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Th to Th po of filr Or be th< ale oti fin sic or Th ahi Til wl Ml dif en bei rig rec mc 10X 14X 18X ZZX 26X 30X y 12X 16X 20X 24X 28X 32X The copy filmed hera has baan raproduead thanks to tha ganarosity of: National Library of Canada L'axamplaira filmA fut raproduit grAca A la g6n*rositA da: Bibliothdqua nationala du Canada Tha imagas appearing hara ara tha bast quality possibia considaring tha condition and lagibility of tha original copy and in keeping with the filming contract specifications. Las imagas suivantes ont 4tA reproduites avac la plus grand soin, compta tenu de la condition at da la nattetA de I'exempiaire film6, et en conformity avac les conditions du contrat de filmage. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated impres- sion, and ending on the last page with a printed or illustrated impression. Les exemplairas originaux dont la couverture en papier est imprimte sont filmAs en commen^ant par la premier plat at en terminant soit par la dernlAre page qui comporte une emprelnte d'impression ou d'illustration, soit par le second plat, salon le cas. Tous les autres exemplaires originaux sont filmfo an commanpant par la pramlAre page qui comporte une emprelnte d'impression ou d'illustration et en terminant par la darnlAre page qui comporte une telle emprelnte. The last recorded frame on each microfiche shall contain the symbol -^ (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Un des symboles suivants apparaltra sur la dernlAre image de cheque microfiche, selon le cas: le symbols —** signifle "A SUIVRE", le symbols V signifle "FIN". Maps, plates, charts, etc., mey be filmed at different reduction ratios. Those too lerge to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent Atre filmte A des taux de rAduction diffArents. Lorsque le document est trop grand pour Atre reproduit en un seul clichA, 11 est filmA A partir de I'angle supArieur gauche, de gauche A drolte, et de heut en bas, en prenant le nombre d'imagas nAcessaire. Las diagrammas suivants illustrent la mAthode. 1 2 3 32X 1 2 3 4 5 6 AC • • • • •• • • • • • • • • • •• • • •• • •... • • • • ••• • •• • • •• • • • ^ • ••• Cv FIRST LESSONS IN ARITHMETIC: COMPRISING AN EASY AND EXPEDITIOUS METHOD OF ACQUIRING THE. FUNDAMENTAL RULES, •..• AND OP BNaSI'V'GC''<1B pupil TO • ■ • • • PERFORM liiE: OPERATIONS • • • • • • • • Wn» ORB AT FACILITY AND"rtORRECTNESS. .• • BY ROBE'RT SCOTT, WBITll«0«fA*TSn, IDIITBrROH. tlB-PRINTBl9«FR01l THB •••• LATEST EDINBURGH EDITION. MONTREAL: PUBLISHED AND SOLD BY CAMPBELL BRYSON, SAINT PBAN^OIB XAVIBR STBBBT. 1842. J. Starke & Co. Printers. i-H -H o r—i ao CO 0^ Q l-H 0..2..0 24 I..4..0 0..3..0 1..16..0 U..4..0 48 2..8..0 0..5..0 (iO 3..0..0 =>. o d 'M oi J '^ "• CO < -OS =i M6 - 00 o • • o o* 1^ o J iO u^ o • c: o • • d ■'*' n H i 'A o ol O d If o • • »j >-^ d • ^^ • O CM C4 O • ^^ • ^' O d ® CN o o d O d d^^ d Taw o CO r^ GO 00 ^® o- CO o • • d^J ::0 --. o d ^O d o ^ o< O • • d^J > • « o • • o» QO 00* d^J o o • • :(N : "^ ^ * Ji2 «> ®icO '^ • • O .-4 = (Equal to J denotes equality: thus 20s. rr £1. -t- f Plus J denotes addition : thus 2 -f- 5 = 7. — (Minus J denotes subtraction : thus 5 — 2 = 3. X f Multiplied hy ) denotes multiplication : thus 2x3 = 6. -r- (Divided hy) denotes division : thus 12-^4 = 3. £ denotes pounds, s. shillings, rf. pence. — a farthing, or a quarter of any thing. a halfpenny, or the half of any thing. i three farthings, or three quarters of any thing. Q H 12; o p-H (-H Tl2 ^x • ■^« o • t " : r^ ". as • — ' d ^ d w ' • '^ 00 >*^ «o ^ • • 1^ X at ": X 1 d ^H d *o • • ao -^■- d 0..9..20..10..0 1101120 5..10..0 6..0..0 ;:co 2 :r-H : to • ^^^ £ 'N -. J f— 1 d 0..12..0 144 7. .4. 0' F- ^^ c^ • ^^^ • d d 00 • _ • d — d iC w d d -^ d • ^^^ d r—t d 9* 1(5 Oi tS « o OB K5 CO fC . • • sj • • •* to .io d CO • • °:X°: Ci '-^ 00 • ^ • r-* .0 QO "^00 o tfl ^* w d d .-^ *; d ^^ d • • d "^J o» ° d 00 • _ • : X : ■«« • • 0= » ,- © :.^ : ■X >-^ to CO «* WW d 00 • • 03 • • d 10 tjt-ti ° d © • • d^ J © ^ O £ s d£ s d 0..2..11 0..S..6 35 42 1..15..0' 2..2..0 o« ^#? X 00 .-s eo ■— d :^ i oV L 0» ...-^ . d ^*^ d to • '."^ • U) >»/ to :-sO : eo d^ tji d A^ "• ■^ d o n ^* in oi • • • ** J^O d ® 0; © • /^^^ • 10 ^-^ © CO Tj^ tfl CN X 00 :(N : 00 : CO '•■f 1H - • • ^^ • >:cO ". * • • CO ^— :'<^ : &4 00 • a d '^ * :Tt : . • •«« X d © o< CO 0..1..2 0..1..9 14 21 0..14..0 1..1..0 0' • • I'M : ►, • • — s.i.' to • »^ '"' • f^^j .'-^ eo .',? • • fJ X d ■:rH -. ° d to • • ot -^^ ^ •^* • « • • ^•Od ■-• 0..1..10 0..2..9 22 33 1..2..01..13..0 © « ■ eo >— ' to © (M © • :(M : »-< - •SH :in Jix'iniv 2 . ^' gX'r- < V CO 09 S^\ .s 1 Sol =2 farthings. I Penny = 4 farthings, or 2 SoZs. 1 QMtnze-so/s,or YorkShilling=7| d. 1 Xfyre or Franc = lOrf. 1 Pistareen = \0d. 1 Trente-sohy or ;|^ dollar = Is. 3 7 8 9 10 11 12 13 14 3 5 7 8 9 10 11 12 13 14 15 4 G 7 8 9 10 11 12 13 14 15 16 5 7 8 9 10 11 12 13 14 15 IG 17 fi 8 9 10 11 12 13 14 15 IG 17 18 7 9 10 11 12 13 14 15 16 17 18 19 8 10 11 12 13 14 15 16 17 18 19 20 9 11 12 13 14 15 IG 17 18 19 20 21 10 12 13 14 15 IG 17 18 19 20 21 22 11 13 14 15 IG 17 18 19 20 21 22 23 12 14 15 IG 17 18 19 20 21 22 23 24 ! ^ote It is indispensably necessary that the pupil should be thoroughly acquainted with the preceding tables before advancing further. ADDITION Is that operation by which we find the amount of two numbers. EXERCISES IN ADDITION. Na 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 or more 22 2 2 3 2 4 4 5 1 6 3 7 5 8 8 9 8:i0 9 2 12 2 1 3 3 4 2 5 4 6 2 7 4 8 6 9 9 10 10 1 12 2 2 3 1 4 1 5 5 6 1 7 3 8 5 9 7 10 8 10 12 2 1 3 2 4 3 5 3 6 5 7 2 8 4 9 6 10 7 11 12 J_ 2 2 3 3 4 4 5 2 66 7 1 839 5 10 6 , _ 9 12 2 1 3 1 4 2 5 I 6 4 7 6 8 2i9 4 10 5 8 12 2 2 3 2 4 1 5 4 6 3 7 7 8 1 9 3 10 4 7 12 2 1 3 3 4 3 5 5 6 2 7 5 8 7 9 2 10 Sll 6 12 2 2 3 1 4 4 5|3i6 1 7 4 8 89 1 10 2|U 5 12 2 1 3 2 4 2 5 2 6 5 7| 3 8 69! 8 10 1 4 12 2 2 3 3 4 1 5 1 6 6 7 2 8 5 9 9 10 9 3 12 2 1 3 1 4 3 5 5 6 4 7 1 8 4 9 7 10 10 2 12 2 2 3 2 4 4 5 4 6 3 7 6 8 3 9 6 10 8 1 12 2 1 3 3 4 2 5 3 6 2 7 7 8 2 9 5 10 7 10 12 2 2 3 1 4 1 5 2 6 1 7 5 8 1 9 4 10 6 11 12 2 1 3 2 4 3 5 1 6 5 7 4 8 7 9 3 10 5 9 12 2 2 3 3 4 4 5 4 6 6 73 1 8 8 9 2 10 4 8 12 2 1 3 1 4 2 5 5 6 4 7;2 8 6 9 I 10 3 1 1 7 12 N.B The pupil should practise, at home, the above exercises, and le following questions, in addition, up and down, without naming the Igures, keeping by one column, till he can add it with great facility ind correctness. o ADDITION. P 723 523 123 362 426 546 642 456 t 426 382 174 876 789 763 \ ' 573 836 354 234 •k 528 265 283 137 567 234 i 123 2562 ,2532 2169 2313 1769 1839 2009 2046 1951 • 1343 2562 2532 2169 2313 1769 1 2 3 4 5 6 1 8 9 213 121 425 254 426 426 423 213 426 321 432 634 423 345 315 145 423 315 132 546 213 156 231 216 256 514 234 123 213 142 ^231 142 324 432 231 521 224 186 433 124 456 543 435 345 354 314 451 578 567 347 454 675 476 687 10 11 12 13 14 15 IG 17 18 256 436 234 234 342 214 314 345 891 782 283 261 234 356 256 576 648 764 314 524 243 423 426 342 941 591 876 265 123 125 142 312 133 759 437 987 462 645 251 625 762 726 627 568 879 245 797 546 908 456 629 892 946 764 49 20 21 23 23 24 36 26 2? 357 684 524 532 623 132 326 623 321 541 594 136 143 432 245 475 524 123 179 176 341 252 123 326 284 132 516 438 654 285 416 564 412 123 426 423 911 813 361 633 763 376 432 313 432 451 861 824 336 879 987 233 634 324 »1 ADDITION. 7 M 99 80 31 33 33 34 35 36 235 234 256 245 324 215 126 235 423 123 125 412 362 235 643 752 234 567 426 342 385 853 674 126 183 483 421 512 213 123 216 231 434 216 384 675 456 124 564 164 746 678 456 908 2 54 ? 464 768 809 456 678 789 890 965 6 43 567 678 789 890 901 234 345 456 567 37 .38 39 40 41 42 43 44 45 234 231 123 756 145 381 352 462 784 567 248 456 189 673 246 236 122 132 801 331 612 302 234 983 418 581 651 234 254 612 454 612 124 142 263 823 123 176 345 436 536 531 367 426 412 522 231 123 512 421 423 123 152 635 678 234 325 426 567 678 897 789 897 46 ii 48 49 50 51 52 53 " \ 456 679 755 678 432 567 789 946 235 437 658 426 790 421 892 234 325 435 326 658 426 345 751 316 567 245 354 245 678 861 435 288 254 245 456 543 334 567 789 432 257 123 468 326 246 1^ 426 837 968 456 234 456 321 158 545 i 123 234 345 465 567 678 689 797 809 ■ AS 56 67 58 59 M 61 63 63 234 426 325 542 623 213 918 654 654 ( 563 345 782 365 584 456 372 382 645 ' 428 834 463 426 276 584 134 765 456 1 156 627 542 321 345 276 625 321 321 1 123 234 345 456 567 678 789 890 901 1 334, 345 456 567 678 789 890 123 234 I 245 456 567 678 789 890 901 564 123 ' ."^ ADDITION. fl rwi cs m t'A 60 70 71 w o< us 176 3S4 425 123 534 456 564 123 4< 1. 2, 45G SS8 623 234 467 123 782 341 459 782 132 516 176 832 456 621 169 617 341 456 7«9 832 456 723 234 747 943 263 124 234 245 723 624 547 791 115 4 7 I 5 428 532 126 384 465 132 426 917 511 i 284 325 621 438 732 645 624 971 151 8*4 342 2lG 843 247 234 246 719 525 n 74 75 76 77 78 79 80 81 ! 4 457 697 651 363 157 345 123 234 435 '^ 557 411 146 234 345 456 567 678 789 A 632 678 619 123 234 345 456 567 678 . 891 392 901 987 876 765 654 543 432 765 567 437 567 778 909 672 987 125 1 X 123 216 789 987 798 978 567 765 665 [■ %j 709 907 248 824 428 842 482 675 567 1 ^1 154 L 566 052 789 824 79s 978 797 654 • 1 1 82 83 84 85 86 « 87 " 88 89 m ^ 1 5« 566 t G55 128 234 345 456 567 678 789 891 231. 245 456 567 678 789 891 923 345 456 567 678 789 890 123 234 456 I 567 678 789 890 123 234 345 456 567 H 678 789 890 123 234 345 456 567 678 H 789 890 123 234 345 456 567 678 789 891 234 345 456 567 678 789 891 234 j H 345 i 456 567 678 789 891 234 465 531 i H 91. Add 56789+6789+45678+3G210+4391 +64357 + 5432. 92. Add 78901+2345G + 902 + 67 + 345+94 + 678 + 6789 + 664. 93. Add 12345+56 + 921+7+678+23 + 678+2456 + 562. ADDITION • 9 94 •• ft vt m 99 100 Q635 1574 3468 4259 9825 4315 2158 4,254^ 2656 2765 2864 4674 2116 4237 1366 3427 3824 1362 3265 3154 8675 2546 9832 5649 9845 2381 2793 2643 8217 1564 1034 6734 3624 7586 1234 4902 3013 7281 1249 3826 1235 3821 7326 2156 4325 3826 4641 3194 9123 1234 4523 2684 4521 3842 2561 4567 5632 1748 1270 6432 6515 3416 8901 4567 4578 4905 4567 5476 1087 4157 101 102 m 104 105 106 107 4721 4361 5826 4294 2164 2483 1235 6138 6746 5826 1787 3845 8547 9367 2451 8456 1489 8346 2367 1385 1906 5748 3547 3565 1467 1418 9456 4234 9134 8126 1454 3535 3584 1563 1364 6257 3454 3547 2159 1758 4281 1583 1453 2341 8163 5861 6145 4561 6701 4567 3456 1966 2346 2817 5146 5432 8194 7345 4238 3402 6321 3216 4168 9087 7860 9708 5419 4097 9078 4647 108 109 110 111 m 113 lU 4361 1234 4635 2746 5678 2625 1691 7856 5672 1243 5428 4563 8427 7961 3174 9803 2834 3276 1845 3216 4559 6784 2716 4216 6417 2561 5844 1235 3267 3461 2356 6614 3842 8523 9362 1673 2345 4967 2345 3236 9654 5465 3854 1468 5876 6894 I76I (1028 5408 1627 4216 3142 2365 2418 3752 4071 8352 2174 5798 1476 3674 5278 9876 4997 4678 9764 9087 7085 7904 4567 V 10 ADDITION. ■■ j 115 . -. 116 117 ■-^m ■ 119 1 953467 435678 479324 318567 123456 Is t 845678 87654 889643 134287 678903 jrrea 538898 976543 463278 675835 2:34567 Mm 953325 547934 48853J 456754 277567 642276 457788 456789 426754 567890 546943 975312 268567 308165 456789 76547S 435678 456789 254978 567890 496534 546789 345778 902345 689760 459787 432536 587975 490776 34678O 24J 13i 345678 708765 432345 423451 787O87 M.tJt 234567 890987 654323 456789 876543 1 431 356789 906534 345678 567899 234567 Ott 234569 890763 456438 778633 987654 36$ 1 V 456789 2346G7 436589 663567 890434 ID 423689 789124 136587 653473 672342 16^ 907523 345678 466867 384667 123566 ; Wi 120 121 I V2i > 123 IS4 i 16; 371267 123456 234567 678901 212345 1 56'. 842756 978923 890123 567894 678901 wk ^^^ 456832 234567 456789 566890 234567 1 6^< •4^1 A Cfi 235078 890123 12345 462134 890123 9 45( 234567 778944 123456 977554 224507 '^B A Ck 890123 567893 789098 321213 897654 m ^^ 456789 213456 765432 455789 323456 a 16 234567 776045 134567 987654 678901 1 ' ^ 890123 678984 890986 321987 234567 ■ 12 456789 324563 654321 654321 654312 ■ ^ 102335 987654 234567 233567 345678 1 56 678901 321234 800123 937654 901234 m ^^ 234568 648114 456789 321335 567890 m ^ 890123 577890 102345 678909 987644 m ^^ 456789 787654 678901 876543 535678 1 4C 224567 321235 234567 212687 234557 1 SUBTRACTION. 11 SUBTRACTION Is that operation by which we take a loss number from a greater, and find their difference. The greater is called the Minuendf and the less the Subtrahend. EXAMPLES. From 76389504160 Take G8152837091 Dlff. 8236667069 Pz-oo/, 76389504160 24342424544 13328204232 74334516475 51232403132 43542343434 34323432242 52435984263 22314623512 36241358536 15761234524 10 40832561263 35361432532 16502101306 9784354138 74932614653 23468667231 54932615334 16493258936 63295162814 38423628676 21 56201032506 34625623454 22 36920051423 35268436938 25 69320020021 45678946563 26 10082367421 4969457989 29 65260143431 42836789345 30 10605040302 4644356783 33 16203345012 9865423678 34 75233311100 42876543219 12340tK)1367 3269876549 38 23451006945 16987667903 56721030028 17064823639 67832ll30142 2 ^ 116284 90066221155 48976346237 46 10036421967 9876546978 49 40268008678 16098765893 50 40000123202 123201 From 13061928719 Take 60809 74532 Diff. 698095 4187 Pa-oo/, 13061928719 48434345656 34224232432 65427681354 32814265133 56832463565 42356548562 10652135265 5436873766 96243951020 36845234567 23 96023428546 43567898677 27 36056001002 12885663456 20234160021 16167852265 35 63920130163 14818234076 39 34097120660 26148938427 78912304050 43028567896 23089367896 19689478969 56120600038 ^8399699 6216464S759 30054241728 24396524685 12152365232 12 62038541242 49567894893 To 36945000423 15768954678 20 12340326546 6542163154 24 16842821063 5384654324 28 45002101012 34636436498 29 31420164013 22345678921 36 21032043054 12743 205262 40 45612335500 36928543696 89016003206 967 7096849 48 83364000002 211769 87654 12000003223 68947899 12 MULTIPLICATION. I,". 92346890190 46998870989 1233214320 1 5198765432 65 10002030203 7896438 56 69696300209 8596961 57 58 59 60 61 62 63 64 65 66 67 From 78901234567 subtract 65432123456. From 105274165 subtract 9628397. From 23456789 subtract 8426483. From 628537546 subtract 207822639. Subtract 92357944 from 235298283. Subtract 39279223 from 56342047. 267534780 — 66936. 8765432986 — 22.34. 267905436 — 234567. 59827684 — 7462354. '. 4892635461—16829951. MULTIPLICATION i: Is a short way of performing that particular case of addition in which all the numbers to be added are equal to one another. The multiplicand is the number given to be multiplied ; the multiplier that by which we multiply ; and the product is the result of the operation. EXAMPLES. 43058 ' ~ 437 5325487 2 Mutipiicandi MuItiplieTf Product, 10650974 4380529 4 17522110 301406 129174 172232 18816346 16 2 25 3 29 4 36 5 48 6 57 7 159 8 571 9 4163 10 1 2 3 4 5 6 32608156 73468326 46805236 76823056 12345678 34208769 2 3 4 5 6 7 12 76432819 23 7 ^8 9 10 11 60843260 49731085 63215643 43268543 52281635 8 9 10 _ 11 12 ■~I3 14' 15 16 17 18 19 20 21 22 23 24 123 234 345 456 567 678 879 982 2345 3456 4567 5678 234 345 456 567 678 789 897 982 987 876 765 654 25 27 28 29 30 31 32 33 34 8956 7891 8912 9123 1234 2345 3456 4567 5678 6789 543 432 321 246 567 678 789 895 784 958 35 78235 4932 34106 5623 124^67898 987654322 87 19274 9032 6789*2345 456789123 38 52097 6245 39 56789 7853 34567895 57894536 40 53125 .34568 456789334 345678978 4163 10 40 53125 34568 .•^ • , DIVISION. iS 45. MulL 982546 by 104 53. MulU 7364895 by 690 46. 465437 234 54. 6854759 340 47. 456789 340 55. 57893456 120 48. 507890 456 56. 67890786 246 49. 678902 567 57. 6843625 72 50. 7890234 678 58. 49368276 4685 51. 890234 783 59. 2783682 7006 52. 837946 X 475 60. 257341 X 38942 DIVISION * ■ Is that process by which we discover how often one given number is contained in another ; or it is a short way for finding out how many times a less number can be subtracted from a greater. The dividend is the number given to be divided ; the divisor that by which we divide ; and the quotient is the number of times the divisor is contained in the dividend. EXAMPLES. •r.i«i Divisor, Quot. Dividend. 2jd6254240 18127120 2 Divisor. Quot. Proof. 4)64085263 Dividend. 4)16389250 1 J 5973 12 4_ 46389250" 5)92658174 Proof. 36254240 1. 2)47186257 2. 3)3261 2344 3. 4)64085263 4. 5. 6)32451760 6. 7)2642 3456 7. 8)46281950 8. 9)32441759 9. 1 1)68274187 10. 6)86754325 11. 7 )87654325 12. 8")7096 5345 13. 9)57893532 14. 8)7800 5432 15. 7)^5970086 16. 6)6780 0543 17. 7)90065945 18. 6)5807 5432 19. 9)52597389 20. 8)78054099 21. 9)98754328 22. 2)54638691 23. 7)75684269 24. 1 2)57426851 25. 3)78965768 26. 8)25467630 27. 7)28739259 28. 4)192 76305 29. 9)843 52678 30. 5)47628466 31. 5)73102064 32. 10)25870846 33. 4)28293697 34. 6)11504287 32. 1)84721089 36. 9)65488638 52)271653 ( 5224/^ 260 ... 52 116 10453 104 26120 125 271653 ■ 104 213 208 5 rem 463) 1245620(2690i||o 926 .. . 3196 2778 : * ." 4182 4167 150 rem. *'- v:-n>: : y 14 MULTIPLICATION AND DIVISION. 7584)6503765(857^fJJ 39406)862354 0(2 1 S^^^ 60672 . . V 78812.. 43656 74234 ; 37920 ' 39406 1 ' 57365 • 348280 V > 53088 1 t • ^' 315248 '[ 4277 rem. " • . '" 33032 rem. Divisors. Dividends, Divisors. Dividends. 1. 31)4.6326452( ' • 6. 17)10856437( 2. 41)68123456( 7. 1 9)282637 19( 3. 52)1234.5678( 9k 23J16428692( - 4*. 62)34281 9i0( ' ' \'' -'K ... .^ - 43)46728164( ' ' 5. 13)43892345( - r 10. 65)12345678( ' . ' ' •}. Divisors. Dividends. ' -<-J Divisors. Dividends, 11. 86)98765432( ;■ ' ■ '■' 16. 642I9)16781234( 12. 328)43602816( -'-i ■> i 17. 54129)34782134? IS. 746)926.32 175( » ' • ' 18. 61247)28263719( 14. 4608)18263457( 19. 43802)34218094( 15. 718.5)61330483( 20. 9103)12346525( 21. Div. 6864545 by 2 30. JDiv. 2345678 by 96 * 22. 1214567 24 31. 3456790 265 23. 2345678 123 32. 78654330 148 24. 9876543 234 33. 75201579 320 25. 8765432 345 34. . 2356785 345 26. 7654322 448 35. "82806540 231 27. 6543234 549 36. 8645673 245 26. 5432345 757 3T. 9754329 954 29. 8096542 -f. 896 38. 85432580 -5- 999 MULTIPLICATION AND DIVISION, BY COMPOSITE NUMBERS. A COMPOSITE number is a number produced by multiplying two or more numbers together, and the component parts are those which, when mul- tiplied together, make the composite number, — thus, 6X6, 3x12 and 4x9, are all component parts of 36. Note.— In dividing by components, if there be remainders, multiply the last remainder by the last divisor except one, and to the product add the last remainder except one ; multiply this sum by the next preceding divisor, to which add its remainder, and thus proceed till you have added all the remainders: tho last sum is the true remainder. EXAMPLES. MULTIPLICATION. Mult, 765324 % 24 765324 4 3061296 6 Ans, 18367776 72 { DIVISION. Div, 76832563 bi/ 72 6176832563 67 ^ 121 1^805427—1 \ Ans, "l067118-~ll j. ^^~ J 1 X 6 4" 1=tI' ^^^^ '**^^' MULTIPLICATION AND DIVISION. 15 1. M^ u//. 153284.26 % 16 1. Div. 53842567 by 16 2. 3284,7633 18 2 52845234 24 3. 43536846 25 3. • •' 42563851 36 4. 72468321 48 4. '- 35462832 72 5. , 35421684 108 5. 63224832 96 6. 71345262 144 6. 32546202 132 7. 63265432 160 7. 24609067 240 8. 78987654 220 e 46756790 264 9. 65432345 240 9. 72354628 486 10. ~ 45678006 660 10. 76542345 648 SUPPLEMENT TO MULTIPLICA.TION AND DIVISION. 1. To Multiply when the Multiplier contains a Fraction. Rule. — First multiply by the upper JBgure of the fraction, and divide the product by the under figure ; then multiply by the integer, and add the product to the quotient. EXAMPLES. Mult. 342052 bi/ t Mult. 156234 156234 by llf 7)312468 44638f 1718574 Ans. J^^2| ^ Multiplicands. Multipliers. 1. 434256456707 5i 2. 148932567890 3. 358402658606 4. 274058345648 12f 5. «48632124567 14^ 6. 538475674523 23f 342852 qi2 ^T7 13)4104624 4 315740y\ 3078468 Ans. 3394208^% ' Multiplicands. Multipliers. 7. 2865427870 57f 8. 2056678908 9. 7265483406 10. 4760124567 11. 2136482564 12. 5274501234 64f 8311 97^ 105j 2. To' divide when the Divisor contains a Fraction. Rule. — Multiply both divisor and dividend by the under figure of the fraction, adding the upper figure to the product of the divisor; then divide the greater product by the less. Div. 2345645 by 3J 3^ 2345645 3 3 10)7036935 Ans. 7036937% [ EXAMPLES. Div. 4632082 by 51 4632082 2 2 "11)9264164 Ans. 842196ft 5i 10 REDUCTION. Divisors. Dividends, 1. 21)7432812345671 2. 3|)346685345678( 3. 4|)612803456680( 4. 6|)263827587897< 5. 8|)489360789074( 6. 10|)127605345678( Divisors. Dividends, 7. 8. 9. JO. 11. 12. 15^ )38256745678( 23f )21836409876( 54U)53468198765( 53J )17402756789( 6l| )27164323456< 65i5)48326012345( REDUCTION V Is the application of Multiplication and Division in bringing money, weights, and measures from one denomination to another, without alter- ing their value. Table. — 4t farthings = 1 penny ; 12 pence «= I shilling ; 20 8hilling8= . . 1 pound; 20 shillings =- 1 sovereign. EXAMPLES. £ s. d. Bed. b 12 6^ to farthings. 20 112 shillings. 12 It 1350 pence. 4 5402 farthings. Red, 5402 farths. to £ 4)5402 farthings 12 )1350 ^ p ence 20) \\2T shillings £5 12 ef" 1. 2. 3. 4. Red. 9. 10. 11. 12, 13. 14. 15. 16. £ 13 96 19 Red. s. 14 19 17 10 d. H 11 to qrs. to hp. to pe. to shs. 5. 6. 7. 8. Red. £ 67 83 145 496 17 13 12 13 d. 6f 8 6 7 to to to 9, 19, 39, 41, and 45 farthings to pence. 35, 68, 112, and 219 pence to shillings. 116, 241 and 32881 shillings to pounds. 1876547643 farthings to pounds. 7846238451 half-pence to pounds. 4827635899 pence to pounds. 8497683 half-pence to sovereigns. 743628478 half-pence to shillings. qrs, hp. pe. to hp. £ s. d. 43 16 m 25 12 H 67 17 8 74 14 IIJ 96 18 4 309 5 265 3 ^ 309 5 JND . ^D] EXAMPLES. £ s. d. 34 13 ^ 67 18 m 81 11 11 46 14 6J 13 19 24 18 5 210 4 10| 244 18 5 £ s. d. 36 18 Hi 74 8 7.^ 80 17 98 11 4 63 10 Oi 354 7 H 317 8 4 354 7 3i r?. COMPOUND ADDITION. 17 £» s, d. £. s. d. 18 13 11 3 36 18 24 17 54 6 4 2 4 3 7 76 14 5 34 12 3 73 4 8 61 13 7 15 3 6 61 11 4 24 6 7 3 5 10 44 8 9 16 17 8 £. s, d. 23 16 10 67 18 11 26 4 8 36 8 2 43 17 8 5 6 7 8 16 15 8 92 9 9 67 4 6 87 16 6 91 16 2 46 13 10 46 18 3 67 13 8 18 5 11 76 13 3 76 12 11 46 17 9 98 8 7 65 11 2 61 11 10 67 17 8 21 17 7 13 13 8 46 13 11 19 18 6 9 10 11 12 36 18 10* 34 13 64 25 16 H 56 8 H 93 13 lU 74 18 H 36 15 5« 96 9 9 37 2 5 63 17 10 47 14 44 10 63 16 4J 74 17 94 3 19 H 91 19 i4 45 19 7 67 14 6 S6 18 6 34 16 4 58 10 oi 14 15 14 H 53 10 54 23 14 84 13 15 16 57 17 10 25 16 44 18 18 14 21 2 3* 16 18- H 36 17 H 90 19 11* 32 13 4* 43 19 4 47 18 6i 37 18 7 43 14 H 58 10 74 53 9 74 16 5 34 54 15 6 41 17 H. 69 15 8 48 14 lOf 65 6 n 71 12 2 43 12 104 36 15 4 76 17 9 41 14 9 16 10 54 48 14 104 83 9 20 104 17 18 19 34 14 H 36 19 54 36 10 6i 70 12 6 45 15 5i 35 5 7 93 12 3J 44 10 8 55 16 6 63 4 74 67 9 10 56 15 H 67 17 74 16 11 "4 83 4 6 66 16 104 78 18 8| 18 9 64 54 16 34 77 8 H 83 19 9 85 10 104 28 14 6| 88 18 ^4 12 11 2 25 15 6 14 1 14 99 9 n 78 6 4 2 12 7i 87 15 6| 12 2 6 18 COMPOUND ADDITION. £. s. d. 21 £. 5. d. £. 8, 22 S?3 d: f. s. d, 24 94 13 8i 17 6 8 96 17 m 89 14 5i 18 15 U| 42 10 9 36 16 H 11 3 2; 64 17 1 83 12 6i 98 10 111 36 18 4| 45 18 llj 43 14 10 16 15 2 38 13 2 74 17 lOi 96 15 7| 36 11 9| 44 14 4i 25 15 6 42 14 8 18 18 10 55 5 5| 36 16 7i 12 17 6 29 9 6i 66 16 6i 47 7 8| 25 27 13 Hi 30 10 26 lU 77 7 7 27 216 16 9 243 12 9 146 14 3i 239 15 lOi 486 10 10: 789 14 5i 348 17 8i • 534 11 1 111 3 2i 419 12 3i 645 2 2i 785 13 Hi 586 1 1 756 13 8J ' - (■! 976 18 1)4 643 19. Ill / 867 4 3| ;. -■; - 463 17 lOi 796 14 4| <,■ 939 15 lOJ *i 565 14 7i 873 12 lOr . •- V 448 10 3 ', _ ' 286 9 10 976 8 9J •> \' 556 8 5i '*v 383 10 1 ^ 785 10 8i - ■': 447 18 6i 760 15 8| 28 • 29 30 i 316 11 6 ■ .. 365 16 8| 956 16 3| 432 15 lOj ~ 296 4 8J *^ ' ' ' 222 2 2 436 18 4| 962 4 3 333 13 3i 224 17 3 123 14 Hi 444 14 41 j 454 6 7 609 3 5i 555 15 5 182 15 2i 482 1 6 912 12 10| 624 6 4 • 376 13 9 206 16^ 7i 3 15 lOJ 268 17 4i 432 9 4i 645 8 9 724 5 2 437 18 7i 467 18 11^ 136 17 lOj 716 17 4i ' 31 32 38 326 4 8i 107 8 5 422 4 7| 836 8 2i 876 12 4i 524 18 6 643 17 8 393 5 2 425 9 8 967 4 6 1 585 9 9 657 8 7 846 13 lOi 643 7 8i 986 16 lOi 976 13 3i 911 16 10 765 9 2| ! 165 11 2i 372 17 3 654 7 9 713 13 8 516 3 8i - 542 10 6i 76 14 9i 439 12 Hi 434 7 9 467 17 8 216 8 3i 246 17 lOi d. 4| 2 H H 7 84. £ «. 2328 11 3462 15 ll!i 3 4532 17 6146 4 2317 16 7819 7 9945 16 3265 3 1287 16 S278 9 1545 15 9678 7 3212 14 8390 19 COMPOUND SUBTRACTION. £ 1234 4586 856 3546 ' 2146 979 2334 6545 9834 1112 3045 2868 8190 3267 4178 19 80 £ s. d. 1346 14 5} 4567 5 6 5678 16 8} 6789 7 463 18 9 2170 9 10* 7356 10 11: 6325 11 1, 4656 12 3; 9 13 0; 6034 8i 8401 16 9 4078 9 H 36 17 7r 3656 4 5 COMPOUND SUBTRACTION. 5 3} 2 2 3 3i % 4i 5 5 26 16 17 18 8 18 2f 26 16 8f 30 12 10 48 7 4 15 9 6 6 26 3 2 7 36 9 4 90 15 11 15 4 44 75 12 3 11 12 63 8 4 54 12 3 23 9 16 3 25 16 5 17 96 11 4f 67 8 5| 9| 57 16 H 48 12 21 22 52 16 H 39 13 10 28 19 26 5f 26 14 4f 75 15 2i 64 2 3^ 29 5 31 8| 42 10 S2 8| 50 13 ^ 80 1 4 45 15 3^ 8| 16 3 37 5i 84 11 7* 32 1 4| 68 12 8} 41 15 2 5^ 132 13 64 29 19 10 EXAMPLES. 42 8 2^ 6| 25 9 16 18 7i 42 8 2^ 3 70 14 6 23 5 4 8 60 3 8 48 2 5 13 65 14 lU 42 9 ^ 18 80 5 2 42 6 3^ 2'J 75 2 4 48 3 8| 28 40 5 4| 34 3 81 33 60 10 11 59 10 111 S8 jl5 1 H 19 3 ^ 42 109 16 0| 30 18 li 48 60 4 50 3 5 12 1 3 9 96 3 1 48 2 -u 20 13 10 16 14 10^ 19 40 3 6 26 5 84 24 98 12 1 49 15 5| 29 40 3 4 25 13 8| 34 57 19 4 50 19 8| 39 90 3 53 45 4 H 2 5 11 17 li ^ 26 13 5 2 8 1 4 10 5G 1 ;^ 42 3 4 is 30 17 4i 14 15 8| 20 45 2 8 40 5 9^ 45 11 3 23 12 8 30 ■ 60 12 4 45_17_84 35 63 18 11 41 12 5| 40 65 4 6 34 1273 796 43 I 1 l\\ 5 Sj 20 COMPOUND MULTIPLICATION. 725 149 16 18 4 * 46 705 13 269 18 7 81 4567 17 7 . 3785 19 Oi - COMPOUND MULTIPLICATION. ' " EXAMPLES • £ 12 6 d. 8 2 £ 7 s, 12 d. £ s, d, 16 7 9j 4 Prorf. 24 13 4 Prof^. 22 17 4i Prorf. 65 11 3 3 6 4i 2 12 8 10 6 13 9 10} 10 13 15 16 7} 3^ 17 12 9i 7_ 10 1 18 4| 11 10 16 6j 4_ 14 10 11| 8_ )6 10 8j 12 137 6i 7__ 516 12 111 10 109 14 19 01 12 8 10 5 15 13 6| 9^ 13 16 5^ 12^ "75 836 17 0} 11 213 17 7J 9^ 598 17 llj 12 What cost 15 yds. at 2s. 9^c?. ? £0 2 9^ 3 "O 8 4i 5 Am, £2 1 10^ 1. MuU. 8 13 5 6y 29 What cost 342 /6s. at Ss. 4|^? £0 3 4|X2=0 6 91 10 1 13 11^X4=6 15 10 10 16 19 7 X3=50 18 9 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 6 12 6^ 25 3 9 4| 36 6 3| 49 1 16 6j 64 10 13 10 70 3 14 0| 96 2 9 6| 120 3 6 8^ 77 18 11 39 1 6| 47 2 7i 53 Ans, £58 14^ IS. Mult, 11 2 by 79 14. 6 13 5 68 15. 2 5 10 74 16. 13 11 6 83 17. 4 16 7| 104 18. - 1 16 lol 112 19. 2 6 10 264 20. 7 6} 340 21. 8| 406 22. 1 10 11 714 23. 3 6 6| 886 24. 1 2 10 342 COMPOUND DIVISION. 21 S3 S6 J7 S8 Mult, £ •. d. 2)29 12 6 Quot. 14 16 3 2 *° 843 31 ^2 768 COMPOUND DIVISION. EXAMPLES. £ I. d. 3) 35 5_3 QuoL 11 13 h 57 76 3146 3472 Proof. 29 12 6 1 8 3 * 5 6 7 8 5 7 37)63 7 ?L 26 20 2)22 3)25 4)27 13 5)32 3 6)37 5 7)41 15 8)49 16 9)52 17 d. 6 4 4 5 2 9 4j 3^ Proof. 35 5 10) 67 13 11)69 1 12)75 19 8)85 6 2^)85 14 3^)162 17 4i)88 12 l|)73 16 9 10 11 12 13 14 15 16 1 3 3' lOi 4 11 7 6 4 5 H £ f. 4)43 5 Quot. 10 16 d. 4 Proof.4S 5 7JL 17 18 19 20 21 2£ 23 24 8(£1 14 SAns. 527 37_ 157 148 ~"9 12 Tie 111 .o •-■■' .'ij:; ':»*) ' r 5 rem. Lf) 141 11)79 2f ) 56 4)29 1J)81 2|)29 3|) 58 5|)66 . d. n 1. JDi». 43 17 6 bit 13 2. 75 15 4 17^ 3. 58 2 6 19 4. 65 1 8 23 5. 48 3 4 29 6. 86 13 5 31 7. 96 5 4 41| 43) 74 17 4|(£l 14 43 20 637 43 207 172 ~35 12 " 424 ' 387 • "37 _4 TsT 129 22 rem. 8. 2>iv. 98 11 10 % 43 9. 108 2 6 47 10. 115 8 2 51 11. 216 18 4 62 12. 120 17 7 9i^ 13. 260 11 84 59 14. 243 5 6 6IJ 22 BILLS OF PARCELS. 15. Div. .340 10 10. 390 18 4 17. 401 10 18. 543 17 5 10. 012 7 11 ^y 07 t 71 75J \ 80 101 20. 21. 22. 23. 24. Div. 04:> 703 850 201 98 8 8 4 18 5 11 5 h lOo 342 342 43 07? SUPPLEMENT TO COMPOUND MULTIPLICATION. £ a. d. 1. 17 10 X 2. 10 13 10 X 3. 13 9 X 4. 2 7i X d. £ 6 13 21 10 9' X 90] 43 2 11 X 123: 13 5} X 68^ 11 0} X 83 J BILLS OF PARCELS. EXAMPLES. Mr Jambs PRVDg. Bought qf Dickson & Cu. 46 reams thick post, at 32u Gd 53 thin do. at Si'^a Gd S6 foolscap, at iSaGd 31 !cartri(If|ro at 138 8d 9 cwt pastf'boarda, at lOa SOOOquills at IsSdV^ieO < ^ Mr Wm . Graham, Bought qf Andw, MBtROSs & C* S9| lbs green tea, at ISs Cd 17; rmperial at IGa 9d 36 Bohea at lis lOd 111 coffee, at 48 3d IG} double-refined sugar, at Is 2|d 7 sugar loaves, l4|lbs each, at lO^d 41|lbasugar, ..M at 9d 8 Mr Jambs Miller, Bought of Robbrt Brown. yards muslin, at Is 8d do at ls94d linen, at 38 lid do at 287fd shalloon, at ^iiiid flannel, at Is 5d Mr J. Cruickshank, Bought of W. Whitb & Co. 16 copies of Davidson & Scott's Arithmetic, at 3s 6d 53 Scott's First Lessons at 3 dozen copy-slips, No. 8, at 5| do. No. 3, at 21 copies of capitals^ No. 19 at 11 Principles of Writing, at 6d 6s 6s lOs Ss6d '. <: *:>: Mr M*Nab, Bought qf V. C. Baird . l^ dozen of port. at 32s 17 sherry, at 308 14| claret, at 548 19 madeira, at 40s 23 gallons of biandy, at 30b 26 rum, at 168 29 Avhisky, atlls6d EXERCISES IN ABSTRACT NUMBERS. 23 •I M« D4VID LiNDiAY, Bought nf yfH. Law. 31 Ibi blark ton nt 3i 'M ' l> < SAf ff"***' at4»H^^t%ht qf Cowan & Stracuan. 20 yarda printed <-aUco, ut '29 3|il 9A jaconet iiiU'^Hn,... nt 3s 8(1 VJ\ black crap, ., nt ns Od 31 black aatln at 7s 4d 9 muslin liandkerchiefa, at'28 5d ^ • ' 13 silk do atls7d • '■'* ~£ " EXERCISES : ON THE FOREGOING RULES EXERCISES IN ABSTRACT NUMBERS. 1. Add together 234567+34567-|-4.5678-f-.34.4.+56789+42253+ 332B1 ; from the sum subtract 233241 ; multiply the remainder by 29, and divide the product by 23- 2. Add together 14565434-87C5'154-23l56V-f 087654.4-9764384. 439876-4-30234* ; from the sum subtract 23484*87 ; multiply the re- mainder by 79» and divide the product by 59. 3. Add together 3278542+8229704-4675609+24329+647234+ 562836+487658 : from the sum subtract 4365298 ; multiply the re- mainder by 68, and divide the product by 156. 4. Add together 2,743,068+27%P42+73,489+ 196,456+243,987 +55,546+52,198; from the sum subtract 3604396 ; multiply the re- mainder by 16^, and divide the product by 86^. 5. Add together 18,426+74,686+184,932+284,723+132,924+ 66,903+29,4324-12,893+34,565; from the sum subtract 786543; multiply the remainder by 30^, and divide the product by 84f. EXERCISES IN ABSTRACT NUMBERS. 6. From the sum of the following products, viz. 944X26, 94X26 4321X28, and 1642X36, subtract 17224, and divide the remainder by the sum of the multipliers. 7. From the sum of the following products, viz. 454X38, 743X26 843X32, and 744X*3, subtract 44515, and divide the remainder by the sum of the multipliers. 8. From the sum of the following products, viz. 4583X57, 8765X76 and 6879X89, subtract 419474, and divide the remainder by the sum of the multiplier!>i. 9. From the sum of the following products, viz. 1378X69^ 7696b^ I12|, 4368X76J, and 5765X97, subtract 1365881, and divide the r"^ mainder by the sum of the multipliers. 10. From the sum of the following products, viz. 58x73i 1794v 47i. 567X621, 5^67X36^, and 743X47J, subtract I545l8i,7nd divide the remainder by the sum of the multipliers. 24 EXERCISES IN COMPOUND QUANTITIES. EXERCISES IN COMPOUND QUANTITIES. 1. Add together L.6H : 16 : 8-f L.854 : 19 : 8+L.4U : 7 : 11+ L.21'1 : 18 : 3?4.L.827 : 9 : SJ+L.Si? : 4 : 3; from the sura subtract L.3456 :I3: 6^; multiply the remainder by 16, and divide the product by 31. 2. Add together L.344 : 7 : If+L.SSS : 18 : 6+L.389 : 14. : 2^+ L.54.: 16:5+ L.47: 18: IOJ+L.64.: 18:a+L.75: 14 : 7J+L.24 : 13 4^ ; from the sum subtract L 484 : 18 : 4 ; multiply the remainder by 29» and divide the product by 65« 3. Add together L.128 : U : lf+L.243 : 18 : 7+L.254 : 8 : 9+ L,75:4: 6+L.84 : 5: 10|+L.29: 17 :6+L.35 : 17:5 ; from the sum subtract L.755: 15: 9 ; multiply the remainder by 87 and divide the pro- duct by 74. 4. Add togi'ther L.808 : 15 :'4 + L.235: 12 : 6£+L.486 : 4 : 6+ L.422 : 14 : 7f+L.123 : 5 : 10+ L. 235 : 18 : 5f+L.432 : 17 : 7+ L.234 : 14 : 7 ; from the sum subtract L.1234 : 14 : 7^ ; multiply the remainder by 365, and divide the product by 85. 5. Add together L.876 : 14 : 7|+L.145 : 7 L.543 : 15 : 10+L;123 : 15 : 6^+L.545 : 9 the sum take L. 1 765 the product by 84^. 10+L.234:5:6^+ 6+34 : 5 : 8|; from 12:2; multiply the remainder by 24f , and divide ( EXERCISES IN COMPOUND QUANTITIES. 6. Multiply L.29 : 12 : 5J by 14, L,37 : 8 : 4f by 17, L.59 : 7 : 7 by 27, and L.52 : 12 : 7^ by 32, from the sum of the products subtract L.3457 : 13 : lOf , and divide the remainder by the sum of the multipliers. 7. Multiply L.37 : 14 : 8^ by 16, L.4S : 16 ; 3^ by 25, L.53 : 17 : 7 by 35, and L.89 : 13 : 10^ by 55 ; from the sum of the products sub- tract L.3202 : 16 : 8, and divide The remainder by the sum of the mul- tipliers. 8. Multiply L.48 : 15 : 4^ by 48, L.45 : 15 : 6 by 57, L.66 : 18 : 5i by 60, and L.99 : 10 : 8 by 84; from the sum of the products subtract L.2754 : 16 : 7|, and divide the remainder by the sum of the multipliers. 9. Multiply L.56 : 17 : 2^ by 17, L.42 :>13 : 10 by 19^ L.85 : 2 : 6 by 44, and L.35 : 16 : 8 by 50 ; from the sum of the products subtract L.2263 : 15 : 2|, and divide the remainder by the sum of the multipliers. 10. Multiply L.46 : 5 : 6 by 22^ , L.56 : 13 : 3 by 31^, L.173 : 8 : 6 by 62^, L.49 : 6 : 9 by 35, and L.55 : 7 : 8 by 74 ; from the sum of the products subtract L.2442 : 5 : 8, and divide the remainder by the sum of the multipliers. 11. Multiply L..34 : 4 : 10 by 16, L.82 : 14 : 5A by 24^, L.91 : 3 : 9^ by 75, L.57: 5 : 2^ by 43^ and L.102 : : 11^ by 19^ ; from the sum of the products subtract L.975 : 12 : IO3, and divide the remainder by the sum of the multipliers. 3 THE END. V J, Starke % Co. Printers^ St. Therese Street, : 11 + ubtract )roduct 24:13 by 29, : 9+ ,he sum he pro* 4:64- 7:7+ ply the :6^+ • ; from i divide :7: 7 subtract Itipliers. : 17:7 cts sub- lie mul- , i 18:5| subtract tipliers. 5:2:6 subtract Itipliers. 3:8:6 n of the i sum o( I .91 : 3 f rom the mainder /