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Quantity is any iliinir that can 1>e in«^roase(l or Jlimnnsliod ; as, •. of a body, \\m weight of an arf iclo. 4. AUnitisaqnantily will, which wo compnr(^ others of tlio same Jdnd. 6. The comparison ofquantity with unity produces three kinds of numl,ers : hUegen, Fractiom and IMhecl Jynvibers. 6. An Integer is anumber wliich contains its unit m exact number of tim.. : as, 12, 15 ; G boys, 4 apples. 2 DRKTNITIONS. a.-l.v,aed ml„ two classes; viz, ^/„/„,, and r'„«. 10 An Abstract Number is a numhor (he naluro of whoso ,.„.t i, ,.ot .l..t,.,mi„,Kl ; as, ,r., 42r,, 7840 tIiO dol J::" "" *""""""'' ^ -■ "' men. 425 days. NUMERATION AND NOTATION. 12. Nim.omtion i. the methcul of reading- num- fnns <'xi)r('sso(l by .•haraotons. 13. N«»tatioii i.s Iho iiu'lliotl of wrilin^r numbers. 14. Numbers may be re])ri'.seiited as I'oHows :— T. JJy jw/v/.s ; as, one, two, three. 11. y>y Ji^urcs, called the Arah/r Method; jis, 1, 2, 3. III. IJy A7/o>-, called the Roimm Molhod: as Tv 15. In llu. Ai-al»ir Mt'tliod, numbers are ex- pressed by tne lollowinii- ten ^is:un..s:,,2, 3, 4, S, 6, 7, 8, 9, O. rV allies : One, Two. Throo. Four. Five. Six. Sovon, EiRht, Nine, Naught- PRINCII'LE. A simple name is ^nven lo enrh oj the first nine num- bers, of which groups are formed. These groups also receive, each, a particular name, and are numbered by the simple names of the first numbers. 16. The first nine figures are called signifwant be- cause they represent a value. But the tenth, by itself, represents nothing. It is only an auxiliary figure : its ofiice being to hold the place of any order 4 NI.M,.;li,AT^O^f ANl, NUTATION. wh„tov..r, whoa thoro are ,k, unit., of that order iu 17. l^]aer whi.-h follows the ninth is cdled fen- r s represented by writinn- the il^are 1 with a naugnt ui'ter it; thus, 10. '' ^ 19. 7Vv. i« I he unit of the ,eron4 order und is eaunl lo ten units of the,/,V.s/ order. ' ^ ^ ^ 20. Tens are counted in tl»e same manner as sin^^lo ^nsUnn has rephiced these words by the followin<.- •- ^^^-^y' 20 Sixty, lo Thirty, Forty, Fifiy, 30 40 50 Seventy, l<:ighty, Ninety, 70 80 90 NotM._The..,yuitl,..s,.wonl«sij^„i,iesten. 21. The names of the numbers included between two <.onsecutive teiis. are formed ),y joinin.- to th -neoftheiirst of tln.et.ns, the L;l.n^^^^^ the hrst nine numbers, sayin- : Twenty-one, Twenty-two, Tvventv -three, Twenty-four, Twenty-live, Twenty-six, Etc. 21 ''' 22 23 24 25 20 Thirty-one, &c. Forty-one, &c. Fifty-one, &c. vSixty-one, &c. Seventy-one, &c. Eig-hty-one, &c Etc. Ninety-one, &c. ^ ^, _^^ The highest number expressed by two fin.u^.s being niuety-nine, 9<). ^ i^oUrts, 31, &c. 41, &c. 51, &c. (51, &c. 71, &c. 81, &c 91, &c." 'esses Sim- NUMERATION AND NUTATION. 5 22. But instead of saying ten and one, ten and two, ten and three,... ten and nin(^ custom has adopted the expressions : Eleven, Twelve, Thirteen, Fourteen, Fifteen, NoTK.-Tlie " toen •' in (lie wonJs liiirlee,,, etc., lo ninetpen, niPans Im. bo lliat, strictly sj.eakints thirteen nipons llirce and ten • fourleon, four and ten ; etc. EA'EJWISES. Copy and read the follovvinn-juunbers, namino- the lena and units in each : 11 12 13 14 15 Sixteen, ►Seventeen, FiulittMMi. Xineteen, 1<) 17 IS 1!) (1) 17 12 11 16 13 87 46 (2) 28 20 30 90 79 69 59 (3) 55 22 37 48 40 31 19 53 87 62 32 43 34 50 (5) 85 44 33 (>7 97 79 60 (6) 29 10 61 99 21 33 54 0) 70 89 64 23 14 74 82 Express the following- numbers by fio-u,.e,s ;_ 73 98 72 27 58 80 49 1. Ten. 2. Thirty-seven. 3. ScA^enteen. 4. Fifty-eight. 5. Forty-three. 6. Twenty-one. ^. Forty-two. 8. Twenty-three. 9. Eighty-six. 10. Ninety-eight, 11. Thirteen. 12. Forty-live. 13. Thirty-six. 14. Forty-seven. 15. lilleven. 16. Ninety-seven, 17. Seventy-six. 18 Sixty-eight. 19. ]']ighteen. 20. Forty-four. 21. Sixteen. oeve nty. 23. Nineteen 24. Twelve, 25. T 26 NUMERATION AND N enty-six. I 83. Eighty. OTATION 26. Seven ty-ont 27. Fifty-one. 28. Sixty-three. 29. I'hirty-niiie. 30. Fifly. Fifteeji. 41. Eighty-three 3J 34. Twenty-fonr.|42. Fifty-six. 3.). Thirty-seven. I 43. Fifty-nine 36. Sixty-two. 44. Seventy-eight 37. Twenty. 45. Forty-six 38. Twenty eighl 46. Sixty-three two naughts after it ; thus lon. " '"' 24. 0,«/,Mrf,-,rfi,the unit of the «,>,/„, 313 } ^ 81G \ 911 15. Throo hiiiidrcd forty-live. l(i. Seven hundred nine. 17. Eiucht hujulred tv^'o. 18. Five iiuudred sovonty-two. 10. Seven hrimli-ed two. 20. Six hundred fii'ly-lbur. 21. One hundred seventy. 22. Three hundred twenty-nine. 23. Nine hundred nine. 24. Six liundred live. 25. Seven hundred .sixty. 2(). Four hundred seventy. 27. Three hundred tw^enty-seven. 28. Five hundred ninety-seven. 20. F\)ur hundred ninety. 30. Two liundred eighty-four. 31. Four hundred seventy-live. o2. One hundred one. 33. One hundred two. 34. Seven hundred seven. 35. Seven hundred seventy. 30. Fight liundred eighty. 37. Five hundred sixty-one. 38. Nine hundred ninety-nine. 30. Eight hund.ed. 40. Three hundred thirty-three. 28. The number which follows 000 is called Hum- mnd, and is represented by writing the figure 1 with three naughts after it ; thus, 1000. 29. Thousand is the unit of the second period. The period of thousands, like that of simple units, com- 10 N U ]\I E II A T I O N A NM) N O T A T I ON, pi'Lscs uiiitis, t('n> Jind limidn-ds. ^j^j. lousamls, and hundreds or jh( 000. ton 111 y are The hundrey and n^ad (he Ibllowinn- numben (1) 1831 4785 TcMO 6837 8001 8788 2027 1456 (2) 1030 2686 1522 7403 5465 1401 6434 8573 I (3) 0184 1025 2222 6807 5273 6600 1020 5409 (-1) 2040 3107 5043 7041 7856 4624 4862 4709 (5) 5083 3174 4065 7831 4563 4000 5980 1036 (6) 8800 5580 1001 2050 3307 3009 2010 3003 n 4 7i 21 8( 4; riON, NUMERATION AND N O T A T 1 o N . 11 mils oftliou- "nhouNuiidN, dvrti ol uiiiiis. 'u; fhouNund. !»000. y tlioiisaiul. tl thousand, )00, 'i two con- >y joiiiinir, lose orders, this order. (6) 8899 5580 1001 2050 3307 3009 2010 3003 154(12 21009 80450 78921 44383 (12.) 442839 750351 290420 807905 431900 (8.) 03041 79S25 3H(;78 10909 8000(1 (13.) 905497 080329 751341 008315 917823 Express in figures, II. (0.) 0848! > 73401 3!M;32 71854 27374 III. (14.) 034584 100091 390400 745001 370492 the Ibllovv I. (10.) 25738 1050(1 8i!ni i2i;u io09(; (15.) 25120(; 358192 870538 704115 171211 injj^ : — (11.) 71392 59!»S9 0300i> 24784 87004 (10.) 9!K)098 431900 829473 110018 980703 1. One thousand eight liundred eighty-lwo. 2. Three thousand nine hundred four. 3. Two thousand, nine. 4. One thousand eight hundred sixty-three. 6. Seven thousand five hundred forty-one. 0. Nine thousand forty-seven, 7. Six thousand five hundred eighty-four. 8. Nine thousand one hundred twenty- seven, 9. Six thousand five hundred eighty-nine- 10. Three thousand one hundred five 11. One thousand one hundred twenty-two. 12. One thousand five hundred fifty-five. 13. Eight thousand eight hundred ninety-seven. 14. Six thousand three hundred forlv- 15. Eight thousand eight hundred ninety-six 12 "UMKnATION AN,, N,,,.....,.,^. ,;!• ^■'"^'''•""••""'"-""iKvo )„„„,, .,,.1. --.Sovo„fy,l.o„„,„„,„i,,|,,.,.„„^ -A K.sl. y..,.v,.„ ,l,„„s„,,„l si,. -^- ieii Ihoiisjmd, ono 25. Tw..,Uy thousand two h,„„l,,,„,,„,,, ^^•;;-. N,„o,y.„,„e thousand f„„,. ,„,„„.,,,, ^'I,,,,,,^.. ^5. Ten thousand, (on. J^-^Ki,Ut hundred .si'J'u.ou.sand nino hundred l-,dJdUv!'"""""' '"--'y--" '"""-..1 oight dreT '*'^'""'d-„s, Tril- hotfs, Sec. Million is the unit of the finrd period ; billion, the niiU ol the./o//rM period; and trillion, the unil of the /iff h period. These three periods, like w.^V*- and llumsanth, com- prise, each, three orders ; viz., the order of units, that of tens, and that of hundreds. 32. The names of the various numbers included between their several orders are formed in the same way as those included between the several orders of thousands. PRINCIPLE. Ever!/ figure placed to the left of anolher, represents mils ten times greater than those of the other; in other words, %t represents mils of the next higher order, 14 N U M K U A T ION AND N f ) T A T I O N 33. From this principle it loiJows : I. A fi^raro 8tandin^r alono, or in the f.rst place at the ri-ht of other li-ures, expresses units. II. A fin-ure stjMulin- in the second place, counl- ins irom the rioht, expresses tens; in the third place, hundreds ; in the fourth ,>lace, thousands ; &c. Til. It IS necessary to have one iigure to represent a number having- only simple units ; two, for one having fens; three, for one having hundreds; four ^' rone having thousands; &c, according to the or^ der ot the units. 34 ^^^'t^ry significant Jlgure has uvo values. One Ls called Its smpfe, or nbso/uf, value ; and the other. Its /oral, 01 re/afive value. The Suupfe Value of a figure is that given to it by Its lorm. •' The W Value is that which it receives from the place that it occupies in the number. ^^"" ^- ^^ e number 430G, the simple value of the is 4 first figure to the left is 4 ; and its local units of thousand ocal value PRINCIPLES. /. Ten nnihnfam, order whatever Jorm one unil of (he next higher order. II. A th„,,,,u,,l „uih of „„y period, « equal to one unit "I Itle next lugliei periml. h-rs i.l,e hg,„es are divid.,1 into ;,«•/,.*, each of which comprises three places. The//™/ ihne place, T A T I O N . > . ho fiivst ])liu'(' at mils. id plaro, conn I - ; ill tho lliird tliouKaiids ; &c. nre to represent > ; two, for one lundreds ; four, 'ding- to the or- • o values. One and the other, t given to it by elves from the le value of the cal value is 4 N ir M E R A T I () N AND \ n T A T H ) N . IT) eonstitule the first, or units perio ii ^ 2 2 S •2.2.2 5 3 n O O o ^ '/J S :=:SS ■^■^■^ ^^;a '^ '^ '^ Hip^ §^S i5i5^ £^5^5 c-^HH p:;p;pq ^<=^?% H c—i r-( ' ©oo ooo ooo -- n3 o '/J '•^ OOO 0) S2.5 15.5 I2.2 -2.2 -2^2 Sr''-* r-;^^ p-SZ- ^-"•'^ -"i;.~ fcljl'.^ u^O)"-" p^jTCI ST2 r-S^ HhP SHt^ ShI^ K^C KhLB Names OF I'ERions. Ni MHiai. TriUiuns, P.illions, :Millioiis, Tliuiisimds, Vnxu, S-^O 02o 0V4 .308 040 ( one unit of the lual to one unit writing num- riods, each of St three places Orders. 'ZlSS -^-tl-^ ^-d^ »o 't CO rM ^ o c: ■X' 1*^ Peiuo ns. 5 S-^-^ r^^ .^ —^ ■"^ w 1/3 '•O -f iTO (? I rH -2 >0 1< CO 'd ns, Quinmons, kexlUlions, Septitlmns, Octillions, X-c, 16 NUMERATION AND NOTATION. MA'i:iiCli6E8 f V NUMEUA TION. AiU'i- tli(. ioiv-oinir (.xi.lanatioi.s, the pupils should 1).' able to remi any numlM>r whatever accorclin«r to the ibllowiiig' "^ RULE. /. Be millions ; tlit^ sh- lionce llie number (5.) V 704«-?5 2 O59037 I 954308 J 100716 > 536900 1 213472 f 360005 800001 780602 f NUMEKATION AND NOTATION. 17 ir. (6.) 2l9M7»i5 377!t843 321167?? 7864321 .>623102 54H220() 9180406 4706204 7601o;?6 4073208 14050(10 8880808 8006807 6000011 20!)0001 2390086 (9.) 4072634 82791640 7006 984270 400200 1807 62876000 900040 900000800 3742680002 8632073009 862794846704 2872819642 34006411H (7.) 23 7s 2621 486:51425 77666555 43125789 52706000 60300001 72060:584 10010010 83000505 758(10207 31500004 90088050 60500283 200O2021 53700006 69014789 III. (8.) 978564123 HO«;273S7l 55211S622 4H(;.37462H 1112223,^3 7090,S()O(;2 203100000 840601007 320000006 786400200 842900601 120340560 400300600 910004576 475462394 800006301 (10.) S563400024 7462007302 82367400210 53024046070 86920000030 17629080406 294635112211 909009008007 842780062004 1303000170410 327864219741(3 14000075001004 167008634216786 3462184390075819 rl 18 N U :\I E 11 .\ T I O N ^ N D NOTATION EXEllCISEH JN NOTATION. R U I. I^ . /. Be^-innin. J^lig-hty-eiglit. »Seventy-seven. Fil'ty-live. 1. Forty-nine. Twenty-six. l^lighty-nine. 8. Ninety-two. Thirty. Seventy-three. • 9 One hundred five. One hundred eleven. 10. Three hundred ten. Two hundred sixty-five. 11. Four hundred nine. Three hundred twelve. 12. Five hundred thirty-eight. Six hundred eighty- one. 1\ Nine hundred lliirty-two. Eight hundred ninety-nine. 14. Three hun'.-red sixty. Five hundred eighty-two. 15. Nine hundred twelve. Three hundred fourteen. 10. Seven hundred nineteen. Nine hundred three. ATION WN. ". hiij^hcat periody rh period in the vo thonmnd four Ills, thousands and tie onJcr, wliicli is "I isands ill llie Iburtii L (0) in Uio second t [liaco. Jlence these ivcii number. liguivs : wo. lireo. irty-oiic. il'ty-livo. '-nine. reo. I olovon. •ed sixty-five. Ired twelve. nndred eig-hty- light hundred red eighty-two. idred fourteen, liuudred three. NUMERATION AND XoTATloN. 19 lY. Three liundred twenty-two. Two hundred sixty-six. 18. Seven hundred eighty-eight. Four hundred four. li». Five hundred twenty-eight. Eight hundrc^d twenty- five. 20. Three hundred eigdity-five, Six liundred sixty. 21. Seven thousand, sixty. vSix (housiiiid, seven. II 22. Nine thousand, seven hundred eight. 23. Three thousand, seven hundred fourtcHMi. 24. Three thousand, two hundred foriy-iive. 25. Seven thousand, six hundred ninety. 20. Three thour;and, seven hundred fifly. 27. One thousand, four hundred seven. 28. Two thousand, two hundred s(U'enteen. 20. S(»ven thousand, threi^ hundnnl twelve. 80. Two thousand, four hundred ten. 81. Three thousand, eight hundreen thousand, seven hundred. Foriy thousand, six. 88. Fifty thousand, eight hundred forty-one. 39. Seventy-three thousand, one hundicd twenty- nine. 40. Eig-hty-seven thousand, four hundred t\n3nty- two. 41. Seventy thousand, one. Twenty-four thousand 20 W U M E 11 A T I () N AND NOTATION. 42. Twenty-four thousand, nine hundred sixty- eight. 43. Twenty-nine thousand, two hundred. 44. Seventeen thousand, one hundred ten. 45. Forty thousand, three hundred ninety. 46. Twelve thousand, eighty. Six thousand, two. 4*7. Nineteen thousand, sixty-two. 48. Ten thousand, one hundred ten. 49. Twenty-three thousand, five hundred eighty- nine. III. 50. Sixty-three thousand, twenty. 51. One hundred forty thousand, five hundred seventy-five. 52. Two hundred ninety-ono thousand, seven hun- dred forty-six. 53. Nine hundred sixty thousand, ninety. 54. Nine hundred thousand, nine. 55. Three million, five thousand, one. 56. Five hundred million, five hundred. 57. Six hundred million, five thousand, four hun- dred seventeen. 58. One hundred eleven million, one hundred eleven. 59. Two hundred ninety-seven thousand, forty-one. 60. Four billion, six million, one. 61. Five billion, seven million, two thousand, five. 62. Eleven million, eleven. 63. Four hundred six thousand, seven hundred eight, 64. Eight hundred nine thousand, sixty-five. 65. Two trillion, twenty-five million, five. 66. Sixty-six million, ten thousand, nineteen. '•'■VilJWrW ^•''^*iK-bi*A;9liaiti\^-^t,\giYi M T I O N. hundred sixty- undred. trcd ton. 1 ninety. : thousand, two. n. lundivd (Mghty- . five hundred and, seven hun- ninety. lie. dred. and, four hun- one hundred sand, forty-on e. thousand, five. even hundred iixty-five. ri, five, nineteen. NUMERATION AND NOTATION. 21 67. Fourteen million thirty-five thousand, one hundred ninety-four. 68. One million, three. 69. Seven million, three hundred thousand, ninetv- [four. ^ 70. Forty million, four thousand, seven hundred. 1h Six hundred three million, fifteen thousand, sixty-one. ^^ 72. Fifteen billion, seventy-one million, six thou- ' Rand, four hundred. 73. Three hundred thousand, five hundred eio-htv- I two. ° ^ ' 74. Two hundred million, fourteen thousand, one hundred. ^5. Eight hundred thirty billion, twenty thousand twenty-two. ' 76. Five million, two hundred six thousand nine- teen. 77. Nine hundred billion, sixteen million, eiffht thousand. ^ 78. One hundred nine million, four hundred twenty thousand. 79. Five hundred twenty-one million, three thou- sand, ten. JX^d''" ''""'''■"' '"""°"' '"'"''y "^»'«»>"i. '""« 83. Three trillion, one hundred twenty billion, two milUon, five thousand, one. 00 NUMERATION AND NOTATION. 84. Thirty-sovoii trillion, one billion, ninety-nine 80. Four trillion, eighty-one billion, one thousand two. Roman Notation. 38. Tn the J^omm Method of Notation, numbers are expressed by the Ibllowing- seveii letters of th. Jvoman Alphabet : Lrller,. I, V, X, U C 1), M. ^dho'^. 1, 5 i(>^ ,-^ 100,500, 1000. PRINCIPLES. I. The mine of the letter is repeated as often «.« the tetter Itself I, repealed ; ax, HI expresses the numher three ; XX expresses tinentn. II. A letter placed to the right of one of ^greater value adds Its own to that of the other ; as, X V represents f,J teen \ VII, seven. Ill The valneofa teller plaeed to the left of one of grenter value, must be subtracted from that of the other; as, IV expresses four ; IX, nine. IV. The value of a letter or a combination of letters, is increased a thousand-fold by placing a dash over it. Thus. X, LX, denote, respectively, ten thousand, and sixty thou- sand. NoTi.:.-l. Ifa lelK'r Ihat denotes a less niiinber be placed betwvrn two that denote greater numbers, it diminishes the latter, but do,.^ not atToct the former. Thus in the combination LIX, the value of 1 must be lalven Irom that of X. Hence the number expressed is fiftv- nine. (59). ^ II. It. must also be observed that no letter is written four limes in succession. T A T 1 N NUMERATION AND NOTATION. 23 Ilioii, ninety-nine. 39. The application of tliese principles is shown ion, one thousand, i» the following roN. otation, numbers 'en letters of the 1), M. .^00, 1000. as often as the tetter limber three ; XX, of greater value, ^ represents fij teen : the teft of one of hat of the other; wtion of letters, />• 'ish orer it. Thus. and sixt// thou- erbo placed belwi'rii tlie Jailer, hul diM- LIX, liie value of I >er e.xprossud is fifty. TABLE. One Two Three Four Five Six Seven Eight Nine Ten Eleven Twelve Thirteen - Fourteen Fifteen Sixteen Seventeen • Eighteen XIX - XX XXX ^ XL L LX LXX . LXXX XC C CC - CD D . DC CM ~ M MM - MDCCCLXXXIII 19 ■ 20 80 - 40 50 - (10 70 - 80 90 100 200 400 500 600 900 1000 2000 1883 wriWen four linicb 24 NUMERATION AND N () T A T I O'N . EXERCISES. Eoad ihe following lumibors and express Jhem in figures. (^•) (2.) IV XXII XV XXXII XLIV XVI LXXV LY XXVIII LI XXXIX LXII XI XCI XLIX LXXVIII (3.) (4.) LXXXIII LXVIII XIV Lxxxrv LXXXVIH XLII LXX LIX XCIII XXIII XCVII (r>.) CCXLIX DXXVI CMLX CDXXVI (G.) DCVIII CXIV DCCCXCI DCCLXXVII (8.) MDCCCLXXII MCDXXII VDCCXI IVXC LXXIII X XIX XLIX XXXIII il.) CXVIII DCLIII DCCXLIII CCCLXXXI (9.) MMDXCVII MDCXLVI LIXV MDXLIX (10.) MMCXXIV CIJXXXIX XXVLX MI NOTATION. lul ('xi)r(;s.s lliom (4.) II LXVIII LXXXIV an xLii LXXIII X XIX xux xxxrir CXYIII DCLIII DCCXUII CCCLXXXI (9.) MMDXCVII MDCXLVI LIXV MDXLIX NUMERATION ANO NOTATION or. 'rite tho following mnnbors })y the Roman Melhud • ■) lo. 402 (2.) 24 18 64 38 27 13 (3.) 34 40 12 80 77 08 41 177G 18G0 1783 2570 (14.) 51 G3 42 80 14 15 80 (20.) 1342 ]()35 1883 1206* (15.) 02 10 48 25 01 20 02 (21.) 1402 1184 1203 1035 (4.) 30 07 70 82 00 00 2!» (10.) 2132 8004 4040 7032 (10.) £8 47 62 60 11 41 73 (22.) 5048 2732 1704 1500 (5.) 830 501 320 270 105 014 182 («5.) 402 080 084 583 372 007 300 (11.) 2358 8422 4004 8743 (H.) 83 00 10 33 50 04 70 (23.) 3058 4032 0004 2801 (18.) 37 2r> 14 85 70 05 0) 202 100 470 324 712 410 007 (12.) 0008 12074 11402 21800 (10.) 40 68 13 55 87 38 44 (24.) 4010 0020 1000 5000 1;. ADDITION. -.o:- 40. A and and C and G and G and G and (T and *7 and V 1 and 7 and 7 and 7 and 7 and 8 and 8 and 1 are 2 are 8 3 are U 4 are 10 5 are 11 G are 12 1 are 8 2 are !) 3 are 10 4 ar(^ 11 r> are 12 G are 13 7 are 14 1 are (» 2 are 10 fr--S3&n^--^--,^^^-5^-3^^^.., ADDITION. 27 ORAL EXEltCIHES. nindinn- jIk, g^^, ' "ff I ; (' .111(1 2 aro ',\ 8 and 3 aro H and 4 aro 8 and 5 aro 8 and are 8 and 7 aro 8 and 8 aro and 1 aro ^ and 2 aro and 8 aro and 4 aro and 5 are and (5 aro and 7 are and 8 aro and 9 are low manv and 1 ? and 8 i and 1 ? and 4 :* and 'Z ? and 2 ? and 2 ? and 1 ? and 2 ? I and i aro 4 and 1 ? •3 and 4 ? 3 and ? n and 3 ? 7 and 2 ? 4 and 4 ? and 2 ? 1) and 4 ? 3 and 8 ? and 1 ? II. 1 and 1 ? 5 and (> ? 4 and 5 ? 5 and 4 ? 1 and 9 ? 7 and 3 ? (3 and 2 V 3 and 9 ? '') and 7 ? 7 and ? f3? 3 f-1? 5 + 8? 6- |9? G- 1-7? 4|G? 3- [8? f) 5? 7- 0? 5 6? G and 4 ? 8 and 8 ? 7 and 8 ? r> and 3 ? 9 and 7 ? 4 and 8 ? and G ? 2 and 8 ? 9 and G ? 8 and 5 ? 4+7? 7+8? 4+9? If 8? 2+6? 3+5? 2 + 7? 2+9? 0+8? 5+9? w >l 28 ADDITION. III. 1. (i })ats and -^ l)ut.s arc how luaiiy bats ? 2. 4 l)()y« and T) })()yN an; liovv many hoys ? J3. V dollars and 2 dollars an; how many (h>llars ? 4. 2 (H'nts and T) i-cnts aro how numy ccnls ? 5. 4 g'irls and 3 girls arc how many <^irls ? (). 7 houses and 5 houses aro kow many houses? 7. A fishes and 8 lishes are liow many lishes V 8. !) toi)s and 1 loi> are how many tops ? A boy pnid 1 cent lor a slick of candy and 2 cents for an apple ; how many cents did ])oth cost ? Sou;TiON.--If a stick of candy cost 1 cent, and ;iii applo cost i CHiits, l)olli must cost the sum of I cent and 2 coiils. Tlio sum of I com and .: conls is 3 ecu's. Tlicrcl'uro bolli cost 3 otiils. 10. John's lather gave him two ui>])les, and his mother gave him two more ; how many ai)i)leB had John then ? 11 George had 4 chestnuts and Joseph gave him 3 ; how many had George then ? 12. If a pencil cost 2 cents, and a co])y (5 cents, how many cents will both cost ? 13. "William lost 7 marbles and has remaining ; how many had he at first ? 14. There aro 8 birds on one tree, and on another; how many birds on both trees? ir>. There a-re 4 hens in one coop, and 5 in another; how many hens in both coops ? 16. I travelled 4 miles one day, and 7 miles the next ; how many rniles did I travel ? 17 There are G eggs in one nest, and 8 in another; how many eggs in both nests ? jj^ A D i:) I T I O X 29 ly biits '^ iiy ))«)ys ? : iiuiny dollurs 'i any rciitts i 11 y skirls ? ' many Iiounos? laiiy lislies ? T tops V of ciuuly a I id 2 s did both cost 'i and iiii ai'plo oost '2 ceiils. TIhj t-uin of 1 •I 3 oeiils. itp])l(\s, and his lany ai)[)les had osoph i>'avo him a copy coiits, IS G remaining ; ndOon another; ind 5 in another; nd 7 miles the nd 8 in another ; 18. raid 5 cents ll.r a kit.., and '. cents lor some String; how nmcli did holli co.st ? I 10. A man Imu-ht ;| |,„rsc,s „n \Vcuy v L'd. .lames put S .hairs in the parlor, and C in (I,.. nt<-hen; )i<>\v manv <-}iairs did lie ■,u( ju the two fooms ? 21. I paid n dollars for a hat, and ll dollars f<,r a #airol pants; liow miirli money did I sj.end '^ I 22 Mirwards w<.n f ; how many marbles had lie then >■ Add: 1 . 1 and 0, 12. 51 and 2, f^. 2 and 1, fl. /i;5and3, |A. 4 and (J, f 1 and 4, 12 audi, G3 and 4, 14 and 6, 05 and 8, l(>and8, 87 and 1, 18 and 3, to. GO and 1, 1 50 and 0, IV. 20 and 5, 71 and G, 22 and 2, 73 and 4, 24 and 7, 75 and 8, 2G and 7, 77 and 2, 28 and (5, 70 and 0, 30 and 7, 81 andO, 32 and 2, 83 and 5, 34 and 7, 85 and 0, 3G and G, G7 and 3, 40 and !>. 1 and 0. 42 and 3. 03 and 5. 44 and 0. 05 and 4G and 5. '")7 and 4. 38 and 8. | 48 and 4 80 and 2, | UO and 5. HI-? |2+6n=? i5 + 0-='<» 64+3==.? 72-f-5--^? 60 + 7:::r.? 34-j-O:..? 88+4=? f4+8--? 62+9=? Gv I b=; o /+8^-? 47+7=? 63 + 5='? 11+8=? I 23+0=? V. 01+ 9-.? 21+ 8=? 7+14=? 03+ 7--? 46+ 5=? 13+ 8=? 40+ 0=? 61+ 8=? 32+ 1=? 63+ 0--? 78+ 6--? 53+ 9-=? 82+ Q=--'i 9+31--? 8 + 12=? 00+ 7=? 68+13=? 40+ 7_? 02+ 7---? 86+ 3-? 72+ 9=? 6+12=? 7+99=? 55+ 2-=''^ 93H- 9=? 27+ 6=? 7+84=? I fl 80 ADDITION VI. Add : 1. l^y thrct's, from '2 to 110. Tluis, 2 and '? arc T), and H arc H, and ;'. aru 11, &c. -. \)y twos, from .'} to 81. 3. By throes, IVoni 1 to 01. 4. J5y lours, from 8 to 115. 5. liy lives, from 2 io 11. 0. By lives, from 4 to 104. 1. By sixes, from 3 to 57. 8. By sixes, from 5 to 83. 9. By sevens, from 4 to 11(5. 10. By sevens, from G to 118. 11. By eiii'hts, from 1 to 80. 12. By eights, from 5 to 69. 13. By eights, from 7 to 55. 14. By nines, from 3 to 102. 15. By nines, from 4 to 76. 16. By nines, from 8 to 116. 17. By threes, from 11 to 44. 18. By fives, from 7 to 47. 19. By sevens, from 9 to 86. vn. 1. A news boy sold 10 papers in the morning and 7 in the afternoon ; how many papers did he sell during the day ? 2. If Joseph has 3 e»»nts in one pocket, and 10 yents in another ; how many cents has he? 3. AVilliam paid 12 cents for a slate and 1 cent for a pencil ; what did he pay for boili ? how There are 17 trees in one field and 9 in another many trees in the two fields ? ADDITION Bl I ;{ aro 11, &c. he morning and pors did ho sell 5. If there are 15 panes of jrlass in one window and 8 in another ; how many panes in both windows ? 6. Francis had 2r> cents and liis uncle gave him 5 more ; how many cents had Francis then ? 7. Albert took 1 4 roses from a bush, and Mary took j !• from the same bush ; how many roses were takeu I from the bush ? 8. If John say (34 words in a minute, and Thomas 18, how many words will both say in a minute? 9. Thomas plucked 47 plums from a tree, and picked off the ground ; how many plums had Thomas ? 10. In a company there are 50 private soldiers, I and (i officers ; how many men in the company ? 11. How many cents must I pay for a pound of butter worth 3G cents, and a pound of cheese worth 1 9 cents ? 12. llobert having 05 marbles, won 8; how many I had he then ? 13. There arc 19 books on a shelf and 6 on a table ; I iiow many books in all ? 14. During a recitation 25 queslions were an^ Bwered correctly, and 8 incorrectly ; how many ques- jtions were asked ? 15. Aleicander is 3(1 years old, and Jacob is 9 years roJder ; how old is Jacob ? IG. During a game of base-ball, one side made IG runs, and the other five ; liowmany runs were made I by both sides V 17. In the park 45 boys were plnyin^ ball and 1 fwere playing leap-frog; how many boys were en- gaged 111 both games '^ (, 14 n- I 82 ADDITION iRWl,-,! '"'"""""I' '""».»» .0.1. JIJ Ac 63 10 id; 42 25 57 30 54 45 39 60 2i 75 57 11 31 26 68 31 48 56 47 61 18 86 46 32 2!) 27 7!) 42 32 57 38 62 38 87 35 13 92 38 81 43 29 58 47 73 59 98 24 24 80 . 89 72 44 38 59 66 74 62 99 82 41 07 14 19 93 27 86 45 63 54 75 ADDITION. 3, and 9o cents for )r both ? ^•^igo., and 38 milos its, and sold it for vv many cents did S3 39 2i 00 75 47 . 18 61 80 38 38 62 87 47 50 73 98 66 71 02 99 45 G3 5t 75 IX Find Ihe sum of 10 and 10 U4 and 10 132 ami 47 25andll 24aiid30 25and27 ...„uo4 J^ and 13 T3and38 02and37 07and58 J 2 and 27 -^ - ' 14 and 40 ';fandl2l39and32!04and48!88andI5 4/ and 10 J^5and27 49and50 12and03 ^^^^iind39|92andl8 70 and 54 nand57 17and92 44and03 87 and 32 19 and 91 80 and 57 ;:!!:;:J!fi!^»"^^^"-i2«i2«a;;a;;; 28 and 21 30 and 33 £7 and 12 80 and 40 47 and 52 77 and 07 -2and2o Iand27 29and34 .....,, 83 and 4 J 47 and 08 50 and 33 54 and 98 44 and 07 1 01 and 92 1 10 and 10 I 07 and 99 X. 1. William has 54 cents and James has 43- how much money have both ? ' ^ 2. A farmer havino- 47 /in/^l-c u i i .^ how many auofa,,i|ht\f,:tnr''' '«■"-; ■^U\onZ T7 t""'' "'"' "^*' *■"■ =' '^''"Wl worth -7 do la,.s, and ,, divss worth 45 doUar.s '' 6 Purchased two tu],s of butter iho hv * *-»i"S- 03 pounds, and the smalW 5 j ' f ' T'^" --'h butter dKl I purchase ?' '"""'^ ' ^^^^' 7. A real estate agent sold two lots containino- on^ 83 acres, and ihe othr^r j 1 • 1 "lauuiio^ one, sell '^ '' ^ * ' ^'^^^ ^"^^»y a^'res did he 34 ADDITION. 9. In a school consistiiiR of two oIn<,<.„. ti. > « i class has 42 p„pik, and *he secrd VT hoi ' Pnpils in the school '^ ""ona 71 , how many bo'i'oitXnrr''^^'-'^''^''^'''''--''' »■'"'>« 11. Jeae's library contains 8r, books, and Charles'. 2. how many books in bolh libraries ? were received by both ? ^ ^^^ IG. How much money will be ronm-r..^ + i. a hat worth 65 cents a/d a ba^^Z^O '^I^" 17. Andrew bought a pair of skates for 95 eonfs and sold them so as to gain IC cents ; what w^ h^ celling price ? vv"<^ii was nis 18. February has 28 days and M-iivfi qi i days in both months? ""^ ^^'^^^^ 31. how many 19. A tailor sold 4G yards of cloth to ^VTr Q ui. «.oMr.W;howmanyytd::f";,,^:^ lines has he to write ? " ^ ' ^'"""^ "^^"7 ■i-j classes, the first ^1 ; how many how old will ho v's, and Charles's ies? ^ for arithmetic ny good points Ivanced Reader, how much did neck-ties, and class ? . one class re- V m.any credits fed to purchase 80 cents ? for 95 cents, what was his 31, how many o Mr. Si^Ath of cloth did ADDITION. 35 25 lines im- • ; howiiiuiiy OPERATION OF ADDITION ^u™r"J::i::'';;i!^---^'^T5,854,and.oo. 854 wo hogin at f|,o ri.,, . ' '""" '°''"""' (JOt; atdy. Tl, s ' 'r '■"''' ''''^' ^""""" ^^P'"- — - and .0 „ s ,^," ,' 'T """ ' """^^ '^ "^ »"'^« ^ .0.5 -'-• - Ho;:;;;; rr w:^;r ;;'"^'* ^^^ "- ' ^eu wl,id. .0 car ," , 'unrJ"7 ''^ '^"^ ^^^"""'""^ -*'" ■«'"' '^ lens, is iOtons, an 5 is " r 7" '"" ^"" °' ' '"^^ l""«; t'-alis, 2 l,undro,ls and 2 f n W v ' '"Z' ' ^'"^ ''' ^ '"'"nH.oflons, we carry 11,02 1.,, '"^ "'' ^ ^«"^ '" "'« ''-tis.2t,,ousandslnd trr^^^^ -t 'lown Iho entire s„m. Tl, n ',., V'o! " ^ ? '''' -'"-" we '/""■od sum, because it is the 'um n i "' ^''"''''''''^' ^''^ '^- "'•l''e given nuuWs '"'''"•'"'" ^^^^''^ »"'t-S tons, and hundreds 412 348- (5.) 542 feet. 717 " 203 !*71 <( 12087 (7.) 278 pounds. 24'8fcet. 1314 d„y,. U 2293 pounds. IiVTmn. Ti •'"■ -^-1^^ pounds. ^- 3t;J^liS;;^i:;;-;i|^'^^Jo.umn oniguros should be ab- ;'mp)e r,, the pupil should "a^^nl3^T,^ 'I'P- '^''"^' ^" e'^" 8(5 A D 1) I T I () N . 1 1 7t'/ TTEX EXERCISER. Adtl the fjllowinir : 1. Tliroo Imiidrod uinoty ; eight huiKlred thirty- six ; throe hundred tweiity-.six ; and two hundred ""^^ Am. nCl. 2. Tlire.> thousand, forty-eight , one thousand, four hundred eighteen ; one thousand, two hundred fifty- two ; and one thousand, nine luuidred ninety-one. Ahs. 7700. 8. Eight hundred two ; two hundred seventy-two ; tw^o hundred sixteen ; and five hundred thirty-nine! Am. ISiiO 4. Six hundred ten ; one thousand, seven hundred thirty-six ; four thousand, eight hundred ninety-se- ven ; seven hundred one ; eight hundred thirty- three ; and seven hundred ninety-six. An^i. 0573. 5. One thousand, two hundred tw^o; five thousand live hundred five; six liundred seventy-eight; tw^o thousand, fifty-on(,' ; and one thousand, three hun- dred thirty-nine Am. 10775. 6. Two thousand, three hundred sixty-seven ; eight hundred seven; five hundred twenty-four; and three thousand, one hundred seventy. Am. G8G8. 7. Four thousand, five hundred seventy-eight; nine huiulred sixty-one ; five hundred seventy-tw^o; and three hundred sixty-three. Am. 6474 8. One thousaiul, three hundred nine ; four thous and, three hundred twenty-nine ; one thousand, two hundred sixty-five ; three hundred eight ; and four hundred twenty-six. Am. \ 337. 9. Eight hundred ; four thousand, one hundred ADDITION luli'od thirty- two hundred Ans. 11GL housand, four luiidrod fifty- L ninety-one. Ahs. 7709. soventy-two ; d thirty-nine. Ans. 1S20 'ven hundred ed ninety-se- idred thirty- Ans. or) 73. ive thouso,nd ^-eig-ht; two , three hun- Ans. 10775. sixty-seven ; twenty-four ; y. Ahs. G8G8. venty-eij^ht ; leventy-two; Ans. 6474. ; four thous ousand, two it ; and four Am. \337. ne hundred eigrhty-three ; two thousand, one h three hundred twenfv 37 10. 11. 12. 13. 14. 15. 10. 17. 18. 19 20, 17G 674 71.-) 33i5 643 496 1015 5434 3287 4906 7603 21. 2004 (22.) 3416 8743 2655 14814 (26.) 96327 86438 69476 (39.) 333355 766988 544375 und red sixty-four; nnd eight hundred five. jj Ah.^. 827e. 302 523 672 856 129 257 8037 2305 4662 879 46 5087 490. 241. 805. 274. 576. 490. 6191. 1140. 9315. 3402 709. 603. Ilf. (23.) 7422 8674 9830 25926 (27.) 37951 98029 96746 ^31.) 45706 847687 (24.) 6089 7906 4078 (28.) 56789 37454 15079 (32.) 509234 767448 189979 Atfs. A//S. Ans. Ans Ans. Am;. Ans. Ans. Ans. Ans. Ans. Ans. (25./ 6780 3007 5944 (29.) 99777 55444 (OO.) 76815 274867 537967 968. 1438. 21!)2. 1465. 1348. 1243. 15273. 8879. 17264. 9187. 8358. 7694. 3g ADDITION. IV. 34. Three hundred sixty-five thousand, four hun- dred sixty-two; five hundred sixty thousand, four hundred twenty-seven ; four hundred five thousand, seven hundred sixty-three ; one hundred thirty-six thousand, one hundred sixty-six. A?is. 1467818. 35. Three hundred twenty; four hundred fourteen thousand, five hundred ninety ; and eight hundred seventy. Ans. 4151S0. 86. Two thousand, five hundred thirty-seven ; nine thousand, three hundred eighty-one : six hundred sixty-eight ; nine hundred ; and fifty-nine thousand, seven hundred forty-four. Ans. 23230. 87. Seven hundred three ; one thousand, five hun- dred ninety; one hundred twenty; eight hundred thousand, sixty-six ; and three thousand, seven hun- dred seventy-seven. 38. Two hundred ten thousand, three hundred eight ; twenty-eight thousand, seven hundred fifty- six ; three thousand, one hundred forty-two; and thirteen thousand, seven hundred fifty. 39. One hundred nineteen thousand, ninety-four ; two hundred fifty-five thousand, two hundred seven- teen ; three hundred thousand, sixty-five ; and sixty- eight thousand, six hundred. Ans. 946580. 40. Sixty-four thousand, four hundred sixty-seven ; one thousand, five hundred twenty ; seven thou- sand, nine hundred thirty-six; thirteen thousand, seven hundred forty-four ; nine thousand, nine hun- dred fifty-five ; and eleven thousand, eight hundred twenty- two. (42.) (43.) (44. 37 78 68 12 35 14 92 29 71 62 57 (51.) 91 65 42 39 11 13 (59.) 231 462 563 492 (65.) 893 491 682 963 421 506 - 30 34 79 57 (52.) 14 17 36 48 57 36 (53.) 93 12 49 67 82 91 (60.) 896 431 567 624 (66.) 321 402 913 806 201 497 ADDITION. V. (45.) (46.) (47.) (48.) (49 68 79 51 70 29 68 36 92 14 55 72 41 32 93 45 12 68 31 72 19 39 12 77 85 56 89 50.) 21 ) 49 98 87 (54.) 63 47 93 25 12 49 (61.) 729 820 926 409 (55.) 38 48 72 96 57 43 (1^6.) 36 72 46 35 20 93 (67.) 482 371 206 431 502 739 (57.) (58.) 87 79 36 45 32 24 92 (62.) 302 921 426 526 (63.) 429 602 391 402 (68.) 803 413 516 796 385 402 63 45 33 29 64 (64.) 365 893 943 627 (69.) 234 964 757 813 405 691 -i^J ADDITI ON. (70.) .(71.) (72.) (73.) (74.) 205 910 749 102. 482 431 796 322 893 396 304 804 416 421 410 276 510 702 605 516 153 312 512 734 503 421 406 614 896 912 089 527 •735 431 431 (75.) (76.) (77.) (78. 4321 6-93 5002 7893 5078 405 3015 4821 3134 7931 6912 5632 50G3 3144 7896 345 2093 5689 4004 21 7215 3965 7965 4002 2653 £01 4689 3112 203 6009 398 705 5035 3965 4590 3456 UNITED STATES CURRENCY. 41. The Si}rn, $, written before a nnmbor signifies do//ars. Thus, the expression $120 is road one hundred twenti/ dollars. 42. DoUars and cents may bo written together, the ccnis being separated from the dollars by a point. Thus, the expression, $25.35 is read 25 dollars and 35 cents. ADD I 'J" J ( ) N . 41 Ilxpio.s l.ypropor s.-ns niul fi-nivs. Il.o Tollovvin- , ^, , /■:.\ /'-'/>'( 'I s/-:s. ° 1. N'v<-n (i.'llius mid Iwvniy-ihuvvvuis. 2. Sixlccii (lolkirs iind I'orly cdiIn. ^. yoviy-swrn dollms aud'sixty-lluvo roiit«. ^. AiiH>ty-,ni,c dollars niul lourlvon conts. T). ]*.mh!y-s('vcii c'nls. 3.10, and $0.40 ? OPERATION. $10.27 123.00 o 206.90 3.10 0.40 $343.79 Soi.rnoN.-IIaving arranged llienumbors accor.l- H.g to Art. 4,lw.ad,!tl,Pmhy the principles of •■^inii)]*! addition. Tlio sr in li paratinjr point is f)lacH(l numijors 'orosiiliimmodiulHj- under those of tho given 42 A p 1) I T nj N . Ill the same maiiiuT add llie following: (2.) • (3.) (4.) !8;S1.05 1217.75 I78..50 54.02 83.10 151.03 125.84 55.32 90.18 370.(;2 13507 1203 !i!032.13 (5.) (G.) H) $05.14 175.15 !ii!2245.70 91.73 207.45 791.18 182.04 1241.10 33.87 79.30 7907 0.75 20.37 34.81 050.37 11038.24 (8.) (9.) (lo: 15838.24 11840.25 I370C8.75 0183 42 30000.00 6000.00 981.3 I 4700.50 8337.25 89.05 373.33 840.16 320.10 870.45 73.82 4823.03 1950.55 10950.03 $58810.01 11. Find the sum of $75.85 ; $16.05 ; $123.25 ; $475.00 ; $325.50 ; $110M6. 12. Find the sum of $3284.03 ; $87.24 ; $1325.55 ; $1806.10 13. Add $26.45 ; $33.80 ; $70.67 ; $8.70 ; and $63.73. 14. Add $135.10; $0.17; $1.67; $1800.00; $3.60; md $867.25. ADDITION. 43 |H3o, toafor$10.5; InUtor for$l7.10; cheese for $5.70 ; and egg. for $m. What was the amount of his purchases ? , .^, ' 10. A owes 1137,75 to B; .^207.25 to C; $0r>0.00 to D : and MUO to E ; what is his indebtedness V 17. A lady purchased a dress for |27.G0 • a shiwl for 114.75 ; a bonnet for $(3,50; a pair of glovel'for $l.1o , and handkerchiefs for 90 cenls ; how much money did she expend ? Au^m^Q .,lf,fl- ^^^^^^»«.bought a house for $3810.00; paid §^Ir. WIUTTEX AA /■:/,'('/ SKS. (I.) 4i; 27 82 50 9i> 13 07 48 24 (18 52 n7 21 18 75 Ol) 37 12 (4.) !»2 35 24 11 13 (10.) 53 4(1 02 38 84 75 00 (11.) 30 87 12 50 73 (50 (12.) 84 47 30 00 21 10 70 47 03 45 no (13.) ■Id 13 04 21 37 48 (0.) 83 20 88 03 23 (14.) 70 20 18 32 47 53 01 (7.) 40 55 111 72 45 (!•'">■) 02 15 20 08 72 82 (8.) 82 41 8J) 20 73 (IG.) 13 93 00 GO 18 22 87 (17.) (18.) (10.) (20.) (21.) (22.) 214 182 831 231 031 003 477 1 03 (102 003 804 (153 750 022 510 701 411 500 872 502 508 r.ix; 201 roo 410 001 384 243 ix'J .71 785 417 700 832 i<»7 10<) 802 103 402 714 572 831 382 405 o 17 203 (lO « 'ad 031 400 317 508 704 (23.) (24.) (25.) (20.) (27.) (28.) 4'2 837 043 032 050 300 408 191 782 401 810 431 184 756 411 032 345 709 279 83.') (8.) 82 41 8!) 20 73 (1G.) 13 98 22 CO 18 22 87 (21'.) 8I>12 7or)i; 28!>8 1702 410l> (34.) 0132 421G >842 7720 8054 0328 1217 5(580 (30.) 04781 04075 70807 84518 30572 04784 43002 14840 30047 28034 3005 2138 4700 0023 8107 (35.) 4502 3054 1804 0407 5074 3102 1804 5287 ADDITION. (81.) 1045 3023 780 4 5231 2100 (40.) 38303 07084 37400 5 i507 02841 01950 80372 50841 61130 00 110 (30.) 0480 2447 5810 1234 9768 3521 7023 4210 (82.) 7432 5031 8470 0401 7108 (37.) 2345 £081 7108 5043 2731 1852 2040 1508 (41.) 20301 80734 50032 30:i7 400S2 50721 24002 00831 44765 ol3(34 45 (33.) 1000 4082 3875 4023 0742 (38.) 0784 4050 3027 5273 1450 2180 1355 0701 {42.) 80320 7201 ^. 40005 81707 34502 03140 00825 42023 18704 50348 SUBTRACTION. -:o: 43. Subtraction is the process of finding the difTerence between two numbers. SUBTRACTION TABLE. from any number leaves tliat number; thus, from 1 loaves I • from 2 leaves »', elc. 1 FROM 1 leaves 2 leaves 1 3 leaves 2 4 leaves 3 5 leaves 4 G leaves 5 7 leaves 6 8 leaves 7 9 leaves 8 10 leaves 9 2 FROM 2 leave 3 leave 1 4 leave 2 5 leave 3 6 leave 4 Y leave 5 8 leave 6 loa.v« t 10 leave 8 11 leave 9 3 FROM 3 leave 4 leave 1 5 leave 2 C leave 3 *7 leave 4 8 leave 5 9 leave G 10 leave 7 11 leave 8 12 leave ^ SUBTRACTION. 41 4 FROM 4 leave 5 leave 1 6 leave 2 7 leave 3 8 leave 4 9 leave 5 10 leave G 11 leave ^ 12 leave 8 13 leave 9 5 FROM 5 leave 6 leave 1 1 leave 2 8 leave 3 9 leave 4 10 leave ^ 11 leave 6 12 leave 1 13 leave 8 14 leave 9 G FROM G leave 7 leave 1 8 leave 2 9 leave 3 10 leave 4 11 leave 5 12 leave 6 13 leave 7 14 leave 8 15 leave 9 ding- the t loaves I ; ^ROM 'ave 'ave 1 ave 2 ave 3 ave 4 ave 5 ave G ave 7 ave 8 ave ^ 7 FROM 7 leave 8 leave 1 9 leave 2 10 leave 3 11 leave 4 12 leave 5 13 leave 6 14 leave 7 15 leave 8 IG leaA'^e 9 8 FROM 8 leave 9 leave 1 10 leave 2 11 leave 3 12 leave 4 13 leave 5 14 leave 6 15 leave 7 16 leave 8 17 leave 9 9 FROM 9 leave 10 leave 1 H leave 2 1 2 leave 3 13 leave 4 14 leave 5 15 leave G IG leave 7 17 leave 8 18 leave 9 48 SUBTRACTION. OJtAL E.YERCISE8, I. "What remains after takinjr 6 from Y ? 1 from 8 ? 1 from 9 ? 4 from 7 ? 5 from 5 J 3 from 8 ? 1 from 1 ? from 3 ? 2 from 2 ? 1 from 4 ? f) from 1 ? 5 from 7 ? 2 from 6 ? 3 from 7 ? 3 from 8 ? i from 9 ? 4 from 5 ? 7 from 9 ? 1 from G ? 8 from 9 ? 1 from 2 ? 2 from 4 ? 8 from 8 ? from 7 ? 2 from 7 ? from 8 ? 2 from 8 ? 6 from 9 ? 7 from 8 ? 5 from 8 ? *7 from 7 ? 3 from 6 ? 1 from 7 ? 2 from 5 ? 3 from 4 ? 4 from 6 ? 1 from 5 ? from 9 ? 3 from 5 ? 4 from 8 ? 2 from 3 ? 9 from 9 ? 5 from 6 ? 5 from 9 ? 6 from G ? 8 from 9 ? from 2 ? from ? from 6 ? 2 from 9 ? II. 15 7=? 15—8= ? 17—8= ? 18—8= ? 15-3 ? 10 8- ? 11—2- ? 14—7- ? 13 9_? 12—9= ? 12 3=-? 17—9- ? 11 Q=l 12—8= ? 11 1 ? 13— C= ? 13—5= ? 10—2= ? 14—2= ? 18 3 ? 10 9=? 10 6=? 16—7- ? 16—6= ? 11—3= ? 14—6- ? 12—5- ? 14 8=? 14—3= ? 18 7 ? 12 7-? 16 9-? 12 8 ? 17—6= ? 14—4=;? 13 4=? 11 8=? 18 5-? 16 2 ? 13—2= ? 11 0-? 15 9=? 16 4=? 17 9=? 15—4- ? 13—9=? 10—1- ? 17—5= ? 18—3= ? 16—8=5 ? ( SUBTRACTION. 49 5 from 5 '? 1 from 4 ? 3 from 8 ? 8 from 9 ? 2 from 1 ? 5 from 8 ? 3 from 4 ? 4 from 8 ? 6 from G ? 2 from 9 ? 8+4—5=.? 9 + 2—6^-:? •7+7—5-=? 8+6—3.=? 9+8—6=? 5+4—2=? 8+8—9=? 3 + 9—1=:? 14+4~9=? 16 I 2—7=? 13+3—1=? 12-f5— 4=? 15+0—8=? 9+9—6=? 16+1— 7, ? 11+3—5=? III. 6—4+ 1^? 16—3+ 7=? 14—9+ 3=^? 9—8+ 6=? 11- 10+4—8=? 7+9— 6 =? 1 12+4— 'v^? 10— (3+5)=? 18-(7— 2)=? 9— (4+3)=? 15— (6-1)=^? 3+ 9=? 13— (7-j-2)=? 7—4+ 6=? 15—5 + 18=? 16—9+10=? 14—4+ 3=? 9—6+12=? 14— (5 + 4)=? 16-? =.. 9 10—? =,. 6 13_? == >j 18—? =11 15—3= ? 12—9= ? 11—1= ? 18—3= ? 11—3= ? 18—7= ? 14—4=;? 13—2= ? 15—4= ? 16-8= ? IV. 76!"?!^''^ ^■'"' '' ^^'-^''^'^; 46, 56; 66; ^^2. S^ubtract 4 from 14 ; 44 ; 24 ; 94 ; 84 ; 61 ; 54 ; 3. Subtract 7 from 13; 33 ; 23; 43 ; 14 ; 24 • 64- 74. ' ' 4. Subtract 9 from 18 ; 28 ; 78 ; 97 • 67 • 15 • 7^, • 85; 12; 62; 42. '> ^^, li>, 7o, 5. Subtract by threes from 29 to 2. 6. Subtract by sixes from 45 to 3. 7. Subtract by eights from 79 to 15. 8. Subtract by twos from 63 to 1 9. Count by fives from 6 to ^6 and back a.o...„-„ 10. Count by sevens from 9 to 72 and back^again 11. Subtract by 9's from 100 to 1. ' ^ 12. Subtract by 4's from 83 to 7. 50 S U U T K A C T I O N. V. - ]. Margaret >ought 7 cakes, and eat 4; how many had she remaining- ? Solution,— ir Margaret bouglit 7 cakes and eat 4 of tlioiii, she must have remaining tlie clilTerence between 7 caltes and 4 cakM«, wiiich is 3 cakes. Therefore, if Margaret bouglit 7 cakes and eat 4 of them, she has 3 cakes remaining. 2. George picked G quarts of strawberries find William 4 ; how many more quarts did Creorge pick th:m William? 3. A boy had cents and spent 3 for fire-crackers how many cents had he left ? 4. Albert caught T butterflies, but 2 got away how many had he then ? 5. Jane bought live oranges and gave away 2 how many had she for herself? 6. Henry sold for 1 cents a kite that cost him 5 cents ; how many cents did he gain ? I. Charles rises at G o'clock and studies till 8 ; how many hours does he employ in study ? 8. You have 8 fingers on both hands. Close 3 am' tell me how many remain open. 9. If I borrow $12 and pay back $5, how much do 1 still owe? 10. A boy had IG rabbits, 1 of which were killed by a dog. How many rabbits has he left ? II. Mr. Brown purchased $G worth of provisions, and gave the clerk a |10 bill ; how much change did he receive ? 12. In a class of f>5 boys, 9 were detained for bad conduct ; how many were dismissed ? SUBTR/ CTION, 51 i/ 'f!'''^"^^ ' ^ow many wore saved ? July ? "^'"^^ '^^^''^ '"^"^ ^^^^ ^^h to the 27th of 15. I bought a harness worth $22, and paid S'i on It ; how much do I still owe ? ^ ^ IC^ In a company of soIdi<>rs there wore 78 men Ot those f) were Icillr^l nn,i t t , were fit for duty ? ' "'"' ' ''"'""^'''^ ' '^"^"'any 17. Abel is 8 years of 'in-,, tt pass before he i.s\T;„lf ' """ '""'^ ^^^'^ ^'" There torfstTt''' ' """" '""'■^ '^an boys, incro w eie b7 girls ; how many boys 'i fhem ■Ifn"' "":"'' '' '""^ °' ''"5' »»'! -M « of 'ntm , how many tons remain ' 20 There were 16 persons in an omnibus After ;.^t^o.U...n.^3,ot in, how many persons w.eret^^ 21. In a ring there were ]0 marbles. James shot •.way C, and Edward 2 ; how many remained Inthl 22. Ri,hard had 21 marbles. He won 16 and lost ' ■ how many had he (hen ? 23 William had 1 cent and his unele s^ave him 8 nore. How mu,). does he still want to pureh sT a pair of skates worth TO cents " 24. There wei. 8« peaches on a tree. The wind "itw OH o ; how man^' - i tree ? 91^ ly ponchos re mained on the n arithmetic is worth 70 cents, and a si worth 8 cents. What is the dim ate is orence of their prices? 52 SUBTRACTION. 26. James had 17 oranges. He gave 4 to Mary, 5 to Esther, and sold the rest ; how many did he sell? 27. Oliver had 15 lines to v^rrite from his history. He wrote 4 on Monday, and the same number on Tuesday ; how many had he still to write ? 28. James is 14 years old, Emma 4 years older, and Jessie 7 years younger than Emma ; how old arc Emma and Jessie ? 29. 18 boys were going to have a swim ; 3 stopped to hear a hand organ, and 5 ran to a fire. How many went to swim ? 30. What is the difference between 16+11 and 2+8? V. From 20 From 47 From 69 From 74 From 63 From 15 From 37 From 99 From 86 From 28 From 74 From 27 From 83 take 15 take 21 take 36 take 23 take 31 take 11 take 16 take 63 take 74 take 21 take 25 take 19 take 57 From 87 From 43 From 62 From 39 From 38 From 95 From 37 From 46 From 73 From 92 From 54 From 38 From 70 take 36 take 29 take 47 fake 29 take ?9 tabe 46 take 35 take 38 take 66 take 78 take 48 take 36 take 16 From 84 From 56 From 97 Frojn 42 From 22 From 31 From 64 From 91 From 72 From 88 From 69 From 90 From 81 take 69 take e7 take 89 take 26 take 18 take 29 take 17 take 36 take 49 take 67 take 58 take 26 take 37 VII. 1. Martin had 25 cents, and spent 15 cents for a lunch ; how many cents had he left ? SUBTRACTION. 53 2. From a flock of 87 sheep a farmer sold 26 ♦ how many had he remaining ? ' 3. Purchased p watch for $47, and sold it for $34 How much did . lose ? * if' wu^'' ^' ^'^'' ^^^' ^^^^ his father 58 years old What IS the difference of their an-es^ ^ 5. A geog-raphy is worth 70 cents, and a small grammar 36 cents ; how much moro i<\hn t ,, ,, ,, ' ""^*^ ^"^^i more IS the ffeosrranhv worth than the grammar ? ° o^dpny 6. In the last examination James had 75 per cent and Henry 38 per cent. What per cent, had James more than Henry ? ^^® 7. A person spent 37 cents in a store. What change did he receive if he gave a 50 cent piece r 8 Joseph ran 84 rods and William 56 ; how much further did Joseph run than William ^ o.ymucn 9. The sum of two numbers is 75, and one of them IS 25. What is the other ^^ more than i cost ; what was the cost price ? 12 John has 63 cents. If he spend i cents for marbles, 25 cents for a ball, and 5 cents itr p Its how many cents will he have Mi ? 13. A tree 58 feet high was broken off 46 ft. from the top. How high is the remaining piece '^ 14. A foreman receives $80 a month. He pays f f ' *'^'^"'^' ^^^ ^"^ provisions, $3 for a pair of shoes, and $14 for sundry affairs ; how much ha he remaining ? Iwo 110 bills. She spent #3 for ribbons, $6 for vel- f)4 SUBTRACTION. vet $1 for Silk, and |2 for linin^r. How many dollars and she remainging? 16. A farmer having 04 sheep, sold 11 of them to A, 36 to 13, and the remainder to C. How many did C receive ? n. IG. pupils were promoted from a class of 75 ; and on the same- day 11 were received into the class • how many pupils were then in the lass ? ^ 18. John had 26 cents, and his mother gave him 82. Ho then lost 17 ; how many cents had he left ? ^19. Sold a sled worth 87 cents for a penknife, and 15 cents ; what was the penknife w^orth ? 20. Mr. White had .$93 in bank. He took out $87 on Monday ; and put in $26 the .sai >e afternoon. On Tuesday he took out $16 ; how much has he now in bank ? VIII. 1. To 5 add 7 ; subtract 6 ; add 4 ; subtract 9 • add 11 ; subtract 3 ; add 4 ; add 12 ; subtract 15 ; add •> • what is the result ? 2. 7— 2f5— H-9— G^-l2^-l— 5 + 20— 37 = ? 3. 3+17-lH- 37-64-2-1-.- -25 + 7-30..'^ 4. 18—12+4-10+1—1+0-3+7-? 5. 3-1 7-4+5— 1 + 10— 6 + 2-8+1— 3-G- '^ 6. 3-2+8—8+6+3-2+10—6—7+4.-? 7. 17H 8— 6+10— 8— 3+74— 6:-? 8. 47+7+10-25+5-6-4+3-13-7+4-fo , 9. 38— 1+3-30+17+3-10+2— 7 + 1-4-? 10. 67—8+1-50+47-6+7-8+32-2+3-'? 11. 46—26+17+7-8+3-16+2=? 12. 18+7—5+32-6+7-2-8+16-7+23=? SUBTRACTION. OPERATION OP SUBTRACTION OPERATION. Minuend, 837 Subtrahend, 564 order shall stand m the same column Bo- . f "":7 «l «f'e right, we see that 4 unit; f,o,n Remainder, 273 L'l"f '' c""'''' ^'"«'' ^^« ^^^'i« '" .ho from 3 tens, ^ve add 1 hun. red oriot""'.' 'T ''""'' ''« ''^''"'' tens. Now, G tons from ,3 '^s leave 7^ ' ' '""'' '"'^'^'"^ '^ "^r t'.e tens. To compensat for the ,0 '"''" '"""' '"' ^'"''^ ""* to the minuend, we dimin, Mhe « h . ."'' "' ' '"'"^''^"^ ^^"^'J •^> "undreds taken from 7 ^^ d ^jt^^rf^ ^J^ ' ^-"-". Then ton under hundreds ^^^ ^ J'undreds, which is writ- responding P.HS or .b/:;;;':': ^Pri!;:!;;'",?;;"'' '■'" "■"- Illustrations. From 5786 5«tri'7o„i take 3428 qq *7qp j iS">^-'J.o4 yd 736 yds. 2074.18 RemaindT. 2308 493 937 yds. 3746.36 Prool', 5736 '■^«*7 «^o i ^ " o8< 673 yds. $5820.54. WRITTEN EXERCISES 1. 8: ^. 6. 634—231. •748—523. 542—132. 627—221. 876-525- -^ns. 403. -4^5. 225. Am. 410. ^«.='' ^'""'ff- Bhould 15 A ,„erc.,.a„t i„ one d V ' , , ^"''- *'*'«^- Wlmt „.„. l,i.s 1,.,^, ■„, ™ V "'^«'- o-""! »».).XHO. '«■ How much m„V, "'«• «2M1.00. it «I000 y '""" ''" '"•<»« '" «'!7; 38 to u.ake n. A man with iinnnn , . '^"■'•'- S324.(J2. f ods b„.ine.s, pa,, .r C73t T""'; "' »"•' '''T *-"-^ ^"' the ,„odi ?a;r h '::h't;'s'-! 18. If a man receives 41/,n no '^'"■' «'''-'9-25. «32 1-c.r provision,, « /vf ■!,." Vn''"""""' ■•""' ""J'^ bo able to save each mLth ' ' '""' ""''' ""' ^e 19- A farmer sold h.v for *„• ,. '^'"- *^'-^'^- 20. An auctioneer reeeived Tn.. •. '^'''- ^^^■^^• of ^7864, which he ai c o, . 1 a"'" *^ ^^' ^'^i"« on the furniture v ^^^^' ' '''^^^ was the loss ''' ^ ' lo-ht a nair nf 1 . '^''^- ^243.25 '&"i- a pan ot horses for " ' for #60.50, and a <^arria.' for both horses and haj the carriage "? ^ .. 20, a harness i- for ^300 less than I paid "OSS ; what was the cost of Ans. $380.50 . 60* SUBTRACT ION, WRITTEN EXERCISES. X I (1.) (2.) (3.) (4.) (5.) (6.) (7.) (8.) 93 47 82 51 67 89 21 50 86 32 70 49 52 28 19 42 (0.) (10.) (11.) (12.) (13) (14.) 946 423 482 703 681 732 817 206 379 486 397 489 (15.) (16.) (17.) (18.) (19.) 3841 4928 9238 7678 87:8 19'74 2396 5373 6723 5921 V (20.) (21.) (22.) (23.) 47206 80129 79345 20001 39135 £6547 45678 19245 (24.) (25.) (26.) (2t.) 8965 34527 57932 49345 492 10968 9682 30921 (28.) (29.) (30.) (31.) 72145 30924 70093 64983 9062 8921 19027 35897 4 SUBTRAC TION • 32. 493 387. Ans 106 33. 4061—289. Ans 3772 (8.) 34. 537 29. Ans 508 50 85. 601—482. Am 119 42 36. 8971 896. Am 3075 37. 4008 3196. 38. 2134 97. Am 812 (14.) 732 39. 493 281. 40. 175 26. 489 41. 832-746. 42. 201-156. 43. 824—357. (19.) 87:8 5921 44. 923—868. 45. 1002—491. 46. 796 485. 47. S71— 296. 48. 4321 3924. (23.) 20001 49. 862—674. 50. 502—209. 19245 51. 738 21. 52. 892—406. 53. 56892—7964. (27.) 54. 5394—4096. 49345 5o. 792—485. 30921 bQ. 6931—5076. 57. 392—289. 58. 702—498. (31.) 59. 2020—1965. 64983 60. 70065—3962. 35897 61. 8434—7908. 62, 456-390, ei MULTIPLICATION. i I ! 44. Multiplication is the process of taking one number as many times as there are tiiiits in another. Multiplication Table. Once is ; twice is ; taicen any nunibor of times is 0. times 1 is ; limes 2 is ; limes Any niinrb.'r is 0. ONCE 1 is 2 are 3 are 4 are 5 are are 7 are 8 are 9 are 10 arc 10 11 are 11 12 are 12 1 3 4 5 G 1 8 9 4 6 8 TWICE 1 is 2 2 are 3 are 4 are 5 aro 10 6 are 12 1 are 14 8 are 16 9 are 18 10 are 20 Hare 22 12 are 24 3 TIMES 1 is 3 2 are 6 3 are 9 4 are 12 5 are 15 « are 18 1 are 21 8 are 24 9 are 21 10 are 30 11 are 83 12 are 36 4 TIMES 1 is 4 2 are 8 3 are 12 4 are 16 5 are 20 6 are 24 7 are 28 8 are 32 9 are 36 10 arc 40 11 are 44 12 are 48 1 1 li 1 2 3 4 5 6 7 8 9 10 111 12 J king one 1 another. 5 TIME,3 1 is 5 2 are 10 3 are 15 4 are 20 !> are 25 are 30 7 are 35 8 are 40 9 are 45 10 are 50 11 are 55 12 are (10 ^ULTIPtlCATlON. 6 TIMES 1 is G 2 are 1 2 3 are 18 4 are 24 5 are SO fi are 3C *7 are 42 8 are 48 ^ are 54 10 are 00 1 1 are GG 12 are 72 7 TIMES 1 is 7 2 are 14 3 are 21 4 are 28 5 are 35 G are 42 7 are 49 8 are 50 are 03 10 are 70 11 are 77 12 are 84 I 63 8 TIMES 1 is 8 2 are 16 3 are 24 4 are 32 5 are 40 are 48 7 are 56 8 are C4 9 are 72 10 are 80 11 are 88 12 are 06 mos is 0. 4 TIMES 1 is 4 2 are 8 3 are 12 4 are 16 5 are 20 6 are 24 7 are 28 8 are 32 9 are 36 10 arc 40 11 are 44 12 are 48 TIMES 1 is 2 are 3 are 4 are 5 are 6 are 7 are 8 are are 10 are 11 are 18 27 36 45 54 63 72 81 90 99 12 are 108 10 TIMES 1 is 10 2 are 3 are 4 are 5 are 6 are 7 are 8 are 9 are 10 are 100 |11 are 110 12 are 120 20 30 40 50 60 70 80 00 11 ^^MES 1 is 11 2 are 3 are 4 are 5 are 6 art* 7 are 8 are are 10 arc 110 11 are 121 12 are 132 22 33 44 55 GG 77 88 00 12 TIMES 1 is 12 2 are 24 3 are 36 4 are 48 5 are 60 6 are 72 7 are 84 8 are 96 9 are 108 10 arc 120 11 are 132 12 are 144 *' 64 MULTIPLICATION. ORAL EXERCISES. How man 3 times 9 ? 2 times Y ? 5 times G ? 6 times 8 ? 9 times 9 ? 2 times 1 ? 9 times 7 ? 8 times 5 ? 2 times 2 ? 3 times 4 ? y are 2 times 9 ? 7 ^ imes 4 ? 9 times G V 8 limes S ? 5 times 1 ? 2 times 4 ? 4 times 9 ? G times 7 '^ 3 times S ? 7 times 5 ? I. 3 times 2 '? 2 tfmes 6 ? 8 times 3 V 8 time.s G ? 5 times 5 V 6 times 4 ? 5 limes 3 '? 7 times 7 ? 4 times 8 ? 8 times 2 ? 2 times 5 ? 9 times 1 ? 7 times 8 ? 4 limes 6 ? 7 times 1 ? G times 6 ? 7 times 3 ? 9 times 5 ? 8 times 9 ? 4 times 4 ? II. 13 X 4-? 16 X 5—? 11x10—? 18 X 2—? 15 X 2—? 12x11—? 10 X 10—? 11 X 7—? 12 X 7=? 18 X G— ? 18 x 9—? 16 X 7—? 14 X 3—? 17 X 3—? 14 X 7=? 14 X 5—? 11 xll— ■? 14 X 8—? 17 X 8-? 12 X 6—? 10 X 4=? 12x10—? 15 X 4—? 17 X 9—? 15 X G— ^ 15 X 9—? 12 X 12—'^ 10 X 2—? 17 X 5—? 18 X 4—? 13 X 6—? 15 X 8—? ]2x 9—? 16 X 8—? 16 X 3—? 13 X 5—? 13 X 7—? 13 k 9—? 14 X 2—? 18 X 7=-'' times 5 ? times 1 ? times 8 ? times 5 ? times 1 'f times 6 ? times 3 ? times 5 ? times 9 ? times 4 ? 2kftJLTlPLicATlON. 65 6x9-i- 2=? 8x7-1- 9==? 7x9+17=? 12xll-f-8=? 15x6+ 9=? 8xG— 4=? 12x9—18=^^ 7x6— 2=^? 13x8—12=? 11x11—71==,^ 30—6 x4=? 19+11 X ]l = i 37—9 x4=v III. 8X9-1 24=? 16x5—18=? 14x6+60=? 9X5—15=? 17x4—15=? 15x61+0=? 18x8-51=? 8x4—30=? 7x12+3=? 7x7+11=? ''2—12x4=? 28 I 6x16=? ^\ I 9 X8='^ (<5+7)x3--? (14-3)X6-? (l«-4)x9=.-? (11— C)X7-? ^'20-2) X 5-^? (13— l)x4.-f (6+2)xll-- ? (HO) xo---? (28— 15)X2-'? (21-6) + 5--'^ 78—16x4=? 13-4-13x4=.? 99-17+5^? 8x 2—? Ix 7-? 6x 7—? 4x 5—'^ 2x 6—-? 7x 9—? 3x ^_? 5 X 8—? 3x 5—'^ ^x 7=-- ly. Multiply 21 l)v • 91 1 o M U tin V ,37 },v J . ro 1 / > ''MJ), /. V 7 ; 27 hv '-, • n« J n !^ ' ^'^ ^'y '' ; 80 J '-*'>} o , 08 hv 9 : fin K,r Q y ; 99 hv 8. 66 MULTIPLICATION V. 33c»iits. ' " '^""'s •' iioiinds will cosl 2. What cost 2 .pool, of tl„.,.„d ,i 5 eent. a ,.i„.e ^ ^^5.^mat. w.H . po„„„. of cheese oo.,t at 9 r^t „. yo.'solr-nl'V' ' r,"f"'^ " '•''>'• '">- ™-y vvill ? A 9 ,"■'■'■' ^ '^•''>''' ^ ''"y^ ? 2 days ? o James earns *C a week and Henry |3 ; how much "•.1 both earn in 3 weeks ? weeks ? ]3 w" ing if rZh'TsT "'^''-^^ '"" f-'' -^ ^oot contain- 11. John bought C rabber bUls at 16 cents each How mud. change should he receive from a do itr 2. A man travelled by stage nt Ihe rate of 8 miles nn hour. JIow far did he i.-avel in 't hours ? 1 1 t 16 hours ? 18 hours V '"'"'''■. a,„n / !r""'f "^ r""''^ "'■ '*'f •■" ^^ """'-^ ••» POU'"' aiHl 11 pounds of rice at 11 r',.nfc. „ ^ did both cost ? ' ^'''""^ ' ^^'' ^^^ H- What will be th. cost of 7 pounds of c.;, •. ^t ii at 11 cents pounds will cosl 'ich are 33 cents, 'ounds will cost mih a piece ? : how iiiaHV 311S ? I any days in ' 15 wcnks V it 9 ceiHs a. many will days ? ners cost ? liow much weeks ? 'ot conlain- ' a Ion ? at :'en(s oacli. I a dollar ? of 8 miles 11 hours? s apouif id ; vv' '■ r Cvi; "^ at "• Joseph has I , /'" ■•'■"■''"■e for it <• "-y '- 10 row :^^ J' t;';"" '^!-^ « ""'- - i« Ti., "any nas Jleiirv ^ i». iwo meu start from ih.. ... . m opposite directions one S4 tT ^'''"' '""^^ '^^^'^'^ «^hor2G; howiarapa'rtawh " ^^^Y^^^d the 1^- How many hand^^^^^^^^^^ tainino- 25 of them ? ^ ^^^*'^«' ^^'^^h con- 20. Two men traveJhvI i^. i -i/-au ho„n and h ;1h: 7 ''Tr'r ?'«•• -'« -• SK:::i:::S"'^^-'- Piece. , 23. A boy earned 07 c™tfrr '' '^'"''"'^ " P«'' ? inboard ; hov. much had he'!! "'"'r '" *^ "^ " 24. Bought 9 load. „ • u ""-" "'"' "''« J»ys ' f • A carpenter earned *lV '""■ ' ™»k«' *n. How much more ..'"•''-T "'"' " ^^00- "''11 the carpenter have e ",n d ■",'' ""^ ^''«™»k«- 20. If a man d,> -^b,,!' "' ^" ^"^k^ ? how many will bi di.. in 6 I.? 'I"!''""' '" ""^ day, 2V. What is the am'ou^ of the' nf ^^^ • « ""V^' Quarts of soft-soap at ,1 eel '^""wnig bill ; « ^'"*' » auart ; 7 cakes of 68 M U LT 1 I'L I (' AT lO N. soap at 1> coiits eacli ; ami 2 brooms at 35 cents a piece V 28 11' 1 men do a pieee of work in 10 days, how long will it take one man to do it V 29 IIow many pounds of coffee in 4 bags, each containing U] pounds? 3t pounds? 50 pounds? 30. If 12 men build a wall in 12 days, how long will it take one man to build it ? 31. There are 16 ounc(?s in one pound ; how many ounces in 5 pounds ? pounds ? 3 pounds ? 2 pounds ? 32. If 14 yards be required to make one suit of clothes, how many yards will 5 suits nxpiire ? 3 suits? 7 suits ? 33. If a pound of butter cost 23 cents, what will pounds cost ? 34. A farmer sold 10 bushels of potatoes to one man, 20 to another, and 32 to a third, at $2 per bush- el ; how much did he receive ? 35. William is 15 years old and his uncle Charles is 4 times as old ; w^hat is the sum of their ages ? 36. A farmer exchanged 17 barrels of apples worth $5 a barrel, for 12 cords of wood at $7 a cord. Did he gain or lose, and how much ? 1 1 1. 6x4,— 3,-|-9,x2,— 10,+5,x4-« 2. 18— 8,xl0,—75,x2,— 50,-1-1=? 3. 37— 3,— 30,x6,-f 17,— 65,X8=? 4. 14x4— 6,+13, -1-17—65, y8,xll— 41=? 5. 12x9,— 90,x3,— 4,+ll,— 37,X5,— 16=? 6. 130— 75,+5,x8,— 400,-1-20,— 68,X3=? 7. 7+3,— 4,+27— 6,— 12,X8,— 26=? cents a fs, how MULTIPLICATION. 8. 144-24, i80,~n0, x 2,+4,— 30, x 2-04 ? 9. 19 jY, X 5,_i2.-,,-f-0,__.'} :< ]2,— 32,— 1(>-^? 10. 33—18, X 8,-70, I 10, X 3,— 150.—' 2;-):-? . 69 ^s, oarh ids ? )W loiii:^ »v many )ouuds '^ suit of uirc ? 3 it will to one er bush- Charles ges ? ?s w^orth •d. Did Case I. When the multiplier contains only one flgure. 1. Lot it be Tvquirod to multiply 8!)o by 1. Operation. Soi.rrtnx.— After writing the multiplier Multiplicand, 805 ""'''''' ^''" '""'''^^ ord(.Toriii,> muiiipiicand Multiplier, 7 "'"' ''''''^''nf? « I'ne. wo hcgiri to muiliply at I 111- right. 7 times 5 units, are 3."i units, which art' equal to ;{ tons ami 5 units. We write ihe 5 in units j»iace,ami reserve Mnltipiying 9 Product, 0205 the 3 le,is to be ad.l.-l to the ".r^iluj, iriUe'lZ. .nnup.ymg , give 00 tens, or G hundreds and tens. We set down the tens in ens place, and reserve the f) hundre,ls to add to the next product 7 Umes 8 hundreds are 50 hundreds, plus the hundreds reserved make 02 hundreds, or thousand and 2 hundreds. As wa have no more orders to multiply, we put the thousands and two hnn.Ireds m their proper places. The resulting number, G2G:., is the required product. ■ 1"'"=^ Illustrations. (2.) 213 1 (3.) 432 3 (4.) 341 4 (5.) 520 6 (6.) 17.43 7 213 1296 1304 3156 $52.01 '(7.) $5.26 5 $26.30 10 MULT ION. wnrnEN exejicises. Multiply : 8. 871) by 1. Aus. 6153. 25. 604 by 8. Am. 4832. }). ()!)2 by (5. yl//.s-. 4152. 26. 3'n; Ly 1. Am. 1544. 10. lm by 6. Ans. 6368. 27. 915 by 7. Am. 6615. 11. 47G by 3. Am. 1428. 28. 776 by 6. Am. 4656. 12. 582 bv 5. Am. 2910. 29. 525 by 8. Am. 4200. 13. 607 by 6. Ans. 3642. 30. 378 by 7. Am. 2646. 14. 840 by 3. Am. 2520. 31. 267 by 9. Am. 2403. 15. 736 by 2. Am. 1472. 32. 156 by 5. Am. 780. 16. 913 by 4. Am. 3652. 33. 801 by 2. Am. 1602. 11. 619 by 6. Am. 3714. 34. 307 by 4. Am. 1S28. 18. 495 by 3. Am. 1485. 35. 471 by 6. Am. 2826. 19. 856 by 9. Am. 7704. 36. 167 by 9. Aws. 1503. 20. 768 by 8. Aui,. 6104. 37. 516 by 7. Am. 3612. 21. 259 by 7. Am. 1813. 38. 165 by 2. il/«. ^ 330. 22. 387 by 6. Am. 2322. 39. 722 by 8. Am 5776. 23. 954 by 9. Am. 8566. 40. 249 by 4. il«i\ 996. 24. 832 by 4. Am. £328. 41. 3807 by 9. 56. 90038 5 by 6. 42. 2918 5 by 7. 57. 783206 !by7. 43. 479$ !by 8. 58. 405185 !by6. 44. 7587 by 4. 59. 17842C ► by 5. 45. 631£ ►by 6. 60. 218^9;: ;by5. 46. 905^ tby 5. 61. r. -/9? Sbv9. 47. 811^ rby2. ^% 380697 by 2. | 48. 3948 5 by 3. . 790] . by 8. 1 49. 744.8 5 by 8. 4. . 490£ I by 3. 1 50. 2Y93£ > by 7. 65. 30216^ 5 by 7. 1 51. 17092 by 9. m. 235619 bv 6. | 52. 46181 by 4. 67. 81927^ J by 5. J 63. 31953 by 5. 68. 19311] L by 4. 1 54. 67209 by 8. 69. 37495S J by 8. 1 65. 36431 by 9. 70. 506044 by 9. 1 M U LTl V L I C A T 10 S. 71 -■s. the;". : 'rv'"' *''"■ "■"■" ""' '•' '--- -«t ..t baLfflh™' "' """^ ™^' *"■ «'"" "'■" -''« ea4 r''"' "'"""'■"" ""*• "' "'" '•"« "'■ 4-'«»'^« in « mili-" "'" ^^'*" ^"'' "' " '""^'' ''"^^ "'""y f>--^^' 8. How much wilf a grocer pay for 2504 hoads of cabh, ve at 3 cents a head ? coit' ? *^ ' "'"''^ ^^'''^ ^'^^ ^^^^ ^^^'^^ «t^ vvood 11. II it tak tailor 7 days to make a suit of 1 '"I'htratvo""" " '^"^^ ^™ '» ™'k: 42«z ,: in Vyeat I ""'''' '" ^ >'""' ''''^ """'X ^^-k^ ,„, . Case II. one^gSre.*'"' ™»»'l>»«>- ^ontoli.s more tha.. 1. Find the product of 643 by 58. OPERATION. Multiplicand, 643 Solution. — Having wnlirn Multiplier, 58 ^''^ multiplier under Iho mulli. plicand so that units stand Uii- 1st imrtial ^1 i/l n ay o product '^144 643x8 . . --• 2nd partui 3215 ^43 ^ ^n ^c noginat the right liand an. ^ ' -^- ..' J muiiiplyalliheparlsoMhemu: Prodtict 37294 643 x 58 5a is equal to 5 tens and 8 units, 58 limes m'n^Z^l^lufZ der units, tens undo- tons, Ai-., at the right I lUlheparlsot successively, term of tlie multiplier, Sin f 72 MULTIPLICATION, Itiis limofi Oi.] plus 8 units limos 543. Having found S unilft timfts 01.? ly lilt! riilt! uniler Cas.' l,io 1)C 5111, w« sol it down as the lirst parliai product. To ttnil 5 lens times 613, we begin by mulliplyinpS units liy 5 tons, which gives 15 tens, op 150 units, Oinilling tho naught (or units place, we s^tt down the 5 tens in lens pia<-e and carr-y tho I luuidred to I ho next |»roiluct. By multiplying the remaining terms ol the multiplicand by tho T) lens of tho mnlli- plier, and carrying,' as before, wo obtain the second partial product :!•.'!.■)() ; which is equal to 5 tens or 50 times (113. Now, by adding the partial products, :>\U and 3'!l,".0, we find the entire |irod)i(;t 37'2',)4. In like manner we may lind the products of any two num- bers, being careful to place tho first flgupe of each partial product under the corresponding figure of the mulUplier. Illustrations. (2-) (3.) (4.) (6.) 327 4<; 816 436 46 827 63 78 1902 822 948 3480 l.",08 92 1 i\R 1896 3045 ir)Oi'> 19908 33930 15042 (0.) (t.) (8.) (9.) (10.) 2(i3 425 548 318 862 32 21 4& 25 59 WRITTEN EXERCISES. Multiply : 11. 354 by 19. ^Ais. 6726. 12. 295 by 23. .,is. 6785. i:'>. 359 by 36. Am. 12924. 14. 487 by 28. Ans. 13636. 15. 546 by 32. Ans. 17472. 10. 674 by 45. Ans. 30330. 17. 906 by 53. Ans. 48018, 18. 863 by 25. Am. 21575, 19. 735 by 42. Ans. 30«70. 20. 683 by 56. .4, . 38248. A ^ MULT I I' LI CAT I ON. nilft lirafls (luWIi US begin by loU UlillS. IIS in Ituis ull'plying tho miilli- tl product l)y adiling •0 |iruiliu;t two mirn- li product (5.) 435 78 8480 a045 33930 (10.) 862 50 nz 30330. 48018, 2157rv 30«70. 38248. 21. 521 by ;{<). Ans. 20310. 22. 044 hy 7(5. /1«.s. 48044. 23. 078 by 41. /J/?.s. 400O8. 24. 872 by 47. yl//.s. 40084. 25. 7()1 by 58. Ans. 14138. 20. 408 by 00. Ans. 2Kl,-)2. 27. 007 !»y 78. Am. 47340. 28. 320 }>y 84.. Am. 27030. 20. r)341)y03. A„s. VMWyl. 30. 285 l)y 74. Am. 210!>0. 31. 802 by 40. yl//,v. 42238. 32. 704 by 24. Am. 10050. 33. 827 by 52. .-Ia/x. 43 .04. 34. 502 by 71. Am.^biJA'l. 35. 288])y42. /1«.s. 12090. 30. 830 by 80. yl //,s. 74071. 80. 75. 37. 310 ])y 75. Am. 23025. | tj7 38. 417 by 93. Am.mi>^\. 30. 523 by 87. Am. 45501. 40. 108 by 70. ^«.s-. 15048. 41. 879 by 34. yl/i.s-. 29880. 42. 725 by 77. ^//.s. 55825. 43. 300 by 37. Am. 11322. 44. 090 ])y 58. yl«.s. 40308. 45. 287 by 09. ylw.s. 10803. 40. 014 by 28. Ans. 25592. 47. 540 by 08. Am, 37332 48. 705 by 00. Am. 00705. 40. 307 by 52. ylw.s. 10084. 50. 497 by 44. Ans. 21808. 51. 447 by 03. ylf/A-. 28101 52. 310by 18.^/<.s-. ^(jyg 53. 8730) by m. Am. 838050 54. r>485 by 88. Am. 482080 55.^/l;}7by25.^1/y.v. nS425 50.8409by03.^/„.s.r,2J>707 57. ()523 by .'}5. Am. 228305 58. 0040 ],v 47. J A/s. 425102 50. 52877 by 28. 00. 018024 by .38. 01. 270301 by 02.105107 by 03. 2304 by 271. 3104 })y 815. 1282 by 430. 4730 by 810. 5321 by 427. 3240 by 245. 4871 by 502. 0547 by 374. 0293 by 853. 0785 by 070. 5482 by 735. 8073 by 103. 75. 007284 by 352. 70. 7S0ir25by 039. 77. 2842753 by 784. 78. 9310924 by 028. 70. 0454705 by 475 04. 05. 00. 08. 00. 70. 71. 72. 73. 74. iii. 74 M U L i T I P L I C A T I N . 1 ^^H 1 45. Aiinoxiiig" a cipher to a number moves each of ^^^H/ its digits one place to the le ft, thus converting units H^l into tens, tens into huntlrecU &c, ; which is the same ^^^H as multiplying the number by 10. Hence to multi- 1 ^^^H ply a number by IC ), wo annex one cipher ; to mul- m^l tiply it by 100, we annex two ciphers ; and so on. ^^^H I r.LUSTRATIONS. ^^H 1. Multiply 35 by ' 240 2. Multiply 3500 by 240. ^^^H OPEliATIUN OPERATION. ^^^^H 35 35 00 ^^^^H 24 24 ^^H 140 140 70 70 840 840 000 ^^H Multiply : ^ ^^m ' 3. 8607 by 10 Ans. 86070. 1 ^^H : 4. 68038 by 100 Ahs. 6803800. 1 HH 1 5. 780 by 100 Ans. 78000. 1 6. 38600 by 10 Ans. 386000. 1 ^^1 7. 37862 by 1000 Ans. 37862000. 1 ^^H 8. 98630 by 1000 1 ^^B 9. 86421 by 10000 1 HH 10. 378200 by 100000 11. 394 by 200 ^^^H 12. 5860 by 320 ^^^^M 13. 8790 by 4600 ^H 14. 1576 by 3000 ^H 15. 1700 by 16. 2030 by 4200 5000 ■i Ans. 10150000. i ■ 17. 10800 by 250 Ans. 2700000. 1 ■ 18. 46200 by 7130 3S each of ing- uiiitw tho same to multi- to mill- so on. by 240. ). 15 MULTIPLICATION. 39. 47300 by 16000 20. 25000 by ](5500 21. 70500 by 40500 22 40000 by 82000 23. 08000 by 7(5000 24. 53200 by 10300 25. 386000 by 147000 2(1. 70200 ],y 20(J0 27. 4030 by 74000 28. 405000 by 3070000 UNITED STATES CURRENCY 46. When one of the factors contains cents or ./oA /«- and ..nls, mnltiply as in simple nnmbers' ^nt SourriON.— If one ton cost $5,75, 27 Ions will cost ^7 limos $5.75, wl.icliis$l55.'.'5. Since Ihe mulli- rlicand contains cents, ve must point onriwo places in the product. -.75 27 4025 1150 155 25 J^^Whai will 37 ),arrels of /lour cost at .*6.85 a barrel ? 3. Multij)ly $472,06 by 27 4. Multiply }i^]826 37 by 160. n Tir Multiply 1802.06 by 327. A -"Hiply ^20.!i2.25 ],y 1408. Aus. |4128G08 7. If an acre of land 462 acres worth ? Aus. 1253.45. Jns $12701.82. Ans $202210.20. $201703.62. 00. IS worth $237.82, what aro 4ns. $1146£9.2^ •76 MULTIPLICATION. 8. At $4.80 a bushel, what will 625 bushels of flax- ""^f Z^^ ' ^^'^- $3000.00. 9. What cost 83 bushels of corn, at 15 cents a ^"'^^^' Ans. 62.25. 10. What cost 145 yards of sheeting at 8 cents a y^;t\ An.s.nSO. 11. At $4.03 a head, what will 378 sheep cost? io wi, . ^//- $1750.14. 12. What cost 8 pieces of calico, each piece con- taining 25 yards, at 7 cents a yard ? Ans. $14.00. 13. How much will a grocer pay for 2 chests of tea each containing 65 pounds, at 65 cents a pound ? 14 Txri ^^*'- *i84.50 14. What will 19 hogsheads of vinegar cost, each containing 63 gallons, at 23 cents a gallon ? Arts. $275.31 15. Bought 9 cows at $30 each, 13 horses at $135 each, and 300 sheep at $3.50. each ; what was the *'"*''^ ^««t ^ Am. $3075. 16. A merchant purchased 27 pieces of cloth each containing 54 yards, at $3.33 a yard, and sold it for $3.45 a yard ; how much did he gain ? Ans. 174.96 17. A Hour merchant bought 450 barn^ls of Hour for $3262.50, and sold them for $8.63 a barrel • what did he gam? .1/^... $621.00 18. A man earns $3.25 a day, and his daily ex- penses are $1.89; how much will he save in' 365 '^""Z-, ,, ^//.v. $496.40. 19. I sold 13 bales of cotton cloth, each bale con- taining 10 pieces, and each piece 19 y.ards at .05 iicr ^ard ; what did J receive for the whole { ilsof flax- $3000.00. 5 cents a ins. 62.25. ^ cents a ins. 11.60. ) cost ? $1750.14. iece con- ta. $14.00. L^sts of tea I pouiKl ? IS. $84.50 ost, each . $275.31. at $135 was the IS. $3075. oth each 'Id it for s. 174.06. of flour 3l ; what $621.00. Inily ox- ^ in 365 $406.40. ►ale con- t .05 per HULriPl.iCATlON WRITTEN EXERCISES, (1.) 356 7 (6.) 7002 28 (11.) 3063 49 (16.) 3073 42 (21.) 7006 235 (26.) 10034 • 806 (2.) 392 % a) 5062 15 (12.) 7802 25 (17.) 4063 55 (22.) 8067 007 '27.) 4006 450 4 (8.) 7803 26 (13.) 5632 78 (18.) 0063 75 (23.) 4063 204 (28.) 70632 0/\rt .(4.) 1056 (9.) 3056 88 (14.) 7032 51 (10.) 6803 123 (24.) 80{}3 204 '20.) 45632 6o7 77 (5.) 305 5 (10.) 4063 42 (15.) 5062 97 (20.) 4563 2')7 /25.) 7006 752 ,'30. ) 8963 404 is MULTIPLICATION .^ Multiply ''H. 0G5 })y 1. 'iS. 805 })y 45. 84. •7302 ])y 71. 85. 062 by 15. 86. 2008 by 9. 87. 850 by 10. 88. 4000 by 21. 30. 70602 by 50. 40. 70032 by 01. 41. 80213 by 70. 42. 5008 by 101. 43. 0032 ])y 500. 44 7820 by 20. 45. 80032 by 108. 40. 7003 by 75. 8032 1] y 270. 48. 8584 ])y 002. 40. 70021 ],y 008. 50. 50032 by 403. r>l. 8084 ])y 132. 52. 28501 by 175. 53. 3002 by 581. A4. 8008 by 705. 55. 7003 by 300. 50. 50002 l)y 280. 57. 85032 by 5003. 58. 7000 ])y 304. >y 702. /;q Anr.o-t i, -X'JXJU i. fO- 20068 hy 142. Ans. 0755. 82. 1008 l)y 150. ' Am. 1 A A na. 05828. 10425. m. 522702. Am. 14480. Am. 1S507. Dimm. 47. I^ivisionis'th6-processofiindino. how inanv ^ one number i. contained in anot W of :L:;:! DIVISION TABLE. divided Ly I equals 0; div any numbor equals 0. ided h\ 2 equals 0; () divided by .V^-^^W- ■ .i TMfTMWIwWHwiT >| ii ii-. ^ ff ;^ | ,^|rt,^ fui ^ 80 9-^9=1 18-:-9=2 27-9=3 36 ;-9=-4 45-^9=5 54-^9=6 63-^-9==7 72-^9=-8 81-^-9=^9 DIVISION. 10-HlO=l 20--10=2 30-10=3 40 -.-10=4 50-:-10==:5 60^10=6 70 rl0=7 80--10=-8 90-10=9 11^11=1 22--ll=:2 33-11=3 44-:-ll=:4 55--ll=5 m --11=6 77 :-ll=7 88-11=8 99-:-ll=9 12 24- 36- 48- 60 72-; 84 96 108 12=1 12=2 12=3 12=4 12=5 12=6 12=7 12=8 -12=9 OJiAL EXEMCISES. 6--2=? 8-1=? 9-^9=? 4-f-2=? 6-f-3=? 8-^4=? 9-^3=? 8-2=? 7-f-l=? 16 2 1 8 ? 8 • 24 3 • 36 9 4 i 24 9 6 ' f=? 16 9 8 • 14-:-2=? 18-3=? 16-f-4=? 15--3=? 12-^2=? 12--3=? 18—2=-? 25—.^=? 24-4=? 27-- 3=? 27. 28 30 33 9 11 • 35 42 45 t 56. 12 63 '=•? II. 24-4-8=? 28-4=? 20-:-5=? 32-.^4=? 30-6=? 35_._7=? 36--9=? 32-^-8=? 36—6=? 40-5=? 72 ? 81. 84. 12- =? 36 ^? 12 • 48 9 8—-, 3() 9 10- i 10 9 5 — L 99 ? 11"^ 80.^9 10—% < I 12 — L 48 45 48 44 49-: 56 50-: 54 64 63 6=? 5=? 12=? 11=? - 7=? 8=? 10=? 9=? 8=? 7=? 10 9 •2 i 54 9 6 1 91 9 12 • 72 9 8 • 40 9 5 iK) 9 10— i, •am ' 42. :7- :? >' * •< 77 9 (11 • 18 *> 40 — ; \ ^ V 12-^-12==:l 24-f-12=2 36-^12=3 48-12=4 60:-12=r) •72-M2=6 84-:-12-:7 96-:- 12=8 08 ;-12=-9 i>ivisiojv. 8-; 5- 8- 4-: d- y 1 ;- 6=? 5=? 12=? :-ll=? :- 1='? 8=? 10=? 9=? 8=? J-f- 1=1 10 2-—' 54. 6- 40 ? 8~v 15--5=? 16-^5=? 12-6=? 14:6=:? 21: Y=? 24-f-7=? 40-:-8=? 46-:- 8=? 18-9=? 26-^9=? 22-^2=? 36--3=? 48-^^4=? 55-^5=? 88-f-4=? 28^2=? 46-f-2=? 69-:-3=? 77-^7=? 64--2=? (12+ 6)- 3= (20+ 4)-^l2=. (17-f 1])-- 2= (26- 6)-^- 4= Si 23; 3= ? 10 : 4=? 42:-8=? 17-^-6=? 12:-7=? 19-;-3=? 25 ^6=? 34-^5=? 43-^5==? 53-:-9=? Ill •37 : 10=? 73 : 8=? GC) :- 7=? 69;- 8=? 95M1=? 87-:- 12=? {]d~ 9=? 18--ll=.? 44-:- 7=? ' BS-r- 9=? IV 03-:-3=? 68-; 2=? 50-:- 5=? 66^6=7 86-:- 2=? 8i-f-4=? 63-f3=? 06 : 8=? 44 : 2=? I)f>-: 9='? 48-;-3=? 75^5=? 60v-5=? 96-:-8=? 84-:-7=? 91--7=? 78-^6=? 85-:-o=? 42-:-4=? 51-:-3=? (47- 5)-: ;? 2^? - 6==? (19-1-17)-;- 5^? I ( 5 V (37-1-16)-- 9=? (29-13)-.. 6-? (48- 7)-^ll=.? ( 7x 6)~- 3=? ( 8x 9)-- 6^? ( 6x 4)-- 2='? X 8)-- (6 4S 72 X -( ^( 81 82^10=? 74^11=? 35-:- 4='^ 27 - 4=? 99 --12=? 55 ~- 7==? 81 :-12=? 75-- 9=? 63-;-lG=? 51-f- 6=? 78--7=? 43-:-S=? 61--4=? 79-f-5=:? 75-;-4=? 94-6=? 82-7^? 33-^2:^? 47-^^3=? 58-^4=? ^)^ 7=? 2X 6)=? 3x 4)=? 4x 2)==? '^4^-( 3x 2)=? 4=? 84 96--< 8x 3)=? -( 3X 4)^? 'Jj ill "mm 82f (18- G) (30— 9)-: (84— 4) (63— 8)-; (76 + 12)-: (36+ 7)- (42+23)- (80+ 4)- ( 7x 8) ( 8x 9) DIVISION. ;-( 4+2)=? ( 1 + 4)-? ( 3+7)-? (11-6)-? (14-3)-? -( 8—1)-? -( 3 + 2)-? -( 6+3)-? -( 4X2)-? ;-( 4x3)-? (47- 7) (93- 8) (43 I- 7) (48+12) ( 8X it) ( V-^ 0) ( 8X11) ( 7X 9)- (78-^- 6) (93-^ 3) ( 3X1)-? ( 6x2)-? -( 3X5)---:.? ( 6x4)---? ( 4X3)=? ( 9+1)=? ( 3 [6)-.? (17-3)-? ( 3x4)-? (72-: 9)=.-:? VI. 1. At 4 cents a piece how many oranges can be bought for 16 cents ? 28 cents ? 32 cents ? 20 cents ? 8 cents ? 2. A man earns 1^2 a day. How long will it take him to earn ^18 ? $4 ? !^6 ? $12 ? $2'? 3. How many yards of muslin can be bought for 72 cents, at 6 cents a yard ? 8 cents ? 12 cents ? 9 cents ? 4. How many times can 5 yards of cloth be taken from ii piece containing 25 yards? 45 yards? 60 yards ? 30 yards ? 5. By writing 8 lines a day how many days will it take John to write 56 lines? J 6 lines ? 64 lines ? 88 lines? 40 lines ? 6. At 11 cents a pound, how many pounds of sugar can be bought for 88 cents ? 55 cents ? 99 cents ? 22 cents ? 7. If one man can do a piece of work in 36 days, how long will it take 9 men to do it ? 4 men ? 6 mer ? 3 men ? 8 men ? 8. Divide 24 into 3 equal parts. Into 6 equal parts. IM V ' . : o N 83 3X1)--? 6x2)-? 3X5)==? (3x4)-? 4X3)=? 9+1)=? 3 + 6) r:r? 3X4)-? r2-;9)=n? 5 can be !0 cents ? 1 it take :ht for "72 9 cones ? be taken rds? 60 rs will it ncs ^ 88 unds of iits? 09 36 days, (] Trin-ji ? al parts. 0. How many dozen of Qo-crs at 9 ro.if^ o .i lots ot 10 acres each can be sold '^ ^ 14. In what nunil)or of davs will n ^ ^ miloa. at ,ho rate of 5 n.ilo.?;!;'" """ "''"■^■' '' 15. How many tim.-s 9 is times 1" ' for «3.'' WsTiro'A;^^"""'^ '^'^ '^"" ''^' ''"^'■''-<' IT. Mr. Jolin-soii travelled 140 miles in T ,i how many miles did he travel eaeh day , " ' '''"'^ ^ 18. How often is 5 contained in T-fi ? ft,> ? co ? l.». How many barrels of apples of sq , u . ' be purchased for m ? $i}r, ? |3o ,' * " ^''"'^' «»'' 44Th'^ ["'T '""'°'" '''"''" '^ *«0. •-" 'he rate of »4ahead. How many did he buy ? ati^i^L:;:;7'^^^'^^^^^^^^'"--^-oid..ii2o relsts^^""''''"'"^^^^**'^''^^'^^^-"'^ 2a If a man earn $.x> in .» weeks, how much xvill ho earn in ] 1 weeks ? ^^ "* 24. If 8 yards of cloth cost |48, what will 12 cost 1 Ir, yards ? 9 yards r 14 yanis ? 25. What will 5 tons „1 hay ci>st ^26? 118 ? 130? 36? iftw 12 yards ons cost it 84 DIVISION i i 26 How many bottles of mucilage at 10 cents a bottle, will pay for 40 copies at 4 cents each ? .7 At the rate of 28 miles in 7 hours, how far o" V ""''" ^''"''^^ "' ^^ ^^^^'•« • ^1 hrs. ? 14 hrs ^ 28 How many bedsteads at $6 each, can be bou-ht or 11 boxes of oranges at $G each, and |18 worth of lemons ? 2it How many fancy lead-pencils at 9 cents each will pay for 5 tops at 6 cents each, and 11 three-cent stamps ? 30. How many times can a father divide r among his three sons, giving each |5 every time ? VJI 1. 5x4,-2,+X.-.4i.;6,-f>4,+6,-ll,+4:= ? ^- ^^ 1^'X^' ^^^^-'- 5,X3,l-4,^7,-2,-|-8,x3= ? 3. 27-'3,^8,+« :«3,-r,0,X3,-l^,-f 25,-^8= ? 4. 48-^6,+3,X9+l~10,-4,X13,-8,-^7.-f4:^? 5- 144^12,-l,xll,--13,-^9,-5,XG,-2,^10:^? 6. VX9,-3,-^4,+3,X3,-4,X2-19,^9^? 7. 3C+9,-4-5.+2,-^3,+4,x5,-25,-^-8,+6= ? 8. 21-+9.X4,-10,H-ll,+iG,-^2,-3,-l,x9=. ? 1). ]08-f-12,+llH-4,^4,H--l,x7,-2,-^3,xY=^ ? 10. 86~.31,-^ll,+i7,_4,^9^_|.^X4H 11,-2= ? ) coiits a how far 14hrs. ? bought worth of its each, ireo-cent ide $90 time ? 3=? = 7 10= ? - ? : ? DIVISION. Q^ SHORT DIVISION. 1. Let it he required to divide 32540 by 5. OPERATION. So^t;Tro^^^Traving•w^iUon the 'divisor at _ . . Dividend ''« '^^^' 0' t"e dividend, with a .'' ved in Divisor 5 ) 32540 'l'^^^^" l''^"'- we begin at Uw j.vide '''. '^''^'''"' P°'-tB of the divi. M ,,e Quotient (3508 '1^'%. ?"f ' '^ "^^ ^^"^"^'""^ '"3 we a quoiienl and 2 thouonndir '' '^'"' ^''''''' ^ thousands for sandsunder ho t "orand^anVrr'^^^ ""' ^^''^^ ^"^ « ^''-'• annex the next i^J^^l^^^^^rtZ ' 'T''^'' ^ hundreds are equal to 25 hundred.^? .^^^^«"^«"''s and Hve 6 hundreds times LcVZt ^ '^ «°"^«'"ed in 25 hundreds, than 5, there are no t n in tho "r '''"''"'''' ^"'^ «'"^« ^ '« ^^^ t"e pi;ce Of Is anr nn?x r flw•^^'""'°" "^'^« ' '" 'naking /.O units. Dividing ^n is bv 17 T' 'o '''' '°"'' ^^"« ParJofthe^vri^K^-lr^^^^^^^ (2.) 4)672 Ans. 1G8 108 4 Proof 672 Illustrations (3) (4.) 6)287 7)908 (5.) 8 ) 8145 475 47 6 282 6 287 129 129 903 1018>^ JWi 8145 IMAGE EVALUATION TEST TARGET (MT-3) /. i< & ^ 1= 11.25 1^ 12.2 2.0 1^ U 11.6 I ihic Sciences Corporation 33 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 873-4503 '^^\ iV :1>^ s> V ;\ .1^> I - 6 29. 5837 -^ 4 47. 8077636 - - 8 30. 4002 4- 3 48. 6300857 ^ - 4 31 73504 ~ 8 49 90437284 -. -9 50. 76110884 -- 3 n l"r h( w of cu ^lYlBlON. 87 x^- A gentleman divided Jisn » P«reon», giving j4 t„ 2 h' "*>' """« P"'^-- were MieTc ? '' ' '"'"' ™*nr Poor persons bu'/io^JTsV?""' ''^^"' """"^ ''""^ »f wood could . 55. At the late of T *v -i -M u ,,, , ,„„/J, -'^^^ a„^ -. ^ho. ,o., «u 1820 days > ' ^*^^ '"^"X w^^^ivs t>2 A 1.U ichaut yained 139875 dolk,, ,•„ ,, what wa» his average yearly gainT"" " '"'"' ^'i- How many loads mav b.^ f ,t.„ r oi gravel of 82806 cubic feel i' e, i in T ' '"'" cubic feet ? - *^" ^^^^ contani 1 [ MM 88 D I V I S I O JT . rh LONG DIVISION. 1. Lot it be required to divide 50289 by 3t2. Operation. Solution.— since 372 is not contained in 5 tens of tliousands, or in 50 tliou- santls any thousands times, there are no tliousands 'n the quotient. Annexing the next figure, 2, we have 502 hun- dreds. 372 is contained in 502 hun- dreds 1 hundred times with a remainder. Write the 1 hundred in the quotient and multiply the divisor by it, subtracting the product from the 502 hundreds. This gives for remainder J 30 hundreds; to which we annex the next figure 8 tens, making 1308 tens for the next par- bivifor. Dividend. Quotient, 372 ) 50289 ( 135 372 , 1308 1116 1929 1860 69 Remnindert tial dividend. The quotient of 1308 tens, by 372 is greater" "than 3 f.n.l less than 4 ; hence there are 3 tens in the quotient. Multiplying "~^ by tens, we have 1116 tens, and this taken from 1308 tens 37 leaves 192 tens ; to which we annex the next figure 9 units, makin'^ 1929 units. 372 is contained in 1929 units, 5 times with a i-emain"- der. Writing Uie 5. units in the quotient, and multiplying and sub- tracUng as before, we obtain the remainder G9. Hence the quotient )s 1 hundred, 3 tens, and 5 units or 135, with a , ader of 09, 2. Divide 1062934 by 306, and prove ft. Operation. Proof. l>ivi8or Dividend Quotient. 306) 1062934 (3473 918 3473 QuoJent. 306 Divisor, 1449 1224 2253 2142 1114 918 Remainder 196 20838 10419 1062738 196 Homainder. 1062934 Dividend. not contained ' in 50 tliou- s, there are no It. Annexing ave 502 hiin- in 502 Jiun- 1 a remainder. 5 quotient and ;, subtracting 02 hundreds. 30 hundreds ; next figure 8 the next par- reater than 3 Multiplying n 1308 tens, inits, making ith a rema in- king and sub- the quotient ler of G9i 3 QuoJent. '6 Divisor. 8 8 6 Boniainder. 4 Dividend* 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 80; 31- 32. ^VlilTTEN KXEliciSEs. 89. 3- 888 --37. 4- 936--52. "'• 975-25. 45G--24. 924-33. 54G-13. 804-G7. 946 :-43. 608-38. 894-76. 247-^19. 498-27. 816-80. 306-18. 537-46. 732-61. 364-29. 604-54. 477-^53. 836-44. 4214-49. 1335-15. 1617-21. 1081-^23 6184-:-58 8476-83 7581^-47 3544—93 6450-25 Aus. Ans. 24. 18. Am. 39. Ans. l!>. 28. 42. 12. Ans. Ans. A ns. Am. 22. Ans. 10. Ans. 11^ An.-i. 18. Am I827. ^ns. 10^. Ans. Ans. 8^43-34 I 39 17. ^ns. 12. ^ns. 12]J. Ans. llJJ. Ans. 9. Ans. 19. Ans. 86. Ans. 89. Ans. 77. 8864-^92 5621-77 1209-31 2151-57 3864-86 12194-67 13314-42 lis 90 DIVISION. it fl 40. 38584---53 41. 1010(1 -2() 42. 70308: 37 43. 430501-95 44. 45. 40. 74009 04584 72259- -83 :-7l 41 80819-:- 32406-f- 40950-:- 72828-:- 51084-^ 47025-:- 47. 48. 49. 50. 51. 52. 53. 80257- 54. 74670-f 55. 145132- 56. 143082-: 57. 734530-:- .■>,s. 350479 - 59. 504800:- 60. 3971954- 427. 61. 8450834 :-^ 889. 62. 1317296 : 232. 63. 6131043-- 681. 64. 1880810-- 397. 65. 4020621-5007. 66. 5718006: 6873. 67. 609960-:-1326. 68. 122031 3 -:-4503. 69. 4G05430--7663. 64. 33. 126. 867. 396. 627. 913. 108. 307. 462. 136. 320. 208. Affs. Am. A /fs. Ans. Ans. Ans. Rem. Rem. Rem. A as. Am. Ron. Rem. Am. Am. Am. Am. Rem. Ans. 982. 325. 84. 129. 75. 70. 187790-:-2110 71. 273631-^-7329 72. 408576 ---4864 73. 1395940-3068 74. 2987620-:-6020 75. 76. 77. 78. 79. 826. 42. 228. 311. 5401 79. 192. 9302. 9506. 5678. 9003. 221, 803. Rem. 6543. Am. 460. Am. 271, Rem. 7630. 4268004:^5300 2462776-3709 846301--8219 11590744-1352 16815620->-3470 80. 81. 82. 83. 84. 85. 24L34744 32174272 12(Jr>5()9(> t>3000180 7047400 5787088 UNITKD ;»IVlsiON.i '^4072(86. 28898922 "77432 87. 7292924368 ''5<5752 88 3289054376 86420 89, 10824675400 '^3400 90. 65642058 44671 1 STATKS CURRENCY. 88647 846007 ' 13792 520117 326474 the answer in conK wi i '^"^^'^^"^ ^^^^^ ^o dollars and CO s,;!,:!"/^ ^"^^^ ^^ -^«e.d to places from the ri'ht ^ ' "^'""'^"^^ ^^^"^^ *^'<^ as ill simple nxunbers Th T"^' "^^ ^^^'^^« required number " ^""''^"^^ ^^" ^^^^ ^^^ 1 r^- •, . Jr.LUSTKATIONS. ]. Divide 1187 equally among 13 men (1) cents, cents. 13 ) 187.00 ( 1438 13 $14.38 57 52 50 39 110 104 (2) ^•50 ) 600.00'( 80 barrels. 3 92 PI VISION. « :- < $5G. 908. 210. 47 12 2401. 30. Ans. Ans. Ans. Afis. Ans. Ans. Ans. Ans. WMITTEN EXERCISES. >^ 3. Divide $396.76 bv 28 a a,. ^ 4. Divide 11308.24 by'': ^'^ ^^^-^^ •'>• Divide $0048 by 108. «. Divide $'37806.2{) by 30'> l V}''''^'' ^'^'^88 by ll^ents. 8. Divide $137.07 by 63 cents 9. Divide $15275 by $325 10. Divide $9672 by $806 11. Divide $0003.75 by $3 75 12. Divide $276.00 by $0 20. ^,,, o. eo'A '''' "''' ''^""^ '''' ^''^^^ ^^-fwill laere ^^^^ If 516 cW cost $2012.40, what wia'^;!;!^ co:f$^:;r^^^^^^-^^^^i^^y^^^et^S 19. Bought a barrel of vinegar for iu!t ^^If rate of 21 cents a o-ilinn -v. SI^-23, at the barrel » ° "" ' ^""^ """y S»"ons in the 20^ How ^„ch does a laborer receive^r dafif lor 42 days, he earns $56 70 'i . ^' " 21. A. $7 a barrel, how n,any barrels of L^'''- be bought for $273 ? "^^rreis ol ilour can 22. How manv Trlr^e f i ,^ JlAm. 39 bbl. =33.50 at .3 62 LrlV^'^'" ''^^ P^-^^-ed for $633.50 at $3.62 per yard ? ^^. 115 ^ds. «jf. §16.50. «»■ 908. 210. '47 12. 2J01. 30. t will 1 acre Ans. 1126. ^^l 1 chair Ans. 3.90. leep, if 280 ^«.v. $;j 00. iwd, when ^«s. o5t. ohI ca^ be «s- 13 tens. >e bought 24 baskets. '3, at the >ns in the ^ 63^ra/s. r day, if ^s. $1.35. lour ran s. 39 ^6/. Glased for 175 2/ds. Divide : 1 2. 3. 4. 5 6. 7. 8. 9. 10. 11. 12. 13. 14. 35. DIVISION. M'PITTJ'JN ILXEliClSES. 9& 408 by 2. 078 l)y 0. 525 by 7. 392 by 8. 504 by 9. 455 by 5 •792 by 8. 843 by 3 4080 by 4. 3961 by 12 4802 by 34. 39623 bv 61 43693 by 36. 35021 by 70. 49680 by 35. 16. 185952 by 20. 17. 38284 by 28. 18. 16967 by 47 96720 by 304. 8352 by 427. 6533 by 307. 18538 by 806. 32445 by 45. 4962 by 23.' 89322 by 756 4821 by 73. 19. 20. 21. 22. 23. 24. 25. 26. 34470 -'8. 53084 29. 41097 30. 57353 33. 0845 32. 23344 33. 26000 34. 8232 35. 25830 36. 3001443 37. 72072 38. 833405 39. 03045 40. 03984 43. 95048 42. 232002 43. 255045 44. 8430 45. 15341 46. 3450 47. 109440 48. 72134 49. 450203 50. 0024 51. 56396 by 08. hy 831. hy 57. by 83. by 07. by 392. by 208. by 147. by 246. by 5789. by 572. by 6883. by 791. by 356. by 98. by 5740. by 6b. 6. by 1405. by 529, by 27, by 608. by 329. by 856. by 72. by 184 H INTKOPUCTOKV FRACTIONS. i i I- i INTRODUCTORY FRACTIONS. h 1 unit = I * I k I 50. Ifa unit is divided into two equal parts, one ol iho parts is called one half. f l^^^"" "»it is divided ipto i\t\ '^'■^« ^*1"«1 parts, one of tho M ""^^ =3 1 ^^'*' ^' ^'«IWonc third ; two ' ofthej.arts are called two thirds. inheunitis divided into lour equal parts, one of the i i i — J-". 113, Kjuii oi ine lunit = i ^^r'%V'"'^'"'^""^^^' 4 two of the parts are^ called two fourths, and three, three . lourths OJtAL EXERCISE S^ 1 How many halves in a unit ? in 2 units ? in ^ units ? in 4 units ? in 6 unit, f ''' ^ 2. How many thirds in a unit ? in 2 units? in q units ? in 5 units .? in 8 units ? '"^ ^ 3. How many fourths in a unit ? in 2 units ? in 4 nnits ? in 10 unitt ? . "* 4. How many halves in a unit and a half? i„ o units and a half? in 3 units and a half? '^ ^ 5. How many thirds in 3 units and a third? in k units and two thirds '•• ^^ * ^^ ^ oNa. ONS. i divided into 'i one ol ihc >ne hair. Jividcd into s. oue of Iho e ^hird ; two called two ivided into one of the 5ne fourth; are^ called three, three nits? in 3 nits ? in 3 nits ? in 4 alf ? in 2 ird? in 5 ^NTRODUCTOKV FRACTiOI.s. II 95 I Find i of 4, I of 8. Solution To fin.? i ^r 2- Tim., j of 4=.4 J2I2 Z '""""'" ""■'''•' """ "">"'»r by If. ^ of 8=r3 tinios 4 nf « *o- S of 8=,3^4, X 3 j;/;f; •^...o... .t of 8=8^4, tloreforo 2. What is i of 6 ' of 10 ? r , ^ „ 30?of50? '^"-"f^JofSOJofa^, „f moT?:V'^"'''^°^^^^''f''5^ofl8,of04,of ofteJ^'oti^^/^-^^^^^^'^^^^^ofso.or^s. «o'ont^^*r/''^^^^»^^«?of.onofeo*of 7. At 20 cents a notind fm. i, P'-^y for half a poundT '""'^^ ^^^^* ^«st you 8. When coal is worth « ^ n IH' paid for i of a toll ? '"'' ^ '°"' ^^at ™„st B. If tliere are 12 on i ■ <, ;„ onncesin jofaj,o„„d^ " ^"""''' ^<'"' Wany eel- in foTa dll7^'="'^^" »'■«''-. W. a.., .sLTtL^;i!tr:^:;^^i':ieo..at*4a,^ y«* will coat $288;i3rrMo™;lf "' *' ^ *'■ "-- ^^1 will «3 ix>„„d, of tea j. At . WJiat must a n ro( toes at noj ,MMilsa }>iisli,.] ? or pay for 3f) bushels of pot) "• What will ;-,2 Ji ])()uikI 7. A pounds of sunj-ar cost at 11 J centj jnan havino- $uoo, si>cnt ^ of it. How much Jiad he loft ? S. AVhat cost 1L>!I7 (I dozen ? ozon of eggs at U)^ conis a Ans. 1214.005 ^' ^t <>| cents a spool, what cost <)245 thread? 10. IVliat cost 7842 yards of muslin at 33i spools of Ans. $r)77.H125. yard ? 11 AVhat is the cost of 525 pounds .of rents a pound V 12. Find the cost of 2500 melons at 2 cents a Ans. ^2(J14. sugar at 12 J Ans. v$f35.025. 5 cents each ? 13. Wliut must be paid for bales of cotCoi' tainin 120 Dound 1'.'). on, cou- s eac at 10 2 cents a pound ? 14. "WJinl will 18 45 yards co.st, at 25 vaut pieces of calico, each cont Af/s. |;420. !unijij>- 15. If a wlieel turns 480 t s a yard ? Ans. $20-2.r)0. imes in going- a mile, how many times will it turn in going ;;. of a mi^le 1 Ans. 300. 16. At $2;^ a yard what will be the cost of 240 An.utter at 20 c^mts a pound, and 12= yards of ribbon at 3 cents a yjird. How much is still djie hyij ? ONS. do/liir ii box, shds ofi)ofa- t nt 11? rents How mmh H)J conis a h/s. !|214.00r> 45 si)0()ls of s. $r,77.H125. fc 33^ colli s a Ans. $2(n4. su^ar at 12 J l«.s. .I65.G25, cents er.ch ? Ans. s|G2r). cotton, con- )ouik1 ? ^//.v. !ii420. I contaiiiiii*'- «.s. #202.r)0. aniilc, liovv e?/l/^.v. 300. cost of 240 Ans. $GGO. week, how :? ^«.s-. 30. ntsa piece. Litter at 20 t 3 cents a TABLES. A • I* (Canadian Money. ''^ "'ills mako I ,-,.,,1 , ', . JO corns .. ,:"' "'''"•'^"'' CI. ' nollar, « 0, United States IVIonev. I'Oonnls u i ,,. "Kirk.vl cl. t').nn,os . r " .1. c<-»ts ^ i„ eents ? in 8 cent. ' ',- t . "''"'" • "» ^ 2. How many cents in? ?^^''^"''^- ^i«^^^« ? in dimes r ^^""^^ • ''' ' ^''^"-^ '^ in 5 5 "own,anymilIsi„5,ents^dn • fonts m G dimes ? '^""^'''^ "> •' dollars ? <^. How many dolJ-.i-v. ,„ i 12 eagles ? ^ '^''^' "^ ^ '^^^^"I^^^ ? in V eagles .> in 7. How many rent, i,, m i, ^« "^iiLs ? in 30 miJil , "'^^^'^ ' ^'" '^^ "^'"s ? in 97 niilh m Jr "^"I-''^ -ul ,„,„. 9.- How in o< mills .<' in 98 mills ^^^ It) mills ? cen many dimes and i^h}U,nuf^ '''''' '''''^ --nisi in 8(> m G3 98 TABLES. • ?o ?T ""^"^ ^^^^^ ^'^^ dollars in 36 dollars ? m 49 dollars ? in 72 dollars ? English or Sterllxg Money. 4 faKhings, fur., make 1 penny, marked d. -'shillings . ,gm„,^^ Mi «■: Oi?^Z EXERCTSES. 1^ How many farthings in a penny ? in 3 pence - m 7 pence ? in 9 pence ? ^ J' m d pence . andl^rj'""'^'™"^^^^" ^4. and .5s.. in £10. •7. How many d. in 9s. 8d. ? in 12s Od v J^.^Howmany pence in 20 forthings ? in 48 far- ini}Z:r^"^^'^-^-^^^--^in9ed. 10. H( low shillii] many .€ and s. in 25 shillirm-s ? gs ^ m 14G shillings ? gs V m 68 I 36 dollars? EY. Bdd. s. £ ill 3 pence ? 4 shilling's ? n 5 pounds ? 1 6 guineas ? fjir. ? in 8d. *. '^ in £10. ? in 48 fai- ? in 96d ? gs ? in 68 TABLES, Troy Weight. 99 Tiie denominations of Trnv w„- i < weights, and grains. ^ "^''^ ^'^ P^^nds, ounces, penay Tl'opoun,, Troy c„„,.i„, 5,700 ,,.,„,. "■ , *.-M, OiUL EX'-^CJSES, 3. How many trrains in „ l^eunyweights ? i„°6 dwt ^ P«"°y"'«Sht ? in 3 o..'"°iTrr'^«''-"—e. in, „,,,„, 3. How many ounces n, « v. ^^5.^Ho,w „.„, ounces i„ 10 dwt. Uu 80 dwt. i„ .rln~^r -•»«-.» 49 grains, in 8„ 9. How many dwt \n 4 «-, 5 dwt. ? ^ • ''' ^ ^^- '-^^d 3 dwt. ? in ^ _ — ♦ vii, XO. rintlir rv»r»«,— _ ounces m 6 pounds and 8 «z- ? in 5 lbs. 9 oz. ? oz. ? in i iap 100 TABLES. Avoirdupois "Weight. Avoirdupois Weight is used lo weigh all common goods, such as groceries, hay, grain, and ail nielals, exceitt gold and silver. The denominations of Avoirdui)ois Weight are tons, hundred- woiglils, quarters, pounds, ounces, and drams. 10 drams, ur, IC ounces 25 pounds 4 quarters 20 Jiundredweighl make 1 ounce, marked oz. " 1 ])ound, " lb. " 1 (juartor, " qr, " 1 hundredweight, cwt. " 1 ton, T. The pound Avoirdupois contains 7,000 grains. OliAL EXERCISES. 1. How many ounces in a pound ? in 4 pounds ? in 8 pounds ? in 10 pounds ? 2. How many lbs. in 2 cwt. ? in 7 cwt. ? in 9 cwt. ? 3. How many cwt. in a ton ? in 6 tons ? in 9 T. ? in 12 T. ? 4. How many ounces in 3 pounds ? in a hundred- weight ? in a ton ? 5. How many pounds in 32 ounces ? in 64 oz, } in 128 oz. > in 144 oz. } 6. How many cwt. and lbs. in 120 lbs. .' in 260 Ibs..^ in 340 lbs. > 7. How many pounds and ounces in 39 ounces ^ in 84 oz. .' in 90 oz. } 8. How many ounce ■ in 5 lbs. 11 oz. } in 4 lbs. 12 oz. .? in 10 lbs. 3 oz. > 9. How many lbs. in 6 cwt. 25 lbs. ^ in "7 cwt. 36 lbs. } 10. Howmany tons and hundredweight in 45 cwt.? in 92 cwt. ? in 130 cwt. ? foods, such as silver, )ns, hundred- oz. lb. qr. cwl. T. 4 pounds ? in 9cwt.? ? in 9 T. ? I hundred- 64 oz, ? in in 260 lbs.? 9 ounces ? n 4 lbs. 12 ^ in *7 cwt. in 45 cwt..' TABLES. Apothecaries' Weight. 101 This weight is used J,y apothecaries and nhvs'-ciin. in ,.;.• .. • medicines, but medicines are generally .o 7 i ,, " """" avoirdupois weight. ^ ^' '" ^'"' a"anl'ty. by Its denominations ;fp nniin,io ^ grains. ' '""'^'' ''''''''' '^'^^^'' ^oruples, and '^^0 grains, gr., make I scruple, marked so. 3 scruples <• i d,.am, - j^ 8 drams, .- i ounce, « oz' r:j ounces •< i pound, u j^' C^^Z. EJCERCrSES. 1. How many grains in a scruple ^ in 2 s.-ruplos > m 5 scruples ? m 7 sc. .? 2. How many sc. i,i a dram ? in 6 dr. ? in o ,],. ? m 20 dr..? ' ^^- • 3. How many sc. in 40 g-rs. .? in 90 .-rs ? in 1^>() grs. ? in 140 grs. ? ^^ 4 How many drams in an ounce ? in f, oz ? in 8 oz. ? m 15 oz. ? ^- • in » in s/^^'^T "'''''^ '^'''''' "' '^ '*'• • "' ^^ ■'^^- • i'^ '^^ «c- ^ 6. How many ounces in 24 dr. .' in 48 dr ? in 64 dr. ? m 96 dr. > ' ' ^ 7 How many ounces in a pound ? in .'} pounds > 111 5 pounds .' in 15 pounds > in 20 pounds ? 8. How many pounds in 48 oz. .? in 108 oz > in 240 oz. ? 9. How m-jny sc, in an oz. ? in a lb. ? in 1 Ih 6 oz. ? 10. How '' \ dram IS many grains in a dram ? scruples in 4 drams in 5 lbs. ? 102 TABLES. pi WiJVE Measure. Wine Measure is used for measuring all liquids, except ale, beer and milk. The denominations of Wine Measure are tuns, pipes, hogsheads, tierces, barrels, gallons, quarts, pints, and gills, 4 gills, gi., make t pint, marked pt. 2 pints 'i quarts 31 J gallons 4'2 gallons t)3 gallons 2 hogsheads 2 pipes qt. gal. bbl. tier. hhd. pi. tun. 1 quart, 1 gallon, I barrel, 1 tierce, 1 hogshead, 1 pipe, 1 tun, . The gallon of Wine Measure in the United States contains 231 cubic inches, and is equal to 8,339 Avoirdupois lbs. of distilled wafer, very nearly. The English imperial wine gallon contains 277.274 cubic inches and hence is equal to 1.2 times the wine gallon of the United States! OliAL EXERCISES. 1. How many gills in a pint > in 4 phits .? in 6 pints ? in 12 pts. .? in 20 pts. ? 2. How many pts. in a qt. > in 6 qts. .? in 8 qts > in 15 qts. ? * ^ • 3. How many gallons in a barrel ? in a tierce } in a hogshead } in a pipe > in a tun > / 4. How many pints in 12 gills ? in 26 gi. } m 3t gi. } in 50 gi. .? 5. How many quarts in 10 pts. } in 24 pts. > in 50 pts. ? in 84 pts. } G. How many gallons in 1 hhd. 10 gals. > in 2bbls. 15 gals. } 7. How many quarts in a barrel } pints in 2 gal- lons .? gills in 6 quarts ? 8 How many gallons in 72 quarts.? in 104 qts..? in 4 bbls. 4 gals. ? ^ 9. How many pts. and gi. in 18 gi. .? in 31 m. } m 53 gi. > in 74 gi. } 10. How many hogshead gals. } gallons in 3 pipes s in 6 tuns.? pint-s in 8 cept ale, beer s, hogsheafJs, contains 231 . of distillod cubic inches, Jniled Stales. ■nts? in 6 n 8 qts. ? tierce ? in ji. ? in SI ts. ? in 50 in 2 bbls. in 2 gal- 104 qts.? 31 gi. ? m inis in 8 TABl^ES. Ale or Beer Measure. 103 By this measure, beer, porter, and milk are measured. ThodenommotionsofBeer Measure .re hogsheads, barrols gal- lons, quarts, ana pints. . ••"Ills, gai. pmt 2 pints, pt., 4 quarts 36 gallons make 1 quart, marked qi. " 1 gallon, « gal. " 1 barrel, << |j^)| 1J barrel or 54 gals- » i hogshead, •< hhd.' OJiAL EJiEIiCJ8E8. 1. How many pints in a quart ? in 3 cits. ? in 8 qts. ? in 12 qts > i ■ i o 2 How many qts. in a gallon > m 5 gals. > in 7 gals .Mn 22 gals. .? ^ ^ 3. How many gallons in a barrel } in 3 barrels > m 5 barrels > in 8 barrels > 4. How many gallons in a hogshead > in 2 hhds > m 4 hhds } 5. How many qts. in 10 pts. > in 19 pts. > in 31 pts. > in 56 pts. > 6. How many gallons in 11 qts. } in 32 qts. > in 2 bbls. 2 qts. ^ ^ 7. How many qts. and pts. in 17, pts. > in 73 pts ? in 85 pints > ^ ' ' 8. How many barrels and gallons in 75 gallons ' in 110 gallons } 9. How many gallons in 2 bbls 5 gals > in 2 hhds 8 gals, ? 10. How many quarts in 18 pints .? gallons in 68 qts. J barrels in 144 gals. ? 5 i 104 TABLES Cloth Measure. Clolh Measure is used for measuring goods sold by the yard. Jts denominations are ells, yards, quarters, nails and inches. ^ inches, in., malio 4 nails •• 4 quarters " 3 quarters " 5 quarters " 6 quarters " nail, marked na quarter, " yard " Flemish ell, " Knglish ell, " qr. Fi. e. E. e. Frencli ell, " Fr. e. OJiAL EXERCISES. 1. How many inches in a nail > in 4 nails } in 6 nails } in 8 nails > in 10 nails > 2. How many nails in a qr .? in 5 qrs. > in 6 qrs. } in 12 qrs. .? in 20 qrs. } 3. How many qrs in a Fl. e. > in 5 Fl. c. > in 10 Fl e. > in 15 Fl. e. .? 4. How many qrs. in an E. e. } in 8 E e > in 30 E e .? in 50 E. e. > 5. How many quarters in a Fr. e. > in Fr e ? in 25 Fr. e. } in 40 Fr. e. > 6. How many yds. in 20 qrs. .? in 56 qrs. } in 96 qrs. } in 124 qrs. ^ 1. How many quarters in 1 Fr. e. and 5 qrs ? in 9 E e. and 2 qrs. .? 8. How many English ells in 25 qrs. > in 30 qrs. ? in 65 qrs. ? 9. How many nails in 3 Fl. e. .> in 6 Fr. e. ? in 8 E. e. .' 10. How many quarters in 5 yds. and 2 qrs. > nails in 1 qrs. and 3 nails ? inches in 2 Fr. e. ? yard. Jts s? ill 6 6 qrs. ? u 10 Fl. ill 30 E. '. e ? in ? in 96 |rs. ? in qrs. ? inSE. ? nails TABLES. Long Measure, 105 b.e':z.f;r;;' ""■' '^ '"^^^"^'""^ ^^-^^^^ -'^'^-^ -^-'^ to Us denominations are circles, degrees, leagues, miles furlom^s rods, poles or perches, yards, feel, inches, and barleycorns ' ' 3^barleycorns, b. c. make 1 inch, marked in. 12 inches 3 feet « r)J yards, or iq iVet, " •40 rods a 8 furlongs << 3 miles « C9J statute miles " CO geographical miles " 360 degrees •< 1 foot, 1 yard, I rod, pole or perch, 1 furlong, 1 mile, I league, I degree, 1 degree, I circle. It ft. yd. rd. fur. m. lea. deg. deg. cir. OUAL EJCEMCISES. 1. How many barley corns in an inch.? in 3 in- ches .? in 10 inches .? in 20 inches } in 9 ftHiATy""^"' "' ^ ^""^^ ■ "^ ^ ^^- • ^^ ^ ^t- •' int fdr; rrjyt' r ^^ ^-^^^ • "^ ^ ^^« • "^ ^ y^- -^ in 63^tT '"''''^ ^^''^' '" ^^ ^- • "' -^ ^*- • "^ 57 ft. .? in.'p inT^ T>\^^1 '^^ "^^^^^ "^ -^^ -^^- -^ "^ 3« in 49?tTr62Yr'^ "^^ '^^^^^ "^ ^^ ^-* ' "^ -^9 ^^- -^ 8. How many furlongs in 12 miles > leagues in *>! miles ? degrees in 360 geographical mileK ? ^ J. IIow many rods in 2"miles ? in 3 leagues > in 16 furloncrs } m 1 miL. a«/i .i f.,..! ^ ^^^^ " "^ furlongs > in 1 mile and 4 furlon^« . .0. How many feet in 16 yds. 2 ft. } inches !l 10 in. } in 8 ft. 106 Sq,uake Mkasubb. This measure is used for >»>asurinp all kinds of surfaces, such as land, boards, plaslcring, and every thing elso in which length and breadth only are considered. Its denominations are square miles, acres, roods, scpiare rods or poles, square yards, square fret, and square inches. Ii4 square inches make t square foot, marked sq. ft. •J square feet " I square yar.i, " sq. yd. 30^ square yards, " I sq. rod or pole " p. 40 sq. rds. or jioles '< t rood, « 4 roods " I acre, « 640 acres " l square mile, " A. Sq. M. ORAL EXEUCISEfi. 1. How many sq. in. in a sq. ft. ? in 4 sq, ft. > in 6 sq. ft. } in 8 sq. ft. ? 2. How many sq. ft. in 288 sq. in. > in *720 sq. in. .? in 1008 sq. in. .? 3. How many sq. in. in 2 sq. ft. 12 sq. in, > in 5 sq- ft. 80 sq. in. .? .' 4. How many sq. ft. in a sq. yd. .? in 12 sq. yds. .? in 20 sq. yds. } 5. How many sq. yds. in 36 sq. ft. } in t2 sq. ft. .? in 99 sq. ft. .? 6. How many sq ft. in 4 sq. yds. Ysq. ft. .? in ^ sq. yds. 8 sq. ft. > Y. How many sq. yds. in 5 sq. rds. .? in t sq. rds. } in 10 sq. rds. } 8. How many sq. rds. in 3 acres ? in 6 roods > in 5 acres ? l\ How many acres in 2 sq. m. ? sq. yds. in 81 sq. ft. } sq. rds. in 5 roods ? 10. How many sq. ft. in 5 sq. yds. 4 sq. ft. ? acres in 640 sq. rds. ? sq. it in '720 Bf^. in. ? Cables. 107 Surveyors' Measure. TI1.J Surveyoi's or GumUt's chain is generally used in surveying land. It is 4 poles, or fiC feet, in lenglli, and is divided into 100 links. 7 95/100 inches, in., make I link, marked li. 25 links << j rod or pole, " p. 4 poles, or 100 links « I chain, «< cha." 10 chains « 1 furlong " fur.' 8 fur. or 80 chains " 1 mile " M. 10 square chains " 1 acre, '< a. acres OMAL EXERufSES. 1. How many links in a rod ? in 4 rds. ? in 8 rods ? in 10 rds. ? 2. How many poles in a chain ? in 3 chains ? in 5 chains ? in 20 chains ? 3. How many chains in a furlong? in 4 furlongs? in 15 furlongs ? 4. How many furlongs in a mile ? in 12 miles ? in 20 miles ? in 30 miles ? 5. How many square chains in an acre ? in 7 acres ? in 12 acres ? 6. How many acres in 120 square chains ? in 150 s luare chains ? in 200*square chains ? 7. How many links in 2 furlongs ? chains in 2 acres ? poles in one furlonjr ? 8. How many chains in 5 furlongs and 6 chains ? in 7 furlongs and 8 chains ? 9. How m.any acres and chains in 37 square chains ? in 86 square chains ? 10 How many poles in 2 chai 6 chains and 2 poles ? ns and 3 jioles ? 11^ 108 TABLES. Solid or Cubic Measure. I '. This is used for mensuring solids, llmt is, things tiut liavo thro.) dimensions, viz., lenght, breadth and depth or lliickncss ; as wood, limber, stone, masonry, etc. 1728 cubic inches, c. in. milie I cubic foot, cu. ft. V cubic feet " t cubic yard, cu. yd. 40 cubic feet round timber " I ton, T. 4'2 cubic feet of shipping " 1 ton, T. 1)0 cubic feet hewn timber " 1 ton, T. 16 cubic feet " | cdd foot, c. ft. 8 cord feet or 128 cubic ft., " 1 cord of wood, C. OMAZ EXEJiCISES. 1. How many cubic inches in a cubic foot ? in 2 cu. ft. ? in 3 cu. ft. ? 2. How many cu. ft. in a cu yd. ? in 3 cu. yds. ? in 10 cu. yds. ? 3. How many cu. ft. in 2 cord feel ? in 10 cords of woo»«''^"^ P-ks, 2 pints, pt., 4 <|uarts H quarts -4 p pecks in a bushel i f,«»*"u . V^^Sr^^^^' quarts, bushels in 32 els'. hTo busYelir "'^ '^ '' '"^'^^« ' "^ '' '^^^'^- b/ ? ^^u'c b?'"v^ ^"""'^^ '" "" ^"'^''^ • "' ^ ^''- • ^*" '^ 6 How many pks. and qts. in 42 qts. ? in '^ ots ? in 50 qts. ? in 37 qts. ? M'^- • m .7 qts { pk pts 7. How many pints in a peck? in 4 pks.? in G 2 pks. i m 10 pks. ? many quarts and pints in in 39 pt s. ? in 43 pts. ? pints in 2i 9. How many gallons in 16 in 64 pts. ^ in 72 pts. ? in 80 pts. ? 10. Hqw many quarters pints? iu 48 pints? iu IS loads and 2 in 10 loads and 3 quarters ? f jn ^Q iQadg and i (juarter i 110 TABLES. CiRCL TiAR MeAHUUE. Circular Monsiire is applied to the divisions of the circle, and is iisnd in roclconing latitude and longitude and tho motion of the lii'uveniy bodies. It is often called Angular Measure, and is chielly used hy astronomers, navigators, and surveyors. Its denominations ure circles, signs, degrees, minutes, and seconds. on seconds,", malte 1 minute, marked '. ()() minutes " 1 degree, " **. 30 degrees " 1 sign, '< s. 12 signs, or 300", '< 1 circle, " c. OBAL EXERCISES. 1. How many seconds in a minute? iu 3' ? in 4'? in 6' ? 2. How many minutes in 120 seconds ? in 240"? in 360" ? in GOO" ? 3. How many minutes and seconds in 245 seconds ? in 195"? in 370"? 4. How many minutes in a degree ? in 4° ? in 8°? in 10° ? 5. How many degrees in 300 minutes ? in 420' ? in 480' ? 6. How many minutes in 5 degree^s and f!0 mi- nutes ? in 4° 15' ? in o^ 35' ? 7. How many degrees in a sign ? in 4 s. ? in 6 s. ? in Os. ?in 12 s.? 8. How many signs in 150 degrees ? in 270° ? in o'0ovin90°? ■. Ecv' many .sifrns in a circle ? in 6 c. ? i] 10 c. j»i ti c? in 30 .? ! lu. How many circles and signs in 20 signs ? iu S s. ? iu 63 s. ? iu 74 s. ? :lo, and is Lion of iho (I is cliii'lly oniinalions ?in 4'? 1 240"? econds ? n 420' ? •?0 mi- in G s. ? ?0° ? in 1 10 c. ? JUS ? ill BlSTANCE—DEPTHfti—IlEiailTa. Ill \ inches malcc 1 liand, used for measuring tho Im^ihi of hor^os 6 points " . I line, for measuring lengll. of pendulums for .looks 1 geometrical pace, used for moasuring uistancos. I laUioui, for measuring depths ai s.-a. I league, for measuring distances at soa. VI lines 5 feet ■ in 8 leagues ? in 15 leagues ? in 30 leagues V 6. How many lines in 24 points ? in 18 points ? in 48 points ? in 30 points ? •7. How many flithoms in 36 feet ? in 60 feet ^ in 47 feet ? in 108 feet ? 8. How many paces in 35 feet ? in 60 feet '? in tS feet ? in 00 feet ? 9. How many inches and lines in 4" lines ? in 65 lines i in t8 lines? in 17 lines ? 10. How many leagues and miles in 22 miles ? in M miles ? in 58 miles i -flp 112 TABLES, Time. 1 hour, h. Iday, d. 1 year, Y. I week, w. 1 month, mo. 1 year, Y. 1 month. nio. 1 year, Y. 1 century, C. This is reckoned by centuries, years, months, weeks, days, liours, minutes, and seconds. CO seconds, sec. make I minute, marked m. GO minutes " 24 hours " 305 days '« 7 days '< ■4 weeks (com. reck'g) " 52 weeks " " *< , 30 days '" " " 12 months ' " 100 years '< The following are the numbers of days in each montii : January, 31 days. July, 31 days. February, 28 days. August, 31 days. .March, 31 days. September, 30 days. April, 30 days. October, 31 days. ^ ^- May, 31 days. November, 30 days. June, 30 days. December, 3 1 days. ' The days in each month are often expressed thus : — Thirty days hath September, April, June, and November. February hath twenty-eight, and thirty-one the others rate, ^ Except in leap-year, happening once in four, When we give to February one day more. "^ A natural day has 24 hours. A Lunar month has 4 weeks, or 28 days, A Solar year has 365 days, 5 hours, 48 minutes, 48 seconds, nearly, , A Civil year has 12 calendar months, or 365 days. A Julian year has 13 lunar months, 1 day, 9 hours, or 365J days. ORAL EXERCISES. 1. How many seconds in a minute ? in 2 min. ? in 4 min. ? in 8 min ? in 10 min. ? 2. How many minutes in 360 seconds ? in 120 seconds ? in 240 seconds ? in *720 sec. ? 3. How many seconds in 4 minutes and 12 sec- onds ? in 3 min. 15 sec. ? ; .TABLES; 118 4. How many noUrs m 120 minuteslin 360 min- utes ? in 420 min. ? 5. How many minutes in 3 hours? in 5 hrs. ? in 8 hrs. ? in 12 hrs. ? in 30 hrs. ?^ 6. How many hours in a day ? in 3 ds. ? in 6 ds ? in 9 ds. ? in 12 ds. ? ,7. How; many 'days in 3 weeks? months in 5 years ? years in 3 centuries ? 8. Howjmany'days in' May ? in August? in March IJii January ?^in June ? ; 9.^ How many years and months in 15 mos.? in 29 mos. ?^in QS mos. ? in 42 mos. ? -^lO.^How'many weeks and daysjn 25 days ? in 34 days^?_in G9 days ? ' " -- - , Books and Paper. ^The terms folio,' quarto, octavo, duodecimo,' etc., indicate'the number of leaves in which a sheet of paper is folded. f" A sheet folded in two leaves is called a folio.. \ four « quarto, or 4to. <4 undles ? ales? in ims ? in, undies ? its in 2* ;s in 63 14 lbs. " t peck of salt. " 1 lirkin of butter. " t fagot of steel. " 1 barrel of potash. 1 barrel of raisins. " 1 barrel of soap. " 1 barrel of shad or salmon. " 1 gallon of molasses. " 1 stone of meat. " 1 tod. " 1 firkin of soap. " 1 sack. 1 barrel offish. " 1 barrel of cider. " 1 barrel of herring, Engl. " 1 hogshead on shore. " 1 hogshead at sea. " 1 bushel of oats. " 1 do. of buckwheat or barley. " 1 do. of Indian corn or rye. " 1 do. of wheat. OEAL EXERCISES. 1. How many dozen in a gross ? nnits in a dozen ? things in 2 scores. 2. How many pounds in a barrel of flour ? in a bbl. of pork ? in a bbl. of raisins ? 3. How many pounds in 2 gallons of molasses ? in 3 stones of lead ? in 5 stones of meat ? 4. How many pounds in a firkin of soap ?^ in a barrel of potash ? in a bbl. of shad ? 5. How many pounds in a bushel of wheat ? in 4 bu. of oats ? in 2 bu. of rye ? 6. How many dozen in a great gros.s ? inches in a cubit ? pounds in a peck of salt ? •7. How many gallons in a barrel of cider? in a "bbl. of fish ? in a bbl. of herring ? 56 lbs. 120 lbs. 200 lbs. 112 lbs. 250 lbs. 200 lbs. 11 lbs. 8 lbs. 25 lbs. 94 lbs. 364 lbs. 30 gallons 32 gallons 32 gallons 7J bushels 8 bushels 30 lbs. 46 lbs. 50 lbs. 60 lbs. 116 TABLES 10 cwt. :r= J ton. 5 4 2 1 Table of Aliquot Parts. Aliquot parts of Avoirdupois tveight. 121 lbs. == 1 qr. ^ " -= i " 8 oz. = I 11). 4 " =j » 2 1 1 = 5 1 = 10 __ 1 — 20 2 qrs. = 1 cwt. 1 " =4 " Aliquot parts of time 6 months ~- J year. 4 3 2 1 8 <( u << = i 1 = 6 1 — 9 1 — 12 15 days, = J month. 10 6 5 3 o 1 1 = 5 1 — 6 1 = 10 1 = 15 1 — 30 ORAL EXERCISES. ^ 1. How many cwt. in i of a ton ? in J of a ton ? m jig ot a ton V in ^ of a ton ? • 2. How many lbs. in | of a qr. ? in | of a qr. ? in I ot a qr. ? ^ 3 How many ounces in I of a lb. ? in J of a lb. ? m /g of a lb. ? 4. How many months in i of a year ? in I of n year ? in J of a year ? .^ ? u, 5 How many months in \ of a year ? in ?, of a year ? in jig of a year ? j i > 6. How many days in | of a month ? in i of -i month .^ in J of a month? ^ ^ •" 7. How many days in ,], of a month ? in ,\ of a month ? m J^ of a month ? i5 "^ •* TABLES IIT Aliquot parts of American Money. PAHTS OF !|1 IN NEW YORK l^ARTS OF $1 TN N. EN- CUIlRENCr. GLAND CURRENCY r. 50 cents — 4s. — %l. 3 shil $2- 33J — 2s.8a. — %h 2 " V3* 25 — 2s. — 41 Is. 6d. «• 20 — ls.7id- -% Is. t;,- 16s — Is. 4d. - - $(■>• [) ponce $8' 121 — Is. ~ n- 6 " •iPl2* ^ -8d. = 'Pi 2* 6 " |s. 6J — 6d. (ft] •IPltJ' 4 " is. 4J •< -4d. * 1 3 " is. 3| li — 3d. (ft 1 ^^ — i«. Aliquot parts of Sterling Money 10 shillings — £1 6 pence I shil. 6s. 8d. £h- 4 " * (( 5 shillings — £k. 3 " i it 4 (( 4- 2 " 1 ti (( 3s. 4d. 4- n " i (( 2s. 6d. £1 1 " 1 12 <( 2s hillings £^Q. 2 farth's iP enny Is. 8d. 12* 1 " ' i u ORAL EXERCISES. ' 1. How many cents in 4s. ? in 2s. ? in Is. 4 d. ? in 8d. ? 2. How many cents in 4d. ? in 3d. ? in 6d. ? in Is.? 3. How many shillings in $i ? in li ? in |J ? in $i ? 4. How many pence in is. ? in }s. ? in Js. ? in Js ? 5. How many shillini^s in £\ ? in £\ ? in £l ? in Xi?in,i„? 10 12 6. How many farthings in | of a penny in J of a penny? ^' 118 1^ ^ SI I ^- W X H O TABLES ^ 22 i!J sj; ^ S' *^"^' ^ '--^ 1^ -t* ^1 ^ ;^ 2 12 1' ^- ^ =^ ^-^ ^ o fi^l fl^l f?! I-H r-l rH CO CO CO 32 22 ^ ^ 2^ '^i '^T '-' "^ ^o -t^ -H (MO, r^^rt COCO^G^ rHQOrO(>ICrjX>COCOCOOi^'4l ^« r-< rH rl CO CO CO Ol (M ;!^ ?? IX] ^T* n! "^ "^ "+* <^ 1^ Ol ofMCJ':oco<:ocoot--trH '-' "-^ rH CO CO CO CM (M (M i"^ '"^ '^ 'M '"^ 1— I 10 10 "^ CO CO fvi Ol ^'>iai^cococoof2^^^ " '-< CO CO CO 01 (M Oi i-( O Ci T— ( O to •rt< -+( CO fM r^i _j _j '-< O-t-tiCOCO(MrHT-^ -< . .0 oi :o CO o 1-^ 2^ ^i; SS ::^ ^ g f^ I CO CO CO CM CM (M r-l ^ n! "^ ■'^ '^ ''-^ 'O 10 -f CO 00 01 n W CO :0 00 O 1^ -t* rH OD LTs rvi — ^ fiH 00 00 CO (M ?; 55 s i5 ^' ^^ -^ ^ < ^ >-0 -f "O tc 10 -t< -H CO C^l 1^1 1— I T-H 30 CO O I- -H r-l 00 .0 C' Ci S CS CO CO CO C-1 ^I CM rH T-i tH (ago) ^1' !3 fH o :::; H S m «. I— « TABLES. 119 I Rule /or fmdmg the number qfdai/s between any given periods by table on opposite page. Find the first given month on the horizontal litie in the left-hand column, and the other given month in the line at the top of the table, and to ifee number Oi days found at the intersection of the two Wnes add the difference between the days mentioned in the two gi\^n months. NoTE.-n must be observed, however, that when the number of tZT'^l- T '^ "''' mentioned month is greater than the given number of days In the second month, then the difference of days Zles '"'**'^''*^ '^^'^ «he number found at the intersection of Example l.-How many days from March ICth to the 24th of the next July ? The number of days at the intersection of the lines IS 122, and 24- 16:=: 8. the difference of days in the two given months. Hence, 1 22 + 8 = 130 days. Example 2.— How many days from the 25th of June to the 18th of the next April ? The nnmber of days at the intersection of the lines IS 304, aiul 25-18 = 7, the difference of days of the given month. Hence, 304 — 7 = 297 days. 3. How many days from May 15th to the 22d. of the next September ? 4. How many days from August 6th. to the 18th of the next October ? 5. How many days from January 10th to the 14th of the next July ? 120 MISCELLANEOUS WRITTEN EXERCISES. 1. How many pencils in a box containing' 2 great gross? An$. ll'2H pencils. 2. What cost 2Y boxes of writing ink, each 2J dozen bottles at 9 cents a bottle ? Ans. $72.00. 3. How many reams of paper in 40*78 sheets ? Ans. 9 reams, 15 ouires, 18 sheets 4. "What will 1 reams of legal cap cost at 35 cents a quire ? Ans. $40. 5. What cost boxes of fancy pen-holders each containing J gross, at 2J cents a piece ? Ans. |1G.20. 6. What cost 2 oz. of gold, if 3 dwt. cost !|2.*70. *7. What will 2 quarts of kerosene cost at 40 cents a gallon ? 8. What will 3 quarts of tomatoes cost at $1.20 a bushel ? 9. How many feet high is a horse IG handsxhigh ? 10. What is the difference between two square feet and two feet square ? 11. At 8 cents a peck, how many bushels of apples can be bought for $6.00 ? 12. If 25 lbs. of flour cost $1.25, what will 2 cwt. cost ? 13. How many half-pint bottles may be filled from 2J gallon of wine ? 14. What will 7 quires of paper cost at $3.20 a ream ? 15. What will 8 eggs cost at 18 cents a dozen? IG. If G oz. of tea cost 3G cents, what will 3 lbs. cost ? 17. What will a gallon of molasses cost at 5 cents a pint ? 18. At 8 shillings a pair, how many pairs of shoes can be purchased for 2 sovereigns ? M I « C E L 1. A N E (J U S , 1^1 >• 2 groat 18 penrih. oach 21 . 172.90. 3ts? 18 shce/.s 35 ceiiis 4w.s'. $40. ers oach S-. $10.20. 12.10. 40 cents 11.20 a IsJiigh? ) square of apples 1 2 cwt. led from $eS.20 a )zen ? 1 3 lbs. 5 cents of shoes 19. At what price must J dozen of chairs, worth |1 o.OO a dozen, be sold in order to gain 50 cents a piece ? 20. How much will a peddler gain by selling 3 dozen combs worth 30 cents a dozen, at 5 cents a piece '? 21. What will f of a lb. of candy cost at 2 cents an oz. ? 22. How many tablespoons each weighing 2 oz. can be made from 1 lb. 8 oz. of silver ? 23. How many leap years in a century ? 24. How many pills of 5 grains each can be made from J an ounce of quinine ? 25. If a gallon of wine cost |5.00, what will 3 pts< cost ? 26. What will it cost to paint a ceiling 12 ft. by 29 ft., at 25 cents a square yard ? 27. How many yards of Carpeting, a yard wide, will cover a floor 20 ft. long and 21 ft, wide ? 28. How many quarts of milk will a boy drink in a week, if he drink a pint a day ? 29. What is the weight in tons, &c. of 3 loads of potatoes, averaging 22 bu. each ; 1 load of wheat, 19 bu. ; and 4 loads of oats, each 25 bu. ? Ans. 4t. Scivt. 30. What will it cost to ship 75 t. 8 cwt. 70 lbs. of freight at G cents a pound ? Am. $9052.20. 31. How many farms of 75 acres oach in a tract of land 6 miles long and 5 miles wide? Ans. 2i)C) farms. 32. What is the height in ^eet of a horse 17J hands ^^S^ ^^ Ans. 5 ft. 10 in. ''?''* 'X I CONTENTS. SIMPLE NUMBERS, Introductory Definitions.. 1 Numeration and Notation. , 3 Arabic Notation ' 3 Numeration Table 15 Eoman Notation 32 Addition 26 Subtraction 46 Multiplication.. 62 Pivision ,...' 79 Introductory Fractions.... 94 TABLES. Federal Money English or Sterling Mo- ' ney Troy "Weight Avoirdupois Weight Apothecaries' Weight AVine Measure Ale or Beer Measure...... Cloth Measure Long Measure Square Measure 97 f< 98 99 100 101 102 103 104 105 106 Surveyors' Measure 107 Solid or Cubic Measure... 108 Dry Measure 109 Circular Measure HQ Distances — Depths — . Heights Ill Time 112 Books and Paper 113 Miscellaneous I14 Aliquot Parts 116 Given Dates .7.... 117