cents = 28 cents. 5. What cost 1 pound at ^i per cwt.? 6. At $6 per cwt., what cost 2 pounds? 5 pounds? 23. What would 15 brls. of beef amount to at C cts.per lb? 24. What cost 65 cwt of cheese at lOJ cts. per pound? 25. At $15 a barrel, what will 32 lbs, of pork cost? 26. What cost 375 bricks at $8 per thousand ? Solution. — If 1000 cost $8, 1 brick will cost tx,Vit of $8 $8 $8 = , and 375 bricks will cost 375 times 1000 $8 X .375 1000 = $3. 1.000 27. At $252 a thousand, what cost 7896 cedar rails? 28, What cost 897G9 feet of boards at $25 a thousand ? 29, What will 125 barrels of fish cost at 2^ cts, per lb.? 30. 24i yards of cloth cost $107.80; what is the price of 3 yards ? 31, What cost 15 brooms at $20 per hundred? 32. How many hoes will amount to $45.50, at $8.40 per dozen? 33. What cost 17 thousand bricks at 10 bricks for 3 cts? 34, Paid $262.20 for 276 gallons of molasses; what quantity can I purchase for $452.50? 88 ANALYSIS. 1. How long would 3 men be employed at a piece of work that 4 men can accomplish in 10 days? Solution. — If 4 men take 10 day^!, 1 man would require 4 times 10 days = 40 days to do the work. If 1 man take 40 days, 3 men would do the work in i of 40 days = */' = 13i days. 2. If 2 men can do a piece of work in T days ; in what time would 5 men do the same ? 3. If T) men can mow a piece of land in 8 days, in how many days should 10 men mow it?. 35. How long should 18 horses feed on a quantity of oats, that would last 6 horses 21 days. 3G. If 7 men build a house in 24 days, in what time should 18 men build it? 37. If Ann can spin 20 bkeins of yarn In 4 days, in what time can she spin ;{5 skeins? 38. If li cwt. of sugar coal .f9.90, what will 25 pounds cost? 39. How many yards of cloth, 3 quarters wide, will line 27 yards that is 5 quarters wide? 40. If 5 coats be equal in value to 9 cloaks, how many coats will be equal in value to 25 cloaks? 41. If 2000 men have provisions for 6 months, how many men would the same quantity serve 8 months ? 42. If 275 reams of paper cost $330, how much can be bought for $1188? 43. If 56 pounds of tea cost $34, what will 7 boxes each 2| cwt. cost? 44. What cost 8973 shingles, at $8 per thousand? 45. If 7 men can build a wall in 20 days, how many men should build it in 7 days ? 1. of wo^ SoM |$2.15 J them in$2l| 2. II ifor 20[ 3. l| ,i i |4G. H reqmr 47. Hi 48. Pi 49. W 50. If 51. H 52. V V 53. I 54. I 55. ^ I 56. : M ANALYSIS. at a piece of I? man would e work, the work in ys ; in what ays, in how quantity of I. wliat time 4 days, in 25 pounds wide, will how many b? aths, how T serve 8 ch can be I 7 boxes 1. Bought 100 sheep at $2.15 each ; how many pounds of wool at 30 cents will pay for them? Solution. — 100 sheep at $2.15, will cost TOO times $2.15 r= $215 ; it will take as many pounds U> pay for them as 30 cents, the price of 1 pound, is contained times $215 in $211 = "riGj pounds. $0.30 2. How many pounds of teaat 40 cents, must be given for 20 pounds of butter at 12 cents per pound? 3. How many pounds of butter at 15 cents will be required to pay for 3 cows at $25 a head? 40. How many acres of land at $6.60 should be given in exchange for 630 acres at $3? * 4*7. How many barrels of flour at $4.90, are equivalent in value to 1000 bushels ofwheat at $1.09 per bushel? 48. Paid $49.60 for 32 yards of silk ; what quantity can be purchased for $223.20? What is a man's wages for 146 days, at the rate of $148.80 per annum? If 2 horses be equal in value to 5 cows, how many cows must be given for 20 horses ? 51. If 2 springs of a dog be equal to 3 springs of a hare, how many of the dog's springs equal 150 springs of the hare ? 52. What is the assessment on $767.25, at 2 cts. in the $ ? 53. If 4 casks of raisins each \\ cwt. cost $92, what quantity can be obtained for $2.30 ? ' 54. If 75 cwt. be carried 20 miles for $2.50, how far should 325 cwt. be carried for the same money? 55. What will 46 pieces of cloth, each containing 57 yards, cost at $4 for 3 yards ? 56. 14 packs of wool each 420 pounds cost $896, what is that per hundred weight ? 49 50 l:i 90 ANALYSIS. 1,1 i 1. Kittj's age multiplied by 12, or Colin's by f), will malre 144; what is the difTercnce in their nges? 2. W, t number added to 5 times itself will make '24? 3. A woman sold 3 dozen egg3 at 1 touts a dozen, and 10 pounds of butter at 15 cents a pound. She took in pay G yards of print at 20 cents a yard, and the balance in sugar at 12 cents a i)onnd; how many pounds of sugar did she receive ? 57. If 7 men consume 1 2 pounds of bread a day, how much bread will serve a garrison of 350 men a year? 58. How many feet of sawed lumber, at $15 a hundred, would be equivalent to 62368 foot of timber, at $70 A thousand ? 50. If 28 reapers finish a harvest in 36 days, how many reapers will do it in 9 days? 60. If $100 gain $6 in 1 year, how much should $030 gain in 2 years? How many books at 85 cents, can I buy with the avails of 1 cords of wood, sold at the rate of $11 f -r 3 cords? A )i;an sold 15 hundred weight of cheese at 11 cents a pound. He received in pay $60 in cash, 17 yards of cloth at $3.27 a yard, 52 yards of cotton at 18 cents, a hat at $2.10, and the balance in tea at 75 cents a pound ; how much tea did he receive ? 63. If a man earn $2.50 a day, and spend $4 a week, how many acres of land at $1.75 can he purchase with the earnings of a year, (313 days) ? 64. A grocer bought 7 hundred weight of beef at 7 cents a pound, and paid for it in tea at 95 cents, sugar at 13 cents, coir«e at 32 cents, giving of each an equal quantity ; how many pounds did he dispose of in all ? 61 62 02. but on( 03. nomiii Tabl NOTK roiiiifct with H( The cent p Tlie weigh *1. ( 2. ( COMPOUND NUMBERS. 91 02. Simple Numbers are those that express things of but one kind or denomination, as 2 shillings, also 4, G, 8. 63. Compound Numbers express more than one de- nomination, as 1 pound 5 shillings. Tables of Money, Weights, and Measures. NoTK.- I'lio tablps nnd mciitiil exorcises hIiouUI 1)o tnnRht In cniiiiectioii with n'duction; tlie first HerioH uf mental exercises* A\ifli Keductiuii DoHCendinp:, (67.) and the eecond sorios t witli Kodiu tlon Ascending. (68.) CANADIAN DECIMAL MONF-^V 100 cents (ct.) make 1 dollar, ' *^ The CM ns are a 5 cent piece, a 10 ci nd a20 cent piece of silver, and a one cent pit )nze. Tlie cent piece is one inch in diameter, and 100 cents weigh one pound Avoirdupois. UNITED STATES OR FEDERAL MONET. 10 mills (m) make 1 cent marked ct. 10 cents " I dime 10 dimes " 1 dollar 10 dollars " 1 eagle *1. Give an example of a simple number. 2. Give an example of a compound number. 3. Repeat the table of Canadian decimal money. 4. Repeat the table of Federal money. (1 d. i( $ (( E. 5. In 3 dollars and 25 cents, how many cents? Solution.— 1 $ = 100 c. ; 3 $ = 3 times 100 c. = 300 c. 300 c. + 25 c. = 325 c. 6 How do you multiply by 100 ? 1000? 7. How many cents in $7? $7.90? $19.50? 8, In $8 and 2 dimes, how many dimes, cents, and mills? fl. In 325 cents, how many dollars? 2. Reduce 600 cts., 725 cts., and 1508 cts., to dollars. 3. In 8000 mills, how many dollars? > r ^V ■*•" ^^. '/ IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I ^ lii 122 us. 12.0 lU lU lit I 11.25 U 11.6 Hiotographic Sciences Corporalion 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716)872-4503 '^^ ^z,^ ^^> ■i 6^ ' 92 WEIGHTS AND MEASURES. OLD CANADIAN CURRENCY. make 1 penny marked d. s. (I II 4 farthings 12 pence " 1 shilling 5 shillings " 1 dollar 20 shillings or $4 " 1 pound 1 farthing is written | of a penny. 2 " " i 3 " « J 1. Repeat the table. 2. Repeat the table backwards, thus : 1 pound = 20 shillings. 1 shilling = 12 pence. 1 penny = 4 farthings. 3. In 3 shillings, how many pence ? Solution. — 1 shilling =: 12 pence ; 3 shillings = 3 times 12 pence = 36 pence. 4. How many pence in 5s., 9s., 4s. 6d., 7s. 9d., 15s.? 5. In 1 shilling how many farthings ? In 2 shillings ? 6. How many shillings in £2, £4, £6, 2s. ? 1. How many shillings in 36 pence ? Solution. — It takes 12 pence to make 1 shilling; in 36 pence there will be as many shillings as 12d. is con- tained times in 36d. ; 36d^ 12d= 3. Therefore, 36 pence = 3 shillings. 2. How many shillings in 24d., 36d-., 70d., 40d., 44d., '72d.j 80d., 96d.? 3. How many pounds in 40s., 70s., 60s., 45s., 90s., 48s., 70s., 240d., 960 farthings. ENGLISH OB STERLING MONEY. ' 4 farthings make 1 penny, marked d. 12 pence " 1 shilling " s. 20 shillings " 1 pound " £ The sovereign represents the pound sterling; 1 guinea is 21 shillings ; and 1 crown, 6 shillings. 1. Repeat the table. 2. In 5 crowns, how many penc6? WEIGHTS AND MEASURES. 93 AVOIRDUPOIS WEIGHT. This weight is used for all ordinary purposes of weighing. 16 drams (dr.) make 1 ounce marked oz. 16 ounces " 1 pound " lb. 25 pounds " 1 quarter " qr. 100 pounds or 4 qr. " 1 hundred weight, cwt. 20 cwt. or 2000 lbs. " 1 ton " T. 28 lbs. to the quarter, or 112 lbs. to the hundred weight, was formerly allowed. 1. In 4 pounds, how many ounces? 2. How many ounces in 3 lbs.? 3. In 7 cwt., how many pounds? 4. In 4 tons, 16 cwt., how many pounds ? 6 lbs. 2 oz.? 1. In 48 ounces, how many pounds ? 2. lu 310 lbs., how many hundred weights? * 3. In 4800 lbs., how many tons? . ^ TROY WEIGHT. 24 grains (gr.) make 1 pennyweight marked dwt. 20 penny weights " 1 ounce " oz. 12 ounces " 1 pound " lb. Troy weight is used in weighing the precious metals, also in scientific investigations. 1. In 3 lbs. 2 oz,, how many ounces? 2. In 1 ounce, how many grains? -^ 3. How many pounds in 50 ounces? 4. How many ounces in 65 penny weighty? APOTHECARIES WEIGHT. Apothecaries mix their medicines ly this weight, but they buy and sell by Avoirdupois weight ? 20 grains (gr.) make 1 scruple marked scr. 3 scruples " 1 dram " dr. 8 drams " 1 ounce " oz. 12 ounces "1 pound " lb, 94 WEIGHTS AND MEASURES. DRY MEASURE. 2 pints make 1 quart marked qt. 4 quarts " 1 gallon *' gal. 2 gallons" 1 peck " pk. 4 pecks " 1 bushel " bu. 36 bushels" 1 chaldron " ch. Grain is often sold by weight, allowing for a bushel, 60 lbs. of wheat, peas, Timothy or red clover seed, 56 lbs. of rye or Indian corn, 50 lbs. of beans, 48 lbs. of barley, 40 lbs. of buckwheat and 34 lbs. of oats. 1. In 1 peck, how many quarts? pints? 2. In 1 bushel, how many quarts? . 3. Reduce 8 bus. 2 pks. to gallons. 1. How many gallons in 40 pints ? , ^ ; 2. In 40 quarts, how many pecks? , . ; 3. In 32 quarts, how many bushels? -ri LIQUID MEASURE. 4 gills (gi.) make 1 pint 2 pints 4 quarts 31i gallons 2 bar. or 63 gal. 2 hogshead 2 pipes 36 gallons 54 gallons 1. In 4 gallons, how many pints? 2. In 1 barrel, how many quarts? > 3. In 1 pipe and 1 barrel, how many barrels? 1. In 48 pints, how many gallons? 2. How many hogsheads in 189 gallons? 3. In 9 barrels, how many pipes ? "* ' marked pt. " 1 quart " qt. " 1 gallon " gal. " 1 barrel " bar. " 1 hogshead " hhd " 1 pipe " pi. 1 ton " tn. 1 barrel of beer. " 1 hogshead of beer. WEIGHTS AND MEASURES. 95 OLOTH MEASURE. 2$ inches (in.) make 1 nail 4 nails " 1 quarter " 4 quarters " 1 yard " 3 quarters " 1 Flemish ell. " 5 quarters " 1 English ell. " 6 quarters " 1 French ell. marked n. qr. yd. Fl. e. E.e. " Fr. e. In 3 yards, how many quarters ? In 1 yard, how many nails and inches? 3. In 4 E. e., how many quarters? 1. 1 1. In 20 quarters, how many yards? 2. In 36 inches, how many yards? 3. In 2 yards, how many Fl. ells.? LINEAR MEASURE. Linear or Long measure is used in measuring lines. 12 lines (1.) --' 12 inches 3 feet 5 J yards r- 40 rods ' 8 furlong's or 320 rds. 3 miles 69^- miles (nearly) make 1 (( inch, marked in. 1 foot, " ft. 1 yard, " yd. 1 rod, pole, or perch, " rd. p. 1 furlong, " fur. 1 mile, " m. 1 league, " lea' (t (( t*^5 ■- -J- 1 degree, " deg. or 4 inches make 1 hand, (used in measuring horses). 18 inches " 1 cubit. 1 pace. *' 1 fathom. 1 cable length. 1. For what is Linear measure used? How many inches in 2 ft. ?-^ Y ft. 3 in. ? In 4 yards, how many inches ? In 1 mile, how many yards and feet ? 180 inches = how many yards ? 3 feet 6 feet 120 fathoms 2. 3. 4. 1. 96 WEIGHTS AND MEASURES. 09 I I I I 30 i square yards 40 square perches 4 roods or 160 sq. per. " 640 acres << (( sq. pr (( r. (( a. 11 sq. m i. It is di- SQUARE OR LAND MEASURE. 1 yd. =3 ft. lu square measure both length and ' breadth are considered. A square yard is a yard long and a yard wide, or 3 feet long and 3 feet wide, equal to 3 rows of 3 square feet each. A square foot consists of 12 rows of 12 square inches each, i.e. 12 times 12 = 144 square inches. Hence : Length multiplied by the breadth gives the square contents, or area of any surface. 144 square inches make 1 square foot, marked sq. ft. 9 square feet " 1 square yard, " sq. yd. 1 square perch 1 rood, 1 acre, 1 square mile. In measuring land Gunter's chain is used, vided into 100 links : -, 7^^,T inches make 1 link. * 100 links or 4 rds. " 1 chain. ,^ - 80 chains " 1 mile. u- „ 10000 square links " 1 sq. chain. >/ 10 square chains " 1 acre. 1. What dimensions are considered in square measure ? 2. What is a square foot ? . 3. How are the square contents of a surface found 7 4. How many sq. ft. in a board 5 ft. long and 2 ft. wide ? 5. What are the square contents or area of a court 10 rods long and 4 rods wide ? 6. What is the area of a room 25 ft. long and 20 ft. wide? 1 What is the length of a room that is 12 feet sq. ? "2. What is the length of a board that contains 20 square feet and is 2 feel wide ? 3. What is the width of a room that contains 120 square feet and is 12 feet long ? CUBIC OR SOLID MEASURE. w 8 feet .a CO la cubic measure, length, breadth, and thickness, are considered. A cubic yard is 3 feet long, 3 feet wide, and 3 feet thick, and is equal to 3 X 3 X 3 = 27 cubic feet. Hence, The solid contents of any body is found by multiplying together the length, breadth, and thick- ness. • re measure ? 1 20 ft. wide? 7228 cubic inches (cub. in.) 1 = 12 X 12 X 12,thati8l2 ' inches in length, 12 in [ width, and 12 in thickness, J 27 cubic feet =3 X 3 X 3 feet 40 cubic feet of round timber or 50 cubic feet of hewn timber make 1 cubic foot, cu. ft. <( (( 1 cubic yard, cu. yd. 1 ton. ton. A cord of wood is a pile 4 feet high, 4 feet wide, and 8 feet long, = 4 X 4 X 8 = 128 eolid fieet. 1 toot in length of such a pile in called a cord loot; hence 8 cord feet make 1 cord. 1. State the difference between linear, square, and cubic measure. 2. What do you mean by a cubic yard ? 3. How are the solid contents of a body found ? 4. What are the solid contents of a block, 3 feet high, 2 feet wide, and 4 feet long ? 5. How many solid yards in a wall, 3 feet high, 3 feet wide, and 100 yards long? In 5 cubic yards, how many cubic feet? ^^ ontains 120 1. In 54 cubic feet, how many cubic yards ? [2. What is the width of a block, that contains 24 solid feet and is 3 feet high, and 4 feet long? " , G 98 CIRCULAR MEASURE. Circular or Anj^lar tnoasuro is used in astronoTnical calcula* tions for reckoning latitude and luugituUc. measuring angles, &c. 60 seconds (") mnke 1 minute, marked '. 60 minutes " 1 degree, " °. 60 degrees " 1 sign, " s. 12 signs or 360 degrees " 1 circle, " c. Every circle is divided into 860 degrees, hence the length of a degree depends on the size of the circle. i TIME ME ASURB. make 1 minute, marked mln. « 1 hour, " h. i( 1 day, « d. <( 1 week, " wk, <( 1 lunar montb, " mo. , V %'. It 1 year, II 60 seconds (sec.) 60 minutes 24 hours 7 days 4 weeks 13 lunar months, 12 calendar months, 52 weeks, or 365i days. The months are January, February, March, April, May, June, July, August, September, October, Novem- ber, and December. ' • ' •• ' The number of days in each month may be remembered from the following lines ;— 30 days hath September, April, June, and November; H ¥■■■ February hath 28 alone, All the rest have thirty-one ; Except in leap year, at which time, February's days are twenty-nine. 1. In 1 day, how many minutes ? x- 2. In 20 weeks and 3 day^, how many days? , 3. In 1 lunar month, how many days? minutes? 1. In 56 days, how many weeks and lunar months? 2. In 600 hours, how many days? * 3. In 9t weeks, how many Junar months ? . , . WBianTS AND HBASUBSS. 99 lical calcula- ^uring angles, the length of lembered from THK ROMAN NOTATION, So called because it was used by the ancient Romans, employs seven capital letters, viz. : One, five, ten, fifty, hundred, five hundred, thousand. I V X L C D . M All other numbers are expressed by repeating or combining these. I, X, C, and M, only, can be repeated, and these but three times. I... II... TIL. IV.. V... .VI.. VII. VIII IX., X... XI. XII. XIII XIV 1 2 3 4 5 6 7 8 9 .10 11 12 13 ,14 XV.... XVI 16 XVII 17 TABLE. . 15 OC XVIII . . . XIX XX a2\.2\w ... XL L LX LXX • . • . LXAX . . • xc c 18 19 20 30 40 50 60 70 80 90 100 ceo CD D DC... DCC DCCC CM M MM MMM MDCCCLXVI.. MXIV 200 300 400 600 600 700 ^00 900 1000 2000 3000 1866 1014 MXIV 1014000 When a character precedes one of higher value it is to be subtracted ; as IV, four ; in all other combina- tions the sum of the characters is der < <;^d; as VI, six, A dash over a character multiplies it by 1000 as V^ five thousand. Read XXIX ; L V ; XXXIX; CI 5 CCCXI; XCIX; MMCLI ; MOX ; CIX. PAPER AND BOOKS. A sheet folded into two leaves is called a folio, into 4 leaves a quarto, into 8 leaves an octavo, into 16 leaves a 16 mo, into 18 leaves an 18 mo, &c. hr" _ .,. ._*,. — . 100 WEIGHTS AND MEASURHs. PAPKR AND BOOKS. 24 sheets of paper makel quire. 20 quires " " 1 ream. 2 reams " " 1 bundle. bundles or 10 reams " 1 bale. V MISCELLANEOUS TABLE. 12 units make I dozen. 12doz. , 1 gross. 1 2 gross 1 great gross. 20 units 1 score. * « 14 pounds 1 stone. ' ' . 56 lbs. of butter 1 firkin. ' :*; 100 lbs. :? i ' 1 quintal. ' ' 200 lbs. of pork or beef 1 barrel. 196 lbs. of flour 1 barrel. ^ REDUCTION. • 64. Reduction is the process of changing numbers from one denomination to another, without changing their value. 65. Reducing numbers from a higher to a lower denomination, as pounds to shillings, is called Reduc- tion Descending. .... ,. 66. The changing of numbers from a lower to a higher denomination, as pence to shillings, is called Reduction Ascending. , J.|< ;-» ''.'.J 67. REDUCTION DESCENDING. ExAMPLB!. — Reduce JE13 lOs. to pence. 13 10 £1 = 20s., XIS = 13 limes 203. 2> =z 260s.; 260s. + 10s. = 270s. n^ Is. =± 12d. ; 270s. = 270 times 12d. 12 = 3240 pence. 3240 pence. REDUCTION DESCENDING. 101 1. In $500 how many cents 7 2. In $7 how many mills? 3. Reduce i;i to pence ; to farthings. To perform reduction descending, RuLV.— Multiply the highest given denomination by that number of the next lower that is contained in one of its units, adding in the given number, if any of the lower denomination ; reduce the result to the next lower denomination in the same manner, and continue the operation till the quantity is reduced to the required denomination. Proof. — By division. »«£1J 3. 4. '). 6. * 1. Reduce to cents $703 ; $72.70 ; $1000. ) 2. Reduce 7E. $2 7 dimes, 9 cts. 2m. to mills.. V.-jil Reduce $25, $91, $.02| to cents and mills. }f Reduce £700 to shillings. In £1080, how many pence ? In £19 3s. 5d., how many pence ? 7. Reduce l7s. lOJd. to farthings. 8. Reduce £1760 198. Gd. to farthings. 9. In 1 guinea, how many half pence ? 10. In 17 lbs. 2 oz,, how many ounces and drams ? 11. In 25 cwt., how many pounds ? 12. Reduce l7l cwt. 3 lbs. to pounds and ounces. 13. Reduce 15 tons 17 cwt. 1 qr. 22 lbs. to drams. 14. Reduce lb lbs. 6 oz. 12 dwts. 13 gr. to grains. 15. In 760 lbs. of silver, how many half ounces ? 16. Reduce 2 lbs. 2 oz. to scruples. ,,, y. ,;-' 17. Reduce 117 lbs. 8 oz. 2 dr. 12 gr. to grains. { 18. How many quarts and pints in 1 bushel ? 4 19. Reduce 17 bus. I pk. 1 pt. to pints, , .„ ; : f' ^ arr U 1*1, 102 REDUCTION DESCENDINQ. 1. la 1 hbd., how many quarts? 2. In 10 jds. 2 qr., how many quarters ? 3. How many sq. feet in a floor 20 feet long and 15 feet wide ? 20. What is the weight of 65 bushels 5 pounds of wheat, and 50 bushels of oats ? ... 21. Reduce 3 hhd. 1 bar. 19 gal. 2 q. to pints. 22. How many quart bottles may be filled from I ton of wine ? 23. In 350 pipes how many pints? •:".;. 24. Reduce 975 yards to quarters and nails. ' 25. Reduce 17 yds. 3 qr. 3 na. U inches to inches. 26. Reduce 31 Fl. e. 3 na. to inches. 27. In 1 mile how many yards? feet? ■ 28. Reduce 5187 yds. 1 ft. to feet and inches. 29. Reduce 17 lea. 1 m. 2fur. 7rds. 1 ft. 6 in. to inches. 30. In 1 sq. mile, how many sq. feet ? 31. Reduce 2 r. 16 sq. per. 19 yds. 8 ft. 121 in. to sq. inches. 32. Reduce 27 sq. m. 2 sq. yds., to sq. inches. 33. How many sq. are perches in a piece of land 200 rods long and 80 rods wide ? 34. Reduce 3 cub. yds. 6 cub. ft. 222 cub. in. to cub. in. 35. In 12^ cords of wood, how many solid feet? 36. How many solid feet in a crib of timber 20 feet long, 8 feet wide, and 10 feet high ? ' " ' '• 37. Reduce 1 lun. mo. 20 seconds, to seconds. 38. How many days from June 2nd to March 22nd ? 39. How many days from Dec. 3rd to Feb. 29lh ? 40. Reduce 9s. 13^ 25' to seconds. 41. Express in the Arabic or common Notation, LIY, XLI, CV, MDVjDOOCIX, MMVI, MDMCCXCVJII, REDUCTION ASCENDINO. 103 08. Example. — Reduce 3240 pence to pounds. 12'3240d. We reduce the pence to shillings by divid- ing by 12, because every 12 pence makes 1 - _^ shilling; 3240d. = 270s. Wo reduce the X'13 10s. shillings to pounds by dividing by 20, because 20 shillings makf I pound, aAd ubtuiu X'13 lOs. the number of pounds ia 3240 pence. RuLB. — Divide by that numbbr of the given denomin- atiou thnt make 1 of the next higher denomination, und so on till the number is reduced to the required deno- minatiuu. The remainders urc of the same name as their divi- dends, ' 1 121 in. to sq. 1. IIow many dollars in 1000 cents? 2. Reduce 15000 mills to dollars? 3. Reduce 000 farthings to pouada. 4. How many shillings in 67d.? 98d.?- «-.87d. ? 44d. ? 29d. ? ■78d.? 1. Reduce to dollars, 70300 cts., 7270 cts. and 100000 cs. 2. Reduce 72792 m. to cts., dimes, dollars, and eagles. 3. How many dollars in 250O0 m., 91000 m., and 25 m. ? 4. In 14000 shillings, how many pounds? 5. In 259200 pence, how many pounds ? 6. Reduce 4G01 pence to pounds. 7. Reduce 858 farthings to pence, shillings, &c. 8. Reduce 1G9053G farthings to pounds. 9. Reduce 504 halfpence to guineas. jlO. In 4384 drams, how many pounds ? ill. In 2500 lbs., how many hundred weights? ' [j3. Reduce 273648 ounces to hundred weights. 104 REDUCTION ASCENDING. 1. What is Reduction? 2. What is Reduction Descending? Ascending? 3. How would you reduce pounds to farthings? farthings to pounds ? — tons to ounces ? — ounces to tons ? 13. Reduce 8127232 drams to oz., lbs , etc. '"'" 14. Reduce 89581 grains to pounds. 15. Reduce 18240 half ounces to pounds. i 16. Reduce 624 scruples to pounds. IT. Reduce 677892 grains to pounds. 18. In 64 pints, how many bushels ? ■ ' 19. In 1105 pints, how many bushels? 20. Of 5605 pounds of grain, 50 bushels are oats, the remainder is wheat ; how many bushels of wheat are there ? 21. Reduce 1920 pints to hogsheads. 22. In 1008 quarts of wine, now many tons? 23. Reduce 352800 pints to pipes. 24. Reduce 3900 quarters to yards. 25. In 647 inches, how many yards? ' ' 20. Reduce 843| inches to Fl. ells. Reduce 5280 feet to miles. Reduce 186744 inches to yards. -. . .- ^ 29. Reduce 3311964 inches to leagues. 30. Reduce 27878400 sq. ft. to sq. miles. 31. Reduce 3789481 sq. in. to sq. ft., yds., etc. 32. Reduce 108391221792 sq. in. to sq. miles. '. 33. A piece of land contains 16000 fn. perches, and is 200 rods long; what is its brenilth? 34. Reduce 150558 cub. in. to cub. ft., cub. yd., etc. 35. In 1600 cub. feet, how many cords. of wood? 36. What is the length of a crib of timber that is 10 ft, high, 8 ft. wide, and contains 1600 solid ft, ? 27. 28. REDUCTION ASCENDING. 105 1. In 1280 cubic feet, how many cords of wood? 2. In 1670 seconds, how many hours? 3. What is the length of a room that is 25 feet wide, and contains 1000 sq. feet? c. 3. hes, and is ^d., etc. >od? at is 10 ft. id ft. ? 31. Reduce 2480420 seconds to lun. months. 38. A note is drawn on the 2nd of June, payable in 293 days ; when will it be due ? 39. When will a note become due, dated December 3rdi and drawn at 84 days ? 40. Reduce 1020300 seconds to signs. 41. Express in Roman numerals 54, 41, 105, 1505, 809, 11006, 16298. 69. To reduce^ old Canadian money, (pounds, shil- lings, and pence) to the new or Decimal currency. Example. — Reduce £3, 16s. 6id. to dollars and cents. Solution.— £1 = $4; £3 = 3 times $4 = $12. p , Is. = 20c. ; 16s. = 16 times 20c. = 320c. i. 3. a. ' 6| 6d. ,-wV ' = loc. 5 i d. = 2 far. = 2 times -j^c. = jf = . 00'^. 3 4 3. 16 20 I 2 12 320 1§ = ^ 3.20 10 $15.30 6* 6 $15.30& Aus. Rule. — Take four times the pounds as shillings ; 20 times the shillings as cents ; reckon 6 pence, 10 cents ; 3 pence, 5 cents; ]| pence, 2 J cents. The remaining pence and farthings, reduce to farthings ; then to cents by multiplying them by -j\ of a cent, the value of 1 farthing. For, 3d. = 12 fiir. = 5 cts., hence 1 far. = -^^^ of 5 pts, ~~ '\ li ct. , ■■MMiinnri 106 REDUCTION. i- ( 1. Reduce £5, 5s. to dollars and cents. 2. How many cents in Is. 6d.?— 13s.?— Ojd.?— 'T^d.? Reduce to dollars and cents, 1. £ 1 10s. 6d. 2. £11 Is. 9d. 3. jEIO Is. Oid. 4. i:i5 15s. 9id. 5. je23 Us. 4Jd. 6. £11 17s. 7id. 7. £ 33 13s. 113d. 8. jei90 17s. lOJd. 9. £295 168. 8id. 10. £180 OS. lid. 11. £190 Os. 6d. 12. £720 193. U^d. 70. To reduce the Decimal Currency to pounds shillings, and pence. Example. — Reduce $25.87 to pounds, &c. Operation.— $25 -r $% the number of dollars in 1 4)$25 87 6. 5 . 20) 187 T. 1 5)21 £6 9s.4^d. Ans. 4^- pound, = £6 and $1 rem. $1 or 100 cts. + 87 cts. = 187 cts. ; 187 -r- 20 cts. the number of cents in 1 shilling, = 9s. and 7 cts. over. 1 ct. = ^d., 7 cts. =: 7 times gd. 3X7 = = 4td- Then add the 5 results which equal £6 93. 4^d. Rule. — Take I of the dollars as pounds, 1/0 of the cents as shillings, and i of the remaining cents as pence (since 5 cents = 3d. 1 cent = J- of 3d. = ^d.) 10 cents may be reckoned 6d.; 5 cents, 3d. ; 2^ cts IJd. Reduce to pounds, shillings, &c., $1, $40, 40 cts., 80 cts., 15 cts., 5 cts., 2 cts. Reduce to old Canadian money, 1. $ 6.10. 2. $68.35. 3. $40.21. 4. $38.37. 5. $47.16. 6. $71.52. 7. $126.09. 8. $377.18. 9. $460.13. 10. $ 71.15. 11. $190.91. 12. $876.99, REDUCTION. 107 i J-. 1. Rfvvice 7 m, 6 fur. 14 rd. 3 yds. 2 ft. 1 in. to lines. 2. In £lj 193. ll$d., bow manj dollars and cents? 3. In 33395236 cub. in., how many tons of bewn timber ? 4. In 100800 cub. feet, how many cords of wood? 5. In X50, how many three-pences ? 6. Reduce JCISO, 10s. to four-pcnces. 7. In 20 half-guineas, how many 7 shilling pieces ? 8. Reduce Jt'l, 19s. lOJd. to cents. 9. How many cents will 27 lbs. 8 oz. of metal make? 10. In 70 E. ells, how many yards ? 11. In 7 Fr. ells 1 qr., how many yards? • 12. How many Fl. ells in 170 yds. 2 qrs. ? 13. How many quart ^bottles may be filled from 4 hogsheads of wine? : -y* :/ v -^^v %ii \W>i« : - 14. How many powders of 3 grains each may be made from 1 i pounds of quinine ? 15. In 16810 bushels of wheat, how many pounds? L In 5832372 lines, how many miles? >-■•:, 2. Reduce $31.90fjj to pounds, &c. 3. Reduce 586 tons hewn timber, 25 ft. 1636 in. to 4. Reduce 787 cords 64 cyb. ft. to cub. ft. [cab. in 5. In 4000 three-pences, how many pounds ? 6. In 903 four-pences, how many pounds ? 7. How many half-guineas in 30 seven-shilling pieces 8. Reduce $7.97^ to the old Canadian currency. 9. What is the weight of $27.50 in cents? 10. In 87 yds; 2 qrs., how many E. ells ? 11. In 10 yds. 3 qrs., how many Fr. ells ? 12. How many yards in 227 Fl. ells 1 qr. ? ' *'- ■ ' 13. 1008 quarts = hovf many hogsheads? ^ * * 14. 2880 powders of 3 grs. each = how many pounds ? 15. 1008600 pounds == how many bushels of wheat? ^^ . « ■( ..M*!mi«;gMM ir-^ 108 COMPOUND ADDITION. Hi! £ s. d. 7 17 9 14 6i 8 8 9J 3 4 45 n 7 3i £36 12 Oi sum. 71> Compound Addition is the addition of numbers of more than one denomination. ' Example. — Findtheamount of £7, l7s., £9, 14s. 6Jd., £8, 8s. 93d., £3, 4s. 4|d., and £7, 7s. 3id. ' • - Having written the addends with units of the same denomination under each other, we commence to add at the lowest denomination. — 1 — 4 — 7 — 9 farthings =, divided by 4 the number of farthings in 1 penny, to 2 pence, and 1 farthing, £36 12 Oi proof, or 2id. ; set down the id., and carry the 2 pence to the pence column. 2 — 5 — 9 — 18 — 24 pence =, divided by ] 2, the number of pence in one shilling, to 2 shillings; set down 0, there being nothing over, and carry 2 shillings. 2—9—13—21—25—32—42—52 shillings, = £2, 12s.; set down 12s., and carry the £2 to the column of pounds, which add as in simple numbers. Compound addition differs from simple addition in the orders not increasing and diminishing in a uniform tenfold ratio. The sam*? principle applies to all opera- tions on compound numbers.* Rule. — Write the addends so that units of the same denomination may stand in the same vertical column. Add first the lowest denomination, reduce the sum to the next higher denomination, set down the remainder if any under the column added, and carry the units of the next order to their proper column. Proceed thus through all the denominations to the last, which add as in simple numbers. Proof. — As in simple numbers, -.- , , \' COMPOUND ADDITION. 109 1 of numbers 1. Peter paid 3 shillings for a fifth book, 2s. 6d. for a grammar, and 6 pence for a slate ; what did the whole C08t? 2. 13s. 6d. + Is. 3d. -f 9d. = how much? 3. What is the amount of 1 yd. 4* 3 yds. 2 ft. -f-4yds. 2 ft. 1 in.? I of the same ical column. ! the sum to le remainder the units of Proceed thus which add as (0 (2) (3) £ s. d. £ s. d. £ s. d. 18 17 6^ n 58 11 18 19 11 15 03 6 10 m 19 12 lOi 1 10 Hi 46 15 lOi 13 14 U 16 16 6i . 68 19 HI 19 15 3i 85 14 10| 93 8 7i 17 19 Al 60 17 9i 56 16 111 (4). (5) (6) £ s. d. £ s. d. £ s. d. 9 7 6i 98 17 72 254 14 Hi *10 19 lOi 87 16 lOJ 715 18 lOi 11 18 9^ 76 19 Ul 916 15 5| 12 17 lU 65 16 9J 175 10 7i 13 16 8^ 48 18 10^ 89 13 4i 14 15 lOi 73 13 7i (8) 7 19 7i • (7) (9) £ s. d. £ 8. d. £ 8. d. 328 14 7i 476 16 6i 816 17 8J 800 17 5i 567 18 8i 389 10| 407 12 8i 678 19 111 31 17 11 670 18 lOi 789 17 lOi 346 18 6i 598 10^ 890 15 4i 407 13 8| 742 8 Hi 910 13 31 748 11 11 967 17 Ul 678 8 111 567 14 4| 864 18 lU 497 7 5^ 687 15 lOi r^T" lid COMPOUND ADDITION. 1 . What is a simple number ?- — a compound number ? 2. What is compound addition ? 3. How does compound differ from simple addition ? | 4. Hoiv do you add compound numbers ? 5. How much is 7 tons -f 3 tons 16 cwt. + 15 cwt.?| (10) (11) (12) t. cwt. lb. oz. pks. gal. qt. yd. ft. in. 13 13 80 4 3 13 17 2 11 90 17 45 3 '6 1 2 20 2 10 16 14 19 14 3 3 8 1 8 16 17 10 10- v\ 2 1 2 7 39 9 90 12 / 19 1 2 13. A man sold on Monday, 456 yds. 3 qr. 2 na. ; on I Tuesday, 386 yds. 3 qr. 3 na. ; Wednesday, 648 i yds. 2 qr. 2 na. ; Thursday, 139 yds. 3 qr. 1 na. ;1 ' ' I Friday, 758 yds. and Saturday, 827 yds. ?J qr ; how much did he sell in the week ? 14. A farm consisted of lire fields ; the first measured I , 24 a. 3 r. 37 per.; the 2nd, 18 a. 2 r. 19 per.lO yds.; . the 3rd, 27 a. 1 r. 12 per. 9 y|^s. ; the 4th, 15 a.l 3 r. 32 per.; the 5th, 21 a. 2 r. 25 per. 20 yds.; how many acres were in the field ? 15. Add together, 1 c. 7 c. ft. 12 cub. ft., 14 c. 2 c. ft. ; 13 cub. ft., 75 c. 7 c. ft. 9 cub. ft. 90 c. 10 cub. ' ft. and 78 c. 6 c. ft. 11 cub. ft. 16. What is the amount of 40 wks. 3 d. 1 h. 5 m. + 16 wks. 6 d. 4 m. + 27 wks. 5 d. 2 h. ? =<; 17. What is the amount of 2 a. 75 p. 248 sq. ft. 72 sq. » in. 4- 3 a. 120 sq. ft. 3 r. ; 177 sq. ft. 85 sq. in. ' + 15 a. 17 per. 84 sq. ft. 80 sq. in. ? COMPOUND SUBTRACTION. Ill pound nnmber? 72. Example. — Ellen purchased a hat at 189. She gave a £5 note in payment ; what change must she receive ? Solution. — She will have the diflference between £5 and 188. ; from £5 borrow £1 = 20s. ; ISa. from 208. leave 2s. She will receive £4, 2s. in change. • 2. 3 yds. 2 qrs. — li yds = what? 3. From £10 18s. 2Jd. take 18s. 3id. Operation. — Jd. — \d. (2 far. — 1 far.) = id. ; we £ s. 10 IH 18 d. 2i H 9 19 Hi Ana. 10 18 2i Proof. cannot take 3d. from 2d., borrow from 18s., Is. = I2d.; 12d. + 2d. — 3d. = lid. ; 18s. + Is. (the one bor- rowed) from 18s. we cannot ; borrow from £10, £1, = 20s., 20s. + 18s. — 19s. = 19s. ; £10 — £1 =: £9. RuLK.— "Write the subtrahend under the minuend with units of the same denominations under each other. Subtract each denomination of the subtrahend from the one above it, commencing at tho lowfist denomination. If any deno- niintition of he subtrahend be greater than the correspond- iug nuinbpr of tho minuend, borrow 1 unit of the next higher denomination, reduce it to the lower denomination, add it to that, and subtract as before ; call the number from which j'ou borrowed less 1, or the one borrowed may bo included in the next figure of the subtrahend and thus subtracted from the upper. rnoOF.— As in simple numbers. (1) ■ 'u': . ^. m^ Y'-- . . r (3) ■ -1 £ s. d. £ s. d. £ 8. d. 10 12 6i 900 1 lOJ .. > i 3 19 4i 98 12 95 03 (4) ' V ' -^^ '•'" (5) " £ s. d. £ 8. d. £ 8. d. 296 3 8i 314 10 4^ 715 14 172 12 n 275 14 5J 620 15 6J r-- ■ i 112 COMPOUND SUBTRACTION. 1. £1 — id. =:howmuch? ' ■ ' 2. Bought a hat at 10s., gloves at 5s. 6(1., paid a pound note ; how much change is due? 3. How do you subtract compound numbers? 0) ■• (8) ' (9) cwt. qr. lb. m. fur. rd. yd. y. d. 17 8 3 3 20 24 7 7 2 38 3 4 17 24 29 h. 12 19 10. From 29 lbs. 10 oz. 2 drs. 1 scr., take 9 lbs. 10 oz. 7 drs. 11. From 16 yds. 2 ft. 10 in., take 6 yds. 2 ft. 11 in. 12. 1 acre — 1 perch = how much? 13. From 18 c. yds. 20 c. ft. 183 c. in., take 1000 c. in. 14. From 19J yards of cloth, cut a coat pattern of 2 yds. 2 qrs. 2 na. ; how much is left? 15. The circumference of the globe — 45° = how much ? 16. A man sold 50 gallons from a tun of wine ; how ! • much was left? ■; ' ■ ' > ' 17. A young man had in the saving's bank £750, lOs. He drew at diflferent times the sums of £8, 18s. 8Jd., • ;. £19 13s. 2Jd., and £27, 6s. 35d. ; how much had he remaining ? 18. Lent 1000 guineas, and received back £680, 153.; how much is still due ? 19. 1000 yds. — [250 yds. 3 qrs. -f- 78 yds. + 100 yds. 1 qr. — 950 yds. 3 qrs.] = how much? Note.— The numbers within the brackets must be considered as but one quantity. 20. How much does 3 pks. 1 gal. 3 qts. larck of 1 bushel? What sum subtracted from 1 sovereign, will leave 3 crowns, 3 shillings and 3 pence ? From 25 cords of wood was sold 13 c. 4 c. ft., and 9 c. 6 c. ft. ; what quantity of wood is left ? 21. 22. COMPOUND MULlPIPLlfeATION. 113 3s. = 27s. which added to 23. 3d. . ) 73. Example. — What is the cost of 9 books at 3s. 3d. each? Solution. — 9 books at 3s. 3d. a piece will cost 9 times 8. d. 3s.3d. ; 3d. X 9 = 27d. = 28.3d.9time8 3 3 XT-^I Ans. = 29«- 3d. = i^l, 93. 3d. 2. What cost 15 sheep at ill, 6s. each? 3. What is the weight of 3 pigs, each weighing 1 cwt. 50 lbs ? 4. What is the value of 12 articles at Id. each ? — - at 2d. ? at 9d. ? at 7d. ? 5. What is the price of 24 articles at 4d. each ? Solution.— 12 articles at Id. = 12d. = Is. ; 12 articles at 4d. = 4s. ; 24 will cost 2 times 4s. = 8s. 6. At 5d. a yard what would be the cost of 36 yards ? of 48 yards ? of 60 yards ? of 1 20 yards ? of 1200 yards ? Rule.— Multiply all the denominations of the multiplicand separately, commencing at the lowest by the multiplier; reduce oach product to the next higher denomination, and carry as in addition. When the multiplier exceeds 12, and is a composite number, multiply by the factors of the multiplier. Find the value of, £14 63. £ 9 8s. £74 18s. £18 1 2 3 4 5. £17 6. £ 4 7. £ 8. £70 9. £19 13s. 10. £12 138. 11. £35 Os. 12. £23 15s. 7Jd. X 7. 4id. X 8. lUd. X 9. Os. Hid. X 10. 8s. 0|d. X 5. 7id. X 6. 4id. X 12. Os. Hid. X 11. 7td. X 4. OJd. X 21. 6s. 9s. 7id. X 22. 0,|d. X 24. 13. £13 17s. Ija. X 35. 14. £ 9 8s. lOJd. X 27. 15. £13 lis. Bid. X 42. 16. £ 17s. Hid. X 56. 17. £ 1 15s. 5id. X 77. 18. £ 4 58. 3id. X 840. 19. £ 8 7s. 7id. X 1080 20. 7 cwt. 2 qrs. 18 -bs. X 9. 21. 151bs. 13oz.8drs. X H. 22. 271 gal. 3 pt. X 22. 23. 8 a. 2 r. 14 sq. per. X 8. 24. 5d. 17 h. 37 nd. X 121. H :!!| 114 COMPOUND MITLTIPLICATION. 1. What cost 20 yards at Is. a yard?— at 38. ? at 9b.? at 198.? What cost 40 yards at lOs.? at 10b. ? 25. Find the value of 144 dozen eggs at T^d. per dozen. 26. " " 99 tin pans at Is. 2Sd. each. 74. When the multiplier exceeds 12 and is not a composite number, Rule. — Resolve the multiplier into any convenient parts, as units, tens, &c., multiply by these several parts, and add together the products. 1. What cost 663 yards at 15s. 7d. per yard? , - Operation.— 663 = 500+604-3 = 10x10x5+10X6+3. £0 15 7X3, 10 '. ; f' 7 15 10 X 6 10 77 18 RuLB 2. — Multiply by the nearest composite number, and add to, or '| subtract from the pro- duct, so many times the multiplicand as the as^ 389 11 8 price of 500 yds. sumed composite number is less or greater than the given multiplier. 4 5 46 15 2 6 9 60 " 3 <« 438 13 5 563 " - i'l'A-'^ .■■-tiSv ' ■-■' Find th 2. £16 3. £ 6 18s. lis. 4Jd. 3 d. X 52. X 66. 4. £ 10s. lljd. X 360. 5. £ 7 188. Oid. X 59. 6. £37 128. 3^d. X 79. 7. £27 143. 5id. X 103. 8. £ 7 138. 7Jd. X 348. 9. £1 5s. OJd. X 7081. 10. £6 78. 8id. X 9008. 11. 850cwt. lelbs. X999.» 12. 60 rds. 4 ft. X 354. 13. 5 dwt. 9 grs. X 436. 14. 6d. 17 h. 44 m. X 137. 15. $178.90 X 100000. * Multiply by 1000 aud subtract once the multiplicand. COMPOUND DIVISION. 115 nd is not a convenient hese several 76. ExAMFLB. — If 3 books cost 2 shillings, what ia tbe price of 1 book ? Solution. — If 3 books cost 2s., I book will cost ) of 2s., 2s. = 24a. ; J of 24a. = sa. Therefore 1 book will cost 8d. 2. What cost 1 pair of scissors at £l 4s. per do?.. ? 3. If 4 acres of lana cost £75 7s., what is the price 1)6 1* acre ? Solution. — 1 acre would cost i of £75 78. i of X75 £ s. d. = £18 and £3 = 60a. remaining ; 4)75 7 60 4- 7s. = 67s.; i of 67s. = 16s. and 38. = 36d. over ; i of 36d. = 9d. 1 acre would cost £18 16s. 9d. Ans. 18 16 9 Rule. — Divide the highest denomination as in simple numbers, reduce the remainder to the next lower deno- mination, adding in the given number of that deno- mination if any ; divide again and proceed in the same manner to the lowest denomination. The quotient is of the same denomination as the dividend. When the divisor is a composite number, divide suc- cessively by its factors. Proof. — As in simple numbers. Find the value of. 1. £100 2. £ 75 68. 6s. 3. £674 lOs. 4. £180 9s. 5. £ 87 Os. 6. £ 25 19s. 7. £ 5 12s. 8. £770 10s. 9. £ 78 143. 10. £265 14s. 4id.-^7 10d-r8. 7id.-J-9. 9id.-f-10. 35d.^5. 9d.4-6. 3d. — 12. Ojd.-T-U. 7d. -7- 4. 3^d.-^21 11. £770 13s. 12. £570 Is. 13. £484 19s. 14. £255 15. £570 16. £ 50 17. £136 18. £3581 3Jd.-J-22. 6d.-r24. 4jd.-J-35. 2id.-r27. 3d.-f42. 6s. lOd. -^56. 88. 8id.-^77. 2s. 6d. -J-840. Os. Is. 19. £9050 128. 6d.-^1080. 20. 69 cwt. 12 lbs. -T- 9. Ah ■ ■■ f J 'its-i; ' m g '( ^ 116 COMPOtND DIVWIO!^. 1. Paid X7, 108. for 15 books; what cost I book? 2. What cost 1 article at Is. a dozou?— — at 3s.? 21. l741bs.4oz.4dr8.-hll. I U3. 68 a. 2 r. 32 p. -{-8. 22. 5970 gal. 1 qt -h 22. | 24. CDSd. 19h. 37in. — 121 25. What cost 1 doz. eggs at jC4, 79. for 144 doz. ? 2G. 99 tin pans cost £6, Is. 8Jd. ; what is the price of 1 pan ? 76. When the divisor exceeds 12, and is not a com- posite number: ,^ ^ Rule. — Divide by long division as follow^* : 1. Divide £4561, 15s. 9id. by 87. £ s. d. £ 8. d. 87)4561 15 9(62 8 8 quotient. 436 211 174 37 20 8 X 11 — 1 =87 419 9 IX 11 4G14 2 8 + 21d. rem. — 52 8 8 4561 15 9 proof. 755 696 69 12 717 69 '» 21 We divide the pounds by 87, and obtain £52, and £37 remaining, which we reduce to shillings, adding in the 15s., and again divide by 87; we reduce the remainder to the nex' lov.or denomination, and divide ageii., anr' ; roceed ' - the same way to the end. 2. £879 15 6-^52. 3. £426 11 3-T-65. 4. £197 6 -r 360. 5. £ 466 3 25 H- 59. 6. £2971 12 8i h- 79. 7. £2855 7 OJ -H 103. iDMPOUND DIVISION. 117 1. How do vou divMe a compound number by an abstract number? '^f what nfime is the quotient? 2. If 1 doz. <(('»8 cost 1" , what is that per ogg ? Solution. — If 1 doz. cost Is. 1 egg = Va of la. = Id. 3. What is the price of a broom at 63. a dozen? 4. If 5 doz. oranges cost 15s., what is that per orange ? lot a corn- Find the value of, 8. £2673 Is. 6d. -f- 348. 9. X'8866 08. id. -f- 7081. 10. £5710 9s. -7-908, 11. £849309cwt. 84lb.-i-999 12. 2l325rd. lITft. 6iii.-7-354 13. ll7oz.3d\vt. 12gr.-7-436 14. 786 d. 5h. 28 m. -J- 137. 15. $17890000 -r- 100000. 77. To divide by a compound number. RuLB. — Reduce both divisor and dividt nd to the lowest denomination contained in either an 1 divide as in simple numbers. The quotient will be a 1 abstract number. 1. How many books at 3id. can be bought for Is. Id. ? Solution. — As many books as 3id. is contain' d times 3id.)ls. Id. (4 books. 4 ^12 ^ 13 12 4 62 in Is. Id.; Is. = 12d., 4- Id- = 13d. ; 13d. X 4 = V2 far- things. 3ld. = 13 farthings. 52 farthings -— IJ farthings = 4 books. Ans. 1. How many times can 1 far. be taken from £1 ? 2. Divide £18 15s. by 8g. 4d, f WMi ' J~ m:7M n »utmmi. -m!m^'- 118 !!( i COMPOUND DIVISION. 1. Divide £16, IDs. 3Jd. by Is. G^d. 2. £87, 6s. 8d. = how many times £1, Ys. 3Jd. ? 3. How often will a cart wheel, 10 ft. 6 in. in circum- ference, turn in 1 mile? 4. A lot of land containing 8 acres is 80 rods long ; what is its width ? 5. How many parcels of 3^ lbs. can be made of 2 cwt. ? 6. 37i yards of cloth will make how many coats, each requiring 4 yds. 2 qrs. 3 na. ? REVIEW OP COMPOUND NUMBERS. 1. What is the difference between simple and com- pound numbers ? 62. 63. 2. How do the denominations of compound numbers differ from the orders of simple numbers? 71. 3. What is reduction descending, and how is it per- formed? 65. 67. 4. What is reduction ascending, and how perform- ed? 66. 68. 5. How do you add compound numbers, and of what denomination is the sum? 71. . 6. How do you subtract compound numbers ? 72. 7. How do you multiply compound numbers ? 73. 8. How do you multiply by a composite number ? 73. 9. How do you multiply by a number exceeding 12, that is not composite? 74. 10. How do you divide a denominate number by an abstract number ? Of what denomination is the quo- tient? 75. 11. How do you divide by a composite number? by a number exceeding 12 that is not composite? 75. 12. How do you divide a denominate number by a de- nominate number ? Of what name is the quotient ? 76. ANALYSIS IN COMPOUND NtJMBEAS. 119 1. If 5 yards of cloth cost XI, 10s.; what will 15 yards cost? Solution. — If 5 yds. cost £1, 10s., 1 yd. will cost ^ of £1, 10s. £1, 10s. = -, and 15 yds. will cost 15 times as 5 3 . . , ,...,,. much = £1, lOs. X 1S{ — £4, lOs. \ 5 ••■'.-:■./■■."; ■■• .',":'' ' . 2. If 9 yds. of cloth cost £2, 28., what will 6 yds. cost? 3. If 2s. 6d. will pay for 3 yards of cotton, how much can be bought for 10s. ? Solution. — If Is. 8d. = 20d. pay for 3 yds., Id. will pay for -sq- of 3 yds. = ip^ yds., and 10s. = 120d., will 6 - -- - ■'■f -■ ■ 3yds. X 1^^ '■• ' "■■■■' ^■ pay for 120 titaes /„ = =18 yds. Ans. 4. How much tea may be bought for £1 4s., when 2 pounds cost 6 shillings ? 78. When a term of both dividend and divisor is of different denominations, they must be reduced to the lovrest denomina- tion contained in either. (In comparing the terms to make the statement, the inferior denominations may be disregarded.) 1. If 6 yards of cloth cost £4, 10s., what will 30 yards cost? .- . 2. If 30 yards cost £22, 10s., what will 6 yards cost? 3. If I pay £4, 10s. for 6 yards of cloth, how many yards can I buy for £22, 10s. 4. If 30 yds. cost £22, lOs., how many yards will*I get for £4, 10s.? 5. If 148 acres of land cost £119, 10s., what will 111 acres cost? 0. If 36 tons of logwood cost £310, Is. 3d., what will 4 tons cost? p I m SE 120 ANALYSIS IN COMPOUND NUMBERS. 1. If 2 oz. of tea cost Is., what will 1 lb. 2 oz. cost? 2. What is the cost 5 lbs. of beef, at XI 10s. per. cwt. ? I. If £89, 12s. 6d. be paid for 111 acres of land, how many acres can be bought for £119, 10s ? 8. What is the cost of 3 cwt. 25 lbs. of sugar at $6,50 per cwt. ? 9. If 36 a. 3 r. of land are rented for $168, what should be the rent of 21 a. 3 r. 20 per. ? 10. How mucb cloth can be bought for £2 8s. at the rate of 50 cts. for li yds. ? II. If 7i lbs. of sugar cost 6s. IJd., what will I3 cwt. • cost? .X ... ,-J ^ V.:.,'-,;',, ._ At 12. If 4 casks of vinegar contain 63 gal. 8 qrt., what will be the contents of 37 casks ? 13. What is a man's wages for 146 days at the rate of £37 4s. Id. per annum ? 14. Paid £9 for 6 cwt. 96 lbs. of flour, what quantity can be bought for £5 18 ? 15. How many yards of cloth at 15s. are equivalent in value to 24 reams of paper at I7s. 6d. per ream? 16. If 3 quarters of a yard of cloth ^ost 1 guinea, what will three pieces each 25i yds. cost? 17. If a man feed to his stock in 7 months 41 bu. 3 pk. 4 qt. 1 pt. of grain, how much is required ibr 7 years? - 18. How much cheese at £4 13s. 4d. per cwt. can be bought for £25 ? 19. How many yards of carpeting 1 yard. wide will cover a floor 25 ft. long 21 ft. wide ? 20. There is a certain pile of wood 120 ft. long, 6 ft. high, and 4 feet wide, what is its value at $2.50 ler cord? MISCELLANEOUS EXERCISES. 121 1. Divide 6 pence between Hal and Hattie, and give Hal 1 farthing more than Hattie. 2. What number is that from which if STS bo taken the remainder will be 187? 3. Printing was invented in 1440; how long is it since? I. The sum of two numbers is 1876, their difference nothing ; what are the two numbers ? 72 X 96 X 70 70 X 90 2. Find the value of ' -f • 48 X 21 X 9 100 3. Find the sum in dollars and cents of one crown, 1 pound, 1 guinea, 1 shilling, and 1 penny? 4. What is the value of 35 barrels of soap, each 254 pounds, at 4Jd. per pound ? 5. How many bushels of wheat at $1.50, must be given for 15 yards of cloth worth 2s. 3d. per yard? 6. A jeweller sold jewels to the value of £1200, for which he received in part 876 French pistoles, at 16s. 6d. each ; what sum remains unpaid? 7. If I buy books at 12^ cents, and sell them at 15 cents, how much will I gain by the sale of 10000 ? 8. Bought 3 boxes of shoes each containing 52 pairs, for £33, 3s., if the whole are sold at $1.25 per pair, what is gained by the transaction ? 9. A. has 24 cows worth 108s. a head, and B. has 7 horses worth £23 each ; if they interchange their droves, how much will make good the difference ? 10. A man's yearly income is £500, and his daily expenses £1, 3s. 6jd. ; what does he save? I I . A man earns £l, 13s. a week, and his daily expenses aye 3s. 10|d., what does he lay up in a year? 122 MISCELLANEOUS EXERCISES. 1. At 4 cts. per pound, what will 100 barrels of pork amount to? . . 2. How many yards of cloth at $2 must be given for for 3 cwt. of cheese at 12i cts. per pound ? 3. How many barrels of flour at £1, lOs. will amount to £30? 12. What is the value of 166^ gallons of vinegar at 3s. 9 iid. per gallon? ^ 13. If 809i acres of land cost £1955, 13s. 9d., what is the price per acre ? 14. How many yards of cloth at $3.50 can I have for 13 cwt. 56lbs. of wool worth 2s. 4d. per pound? 15. From 7 cheeses each weighing 1 cwt. 61 lbs., how many allowances for seamen may be cut each weighing 5 oz. Y drs. ? 16. What is the value of 179 bogheads of tobacco, each weighing 13 cwt. at £2, 7s. Id. per cwt.? 17. Divide $100 between A. and B. giving A. 99 cents more than B. 18. The less of two numbers is 460, their difference 365, what is their sum and product ? 19. 1870744 is the product of two factors, 2468 is one factor ; what is the other ? 20. If 283950000 be dividend, and 75000 the quotient, what will be the divisor? 21. What number divided by 10 mills will give 1879? 22. Two persons take a train at Montreal at the same time, and travel westward, one at the rate of 18 miles an hour, and the other at 25 miles ; hoV far apart will they be at the end of 12 hours ? 23. What is the value of 3 tons, 7 cwt. 60 lbs. 8 oz. Qf metal in cent pieces ? MISCELLANEOUS EXERCISES. 123 vinegar at 1. What coat 12 articles at Id. each ? at 2d.? 6d.? Is. 3d.? 2. At 4 pence each, what is the cost of 24 articles? of 36 articles ? 3. What is the cost of 5 Second readers at 5d. each, 4 Third readers at Is. 3d., and 6 Fourth readers at is. 9d.? ' " 24. How many half pence in 6247 crowns ? 25. In 74962 E. ells, how many Fr. ells ? 26. Divide $1875 among three persons giving one exactly $75.99 more than each of the others. 27. A and B bought a quantity of wine for $340, of which A paid 3 times as much as B ; how much did each pay ? 28. If 28 casks contain 227 gal. 4 pt., what will 7 of them contain ? 29. What is the assessment on $87689.50 at 3 cents in the dollar ? 30. If 1500 men have provisions for 15 days, how many men would the same quantity serve 36 days ? 31. M. White bought of Murray & Co., Montreal : 15 tons of iron at £17, 5s. per ton, 70 hoes at 3s. 3d., 115 rakes at lid., 40 pitchforks at 5s. 2d., 25 shovels at 6s, 3d., 88 spades at 4s. 6d., 50 ploughs at £3, 10s., 15 horse rakes at £1, 15s., 5 threshing mills at £40 ; what did the whole amount to? 32. A merchant had £19118 to begin trade with: for 5 years together he cleared £1086 a year ; the next 4 years he made good £2715, 10s. 6d. a year; but the following years he lost one year with another £475, 4s. Gd. a year. Whet was his fortune at the 12 years' end? 124 ANSWERS TO THE EXERCISES. 90. 73618. 91. 4650. 92. $1675. 105. 66439 trees. 114. 73618. 115. 4660. 116. 239. 139. 68. 140. 918 acres. 149. 1021. 150. $525. 151. $11064. 152. 47296. 153. 26199. 158. 135. 163. 431321. ADDITION. « 164. 336510. 165. 701360. 166. 459152. 167. 343. 168. $337. 177. 14700. 178. 4280. 179. 768790. 184. 2768. 185. 278538. 186. 258611. 187. 88521007. 188. $27067. 189. $2738. 190. $4200. 191. 1300 bu. $612 cost. 192. 1916 lbs. 193. 3846453109. 194. 286615495. 195. 129533167. 196. 238810. 197. 411058. 198. 600 lbs. 199. $380. 201. 883994. 202. 2957. 203. 324628. 204. 1011098. 205. 296984. 206. 1718885520. ADDITION OF THE DECIMAL CURRENCY. 81 1. $98.92 2. $4.91. 3. $2468. 4. $1729( 83. 2226 84. 151K 85. 1871 86. 9723 87. 1587 88. 1883 89. $896 90. 720 91. 120. 96. 873? 97. 473^ 98. 587' 1. $805.92. 5. $34013.34. 8. $6250. 64. $32 65. 166 70. 27 71. $1 2. $5414.69. 6. $866.15. 9. $1386.96. 3. $3866.97. 7. 1325 bu. iO. $17188855203 4. $3065.87. $851.50. * 72. 77 . SUBTRACTION. 73. $9 74. 12 109. 1081. 136. $890. 147. 6999. 75. 54 110. 1499856. 137. 1943 lbs. 148. 12769. 76. 23 127. 158 sheep. 138. 32464. 149. 884374. 89. 7( 128. 69273. 139. 846889. 150. 879687. ■ 90. 2^ 129. 369347231. 140. 9202293. 151. 671. ■ 96. 6 130. 14373. 141. 1548771. 152. $179. ■ 97. 1 131. 1244 yds. 142. 740. 153. 374y.tol866 I 98. 1 132. 60450060196 143. 1708. 155. 5320. 1 133. 397902. 144. $1673. 156. 140000000. ■ 2 9( 134. 999000000. 145. $1090. 157. 2780. ■ 3. 8' 135. 13328591. 146. $30 loss. 158. 1800000. 1 4. 2i Ai^SWEftS TO THi! EXERCISES. SUBTRACTION OF THE DECIMAL CURRENCY. 125 1 • «]piJoit7a. 2. $4.91. 3. $2468.88. 4. $17296.30. 83. 2226120. 84. 15116850. 85. 18712200. 86. 972360. 87. 158760. 88. 1883. 89. $896. 90. 720 yds. 91. 120. 96. 8738496. 97. 473760. 98. 5877. 5. $7310.34. 6. $284.95. 7. $20.«8. MULTIPLICATION. 99. 100. 101. 102. 103. 104. 105. 111. 112. 113. 114. 8. $5935.50. 9. $29533,50. 10. $2.30. ' 168. 115. 804804. ' $676. 117. $939. $1750. 118. 5475 cts. $450. 119. 171000. 158742. 120. 748 days. 1120. 121. $59000. $387. 122. 4320U00 pins 38304. 123. 3650 days. 2242. 124. 16211612. 70116. 125. 17920s. 90985. 126. $95 in debt. Division proves Multiplication. DIVISION. 64. $329. 65. 166^ acres. 70. 27 marbles. 71. $18|. 72. 774 bags. 73. $969966f. 74. 12525«|. 75. 54 sheep. ^ 76. 23 coats, 2 yards rem. 89. 76093. . . 90. 244§ trees. 96. 61.537 + . 97. 121067+ . 98. 181601. 99. 7899643311. 100. 166311402. 101. 27 hats. 102. 362128+ . 103. 15 sheep. 114. $16iV 115. 0. 50, E. 25, K. 25. 116. 132 canisters. 117. 0. 118. 11751^ bags of each. 119. 1000. 120. 559248074824-,V 121. $12750. 2. 96. 3. 87. 4. 280. GENERAL PRIXOIPLES. 5. 8. 8. 36 lbs. 6. 1584. 9. 16 Cts. 7. 7J. ^ ! M l26 ANSWERS TO THE EXERCISES. MISCBLLANEOCS EXERCISES IN PRECEDING RULEH. 1. 6250 lbs. 2. 90906. 3. $*27-05. 4. 1000 times. 5. 57755 sq. in. 6. £11000. 7. 9 yards. 8. 1541. 9. 850. 10. 40 qt. 11. 85 cts. 12. 62-/V tons. 14. 1273989. 16. 70 yards. 16. 81. 17. 89099. ' 18. 13256. 19. 62634005490. 20. 378600. 21. $253.75. ,r^' 22. 12 cents per pair, $17.28 whole gain. 1. $ 2. $ i 3. $ ^ 4. $ ( 6. $ I 6. $ ' 7. $ l: 8. $ 7 9. $11 10. $ 7 BILLS. 1. $109.84J. !■'■ t-! .■■■- 2. $149.44. ANALYSIS. 3. $205.02i 4. 170. 27. $1989.792. 46. 286/jr acres. 6. $20. '■ 28. $2244.225. 47. 222J§ bu. 6. $870. 29. $625. 48. 144 yards. 7. $17,065. 30. $13.20. 49. $59.52. 8. $1092. 31. $3. 50. 60 cows. 9. 25 days. 32. 65 hoes. 51. 100. 10. 625 bu. 33. $51. 52. $15,345. 14, 31 hogs. 34. 476 + gal. 53. 15 lbs. 15. 208 yards. 35. 7 days. 54. 4i^.f miles. 16. $163.40. 36. 9i days. 55. $3496. 17. 75 pairs. 37. 7 days. 56. $15.23^{. 18. 165| lbs. 38. $1.98. 57. 219000 lbs. 19. $72. 39. 45 yards. •58. 29105^ ft. 20. 240 lbs. 40. 13^. 59. 1 12 men. 21. $107.80. 41\ 1500 men. 60. $75.60. 22. 495 yards. 42. 990 reams. 61. 30i«. 23. $180. 43. $1168.75. 62. 503 lbs. 24. $682.50 44. $71,784 63. 328f acres. 25. $2.40. 45. 20 men. 64. 35 lbs. of each LBH. 5. 4006490. 00. L75. 5.02J At^SWBES TO THE EXERCISES. ,.s OF THE DBCmXL CURUKNCY. UBDUOTION OF X"'' rt _ A 127 1. $ 6.10. 2. % 68.35. 3 $ 40.20|. 4. % 63.15iV 5 <$ 94.27i. 6. $ n.52i. 7 $ 134.79-,V 8 $ 163.57. 9. $1183. 33i. 10. $ 720.12H- £ 8. d. 13. 10 ^ 3 9 11 10^ 5. 11 15 9|, 7. 31 10 5?. 8. 94 U 1^^^ 9. 112 10 n- COMPOUND ADDITION. 2i| bu. 4 yards. ,9.52. I cows. 10. L5.345. ) lbs. ,% miles. 3496. 15.23^^ 19000 lbs. 9105^ ft. 12 men. 575.60. ^^5 \- 'M lbs. 328f acres. 35 lbs. of each X £ 108 193. 2. £ 165 15s. o £ 331 3s. 4 X 73 16S. 5* £ 452 3s. 6 £2160 12S. 7* £5381 108. p.; £5490 189. 9 £3996 103. 1U<1- 2jd. lOd. 4|d. 9d. 9id. lOid. 4id. 2d. 10. l77t.l2cwt.46lbs•ll<>^" ll. 35 pk. 1 g^^- 3 ^^• 12. 48 yd. 1 tt. 13. 3218 yds. -gyds. 14 I08ac. 2r. bper. oj 6 ft. 108 in. W 1 *. f t 7 cub. It. 15 261 c. 1 c. 1^ ' ^ 16*. 85wk. 3h.9m. 17. 20a.97p.9yd.5ft 2lm. COMPOUND SUBTKACTION 1 £ 18 139. 2id. o 193. Hi^- ^' « -.* ^ nr 21 lb. 7. 8 cwt. 3qr.^^ 14. 16 yd. 3 qr. 2 na. 15. 350 deg. 16. 202 gal. 17 £694 Us. U-^*^* 7-. 8 cwt. 3 qr. 21 It)- g £309 5s. 8 6m. 7ft. 3 r 4yd. 1ft. 61 L^ 82U yds 9- 16^^^^t^3dr iscr. 20. iqvjart. 10 19lbs.ll02-3. ' ' ■ 17. A. $50,495, B. $49,505. , , r • ' ^ ' 4fS;0Z. 6 q. 11 if OZ. 9500 prod. pence. one and I, each. ;#,^''^] :u ^ % 'tl ••»;V»- LOd. ■ , 6d. . J ^ U -'JA? -■^ JiL ^»i'