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Si" " "■ ~ 
 
 •s,^ irC^^:A 0.^^^/^^^^.^ 
 
 r"'- 
 
 THIS COURSE GMBRACBS 
 
 THREE DIVISIONS ■ 
 
 THE ELEMENTARY. INTE?IMEDIATE AND HIGHER. 
 
 ARITHMETIC 
 
 ELEMENTARY tOURSl;. 
 
 NEW HKRIEH 
 
 VY IHK 
 
 Brothers of the Christian Schools. 
 
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 MONTH EAL, 
 50 COXTE ST" 
 
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THIS COURSE EMBRACES 
 
 TRRKB DtTISIO.VS : 
 
 THE ELEMENTARY, INTERMEDIATE AND HIGHER. 
 
 ARITHMETIC 
 
 ELEMENTARY COURSE 
 
 NEW SERIES 
 
 BT THC 
 
 Brothers of the Christian Schools 
 
 •■ „ 
 
 MONTREAL, 
 30 9OTTE ST 
 
A 
 
 ''I 
 
 ENTERED according to Act of the Parliament of Canada, in 
 the year of our Lord, 1893, by 
 JEAN ROUTHIBR, 
 in the Office of the Minister of Agriculture and Statistics, 
 at Ottawa. 
 
 1. Aritli 
 
 2. A Nui 
 
 ; 3. A Uni 
 
 eomparpd, w! 
 
 A unit ma 
 
 4. A Qui 
 o street, the j 
 
 5. The g 
 I 3 Denominai 
 I 6. Aniui 
 
 AFracti 
 two-thirds, th 
 
 A Denoi 
 of coutiuuoui- 
 
 7. Arith 
 
 8. ArithuK 
 is called Nuv 
 
 9. Xumc 
 them when e; 
 
 10. Each 
 one, two, thrt 
 
 tEach of th( 
 rder. They a 
 formed of c 
 
f Canada, in 
 
 »d Statistics, 
 
 "vV 
 
 ARITHMETIC. 
 
 ELEMENTARY COURSE. 
 
 Introclnctioii. 
 
 !■ Arithmetic is the science of numbers. 
 
 2. A Number is a unit or a collection of units. 
 
 3. A Unit is the quantity to which n quantity of the same kind is 
 isompared, when it is desired to measure it. 
 
 A unit may also be defined to be a single thing or one. 
 
 4. A Quantity is any thing tlmt can me measured. Ex.: </w length of 
 a strtett the population of a city, the surface of a body, etc. 
 
 5. The general classes of numbers are: 1 Integers, 2 Fractions, 
 8 Denominate numbers. 
 
 6. An Integer is a number of integral units ; as, four, six, etc. 
 A Fraction is a number of the equal divisions of a unit ; as, one-half 
 
 two-thirds, three -fourths, etc. 
 
 A Denominate number is a number in which the unit is a measure 
 of continuous quantity; as, three yards, two pound . '^vefeet, etc. 
 
 ARITHMETICAL LANOUAGB. 
 
 7. Aritlimetical Language is the method of expressing numbers. 
 
 8. Arithmetical Language may be either oral or written. The former 
 is called Numeration, the latter Notation. 
 
 9. Numeration is the method of naming numbers and of reading 
 them when expressed by characters. It is the oral expreseion of numbere. 
 
 NUMERATION. 
 
 10. Each of the first nine numbers has received a separate name ; thus, 
 one, two, three, four, five, six, seven, eight, nine. 
 
 Each of these nine numbers express simple units or units of the fir»t 
 )rder. Tbey are formed by adding one to the preceding number, thus : two 
 •*" formed of one aud one, three of two and one 
 
KUMERATION. 
 
 The number after nine is colled ten. 
 
 Ten !• the unit of second order and is equal to ten vnits of the first 
 order. Tens may be counted or read just as the simple numbers ; thus, 
 
 one Un, two Una, three Unt nine tens / but usage has replaced these 
 
 words by the following : Un, twenty, thirty, forty, fifty, tixty, uveiUy, 
 eighty, ninety. . 
 
 The numbers intervening between two tens are formed by joining tUe 
 names of the first nine figures to each of the above tens. Thus lwe;Uy 
 one, twenty-two, twenty-three, till twenty-nine. However instead of saying 
 Un-one, Un-two, etc., usage has adopted the expressions eleven, twelve, 
 thirUen, fourUen, fifteen, sixteen, seventeen, eighteen, nineteen. 
 
 Tiie number following ninety-nine or teu-tcns is called hundred. 
 
 Hundred is the unit of the third order. 
 
 Hundreds are counted just as units are ; thus, one hundred, tvo 
 hundred, .... nine hundred. 
 
 The group of the" first three orders of units forais the first ixjriod or class 
 
 of units. 
 The number following nine hundred and ninety-nine or ten hundreds 
 
 is called thousand. 
 
 Thousand is the unit of the second period. The second period or 
 class of units comprises units, tens and hundreds, just as the first period. 
 
 The number after nine hundred and ninety-nine thousand nine 
 hundred and ninety-nine or a thousand thousands is called million. 
 
 Million is the unit of the third order. The fourth group of a thousand 
 millions is called a billion ; the fifth group a trillion, etc. Each of 
 these periods comprises three orders : units, tens and hundreds. 
 
 11. Remark.— Ten units of any order forms a unit of the ordrr 
 immediately above it. A thousand units of any period forms a unit of the 
 corresjtouding class in the period next above it. 
 
 Numeration table. 
 
 TllICI) l-F.l.li 
 
 First period 
 
 Second period 
 
 )■ First order Units. 
 
 .; Second " Tens. 
 
 Third " Hundreds. 
 
 (•Fourth " Thousands. 
 
 J Fifth " Ten-thousands. 
 
 (.Sixth " Hundred-thousands. 
 
 FoUllTH Htll 
 
 12. Notll 
 
 in three w, 
 letters (Romu 
 
 13. To rep 
 1 2 
 
 one, tw 
 
 Tlie first n 
 a value ; the 
 Hgure ; it ma 
 Willi ting. 
 
 14. Ppin( 
 two following 
 
 1.— When 
 
 I riglitrepresei 
 
 ' thousands ; tl 
 
 I 2.— The ter 
 
 \ 15, Every 
 
 Simple Vs 
 
 alone, the Ix 
 
 \ any other pla 
 
 In the nuni 
 
 5, its local va 
 
 second figure i 
 
 16. How 
 
 reprei 
 
 written succ* 
 
 first, zeros are 
 
 figures 
 
 The numbe 
 representing f 
 thirty is writt 
 
ts of the firflt 
 
 umbers ; thus, 
 
 replaced tliese 
 
 sixty, seventy, 
 
 by joining tliH 
 Thus twe;Uy- 
 
 istead of saying 
 eleven, twelve, 
 
 teen. 
 
 hundred. 
 
 le hundred, two 
 
 it period or class 
 
 r teu hundreds 
 
 econd period or 
 the first period, 
 thousand nine 
 1 million. 
 up of a thousand 
 
 I, etc. Each of 
 
 idreds. 
 
 it of the ordrr 
 
 rms a unit of the 
 
 is. 
 
 isands. 
 
 l-thousands. 
 
 Kl .Ml;|t.\riiJN. g 
 
 r Seventh •' Millions 
 
 Tnira. i-KMn,, \ Eijjhth •' Teu-millions. 
 
 I 
 
 '^^'''"tl' " Hundred-millions. 
 
 ( '''*»th " Uillions. 
 
 KouuTH Htuion .'l Klevnith " Ten-biUions. 
 
 I 
 
 '^ Tuilltli " lluiidit'd-billions. 
 
 NOTATION 
 
 12. Notation is tinj^ method ol writing numbers. This mny be done 
 in three ways : ] By xoords, 2 By figures, (Arabic Method), 3 By 
 letters (Komm Method). 
 
 13. To represent numbers ten figures are used. These are ; 
 
 12 3 4 5 6 7 8 9 
 
 one, two, three, four, five, s'lx. seven, eight, nine, zero 
 
 -in a ^ 1 ""^ naught. 
 
 1 he first nine figures are said to be significant, because they re,)resent 
 a value ; the tenth, zero, represents nothing by itself, it is an auxiliary 
 figure ; it may iiold the place of a unit of any order when this unit i. 
 wanting. 
 
 14. Principles. All number may be represented by means of the 
 two following principles : 
 
 l.-When sevenl figures are written one after the other, the first to the 
 right represents units ; the .econd. tens ; the third, hundreds ; the fourth 
 thousands ; the fifth, ten-thousands. ' 
 
 2.-The tero is put in the place of any order of units that may be want ne 
 
 15. Every figure has two values; a «m;,fe and a /ocai value, 'lu^ 
 Simple Value of a figure is the number it expresses when it stands 
 alone, the Local Value of a figure is the number it expresses when in 
 any other place than units place. 
 
 In the number 6,604, the simple value of the first figure to the left is 
 5, Its local value is 5 units of thousands ; so also the simple value of the 
 second figure is 6. its local value is 6 hundreds, etc. 
 
 16. How to writeanumber.-To represent a number the 
 figures representing the hundreds, tens and units of each period are 
 written successively from left to right ; the highest periods are written 
 first, zeros are used to take the place of missing orders 
 
 The number three hundred and eight is written 308 ; and the number 
 representing forty million five hundred and twenty-seven thousand and 
 thirty IS written : 40,627,030. 
 
4 Nl'MF.RATION. ^ 
 
 17. How to l'eiUlauuniber.--To read a number written in 
 figures, it is divided, at least mentally, into periods of three figures, going 
 from right to left ; then the groups are successively read commencing to 
 the left, and giving to each one the name of the period it represents. If 
 an order of units or even un entire class were wanting, it should 
 not be mentioned. 
 
 Thus 37,409,000,265 would read : thirty-seven billion four hundred 
 and nine million two hundred and sixty-five. 
 
 Roman Figures. 
 
 18. To write numbers tiie Kouiaiis used the following characters : 
 
 J, V, X, L, C, D, M. 
 
 •whose values were : 1, f, 10, 50, 100, 500, 1000. 
 
 19. Priuciplcs.— 1. The letters placed to the right of another, add 
 tluir value to Dial of t/ie other if less than it or equal to it. 
 Thus the numbers : III, XV, ^ XXVll, CLXl, MDCCXVI 
 are re|id . 3, 15, 27, 161, 1716. 
 
 2. Any letter placed to the left of another should be deducted for tlie 
 value of this number if less than it. 
 
 Th3 numbers : IV, XXIX, XL, XCI, CDXIX. 
 are read : 4, 29, 40, 91, 419. 
 
 3. A dash over an expression increases its value a thousandfold. Thus 
 Vlll denotes eight thousan I. 
 
 EXERCISES IN NUMERATION. 
 
 Read the following iiumberM : 
 
 1. 
 
 10 
 
 
 15 
 
 
 17 
 
 
 24 
 
 
 26 
 
 
 29 
 
 81 
 
 2. 
 
 35 
 
 
 40 
 
 
 48 
 
 
 49 
 
 
 53 
 
 
 08 
 
 69 
 
 3. 
 
 62 
 
 
 72 
 
 
 80 
 
 
 86 
 
 
 98 
 
 
 99 
 
 OK 
 
 4. 
 
 100 
 
 
 101 
 
 
 040 
 
 
 160 
 
 
 169 
 
 
 406 
 
 768 
 
 5. 
 
 004 
 
 
 050 
 
 
 505 
 
 
 523 
 
 
 006 
 
 
 796 
 
 801 
 
 6. 
 
 1 027 
 
 1 
 
 060 
 
 1 
 
 090 
 
 1 
 
 126 
 
 2 
 
 002 
 
 3 
 
 019 
 
 5 404 
 
 7. 
 
 11 Oil 
 
 11 
 
 101 
 
 4 
 
 046 
 
 111 
 
 010 
 
 10 
 
 409 
 
 12 
 
 002 
 
 15 040 
 
 8. 
 
 116 096 
 
 273 
 
 459 
 
 430 
 
 590 
 
 246 
 
 689 
 
 386 
 
 211 
 
 406 
 
 804 
 
 679 43-2 
 
 Express tbe following numbers In flgiires : 
 
 9. Ten, eleven, thirteen, eighteen, twenty-one, twenty-four. 
 
 10. Twenty-eight, thirty-four, thirty-seven, forty-three. 
 
 11. Forty-eight, fifty, sixty-four, sixty-nine. 
 
 12. Eighty-eight, uiuuty-five, one hundred. 
 
 13. One hundred and three, one hundred and eight, one hundred and 
 
 ten, one hundred and twenty-three. 
 
 1 
 
 ■f 
 
 33 
 
 1 
 
 34 
 
 1 
 
 35. 
 
 
 36. 
 
 ; 
 
 37. 
 
 
 38. 
 
 '4 
 
 39. 
 
 1 
 
 40. 
 
 41. 
 
 ;i 
 
 42. 
 
 63. 
 
 1 
 
 64. 
 55. 
 
 
 56. 
 
 
 57. 
 
 1 
 
 68. 
 
 1 
 
 \/ 
 
NL'MKllATION. 
 
 5 
 
 nber written in 
 >ree figures, going 
 i commencing to 
 it represents. If 
 anting, it sliould 
 
 ion four hundred 
 
 ving characters : 
 D, M. 
 
 500, 1000. 
 of another, add 
 
 , MDCCXVI 
 1716. 
 
 deducted for tlie 
 
 CDXIX. 
 
 419. 
 
 uandfold. Thus 
 
 'N. 
 
 29 
 
 08 
 99 
 
 406 
 
 796 
 
 3 019 
 
 12 002 
 
 06 804 
 
 arcs: 
 
 ty-four. 
 le. 
 
 81 
 
 69 
 
 09 
 
 768 
 
 801 
 
 5 404 
 
 15 040 
 
 679 43-2 
 
 14. One hundred and lifty-scven, one liuudred an.l sixty-eic-ht, two 
 
 hundred and eleven. ° 
 
 15. Three hundred and twelve, four hundred and thirteen, fivu hundred 
 
 and fourteen. 
 
 16. Six hundred and fifteen, eight hundred and seventeen, one hundred 
 
 and nineteen. 
 
 17. Seven hundred and twenty, one hundred and tweuty-one, tiuee 
 
 hundred and three. 
 IS. Two hundred and ninety-eight, five hundred and nineteen. 
 
 19. Nine hundred and sixty-eight, four hundred and seventy-four. 
 
 20. Seven hundred and ninety-seven, eight hundred and eighty. 
 
 21. Two thousand and five, four thousand and twenty-four, one 
 
 thousand and seven. 
 
 22. Ten thousand and eight, twcnty-four thousand and teen. 
 
 23. Three hundred thousand raid twenty-seven, seventy diousand and 
 
 three. 
 
 24. Two million one thousand and nine, fifteen million five thousand. 
 
 25. Four hundred and six million nine thousand and fifty-six. 
 
 26. Six hundred and six million sixty thousand six hundred and six. 
 
 27. Twenty billion seventeen million one thousand and forty 
 
 28. One hundred and fifty billion forty-five thousand three hundred 
 
 and one. 
 
 29. Fifty-six million ten thousand and eight. 
 
 30. Three hundred and thirty-three million eighty-one thousand. 
 81. Nine million seventy-seven thousand and fifteen. 
 
 32. Five billion thirteen milUon two thousand and twelve. 
 KzprcM In flvures the fol lowing numbers t 
 
 33. 
 34. 
 35. 
 36. 
 37. 
 38. 
 89. 
 40. 
 41. 
 42. 
 
 VII 
 
 IX 
 
 XIV 
 
 XV 
 
 XXI 
 
 XXfX 
 
 XXXIV 
 
 XLIII 
 
 LIX 
 
 LXXXVI 
 
 53. 
 54. 
 55. 
 
 56. 
 
 43. XC 
 
 44. XCVII 
 46. XCIX 
 
 46. cxcviri 
 
 47. ODXXIX 
 
 48. DLXXXVI 
 
 49. DCDLXXVII 
 
 60. MCCXXXV 
 
 61. MDCLXXII 
 
 62. MDCCLXLIII 
 Expresi. ||.« foUowingr numbers In Homnn fiff.ires : 
 
 I 13 16 19 25 31 
 
 » «2 69 76 83 89 
 
 95 
 500 
 
 98 
 540 
 
 101 
 650 
 
 212 
 811 
 
 319 
 
 842 
 
 me hundred audi 57. 1 000 1 019 1 146 1 237 1 328 
 
 347 
 955 
 
 44 
 
 90 
 418 
 963 
 
 58. 1 800 1 824 
 
 1 848 
 
 1 556 1 666 
 
 1 859 1 883 1 900 2 
 
 OOU 
 
/ 
 
 I 
 
 m 
 
 59. 
 60. 
 61. 
 62. 
 
 63. 
 64. 
 65. 
 66. 
 67. 
 68. 
 69. 
 
 Vo. 
 
 71. 
 72. 
 73. 
 74. 
 
 75. 
 76. 
 
 77. 
 78, 
 79. 
 
 80. 
 81. 
 82 
 
 ADDITION. 
 
 Oral exercises. 
 
 What is a unit ? Name the dilFerent kinds of numbers. 
 
 "V^hat is an integer? Define a fraction. 
 
 In how many ways may numbers be expressed ? 
 
 Name the orders of units in the first period. — In the second — In 
 
 the third. 
 How mauy values has every figure ? 
 What is the local value of 7 in 75 ? 
 What is the value of the Roman figur_ps V, X, L, C, D ? 
 What is the use of the figure zero ? 
 How many figures are required to write a hundred units ? 
 How many figures are required to write a thousand units ? 
 How many tens are required to make a thousand ? 
 How many figures are required to write ten-thousand units ? — a 
 
 hundred-thousand ? — a million ? 
 How many (hundreds in ten-thousand ? 
 How many ten-thousands in a million ? 
 How many hundred j in a hundred-thousand ? 
 In a million how many thousands are there ? How many hundreds ? 
 How many units in a hundred 1 How many tens ? 
 How many tens in a thousand ? 
 How many hundred-thousands in p. million ? 
 How many thousands in a billion ? 
 How mauy figures are required to write a number whose highest 
 
 unit is a thousand ? 
 What is the highest unit in a number of five figures ? 
 What is the highest unit in a number of eight figures ? 
 How many periods are required to write a number of twelve figures ? 
 
 1 
 
 FUNDAMENTAL OPERATIONS. 
 
 ADDITION. 
 
 21. Addition is the process of finding the sum of two or 
 more numbers of the same nature. 
 
 The result of addition is called the sum or total. 
 
 22. Ni 
 same del 
 15 doUari 
 they are 1 
 
 23. Ad 
 addition < 
 118+65. 
 
 24. To 
 thorough! 
 the sum o 
 
 and 
 and 
 and 
 and 
 and 
 and 
 1 and 
 1 and 
 1 and 
 1 and 
 
 1 
 1 
 1 
 1 
 1 
 1 
 
 2 and 
 
 2 and 
 
 2 and 
 
 2 and , 
 
 2 and 
 
 2 and 
 
 2 and 
 
 2 and ' 
 
 2 and ( 
 
 2 and i 
 
 3 
 3 
 3 
 3 
 3 
 3 
 
 and 
 and 
 and 
 and 
 and 
 and 
 
 3 and 
 
 8 and 
 
 3 and 8 
 
 3 and 9 
 
>.A> 
 
 'S. 
 
 e second — In 
 
 its? 
 lits ? 
 
 md units ? — a 
 
 fiuy hundreds 1 
 
 whose highest 
 
 twelve figures ? 
 
 
 )NS. 
 
 m of two ov 
 
 tal. 
 
 ADDITION'. 7 
 
 22. Numbers of the same nature are those which are of the 
 same denomination or name. Ex. 25 dollars, 6 dollars, 
 15 dollars, are numbers which have the same denomination ; 
 they are then of the same nature. 
 
 23. Addition is expressed by the sign -f-, called plus. The 
 addition of the numbers 132,118 and 65 is marked • 1324- 
 118+65. 
 
 24. To solve any addition with ease, it is necessary to be 
 thoroughly familiar with the addition table. This table gives 
 the sum of any two figures. 
 
 Addition Table. 
 
 1 and are 1 
 
 I and 1 are 2 
 
 I and 2 are 3 
 
 1 and 3 are 4 
 
 1 and 4 are 5 
 
 1 and 5 are 6 
 
 1 and 6 are 7 
 
 1 and 7 are 8 
 
 1 and 8 are 9 
 
 1 and 9 are 10 
 
 2 and are 
 
 2 
 
 2 and 1 are 
 
 3 
 
 2 and 2 are 
 
 4 
 
 2 aud 3 are 
 
 5 
 
 2 and 4 are 
 
 a 
 
 2 and 5 are 
 
 7 
 
 2 aud 6 are 
 
 8 
 
 2 and 7 are 
 
 9 
 
 2 and 8 are 
 
 10 
 
 2 and 9 are 
 
 11 
 
 and 
 and 
 and 
 and 
 and 
 and 
 and 
 and 
 and 
 and 
 
 are 
 
 1 are 
 
 2 are 
 
 3 are 
 
 4 are 
 
 5 are 
 
 6 are 
 
 7 are 
 
 8 are 
 
 9 are 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 3 and are 3 
 
 3 aud 1 arc 4 
 
 3 and 2 are 5 
 
 3 and 3 are 
 
 3 and 4 are 7 
 
 3 and 5 are 8 
 
 3 aud 6 are 9 
 
 8 aud 7 are 10 
 
 3 aud 8 ore 11 
 
 3 and 9 are 12 
 
 aud are 
 
 7 and are 
 
 7 
 
 7 aud 1 are 
 
 8 
 
 7 and 2 are 
 
 9 
 
 7 aud 3 are 
 
 10 
 
 7 aud 4 are 
 
 11 
 
 7 and 5 are 
 
 12 
 
 7 and 6 are 
 
 13 
 
 7 and 7 are 
 
 14 
 
 7 and 8 are 
 
 la 
 
 7 aud 9 are 
 
 16 
 
 and 
 and 
 and 
 and 
 and 
 
 1 are 
 
 2 are 
 
 3 are 
 
 4 arc 
 .') are 
 
 and 6 are 
 and 7 are 
 aud 8 are 
 and 9 are 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 are 
 
 6 and 
 6 aud 
 6 and 
 6 aud 
 6 and 
 
 5 and 
 
 6 and 6 are 
 6 and 
 6 ami 
 
 are 
 are 
 are 
 are 
 are 
 
 are 
 .ire 
 
 6 aud 9 are 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 8 and are 8 
 
 8 and 1 are 9 
 
 8 and 2 are 10 
 
 8 and 3 are 11 
 
 8 aud 4 are 12 
 
 8 and 5 are 13 
 
 8 and 6 are 14 
 
 8 aud 7 are 15 
 
 8 aud 8 are 16 
 
 8 aud 9 are 17 
 
 9 and 
 
 9 and 
 9 and 
 9 and 
 9 and 
 9 and 5 
 9 and 6 
 9 aud 7 
 9 aud 8 
 9 aud 9 
 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 are 
 
 9 
 10 
 11 
 12 
 13 
 14 
 15 
 16 
 17 
 18 
 
iiii 
 
 "J ADDITION. 
 
 PROBLEM. 
 
 25. WhcU ia the sum of 748, 695 and 874. 
 
 Solution. — The numbers are written so that the Opkbation 
 
 terms of the same order stand in the same column, units 748 
 
 under units, tens under tens, etc ; begin at the right to 695 
 
 add: 4 and 5 are 9, 9 and 8 are 17, or 1 ten and 7 874 
 
 units ; 7 is written under the column of units and the ten 
 
 is added to tlie column of tens : 1 and 7 are 8, and 9 are Total 2317 
 17, and 4 are 21 ; 1 ten and 2 hundreds ; write the 1 under the column 
 of tens and add the 2 to the column of hundreds. 2 and 8 are 10, and 6 
 are 16, and 7 are 23 ; 3 hundreds and 2 thousands, write the 3 under the 
 column of the hundreds and place the 2 to the left in the place of thousands. 
 Hence the sum of the numbers is 2,317. 
 
 26 Remark. —In pn.ctice the operation is performed thus: 
 4 and 5. . . . 9 and 8 . . . . 17 write 7 and carry 1 ; 
 
 1 and 1 .... 8 and 9 . . . . 17 and 4 .... 21 write 1 and carry 2 ; 
 
 2 and 8..;. 10 and 6.... 16 and 7 .... 23 which is written. 
 
 27. Rule. — /. Wrile the numbers so that the units of the 
 same order stand in the same column, and draw a line 
 beneath. 
 
 II, Begin at the units, add the number of each column 
 separately, and write the number under it, if less than ten. 
 
 III, 1/ the sum of any column is m,ore than ten write the 
 units only underneath the column and add the tens with the 
 next column. 
 
 IV, Write the entire sum of the last column. 
 
 28. PrOOfofaddition.— Find the sum of 1543 
 the figures in each column commencing at the 678 
 ^p, the total found should be the sum as that 482 
 found in the first operation. 1074 3783 
 
 29. Secondmethod.— Theproof ofanad- 2156 
 dition compi'ising several lines may be made as 1354 
 follows : the numbers are added in groups of 769 
 five or six, and the sum of these different totals 802 
 is afterwards foumd, this sum should equal that 1G78 GSOi a 
 already found. 10582 10582 
 
 exb: 
 
 83. 
 
 84. 
 
 An!« 
 
 Ans 
 
 8.5. 
 
 Ans. .. 
 
 86, 4( 
 
 Ans. . . 
 
 99. / 
 
 100. 
 
 101. 
 
 102. 
 
 103. 
 
 104. 
 
 105. 
 
 106. 
 
 107. 
 
 loS. 
 
 109. 
 
 110.^ 
 
 111. 
 
 112. 
 
 113. 
 
 114. 
 
 115. 
 
 116. 
 117. 
 118. 
 119. 
 120. 
 121. 
 122. 
 123.' 
 124. 
 
ADDnnioN. 
 
 Opeuation 
 748 
 695 
 
 874 
 
 Total 2317 
 ier the column 
 
 8 are 1 0, and 6 
 the 3 under the 
 ice of thousands. 
 
 1 thus : 
 
 1 and carry 2 ; 
 is written. 
 
 e units of the 
 ' draw a line 
 
 each column 
 than ten. 
 
 ten write the 
 tens with the 
 
 1543 
 
 678 
 
 482 
 
 1074 
 
 3783 
 
 2156 
 
 1364 
 
 709 
 
 802 
 1G78 
 
 EXERCISES IN NUMERATION AND ADDITION. 
 
 Alia ihc rullowiiiir nuinberM : 
 
 83. 
 
 84. 
 
 85. 
 
 Ans. 
 
 Anfl. 
 
 412 
 325 
 
 514 
 342 
 
 87. 
 
 748 
 28.') 
 
 An 
 
 3. 
 
 i 
 
 Ans. 
 
 86. 
 
 6976 
 827845 
 535694 
 
 405789 
 
 6854 
 
 76768 
 
 6304 
 
 10582 10582 
 
 88. 
 
 89. 
 
 7<i.'. 
 
 .\ns. 
 
 Ans. 
 90. 
 
 Ans. 
 
 671079 
 567765 
 
 875449 
 
 996898 
 
 3824 
 
 745+223 
 148+750 
 632+243 
 475+204 
 557+227 
 789+209 
 575+405 
 545+429 
 574+219 
 486+297 
 596+279 
 489+257 
 345+456 
 4.57+754 
 896+944 
 897+409 
 609+769 
 707+797 
 779+776 
 744+659 
 575579+426145 
 973476+595649 
 898423 + 769579 
 574615 + 697470 
 674907+575799 
 477424+648695 
 
 91. 
 
 !»2. 
 
 Ai S. 
 
 8r..]4'.4 
 90727!) 
 
 576r)07 
 447279 
 
 95 
 
 Ans. 
 
 93. 
 
 Ans. 
 
 94. 
 
 6823 
 9S9'347 
 724839 
 
 4927 
 
 98896 
 
 679589 
 
 Ans. 
 
 125. 
 
 126. 
 
 127. 
 
 128. 
 
 129. 
 
 130. 
 
 131. 
 
 132. 
 
 133. 
 
 134. 
 
 135. 
 
 136. 
 
 137. 
 
 138. 
 139. 
 140. 
 141. 
 142. 
 143. 
 144. 
 145. 
 146. 
 147. 
 148. 
 149. 
 160, 
 
 Ans. 
 
 96. 
 
 £76721 
 464934 
 
 853799 
 764581 
 
 Ans. . . , 
 
 97. 
 
 Ans. 
 
 98. 
 
 357047 
 
 79879 
 
 €^49754 
 
 452372 
 
 9694 
 
 877783 
 
 Ans. 
 
 475670+694957 - 
 
 727519+844619 ' 
 
 995676+576644 
 
 789476+617094 
 
 547764+350097 
 
 597091+447089 
 
 895467+301959 
 
 709987+605304 
 
 794691+657784 
 
 829651+728577 " 
 
 789107+695999 H 
 
 894575+876934 
 
 759544^-877409 
 
 657897+794976 
 
 707809+976437 
 
 856437+934579 
 
 576279+495176 
 
 882354+576937'* 
 
 650769+775678 
 
 765097+975985 
 
 578467+854359 
 
 307450+850967 
 
 7456744-.^02966 
 
 980079+395891 
 
 807406+360706 
 
 805464+890316 
 
/ 
 
 10 
 
 ADDITION. 
 
 151. 217904+548254-679yt)4 
 
 152. 897452+920672+746794 
 
 153. 904525+876577+9283i)5 
 
 154. 987864+64247+809456 
 
 155. 741854+7465+3978 
 loti. 327410+7689+456351 
 157. 59827+747365+984576 
 15.S. 677491+5887+976642 
 15lt. 854947+967876+7897t)7 
 KiO. 654576+976787+898694 
 161. 654789+773212+564342 
 lti2. 495837+72224+795477 
 ir;). 676976+799884+685544 
 1(>4. 834905+976827+895795 
 
 165. 954653+497974+68939D 
 
 166. 5276+576423+760554 
 
 167. 654957+78786+547679 
 
 168. 7809+356377+254594 
 
 169. 34827+376956+798898 
 
 170. 87851+676724+375697 
 
 171. 78947+364705+495827 
 
 172. 676+456694+972397 
 
 173. 4.')0017+696459+807576 
 
 174. 576895752+495847967+9954634 
 176. 376457897+453376586+547684794 
 
 176. 654234654+568976456+876889999 
 
 177. 667954+862945677+452789654 
 
 178. 587654927+674987634+486856858 
 
 179. 576795984+687987877+793676785 
 
 180. 376452677+7546984+678667646 
 
 181. 476796675+764579889+507687964 
 
 182. 467676324+6847987+689698798 
 
 183. 74234654+986876497+747987854 
 
 184. 354796452+477689376+766876889 
 
 185. 4347651+865755561+447675384 
 
 186. 645606997+2754884+567875776 
 
 187. 745676462+356789584+789898976 
 
 188. 7652927+535746795+676898888 
 
 189. 798652450+7987987+956896789 
 
 190. 650475875+6984989+889796854 
 
 191. 74678432+7465374+847963459 
 
 192. 7660342+974376457+83085768 
 
 193. 794217476+6964307+954307 
 
 194. 66276454+367796709+6719187+577485S55 
 
 195. 576450079+94196376+65438+560898275 
 
 196. 57874089+4786774+875697897+965665 
 
 197. 789894607+6546754+73836454287948 
 
 198. 6798954+452679687+7665+777423749 
 
 199. 56884569+677958888+3735894+469962 
 
 200. 7847976+46964624+74548935+3856907 
 
 201. 7692762+79764276+736577423 + 4798234 
 
 ?02. 
 203. 
 204. 
 205. 
 206. 
 
 213. 
 214. 
 215. 
 216. 
 217. 
 218. 
 
 222. 
 223. 
 224. 
 225. 
 226. 
 2:27. 
 228. 
 229. 
 230. 
 
 231. Fifty 
 
 232. Si.\ty 
 
 233. Five 
 units, uiiie 
 
 234. Sev 
 teeu units. 
 
 235. Foil 
 thousnud ai 
 
 236. Eig 
 eight, two 1 
 
 237. Fou 
 s^iven huudi 
 
 238. Thii 
 six hundred 
 
ADDITION. 
 
 78;54254+086«7637^+54476+77664986r 
 
 / 808+8867666644-834251+977407307 
 
 796487825+4754954+92236+47623564'> 
 
 452376824+1364795+898987885+856676 
 
 746834232+988978345+75576+89452372 
 
 ^i"f*+^^7976469+89547978+97997807 
 
 96577+476784896+7929654+856934701 
 
 70542+653476+764589985+579698794 
 
 97334+989296857-^97576854+32677496 
 
 ^o^J«fe^+^^^^^*'^^+3«"576376+489236579 
 
 78476854+5995876+889689+979375487 
 
 4809675+307685494 + 96972+807574676 
 
 475879+674275827+7454+3976798 
 
 «^i?i?^^^+^^'^S^ + ^57684754+9767896984.76i5.; 
 
 676401888+765465854+654754976+i89894±j8j? 7 . 7 
 
 507427+834236454+766687935+94879+476372'tH4 
 
 75685378+837456+24359876 + 507876934+89^432 
 *.l^^?i-/'^^^^^«+«»''76+876247689+797685764 
 
 '^f^?I«^50+56437+874954653 + 6788K2+4976569 
 476850+79643279 + 898767984^ 87678797+7709 47^ ^08 156 
 
 95673987+549637709+34907+9871036L+q87%7J?3?8g^ 
 
 Kxpress (he rollowinir numbers aiul flnu their finni : 
 
 ^ T'^'^t" ""'''' "'»«^yfi^« "«»■<*. seventy-eightunrts. 
 
 .3-. Sixty-three unit,, eighty-nine units., seventy-seven u„i/,. 
 
 -33 Five hundred and sixty-five units, four hundred and thirtv-six 
 
 units, nine hundred and eighty-five units. ^ 
 
 teen LS"" '"'""""'"""'"•""" ""■^*' "'"^^^^^ "-■^'. »"- 
 
 235. Four thousand and nine, sixteen thousand and fifty-four three 
 thousand and one. ten thousand and thirty-three 
 
 .if ^^'f*!l""f '''/"'* thirty-aiue. three h mdred and twenty- 
 eight, two hundred and eighty-three, . ^ 
 
 237 Four hundred and stventyuine, eight hundred and fifty-six 
 soven hundred and nineteen. •' ' 
 
 • ^f ■ J^?*''^ *^°"''"^ ''°"'" ^""^''^^ «»d eleven, sixty-one thousand 
 8.x hundred and sixteen, three hundred and seventy-eight! 
 
 11 
 
 ?02. 
 203. 
 204. 
 205. 
 206. 
 207. 
 208. 
 209.' 
 210. 
 
 ^12. 
 213. 
 214. 
 215. 
 216. 
 217. 
 218. 
 219. 
 220. 
 221. 
 
 222. 
 223. 
 224. 
 225. 
 226. 
 227. 
 228. 
 229. 
 230. 
 
/ 
 
 i/ 
 
 ii! 
 
 WA 
 
 12 
 
 ADDITION. 
 
 239. Thirty thousnnd and ninety-six, seventy-eight thouHand and 
 seven, eighteen thousnnd six hundred and nine, twenty-two thousand 
 nine hundred and seventy. 
 
 240. Five hundred and ten, eighteen hundred and forty-four, three 
 thousand eight hundred and ninety-five, six hundred and three, one 
 thousand and thirty-three, nine hundred and ninety-on». 
 
 241. Fifteen thousand three hundred and nineteen, eleven hundred 
 and seventy-six, seven hundred and two, three hundred and thirty-five, 
 thirteen hundred and fourteen. 
 
 242. Eight hundred and sixty-three thousand four hundred and fifty- 
 five, three hundred and eighty tliousand four hundred and sixty-weven, 
 nine hundred and three v.housund six hundred and eighty-two, one 
 hundred and forty six thousand three hundred and seventy. 
 
 Oral Exrirciaes In Numeration and Addition. 
 
 243. How many tens in 1783 units ? 
 
 244. How mflny hundreds in 18860 ? 
 
 245. How many ten thousands in 52465346 ? 
 
 246. What order of units represents : 1° 
 3" hundred-thousands ? 
 
 247. What order of units represents : 1° ten-thoui 
 3' ten-millions ? 
 
 248. How many zeros to the right of a hgtire representing 
 2' thousands, 3° hundreds, 4° millions ? 
 
 249. In what order and period are : 1' tens, 2* hundred-millions, 
 30 thousands, 4" ten-thousands, 5" millions, 6" ten-millions, 7" 
 huntlreds ? 
 
 250. What is the sum of: 1.— 4-f6+5 ; 2.-3+7+9; 8.— 10+6+ 
 4 ; 4._8+l3+6 ; 5.-12+10+9 ; 6.-15+7+14 ; 7.-16+12+9 ? 
 
 251. ^Vhatis the sum of: 1.— 11+6+7 ; 2.— 10+8+6+7 ; 3.-34+ 
 25 ; 4.-35+52 ; 5.— 40+30+6 ; 6.— 46+31 ; 7.-34+25+8 ? 
 
 252. What is the sum of: 1.— 19 + 12-1-8 ; 2.-72+60+4 j 3.-48+ 
 10+30 ; 4.— 13+254 7 ; 5.-29+24+30 ; 6.-33+28+7+35 ? 
 
 253. What is the sum of: 1.-64+40+9 ; 2.— 29+17+12 ; 3.-7+ 
 37+26 ; 4.— 14+394-4 ; 5.-48+31+9 ; 6.— 56+41+10 ; 7.-75+60+ 
 
 22? 
 
 254. What change is made in the sum of several numbers : 1. When 
 one of the numbers is increased ; 2. When one of the numbers is 
 diminished ? 
 
 255. What change is made in the sum of several numbers : 1. When one 
 of the numbers is omitted ; 2. When one of the numbei-s is doubled ? 
 
 tens, 2<= 
 
 •lids. 
 
 simple units, 
 2" hundreds, 
 1» tens, 
 
 I 
 
 Note, 
 Thus, th( 
 dollars. 
 being sep 
 $25.36 is 
 
 In wri 
 together, 
 the colui 
 there be 
 zeros. 
 
 256. Hei 
 
 257. A p 
 age? 
 
 258. Wh 
 
 259. Cha 
 i. years ; in w 
 I 260. Ji'li 
 I 261. Mos 
 |of 120 years 
 
 262. A b( 
 other ; how 
 
 263. The 
 their sum ? 
 
 264. One 
 both receive 
 
 265. A ba 
 Tuesday; he 
 
 266. A ba 
 uring a spc( 
 
 267. In a 
 ing ; how mt 
 
 268. How 
 n class ? 
 
 269. What 
 through one ] 
 
 270. Henr 
 lore; how lu 
 
 % 
 
M 
 
 thouiiand and 
 y-Uro thousand 
 
 "orty-four, three 
 and three, one 
 
 eleven hundred 
 and thirty-five, 
 
 iidred and fifiy- 
 ind sixty-seven, 
 ighty-two, one 
 
 lion. 
 
 ' simple units, 
 
 }, 2' hundreds, 
 
 nting : 1° tens, 
 
 ndred-milHons, 
 jn-raillious, 7" 
 
 9; 3.— 10+«+ 
 
 16+12-1-9? 
 
 -6+7; 3.— 34+ 
 
 25+8? 
 
 iO+4; 3.-48+ 
 
 7+35 ? 
 
 7+12 ; 3.-7+ 
 
 0; 7.-75+60+ 
 
 iberg: 1. When 
 the numbers is 
 
 rs : 1. When one 
 s is doubled 1 
 
 ADPITIOV. 
 
 PRACTICAL PROBLEMS. 
 
 13 
 
 i -ru : ''^° ^' ""''""^ ^'^■■« * ""•"^"'- Signifies dollar.. 
 
 ) Ihus. the expression $120 is read one hundred and twnit,, 
 I dollars. Dollars and cents may be written together, the cents 
 I bemgseparated from the dollars by a point, thus, the expression 
 . S-5.36 IS read twenty-fice dollars and thirt>,.six cents. 
 I In writing sums containing dollars and cents to be added 
 I ogether, care must be taken that the cents be written under 
 I he cohimn of cents and the dollars under dollars ; should 
 , there be no cents in any amount, they are replaced by two 
 ■ zeros. ' ■^ 
 
 256. Henry is twelve years old ; hcv old will he be ,n 27 yoars?A 
 ^^^257. A person was bom in 1792 ; ,„ wbat yey will he be 50 years of 
 
 258. What number is formed by adding 15 to 57 ? 
 
 259. Champlain was born .„ 1570, his career covered t'.e space of 65 
 ., years ; in what year did he die ? 
 
 j 260. Jvlius was bom in 1808 ; .„ what year was he 27 years old ? 
 
 I 261. Moses was bo n 2373 year, a'-r the ci^afon, he died at the ««. 
 
 I of 120 years, in what year did he die ? ^ 
 
 I 262. A bookbinder delivered 75 volumes at one time and 149 at an- 
 I other ; how many volumes did he deliver in all ' 
 
 ithrsul'f '"""'' '"° """'"^ •'^ ''' '''' '""^ g'*"*^^ 362 ; what i, 
 
 ibothtc^:::r'"" ^"^ ''' ^"' ^^« ^^'^^^^^^ »>- -^h do they 
 
 265. A baker receives 20 barrels or flour on Monday and 18 barrels on 
 Tuesday ; how many did he receive on both days f ■/ 
 
 266. A baker left 45 loaves of bread during one trip and 19 loave, 
 iunng a second trip, how many loaves did he deliver ? 
 
 267. In a battle 8945 cartridges were fired, there are 12450 remain 
 png ; how many were there before the battle » 
 
 In !£sf ""^ """^ ^"^"' '" " '^'^' '^'' "' *^««»* «">«» the« are 29 .till 
 
 I 269 What is the capaaity of a tun which is to receive 45 gallon, 
 ■thronsrh onA niru» anA QIC *i u _„QiL . ganom 
 
 270. Henry placed §12.50 in a bank 
 uore ; how miiuh has he in bank ? 
 
 at one time, then $17.60 
 
14 
 
 ADDITIOW. 
 
 ^271. What is the amount of a bill of $5.25 for sugar and 80 centi for 
 
 preserves ! 
 
 272. How long did it take a man to clear a piece of land knowing 
 that a first time he worked 75 dnys and a second time 49 days. 
 
 273. James received $42 from his father and $19 from his mother ; 
 
 how much has he 1 
 
 274. What is the length of a piece of cloth, if after selling 45 yards 
 
 there remain 27 yards ? 
 
 275. A merchant bought goods for $164, for how much must he sell 
 
 them to gain $24 >. 
 
 276. A person bought a house for $15160, he spent $1575 in 
 reparations ; fo. how much should he sell it to gain $2t)00 ? 
 
 277. Peter spent $123 and has remaining $20 more than he spent ; 
 h' .V much has he now f How much had he at first ? 
 
 278. A merchant made three sales during the day : the first was of $45, 
 the second $65 and the -third $97 ; what did he receive ? 
 
 279. $24 w«re taken from a drawer containing money, then $45, and 
 there remain $79 ; how much money was in the drawer ? 
 
 280. In an orchard there are 395 apple-trees, 247 plum-trees and 197 
 pear-treris ; how many trees in all ? 
 
 281. A servant spent $18 for provisions and $23 for wood ; what was 
 the amount spent ? 
 
 282. After paying a debt of $845 ; 1 have $179 remaining; how much 
 
 hSl? 
 
 283. On a certain number of oranges 1 ate 27 and have remaining 15 
 
 more than I ate ; how many had I at first ? 
 
 284. A man cut down in a forest, 445 maple-trees, 514 ash-trees, 423 
 cherry-trees and 536 pine-trees ; how many trees were hewed down ? 
 
 285. A family's expenses for a day were : for milk 8 cents, bread 
 32 cents, meat 28 cents, vegetables 15 cents, cofTee 10 cents, tea 6 cents 
 and sugar 12 cents. What were the total expenses ? 
 
 286. What is the weight of four oxen, the first of which weighs 860 
 pounds, the second 1082, the third 1238 and the fourth 1148 ? 
 
 287. A person bought furniture for $225, linen for $187.50, cloth 
 for $168.00 and provisions for $288. How much did he spend ? 
 
 288. How many men in a regiment of four batallions : the first of 
 which comprises 1209 men, the second 1075, the third 976 and the fourth 
 
 987? 
 
 289. A grocer received 4 boxes of soap : the first weighed 250 poundi 
 the second 150, the third 294 and the fpurtb 214. What was the weigh! 
 of the soap received ? 
 
 290. Ow 
 
 : llaminl of 
 
 J for $1.15, 
 
 ■ How much 
 
 " 291. A 
 
 I $1.75 n da] 
 
 I 90 cents nii 
 
 it nil for a da 
 
 i 292. Wfi 
 
 J ],J5 yii lions 
 
 I 293, WIi 
 
 for $405.50, 
 
 294. A II 
 of pants, $1 
 ihe s))eiul ? 
 
 295. Onii 
 liorses, 105 
 
 296. Inv 
 ilied at the i 
 
 297. At tl 
 ye are now i 
 
 298. To I 
 >ank note of 
 lents. How 
 
 299. Hai 
 low much di 
 
 300. Whai 
 owing sums 
 197.60, and 1 
 
 301. A per 
 mount of $ 
 
 lined $540.; 
 
 302. A mei 
 85.76 from 
 ount of 1 
 
 fore? 
 
 303. A ma 
 960.75 for 
 
 tiaritable pur 
 804. A coi 
 
AnniTioK. 
 
 IS 
 
 of land knowing 
 
 9 days. 
 
 from his mother ; 
 
 selling 45 yards 
 
 inch must he sell 
 
 spent $1576 in 
 00? 
 than he spent ; 
 
 and 80 cent, for 290. Owen bought « Grammar for 35 cents, a Geography for r.5 cents „ 
 
 • or r 5 ^'"'»»-^-/- accents, an Algebra for 4o'ce'ts. a gZ 'ry 
 
 I hL '. "" tr'*'^'"«^° f" ^5 ""'«. " History of Canada for 30 cents '^ 
 1 How much did he spend ? ^ • ov ecu is. 
 
 I $1^ a davTr ^"' 'Z. T" ''"' '" ''"'' "' '^"«^^ = to tf'^ ft«t 
 'oft ? , '"""'^ ^'•°'^' ''^ t'^^ ^hird, 81.20; to the fourth WL 
 
 I In ;::r ::^r "" ''''-''''' '' ""^- "°^ ^-^ ^- "« p^^^^^- 
 
 I 292. What is the capacit, of four casks of wine, if the first contains . 
 I h,5 gnllons. the second 135. the third 120 and the fourth 90 ? 
 
 Ifo.'L'o^'Io'!.""" Tl^ ^'"^ '"'■ ^°"' "°**"'= ♦''•-• fir^t of which is 
 I of ? • "'' TL^ *"'■'"• ''»« ^''"•d S576 and the fourth §179.:5? " 
 
 , r^r * '' '"'. " '"'• ^'' ''' "» °^'^'-"t' «^^ 25 for a pair 
 
 i. al.75 fnr » rano an.) CK ra c .. __ ■ ., 
 
 i.e first wasof J(45, 
 
 I? 
 
 ey, then $45, and 
 
 lum-trees and 197 
 
 wood ; what was 
 
 ining ; how much 
 
 lave remaining 15 
 
 514 ash-trees, 423 
 hewed down ? 
 : 8 cents, bread 
 cents, tea 6 cents 
 
 which weighs 860 
 ii 1148 ■( 
 "or $137.50, cloth 
 le spend ? 
 lions : the first oil 
 J76 and the fourth 
 
 lighed 250 poutflA 
 liat was the weigh^ 
 
 How much did 
 
 f , 4 £,, _ V - -- ■- , v»u lui iiii overcoai 
 
 |ol pants, $1.75 for a cane and $6.50 for a pair of boots 
 |he si)end ? 
 
 %^ mZ^'^H ''" "'"' "'' V'' ^'"''' ''' ^"^^"' ''' o«". 86 / 
 ^lorses, 106 pigs. How many animals were soltl ? 
 
 296 In what year before Christ was Alexander the Great born, if he 
 
 pied at the age of 32 yeai-s, in the year 324 before Christ ? ^ 
 
 -^ 297. At the birth of Our Lord the world had been created 4004 years ^ 
 
 298. To p,iy for a certain quantity of merchandise, I have given a. 
 
 Nuts. How much did the goods cost ? v^ 
 
 I ^^^" ?!i^!!'f '''*"^''* * """*«' ^"'" «^<>' » "Change it for a horsTv. 
 rirt^^ ' ^I '" '^^ '"''''' '' ' «'- ««5 -«h besides 1 '^ 
 
 I 300. What sum does it require to pay 5 clerks who have earned the fol 
 
 I ^"^-Z r.T.L^?^''' * **'"'' ^"^ *"50 ; he made r.parations to the 
 
 'rd"$6to.'3o?-''- '-' ''^ -'-' ''' '^ -" ^^' ^"-^"« t.;:tt 
 
 302 A merchant wishing tc purchase some cheap goods, borrows 
 385.76 from one of his. friends, $76.95 from another one ; wha was 1 
 nou^nt of his purchase, knowing that he had .^47.35 in his pocket 
 
 Sflfio'rf r\!:"^' ^^ T'"'"' *^''*^ ^'' »'»« education of youth. 
 
 8960.75 for the poor. $960.80 to the church. $7,506 for other 
 Imntable purposes ; what is the amount of these legacies ? 
 1804. A contractor baa received for tne construction of a school : 
 
>« 
 
 ADDITION . 
 
 \i 
 
 I 
 
 l" 13643, 2^ $3529, ;" $2675; he has still to receive $1,0825. What 
 #«l the price of the contract? 
 
 30^ An army composed of 6875 m ;i received 3 re-enforcemeuts : the 
 first of 1680 men ; the second, 1500 men, and the third, 2050. What 
 is the total number of the army at present 1 
 
 T306. A person will be 40 years old in 1894. What age shall his 
 father have who is 30 years older than he i& ' 
 
 807. What is the total length of 4 streets which are : the first 342 
 yards long, the second 1425 yards, the third 718 yards, and the fourth 
 866 yards ? 
 
 308. A shoe factory turns out the following work during a week : On 
 Monday 178 pairs, Tuesday 205 pairs, Wednesday 217 pairs, Thursday 
 245 pairs, Friday 256 pairs, Saturday 262 pairs. How many pairs were 
 made during the week ? 
 
 309. The number of pupils attending the schools of the Brothers of 
 the Christian Schools, on the 31st of December 1892, was: in Europe, 
 253280 ; in Asia, 6879 ; in Africa, 4586 ; m America, 40735. Find 
 ho^rmauy pupils in all ? 
 
 310. The population of Bonaventure county is 18908 ; that of Gasp* 
 county, 25001 ; that of Rimouski county, 33791 ; that of Temiscouala 
 county, 25484 and that of Kamouraska county, 22181. What is the 
 population of these five counties ? 
 
 311. A woman currying eggs to the market, bi-eaks 36 of them, she 
 sells 120 on her way, gives 8 to the poor, and when she arrived had 
 665 remaining. How many eggs had she when she left home ? 
 
 312. What is the revenue of a man who spends $160 for food, $120 
 for rent, $125 for clothing, $34 for sundry items ; he gives $12.38 to the 
 poor, and has $150.62 remaining ? 
 
 313. I bought 647 yards of cloth for $2375.40 ; 765 yards of linen 
 for $1036.25 ; 86 yards of ribbon for $126.30, aud 30 yards of calico for 
 $12. How many yards of goods did I buy and what did all uoit ? 
 
 314. A workman received $60, another received $20 mor'. thin i« 
 first and a third as much as the two others. What did ear'. ' ■ .o 't^ . 
 
 815. If 1 could get $41.10, I would want only $2.10 MOio to donble| 
 my money. How much have I i 
 
 "f^^^ 
 
 30. Sut 
 
 tekon from 
 The roaui 
 
 31. Sunt 
 J If 37 w« 
 
 IpcprossuJ b 
 
 4 fmm 
 
 |0 froni 
 
 I 1 1 
 
 1 fron 
 
 21 
 
 lo from 
 
 31 
 
 ? from 
 
 41 
 
 from 
 
 51 
 
 '0 from 
 
 61 
 
 |0 from 
 
 71 
 
 40 from 
 
 8 1( 
 
 from 
 
 9 1. 
 
 1 from 
 
 11( 
 
 1 from 
 
 2 If 
 
 1 from 
 
 3 1e 
 
 1 from 
 
 4 1<> 
 
 1 from 
 
 5 1p 
 
 1 from 
 
 6 1e 
 
 i from 
 
 71e 
 
 from 
 
 8 1e 
 
 from 
 
 9 1e,- 
 
 from 
 
 Oier 
 
 from 
 
 2 1m 
 
 from 
 
 3 lea 
 
 from 
 
 4 1m 
 
 from 
 
 6 lea 
 
 from 
 
 6 lea 
 
 from 
 
 7 lea 
 
 from 
 
 Blea 
 
 from 
 
 Hea 
 
 from 10 leai 
 
 from 11 leai 
 
g $10825. A^'hat 
 
 SULTnACTION, 
 
 17 
 
 iforcemcuts : the 
 rd, 2050. What 
 
 SUHTKACTIOX. 
 
 .hat age .hall his ^^O. Subtraction is . process by which one number is 
 
 .... .he first 342 ^ ^JZh:^^^^''' '''''''''' ^^'^''^ 
 
 is, and the fourth J ,'''"'' "' '^'' subtraction is called the difference. 
 
 J 3^SuuMaction is expressed by the sign-, read minus. 
 ring a week: On ^" ^' '''''^ to betaken from 78, the operation would be 
 pairs. Thursday l^pios.sed by writing: 78 —37, 
 
 .itanir nnira ivnrtt 
 
 many pairs were 
 
 of the Brothers of 
 
 was : in Europe, 
 
 a, 40735. Find 
 
 Subtraction Table. 
 
 8 ; that of Gaspe 
 at of Temiscouata 
 )l. What is the 
 
 s 36 of them, she 
 1 she arrived had 
 t home ? 
 
 150 for food, $120 
 ives 112.38 to the 
 
 ^55 yards of lincu 
 yards of calico for 
 lall .o;t? 
 ^20 moi'. thin the 
 ear", n :.' ieotivii ' 
 10 hioiii to double 
 
 flODl 
 
 from 
 
 from 
 
 from 
 
 from 
 
 from 
 
 |0 from 
 
 |0 from 
 
 40 from 
 
 .0 from 
 
 -4 
 
 leaves 
 
 1 lenvbs 1 
 
 2 leaves 2 
 
 3 leaves 3 
 
 4 leaves 4 
 6 lenvi's 5 
 
 6 leaves 6 
 
 7 leaves 7 
 
 8 leaves 8 
 
 9 leavt's 9 
 
 4 from 
 4 lioin 
 4 from 
 4 from 
 4 from 
 4 from 
 4 from 
 4 from 
 4 from 
 4 from 
 
 4 leave 
 
 5 leave 
 
 6 leave 
 
 7 leave 
 
 8 leave 
 
 9 leave 
 
 10 leave 
 
 11 leave 
 
 12 leave 
 
 13 leave 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1 leaves 
 
 2 leaves 1 
 
 3 leaves 2 
 
 4 leaves 3 
 
 5 leaves 4 
 
 6 leaves 5 
 
 7 leaves 6 
 
 8 leaves 7 
 
 9 leivt'S 8 
 'eaves 9 
 
 2 leave 
 
 3 leave 
 
 4 leave 
 6 leave 
 
 6 leave 
 
 7 leave 
 
 8 leave 
 
 'om 9 leave 7 
 rom 10 leave 8 
 rem 11 leave 9 | 6 from 
 
 6 fiom 
 
 6 from 
 
 6 from 
 
 6 from 
 
 6 leave 
 
 7 leave 
 
 8 leave 
 
 9 leave 
 
 6 from 10 leave 
 6 from 11 leave 
 
 6 fiom 12 leave 6 
 
 6 from ]3 le.ive 7 
 
 6 from 14 leave 8 
 
 15 leave 9 
 
 8 from 8 leave 
 8 from 9 leave 1 
 8 from 10 leave 2 
 8 from 11 leave 3 
 8 from 12 leave 4 
 8 from 13 leave 5 
 8 from 14 leave 6 
 8 from 15 leave 7 
 8 from 16 leave 8 
 
 8 fr, m 17 leave 9 
 
 9 from 9 leave 
 9 from 10 leave I 
 9 from 1 1 leave 2 
 9 from 12 leave 3 
 9 from 13 leave 4 
 9 from 14 leave 5 
 9 from 15 leave 6 
 9 from 16 leave 7 
 9 from 17 leave 8 
 9 from 18 leave 9 
 
 10 from 10 leave 
 10 from 11 leave 1 
 10 from 12 leave 2 
 10 from 13 leave 3 
 10 from 14 leave 4 
 10 ♦rom 15 leave 5 
 10 irom le leave 6 
 10 from 17 leave 7 
 10 from 18 leave 8 
 10 from 19 leave 9 
 
10 
 
 i!i 
 
 »;l!(fll! 
 
 3 from 
 8 from 
 3 from 
 from 
 from 
 from 
 from 
 
 3 leave 
 
 4 leave 
 f) leave 
 
 6 leave 
 
 7 leave 
 
 8 leave 
 
 9 leave 
 from 10 leave 
 from 11 leave 
 
 3 from 12 leave 
 
 8UBTBACTI0N. 
 
 from 7 leave 
 from 3 leave 
 from 9 leave 
 from 10 leave 
 from 11 leave 
 from 12 leave 
 from 13 leave 
 from 14 leave 
 from 15 leave 
 from 16 leave 
 
 The preceding 
 table should be 
 mastered t h o - 
 roughly before 
 taking up the ex- 
 ercises in sub- 
 traction. 
 
 OPr.UATION. 
 
 4795 
 3582 
 1213 
 
 PROBLEMS. 
 
 32. Case I.— To subtract ichen no term of the smalJ't 
 number is greater than the corresponding term of the laryn 
 number. 
 
 Ex. : Subtract 3582 from 4795. 
 
 Solution: Write the smaller number or suUralieitd under tli 
 larger one or minuend, placing the terms of the same order in the saiiij 
 oolurau, and( begin at the right to subtract. 2 units 
 from 5 units leave 3 units, which is written under the 
 units ; 8 tens from 9 tens leave 1 ten, which is written 
 under the tens ; 5 hundreds from 7 hundreds leave 2 
 hundreds, which is written under the hundreds ; 3 
 thousands from 4 thousands leave 1 thousand. There- 
 lore the difference is 1213. 
 
 33. Case II. — To subtract when one or more terms of tk 
 smaller number is greater than the corresponding terms < | 
 the larger number. 
 
 Ex. : Subtract 3867 from 45073. 
 
 Solution : Write the subtrahend under the minuend, and begin 
 the right to subtract. 
 
 7 units cannot be taken from 3 units, therefore add 
 10 units to the 3 units, making 13 units, 7 units from 
 13 units leave 6 units, now since 10 units or 1 ten were 
 added to the minuend the remainder will be 10 units or 
 1 ten too large ; hence to obtain the correct remainder add 
 1 ten to the subtrahend, 6 tens plus 1 ten are 7 tens ; 
 7 tens from 7 tens leave tens. 8 hundreds cannot be 
 taken from ; therefore add 1 hundreds to the minuend ; 8 hundrcl 
 from 10 hundreds leave 2 ; now since 10 hundreds or 1 thousand wf 
 added to the minuend the remainder will be 1 thousand too large ; henci| 
 thousand must be added to the subtrahend. 8 thousands and 1 thousa;^ 
 
 Operation 
 45073 
 3867 
 412U6 
 
 ire 4 thou^ 
 phere are ii 
 thousands 
 
 34. No 
 
 7 from 
 1 and 6 
 
 8 from 
 1 and 3 
 from 
 
 35. Ru 
 mtmber ph 
 i-ind draw i 
 
 //. Ben 
 \iiimber f\ 
 fcriting the 
 
 III If 
 torrespond 
 md then s\ 
 
 IV. Adi 
 yroceed as 
 
 An$ 
 
 Ana, 
 
SUBTKACTIOV. 
 
 19 
 
 The preceding 
 ible should be 
 lastered t h o - 
 nighly before 
 iking up thf ex- 
 rcises in sub- 
 raction. 
 
 % of the small t 
 \rm of the largn 
 
 trahend under tli 
 ;e order in the saiii- 
 lits 
 
 OPnilATION. 
 
 4795 
 3582 
 1213 
 
 the 
 ten 
 -e2 
 ; 3 
 
 sre- 
 
 lore terms of th 
 ponding terms 
 
 lucnd, and begin . 
 
 Operation 
 45073 
 8867 
 41206 
 
 add 
 
 rom 
 
 vere 
 
 I or 
 
 add 
 
 ns ; 
 
 the 
 
 inuend ; 8 hundrc| 
 
 or 1 thousand wtj 
 
 d too large ; henal 
 
 nds and 1 thousa 
 
 Ire 4 thousands ; 4 thousands from 5 thousands leave 1 thousand. As 
 ^here are no ten-thousands to take from 4 ten-thousands, write 4 ten- 
 ^liousands Tlicrefore tiie difference is 41206. 
 
 34. Note :— Iq practiou the procesi* is as follows : 
 I 7 from 13 leave 6 and carry 1 
 
 1 "'"I 6 7 7 from 7 leave 
 
 8 from 10 leave 2 and carry 1 
 
 1 a»*l 3 4 4 from 5 leave 1 
 
 from 4 ler.ves 4. 
 
 35. Rule :— /. Write the smaller number under the larger 
 humhcr placing the terms of the same order in the same column 
 tind draw a line beneath. 
 
 II. Begin at the right and subtract each term of the smaller 
 \iumher from the corresponding term of the larger number, 
 writing the remainder beneath. 
 
 Ill If any term of the smaller number is greater than the 
 corresponding term of the larger nvmber, add 10 to the latter 
 md then subtract. 
 
 IV. Add 1 to the next term of the smaller number and 
 proceed as before. 
 
 Examples for Practice. 
 
 NO 
 
 Ml. 
 
 42. 
 
 149. 
 150. 
 151. 
 152. 
 153. 
 154. 
 
 Ans. 
 
 729 
 417 
 
 925 
 619 
 
 Ans, 
 
 454565 
 7347 
 
 A71S. 
 
 748-534 
 969-733 
 767-548 
 451-323 
 855-548 
 745-254 
 617-429 
 
 343. 
 
 344. 
 
 345. 
 
 356. 
 357. 
 358. 
 3.09. 
 360. 
 361. 
 362. 
 
 454565 
 7347 
 
 1346. 
 
 Ans. 
 
 487654 
 298047 
 
 Ans. 
 
 454500166 
 8893287 
 
 Ans. 
 
 347. 542600741 
 66725746 
 
 780705 
 90877 
 
 Ans 
 
 An> 
 
 348. 274000300 
 92129405 
 
 Ans. 
 
 749-573 
 683-494 
 698 - 299 
 784-395 
 400-245 
 800-501 
 545-484 
 
 363. 
 364. 
 365. 
 36(J. 
 367. 
 368. 
 369. 
 
 476-297 
 754-264 
 745-359 
 976-495 
 874-199 
 741-174 
 842-376 
 
./ 
 
 hi;" 
 ll'll 
 
 iHiii \ 
 
 20 
 
 
 SUBTHACTION 
 
 
 370. 
 
 476 — 
 
 287 
 
 399. 
 
 769 400 007 
 
 371. 
 
 426 542 — 
 
 179 127 
 
 400.1* 879 766 833 
 
 372. 
 
 457 421 — 
 
 178 175 
 
 401. 
 
 705 454 377 
 
 373. 
 
 847 457 — 
 
 457 424 
 
 402. 
 
 879 457 651 
 
 374. 
 
 375 147 — 
 
 196 078 
 
 403. 
 
 457 893 453 
 
 375. 
 
 455 310 — 
 
 8 474 
 
 404. 
 
 104 007 852 
 
 376. 
 
 459 435 — 
 
 88 578 
 
 405. 
 
 678 476 501 
 
 377. 
 
 547 422 — 
 
 268 657 
 
 406. 
 
 405 234 542 
 
 378. 
 
 256 456 — 
 
 74 179 
 
 407. 
 
 587 847 007 
 
 379. 
 
 789 852 — 
 
 49 776 
 
 408. 
 
 657 462 024 
 
 380, 
 
 458 075 — 
 
 75 497 
 
 409. 
 
 867 491 234 
 
 381. 
 
 357 117 — 
 
 87 779 
 
 410.^/ 
 
 645 479 846 
 
 382. 
 
 134 207 — 
 
 70 709 
 
 411. 
 
 875 674 745 
 
 383. 
 
 740 070 — 
 
 471 097 
 
 412. 
 
 745 874 320 
 
 384. 
 
 870 050 — 
 
 757 147 
 
 413. 
 
 874 807 790 
 
 385. 
 
 357 074 — 
 
 196 407 
 
 414. 
 
 997 007 001 
 
 386. 
 
 645 444 — 
 
 452 079 
 
 415. 
 
 847 653 454 
 
 387. 
 
 704 555 — 
 
 375 697 
 
 416. 
 
 546 807 575 
 
 388. 
 
 455 606 — 
 
 375 697 
 
 417. 
 
 956 753 764 
 
 389. 
 
 359 854 — 
 
 204 905 
 
 418. 
 
 950 076 074 
 
 390. 
 
 897 954 — 
 
 541 378 
 
 419. 
 
 477 275 759 
 
 391. 
 
 654 087 — 
 
 87 659 
 
 420. 
 
 876 007 064 
 
 392. 
 
 854 087 — 
 
 98 498 
 
 421. 
 
 564 079 768 
 
 393. 
 
 256 895 454 — 
 
 4 947 872 
 
 422. 
 
 400 076 646 
 
 394. 
 
 754 674 790 — 
 
 64 834 799 
 
 423. 
 
 460 007 646 
 
 395. 
 
 764 675 790 — 
 
 275 987 899 
 
 424. 
 
 650 079 059 
 
 396. 
 
 461 900 797 — 
 
 7 191 989 
 
 425. 
 
 837 040 064 
 
 397. 
 
 810 847 066 — 
 
 614 896 874 
 
 426. 
 
 974 600 700 
 
 898. 
 
 418 030 450 — 
 
 27 740 761 
 
 427. 
 
 846 977 606 
 
 71 900 747 
 19 837 692 
 
 7 792 19S 
 
 97 780 07S 
 
 9 594 327 
 
 72 876 194 
 89 497 354 
 
 53 912 47f 
 
 94 958 09S 
 
 79 834 01 ,- 
 
 91 374 92: 
 
 493 791. 7!*; 
 
 94 789 82:i 
 
 97 905 4,s:) 
 
 65 910 o-i: 
 
 45 124 37; 
 
 74 375 57u 
 
 277 451 79), 
 
 678 404 951 
 
 475 207 Ui 
 
 298 345 84;' 
 
 798 435 49;. 
 
 285 187 g?*) 
 
 93 457 89; 
 
 40 079 452 
 
 479 084 764 
 
 4 134 66; 
 
 93 236 94r 
 
 7 884 m 
 
 Ex|»i . MH in flKares and anbtraet the ftollowlny nnmben i 
 
 428. Fiud the difference between four hundred and sixty-six and throi 
 hundred and fifty. 
 
 429. Diminish eight hundred and ninety-six by fifty-five. 
 
 430. How much greater is seventy-five thousand eight hundred anc 
 lorty-three than sixty-seven thousand and nine ? 
 
 431. Find the remainder when two hundred and sixty-nine thousand 
 seven hundred and fifty-seven is diminished by one hundred and thirteei 
 thousand and twenty. ^ 
 
 432. Subtract one million seventy-eight thousand nine hundred aJ 
 three from nine million three hundred and twenty-seven thousand sii 
 hundred and eighty-one. 
 
 433. What remains if three hundred and two be diminished by sevci 
 hundred and fifty-eight ? 
 
 434. From two million five hundred aud uiuety-l wo thousand cigbij 
 
 \ hundred 
 
 I hundred t 
 
 I 435. T( 
 
 I thousand 
 
 I *36. H 
 
 1 six than r 
 
 I 437. W 
 
 f and one m 
 
 f 438. H« 
 
 I seven thoi 
 
 I 439. Fi 
 
 i thousand 
 
 thirty-sev< 
 
 440. I 
 
 441. I 
 
 442. ( 
 
 443. ( 
 
 444. ( 
 446. ( 
 
 446. ( 
 
 447. ( 
 
 448. ( 
 
 449. ( 
 
 450. All 
 ttwcd him ? 
 
 451. w: 
 
 452. A i 
 ell knowin. 
 
 453. Fin( 
 
 454. On I 
 
 455. The 
 eater. 
 466. A bi 
 
 if there still 
 457. Ap€ 
 lie still owe 
 
SUBTRACTION. 
 
 21 
 
 007 — 
 
 71 900 747 
 
 833 — 
 
 19 837 692 
 
 377 — 
 
 7 792 19- 
 
 651 — 
 
 97 780 07f' 
 
 453 — 
 
 9 594 32? 
 
 852 — 
 
 72 876 HH 
 
 501 — 
 
 89 497 354 
 
 542 — 
 
 53 912 47(' 
 
 007 — 
 
 94 958 09.^ 
 
 024 — 
 
 79 834 01 .■ 
 
 234 — 
 
 91 374 92: 
 
 846 — 
 
 493 791,7!'; 
 
 745 — 
 
 94 789 82? 
 
 320 — 
 
 97 905 4S:i 
 
 790 — 
 
 65 910 o-j; 
 
 001 — 
 
 45 124 3-i 
 
 454 — 
 
 74 375 5/1 
 
 575 — 
 
 277 451 79i 
 
 764 — 
 
 678 404 95) 
 
 074 — 
 
 475 207 45) 
 
 759 — 
 
 298 345 84:' 
 
 054 — 
 
 798 435 49;, 
 
 758 — 
 
 285 187 97*i 
 
 546 — 
 
 93 457 89; 
 
 546 — 
 
 40 079 452 
 
 059 — 
 
 479 084 764 
 
 054 — 
 
 4 134 56; 
 
 700 — 
 
 93 235 94; 
 
 606 — 
 
 7 884 m 
 
 Inv nnmben t 
 
 I sixty- 
 
 sixandthrcf ' 
 
 ty-five. 
 
 1 
 
 . eight hundred anc 
 
 lixty-nine thousaiiii i 
 
 andred aud thirteei | 
 
 i nine : 
 
 hundred ancl 
 
 ■seven i 
 
 thousand aiiM 
 
 minished by sevoS 
 
 I wo thousand ci<'liil 
 
 ^tdtda:/twl^:^"^ '-'- ''- '-'-' -^ --^ ^^--^ three 
 thot'and'tdtTo.*'"^"' '^ '""^^••^' ^"^ seventeen fro. fourteen 
 
 six'than"n1n 7"^ T"^ '' "^°'*y-°"' *'^°"'«'"^ three hundred and 
 .S w^ ! "? / ""'^ '°' '''""^""^ «'^ J^""dred and two ? 
 437. What ,8 the difference between nine hundred thousand and twc 
 
 and one milhon nme hundred and fifty thousand and twenty-eight » 
 
 L^^'J^"^ T. u" f'"''^-'"'^ ''^""^'^'^^ ^"^ t^« «^«««d seventy- 
 I seven thousand two hundred and two ? 
 
 439. Find the difference between one hundred and one million ten 
 
 hn °":,'"°'^f/"^ «-.-<! nine million seven hundred at; 
 I thirty-seven thousand three hundred and fifty-one ? 
 
 Exercise, in Addition and Sabtractlon. 
 
 440. (1207+352) — 1548. 
 
 441. (2713+1065) — 2466. 
 
 442. (21672+67023)— 80471. 
 
 443. (87641— 72320)+4537. 
 
 444. (112796— 10683)+97042. 
 
 445. (71889+13562)-75262. 
 
 446. (87003— 27509)+23709. 
 
 447. (4603+705+3518)-6034. 
 
 448. (7323+687+9346) - (812+5006). 
 
 449. (4503 - 706) — (8003 - 7125). 
 
 PBACTICAL PROBLEMS. 
 
 How much more is^ 
 
 450. A laborer earned $76 ; he has received $55. 
 |owtd him ? 
 
 451. What number must be added to 67 to make it 201 ? 
 
 452. A gardener had 345 melons in his waggon ; how many did he 
 ell knowing he has 79 remaining? ^ 
 
 Ta' n""^ k!;^ "."^^'' ''"** '""'* ^' ''^^''^ *° 138 to make it 450 ? 
 
 454. On a bill of $4217 a man p»ys $427. Find the balance due. 
 
 455. The sum ot two numbers is 1052 ; the smaller is 358. Find the 
 
 t'ttTr!"''V"'V*^'''' '^'''" n^ucl^ has it been diminished 
 in^TS atiii fciuain due $4278 ? 
 
 person owing a sum of $16384, paid $ 
 
 lie still ow« f 
 
 how much does 
 
 • / '/ 
 
 > 
 
::l 
 
 23 
 
 BUBTBACTION. 
 
 i; ilii 
 
 I 
 
 Mllll 
 
 ii! 
 
 liii 
 
 
 458. A person after travelling 9 days, ends his journey 6a the 24th of 
 the month. On what date did he start ? 
 
 469. A woman goes to market with $14.30 and returns with $6.75 ; 
 How much did phe spend ? 
 
 460. Two men working together perform 427 yards of work ; if one 
 has done 174 yards, how mmiy did the second do '( 
 
 461. I had ,$628.75. I bought a farm for $410.90 ; how much money 
 have I left ? 
 
 462. A scholar has 345 lines to recite ; he knows 257. How many 
 more must he learn ? 
 
 463. Having $2128.25, I intend to buy a house worth $3000 ; how 
 much more do I rer[uire to pny for it ? 
 
 464. A voyage is to last 87 days ; how many days is it begun if there 
 are 49 days more to travel ? 
 
 1(r466. The age of a father and his son together is 127 years. The father 
 iS/83 years old, how old is the son ? 
 
 466. A prisoner is in for 270 days ; he has served 187 days. How 
 many more days must he pass in prison ? 
 
 467. The first Crusade was in 1096, and the seventh and last ended in 
 1270. How many yeais did these expeditions last? 
 
 468. A merchant bought cloth for $6364. He sold part of it for 
 $3977.40. Find the value of the remainder ? 
 
 469. Columbus was 51 years old when he discovered America in 1492 ; 
 in what year was he born ? 
 
 470. A grocer sold sugar for $870.45 and by so doing gained $75.60. 
 What did the sugar cost him ? 
 
 471. Potatoes were introduced into Europe in 1586, and coffee in 1644. 
 For how many years were potatoes in use when coffee was introduced ? 
 
 472. I want $420.45 to be able to pay a debt of $746.20. How much 
 have I ? 
 
 473. An army numbering 40300 men lost 7850 in a campaign. How- 
 many men are left ? 
 
 PROBLEMS IN ADDITION AND SUBTRACTION. 
 
 474. Find the total weight of 6 waggons, weighing respectively : 4524 
 pounds, 9425, 7217, 3425, 2027, and 1875 ? 
 
 475. Charlemagne ascended the throne in 768 and died in 814. His 
 son Louis, ascended the throne on his father's death and died in 840. 
 Which of the two sovereigns reigned the lon/crw ' 
 
 476. A 
 nesdny $] 
 $17429,0; 
 
 477. A 
 
 478. C( 
 ninny yea 
 
 479. Ill 
 62446. ] 
 
 480. W 
 I bureau wo 
 J 481. A 
 lowe? 
 
 I 482. Pa 
 I Andrew tl 
 I 483. Tv 
 Jthe shai-e ( 
 I 484. M( 
 |63090 and 
 I 485. Th 
 iliabitants 
 |l 488535? 
 I 486. Ha 
 iK^'ods cost 
 I 487. A ( 
 ^till owe ? 
 483. A h 
 luch must 
 
 489. A I 
 55400 to r 
 »oor. Fim 
 
 490. I be 
 :ain? 
 
 491. Fine 
 
 492. A m 
 'ards, 85 yt 
 
 493. The 
 father is 92 ; 
 
 494. Thei 
 09078 in P 
 
 495. A w 
 |n<i 608 pagt 
 
rney 6a the 24 th of 
 eturns with $6.75 ; 
 ds of work ; if one 
 
 how much money 
 ? 257. How many 
 worth $3000 ; how 
 is it begun if there 
 
 years. The father 
 d 187 days. How 
 k and last ended in 
 sold part of it for 
 
 America in 1492 ; 
 
 ing gained $75.60. 
 
 and coffee in 1644. 
 pvas introduced ? 
 1.20. How much 
 
 i campaign. How 
 
 TRACTION. 
 
 •espectively : 4524 
 
 died in 814. His 
 ii and died in 840. 
 
 SUBTRACTION. 23 
 
 476. A banker received on Monday $2426. Tue&dav «472S ii Wo^ 
 
 $1/ 429.07 ; how much did he receive during the week » ^ 
 
 I 477. A farmer had 345 sheep. Haviui? s..lH 9io j, . . 
 
 17a n». * «avuig sold J49 how manv remain t 
 
 478. Cannons were invented in 1346. and guns in 1430 ^orhoJ 
 many year, are each of these pieces of ordinance if „se? " 
 
 Liul' I a!. *'•' P^'P"'"*'"" «f Quebec was 59699; i„ 1881 it was 
 '80 w!!l "•"■"" •'f P«P"l«t-» for that decade ;f year 
 
 480. What sum is owed a .abinet-maker for a desk worth S!?^ 'in . 
 [bureau worth $48.25 and a table worth $7 ? * ' * 
 
 JSl. A man owes $4567 and pays $3789.65; how much does he still 
 
 uZJZt^r-'"' ""^^^^ '''''■''-' ^- -eh mo. has 
 
 ih:iJ:;i^::s^^" - ''-'' -'''''' ' '^- ''-^^^^^^- ^i-^ 
 
 I 484. Montreal has a population of 220650. Toronto 18190ft n u 
 |63090and Ottawa 44154 F,„H rJ,. i. ^""o^to 181220. Quebec 
 
 I 48R Tl.a V *"'«tlie population of tliese four cities? 
 
 J 485. The population of Ontario is 2114321 • hn,„ "^ ""<'8 f 
 
 |.ubitants has it than the Province of Outh ' 7 """"^ """^ ''^• 
 |l488535 ? province of Quebec, whose population is 
 
 486. Having sold goods for $8795, 1 mined «17i «i u . j-. . 
 foods cost me ? *«'•'. i gained $374.84 ; what did the 
 
 487. A debtor who owes $7887.75 nava SSaos o*: . v. 
 i|till owe ? * o'./o pays $995.95 ; how much does he 
 
 »or. Fiud the sh»te of the poor ? ^"""" "'" "-"■"'ler to the 
 
 m. I hough. . vm. !„ nsm ^^ „« u fo. nm,. wh.. i, „, 
 
 «5. A work comprir ,i " , ' " '"" "'"'™"™ '" P»P"'«"'» ' 
 
 M 50, ^ .. h.„L„; ;.';::- r'rs:? '''- "'• '"- 
 
24 
 
 MULTIPLICATION. 
 
 i! i 
 
 496. A father dying bequeaths his fortune to his three sons as follows : 
 to the eldest he gives $15750 ; to the second, $13800 and to the youngest 
 $11760. What was his fortune ? 
 
 497. In a Ist class there are 38 jiupils ; in the 2nd, 65 ; in the 3rd, 
 78 ; in the 4th, 85 ; and in the 5th, 95. How many pupils attend the 
 school ? 
 
 498. I had $14.20 ; I bought a hat for $3.35, and a pair of boots for 
 $5 40. The remainder I gave for a prayer book. Required the cost of 
 the book ? 
 
 499. Louis has $18930 ; how much has John knov/ing his sum to be 
 greater than Louis' by $5980 ? 
 
 500. I owe my butcher $29.44; my baker $18.75 ; my shoemaker, 
 $33.10 ; my tailor, $67.18 ; my milAmau, $12.30 and my grocer $47.36. 
 How much do I want to cover my expenses knowing that 1 have only 
 $180.85 ? 
 
 501. A merchant has 18547 yds of calico ; he sold at different times 
 760 yds., 200 yds., 567 yds., and 125 yds. How many yards remain 1 
 
 502. A fartaer has three pieces of land which yielded 4500 bushels of 
 oats. The first yielded 1333 bushels and the second 1428. How many 
 bushels did the third yield 1 
 
 503. A workman should receive $45.75 for 5 weeks' steady work, but 
 $8.95 were deducted for time lost. How much did he receive ? 
 
 604. A servant spent $1.25 for linen, 90 cents for butter, 60 cents for 
 cheese, $1.05 for vegetables and $2.35 for sugar. How much must she 
 return to her master on $6 65 ? 
 
 
 To in 
 written : 
 
 1 timt 
 1 time 
 I time 
 1 time 
 1 time 
 1 time 
 1 time 
 1 time 
 1 time 
 1 time 
 
 2 
 2 
 2 
 2 
 2 
 2 
 2 
 
 time! 
 times 
 time! 
 times 
 time!" 
 time.« 
 times 
 2 times 
 2 times 
 2 times 
 
 III 
 
ee sons as follows : 
 ad to the youngest 
 
 iJ, 65 ; in the 3rd, 
 ' pupils attend the 
 
 a pair of boots for 
 equired the cost of 
 
 iving his sunt to be 
 
 5 ; my shoemaker, 
 
 my grocer $47.36. 
 
 ig that 1 have only 
 
 1 at different times 
 ly yards remain ? 
 led 4500 bushels of 
 1428. How many 
 
 s' steady work, but 
 receive ? 
 
 3Utter, 60 cents for 
 w much must she 
 
 HULTIPLICATION. 
 
 MULTIPLICATION. 
 
 25 
 
 36 Multiplication is the process of taking one number, 
 called multiplicand, as mmy times as there are units in 
 another, called multiplier. 
 
 The Product is the result obtained by the multiplication, 
 rhe Multiplicand is the number to be multiplied : the 
 Multiplier, the number by which we multiply. 
 
 the' Ldtt^"^*'^"''''^ ^""^ Multiplier are called Factors of 
 
 38^ The sign of multiplication is X which is read : multi- 
 plied by, times, or into. . . 
 
 JLn^^7xl. *^'' "'"''^P^'^^'^^^ °^ " ^y ^' t'^° ^"'"bers are 
 
 Multiplication Table. 
 
 1 time is 
 
 1 time I is 
 
 1 time 2 is 
 
 time 3 is 
 
 4 is 
 
 5 is 
 
 1 time 
 1 time 
 1 time 6 is 
 1 time 7 is 
 1 time 8 is 
 1 time 9 is 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 4 
 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 
 2 times 
 2 times 
 2 times 
 2 times 
 2 times 
 2 times 
 2 times 
 2 times 
 2 times 
 2 times 
 
 are 
 
 1 are 
 
 2 are 
 
 3 are 
 
 4 are 
 
 5 are 10 
 
 6 are 12 
 
 7 are 14 
 
 8 are 16 
 
 9 are 18 
 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 
 are 
 
 1 are 4 
 
 2 are 8 
 
 3 are 12 
 
 4 are 1 6 
 6 are 20 
 
 6 are 24 
 
 7 are 28 
 
 8 are 32 
 
 9 are 36 
 
 5 
 
 5 
 
 6 
 
 5 
 
 5 
 
 5 
 
 5 
 
 5 
 
 5 
 
 5 
 
 tira^ 
 times 1 
 times 2 
 times 3 
 times 4 
 times 5 
 times 6 
 times 7 
 timi-s 8 
 times 9 
 
 are 
 are 5 
 are 10 
 are 15 
 are 20 
 are 25 
 are 30 
 are 35 
 arc 40 
 are 45 
 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 7 
 
 times 
 timas 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 
 are 
 
 1 are 7 
 
 2 are 14 
 
 3 are 21 
 
 4 are 28 
 
 5 are 35 
 
 6 are 42 
 
 7 are 49 
 
 8 are 56 
 
 9 are 63 
 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 times 
 
 are 
 
 1 are 8 
 
 2 are 16 
 
 3 are 24 
 
 4 are 32 
 
 5 are 40 
 
 6 are 48 
 
 7 are 56 
 
 8 are 64 
 
 9 are 72 
 
lid! 
 
 26 
 
 MCLTIPLIOATIOW. 
 
 times 
 times 1 
 tiniPM '2 
 times 3 
 timi'S 4 
 times 5 
 times 6 
 times 7 
 times 8 
 times 9 
 
 are 
 are 3 
 are 6 
 are 9 
 are 12 
 are 15 
 are 18 
 arc 21 
 are 24 
 are 27 
 
 6 times 
 6 times 
 6 times 
 6 times 
 6 times 
 6 times 
 6 times 
 6 times 
 6 times 
 6 times 
 
 are 
 
 1 are 6 
 
 2 are 12 
 
 3 are 18 
 
 4 are 24 
 
 5 nre 30 
 
 6 nre 36 
 
 7 are 42 
 
 8 are 46 
 
 9 are 54 
 
 9 timeft 
 9 times 
 9 times 
 9 tim s 
 9 times 
 9 times 
 9 times 
 times 
 times 
 limes 
 
 9 
 9 
 9 
 
 Oare 
 
 1 are 9 
 
 2 are 18 
 
 3 are 27 
 
 4 are 36 
 
 5 are 45 
 
 6 are 64 
 
 7 are 63 
 
 8 are 72 
 
 9 are 81 
 
 PROBLEMS. 
 
 39. Case l.—To multiphj when the multiplier is not 
 greater than teji. 
 
 Example.— Multiply 654 by 9. 
 
 Solution.- In this example 654 must be taken 9 Operation. 
 times. Begin at the right and multiply ; 9 times 4 units are 654 
 
 36 units, 3 tens and 6 units. Write 6 in the units place and 9 
 
 cany 3 tens ; '9 times 5 tens are 45 tens plus the 3 tens 53^ 
 carried equal 48 tens or 4 hundreds and 8 tens. W^ite 8 in the .tens 
 place and carry 4 hundreds; 9 times 6 hundreds are 54 hundreds plus 
 the 4 hundreds earned equal 58 hundreds which is written down. There- 
 fore the product is 6886. 
 
 Note.— In practice the process is as follows : 
 
 9 times 4 30 write 6 and carry 3 
 
 9time85 45 and 3 48 write 8 and carry 4 
 
 9time86 54^nd4 68 write 58. 
 
 40. 'RMle.—'-Begin at the right and muUiplu each term of 
 the mHltiplic'and by the multiplier, carrying as in add.tion. 
 Case U.—When the multiplier is greater than 10. 
 Example.— Multiply 3527 by 382. 
 Multiply by the units as in case * Opejiatiok. 
 I, then by the tens placing the 
 fii-st product under the tens 
 column. Multiply the hundreds 
 in like manner placing the first 
 product under the hundreds col- 
 umn. Take the sum of the partial 
 products. The total product is 
 1347314. 
 
 3527 
 
 382 
 
 7054 
 
 28216 
 
 10581 
 
 1347314 
 
 u. 
 
 
 
 product by 
 
 units 
 
 (( 
 
 << 
 
 tens 
 
 « 
 
 « 
 
 hundreds 
 
 Total 
 
 product. 
 
timeS 
 Limes 1 
 times 2 
 tim s 3 
 times 4 
 times 5 
 times 6 
 times 7 
 times 8 
 limes 9 
 
 are 
 
 are 9 
 nre 18 
 are 27 
 are 36 
 are 45 
 are 64 
 are 63 
 are 72 
 are 81 
 
 MUtTIPMCATIOK. 
 
 27 
 
 Itiplicr is not 
 
 n 9 Opeuation. 
 
 are 654 
 
 and 9 
 
 tens 5_38p 
 j;ite 8 in "the ,tens 
 
 54 hundreds plus 
 tten down, "fhere- 
 
 I : 
 
 irry 4 
 
 )hj each term of 
 i in addition, 
 kan 10. 
 
 42. Rule. — /. Bef/in at the right and multiply the multi- 
 plicand hy each term of the multiplier, writing the first term 
 of each product under the term of the midtijtlier ichich pro- 
 duces it. 
 
 II. Add these partial products and their sum icill he the 
 entire product. 
 
 ArraniT.iiicnt mf work. 
 
 uct by units 
 I •« tens 
 « hundreds 
 
 ,1 prodnet. 
 
 . 8527 
 _382 
 
 7054 
 28216 
 10581 
 1347314 
 
 65437 
 
 .'•)3040 
 
 26T7480 
 
 196311 
 
 327185 
 
 3470778480 
 
 Example : Multiply 109080 by 36050. 
 Begin the opi ration by placing a Operation'. 
 
 in the units place there being no 109080 
 
 units. Then multiply by 5 say. 36050 
 
 ing : 6 times are ; write this 5454000 
 
 to the left of the first that is in the 654480 
 
 tens place. Continue : 5 times 8 327240 
 
 are 40 ; write the and carry 4 ; 5 3932334000 
 
 times ai-e 0, plus 4 equal 4, etc. . 
 
 Omitting the occupying the hundreds place take 6 saying : 6 times are 
 0, which is to be placed in the same column as the 6 it being of the 
 same order, thousands, etc. The product of the multiplicand by 3 must oc- 
 cupy the place of ten-thousands as it expresses by itself ten-thousanda. 
 
 I The product is therefore 3932334000. 
 
 Note ;— I. The product of the tens is advanced one place to the left, 
 that of the hundreds two places, etc , because the first figure of each 
 partial product is of the same orde/as the figure of the multiplier. 
 
 , II. When ciphers occur between the figures of the multiplier omit 
 
 I them and multiply by the next significant figure. 
 III. To multiply a number by 10, 100, 1000, 
 
 I add one, two, three ciphers to the multiplicand. 
 
 [Ex. 75X100=7500. Also if there are ciphers 
 
 jat the right of one or both factors, multiply by 
 
 Jthe significant figures and annex as many 312000 
 
 ciphers to the result as there are ciphers to the right of both factors. 
 
B05. 
 
 •'•OS. 
 
 510. 
 5J1. 
 5 J 2. 
 513. 
 5J4. 
 
 2S 
 
 '^- Proof . AT , '"''"^"^"^'^-^o^. 
 
 '"' i»»-actit.©. 
 
 - / r,jQ 
 
 8642076 „ 
 
 515. 
 5Je, 
 
 5 Jr. 
 
 5/8. 
 5I». 
 5-'0. 
 
 r>2i. 
 
 523. 
 
 524. 
 
 525. 
 
 526, 
 
 527. 
 
 528. 
 
 529. 
 
 5ao. 
 
 531. 
 
 532. 
 
 533. 
 
 534. 
 
 535. 
 
 53C. 
 
 537, 
 
 538. 
 
 539. 
 
 540. 
 
 541. 
 
 542. 
 
 543. 
 
 S45. 
 
 546 
 547. 
 5i8. 
 
 Tx 6 
 
 t'^X 4 
 '^^X 5 
 566X 8 
 
 40iX 7 
 436^ 3 
 
 i«4X 6 
 28 -^ ^ 
 
 I't^ 2 
 5'5X 5 
 
 476X 7 
 
 873X 4 
 li^X 9 
 576X 7 
 8760 i 
 
 t^^507X 2 
 »24654 V I 
 &51847Q I 
 
 547854 V I 
 864753O I 
 J^^«27X f 
 
 ?5«r6P 2 
 
 ''45«78y 
 
 S64207V ^ 
 «2<025v I 
 
 «47989P ^ 
 4569070 
 
 »07075V 
 »74834 V o 
 
 : f^ 
 
 529X14 
 540X17 
 
 '54X19 
 359X21 
 669X25 
 
 mxso 
 
 f»7X34 
 
 is^xse 
 fPX'^1 
 
 605X45 
 625X48 
 1^^X53 
 ^57X58 
 S76X62 
 964X67 
 854X70 
 674X74 
 S57X80 
 ^S7X8J 
 667X84 
 457X87 
 657X91 
 »37X93 
 978X96 
 5f«X36 
 
 7070430 ;| ^ 
 
 «%?^|,^ 
 978007X It 
 
 ,7«WX27 
 786795X 20 
 ^53477^ 32 
 
 609834V «| 
 
 «27454X 3« 
 f 7070^ i* 
 60774J^ is 
 74fiS24X S ^ 
 
 6770079, 47 
 
 79645nv !: 
 
 ^^»X48 / la^^- 
 
 jg /»6450X 48 
 
 " «^e854X tf? 
 
 j Wx el 
 
 678967^ fl 
 ^»5437X 7/f • 
 
 674874X if 
 f6&4Q7\^^J^ 
 
 *'^74B9X70S 
 
4 
 
 ' '«t^« same a« the 
 
 >93. 
 
 95. 
 
 96. 
 
 >7. 
 
 S. 
 
 9. 
 
 ). • 
 
 ll^X 83 
 
 ro795^P fi 
 
 '76753$ l; 
 ff«075< 5» 
 i6854X 63 
 
 ^275><e; . 
 
 'yx 4 
 
 967X 72 
 854X 74 
 <37X 75 ' 
 
 7fiX 7» 
 
 '?X257 
 5X618 
 
 »xroff 
 
 (537. 
 
 638. 
 
 «39. 
 
 640# 
 
 641. 
 
 642. 
 
 643, 
 
 644. 
 
 645. 
 
 646. 
 
 647. 
 
 648. 
 
 173. 
 
 674. 
 
 675. 
 
 6/'6. 
 
 677. 
 
 678. 
 
 679. 
 
 680. 
 
 681. 
 
 682. 
 
 683. 
 
 684. 
 
 686. 
 
 887. 
 
 688. 
 
 689. 
 
 690.- 
 
 691. 
 
 692. 
 
 693. 
 
 694. 
 
 695. 
 
 696. 
 
 697. 
 
 698. 
 
 699. 
 
 foo. 
 
 701. 
 
 702. 
 ' 703. 
 
 704. 
 
 706. 
 
 706. 
 
 707. 
 
 708. 
 
 709. 
 ♦710. 
 
 .978457X346 
 
 876574X457 
 
 457974X640 
 
 853473X703 
 
 957456X854 
 
 824956X387 
 
 347653X457 
 
 456824X654 
 
 976489X877 
 
 970546X200 
 
 457834X456 
 
 827669X623 
 
 MULTIPLICATIOK. 
 
 «49. 747898X^07 
 
 650.^ 647I>59X183 
 
 651. 834706X370 
 
 652. 900897X405 
 
 653. 986007X726 
 
 654. 837454X947 
 
 655. 967827X125 
 
 656. 678984X345 
 
 657. 730064X500 
 
 658. 984765X756 
 
 659. 947876X842 
 
 660. 689834X943 
 
 849654X -f'W I 711 
 747876X 7487 712! 
 457854X J»768 I 713. 
 679456X 1304 714 
 895775X 3726 715. 
 70(I789X 1425 716. 
 476895X 4070 717. 
 469889X 2004 718. 
 6y6489X 5360 719. 
 987824X 1076 720. 
 987684X 4567 721. 
 643956X 9475 722 
 8347.'53X 2475 723." 
 690790X 5709 724. 
 674825X 8907 725. 
 807405X 4937 726. 
 457670087X 4564 727. 
 ,„546876X 94347 728. 
 475087654X 7498 729. 
 ^^„764276X 47839 730. 
 679009675X 6689 731. 
 759364X 27895 732. 
 847664857X 9874 733. 
 674307X 42765 734. 
 764897695X 8007 73.5. 
 470076X 742-'4 736. 
 475795834X 2076 737. 
 786789X 69864 738. 
 95376947oX 8421 739. 
 476843X 85654 740. 
 815456789X 3575 741 
 764854X 37654 742^ 
 464879456X 8419 743. 
 966433X 77807 744. 
 654476S8SX 4739 746. 
 897466X 87493 746. 
 866674987X 6321 747 
 876452X 70809 748." 
 
 99 
 
 661. 946634X236 
 
 662. 769487X426 
 
 663. 69.')844X575 
 664./ 654266X429 
 
 665. 346854X537 
 
 666. 650079X935 
 
 667. 965789X327 
 
 668. 697896X938 
 
 669. 157679X937 
 
 670. 747876X945 
 
 671. 789379X849 
 
 672. 874119X927 
 
 497364956X 8470 
 867453X 96207 
 487847207X 2460 
 987407X 9S307 
 689047207X 2460 
 654857X 80076 
 877986755X 6790 
 854307X 67084 
 540090X 6900 
 780000X 4000 
 604000X702000 
 990000X 3490 
 940000X 7600 
 670000X 47600 
 875400X 96600 
 987400X 7000 
 8571O0X 1900 
 914400X 7200 
 977700X 4900 
 742800X 47000 
 890000X 98400 
 648700000X 47000 
 699400000X834000 
 927540000X896600 
 642570000X 69400 
 764600000X629000 
 600301000X400700 
 975007000X457600 
 845004000X700040 f 
 795654000X 84700-^- 
 648745601X474257 
 789407672X587648 
 457465478X459876 
 786745056X954378 
 956543576X376894 
 976432758X976432 
 669754007X649876 
 796030407X87600' 
 
 
 « 
 
 7 
 
 •r 
 
t! 
 
 w 
 
 1 
 
 80 
 
 1 
 
 749. 
 
 760. 
 
 761. 
 
 
 762. 
 
 • ii 
 
 763. 
 
 
 754, 
 
 .' ! 
 
 766. 
 
 , f 
 
 756. 
 
 ■! 
 
 757. 
 
 , :•} 
 
 768. 
 
 iii 
 
 769. 
 
 m 
 
 Ex 
 
 
 MUI.TIPMOATIOX. 
 
 938321676X^68076 
 47rt7-12074y3781»74 
 flo7007428v«8l>073 
 678098789X795409 
 75S507961X146279 
 674907461X307824 
 879421702X376548 
 855807607X976866 
 757489007X900(176 
 879407854X678765 
 787375634X894757 
 
 760. 
 761. 
 762. 
 763. 
 764. 
 765. 
 766. 
 767. 
 768. 
 769. 
 770. 
 
 695769452X976801 
 876454876Xtil5U8u 
 *875849064X76797'I 
 987453970X64581! 
 995296307X48792;) 
 796753769X84968 J 
 794037254X97847'! 
 759097895X760061 
 754827939X477231 
 674396856X28567!* 
 674007906X78456;i ; 
 
 ExprcBM the rollowinir nnmber* In figure* and solve 
 Itae mnltlpllcntion. 
 
 771. "What is the product of one thousand two hundred and thrc 
 units by thirty-two ? 
 
 772. Multiply three thousand one hundred and twenty-one by tliirty- 
 four? 
 
 773. What; product is obtained by multiplying three hundred and 
 twenty-four by two hundred and twelve ? 
 
 774. Find the product of eleven thousand two hundred and twenty 
 three by forty-one. 
 
 775. Take four hundred and tweuty-fonr times the number twelve' 
 thousand and twenty. 
 
 776. What is the product of two thousand and twenty-one by ninety 
 five ? 
 
 777. Give the result of one hundred and three thousand two hundred] 
 and seven multiplied by five hundred and forty-three, 
 
 778. What number is obtained by multiplying thirty thousand and ' 
 seventy-six by five thousand three hundred and forty-two ? 
 
 779. Find the product of nine hundred eighty-four thousand and 
 eighty-six by seventy-eight thousand three hundred and twenty-one. 
 
 780. Find the product of one thousand three hundred and two by forty 
 three units. 
 
 Or.il Exercises In Aaditlon, Anbtractton and SInKiplieallon. 
 
 783. D 
 <|it:»ntity 1 
 hubtracte( 
 
 784. T( 
 answer bo 
 
 785. H 
 
 786. H 
 another n' 
 
 787. W 
 times lai'g 
 
 788. W 
 iii^jer than 
 
 789. Ho 
 '45; 76— 2i 
 
 790. Ho 
 |5); 29-10 
 
 791. Ho 
 [«X2X7;e 
 
 792. Ho 
 I); 93 -(6: 
 
 793. Hoi 
 ') ; 47-10 
 
 794. Hoi 
 0X6 ; 7X 
 
 795. Hov 
 ; 52-22-j- 
 
 796. Hov 
 
 2xn-(ic 
 
 1st by adding the smaller number of a sub- 
 2nd by taking away the ditference from tli 
 
 781. What is obtained 
 traction to the difference ^ 
 larger number ? 
 
 782, What change takes place in the difference of two numbers : 1° ill 
 the larger number is increased ; 2" if the larger niimber is diminished | 
 8' if the smaller number is increased ; 4" if the smaller number 
 dimiuished ? 
 
 Note.- 
 
 iteger th( 
 [hvays be ' 
 
 797. How 
 
 798. How 
 \n each bencl 
 
 799. How 
 [20 shots in ( 
 
 800. A fan 
 

 6t»r)7fl9452XP7fl8'^t 
 87«-J5-187«Xt'l5l^8n 
 *8758490fl4X767»7'l 
 987453970X64581:) 
 995296307X4871*1'! 
 796753709X849681 
 794037254X97847'! 
 759097895X760051 
 754827939X47723 1 
 67439«856X2856rn 
 674007906X7846611 
 
 MCLTIPMCATION. 
 
 tl 
 
 «• and tolv* 
 
 hundred and tliiet! 
 ?enty-one by tliirtj 
 three hundred ami 
 lundred and twenty- 
 
 the number twelve 
 snty-one by ninety- 
 
 lusand two hundred 
 
 t 
 
 thirty thousand am 
 -two ? 
 
 -four thoiinand ant 
 md twenty-one. 
 ed and two by fort\ • 
 
 MiiltlpllenSioii. 
 
 iv number of a 8ul)-| 
 difference from tluj 
 
 ;wo numbers : 1° ill 
 iber is diminisheii 
 smaller number 
 
 » 
 
 783, Does the difference of two numbers change : l._if the sama 
 .,n.>t.ty be added tcTeach of the two numbers ; 2.-if fhe same au^.tit"Te 
 
 iMibtracted Irom each of the two numbers ? ^ 
 
 784. To add 12 times the same number, in what other way may the 
 |answer be found besides by addition ? ^ 
 
 786. How do you call the number that is to be multiplied » 
 786. How do you call the number that indicates how many time, 
 another number is to be taken ? 
 
 tiJeJ'C? " ''' --"'S of the expressions: twice smaller, three 
 
 WlZnZnt rt[i '" '-n'^ "•"" ^"«" ''^"" ' ' 2-12 times 
 789 Hw ' T T """"'-■'■ "'"" ^^ ' ^-^ """^^ «°«'">" than 24 ? 
 /89. How much are: 39-27 ; 43-32; 29-17 ; 53-23 • 61-21 • 67 
 
 ;o.'~u' '' "-'' ' ''-'' ■• ''-'' ■• ^^-22 ; 55-25/ ' '~ 
 
 790. How much are: 25-lOf 5; 26~(10-4): 28-10-4-2 -27 /in l 
 
 15) ;^9 10 + 6 ; 32-(I0+8, ; 34-10+7^ M^-^S V,l'l~'' 
 
 Px:x7";™i:7x:s: '^:^: • '^'^ ' ^x^x« ^^-^^s . 
 
 ;"-^;:;?:^iS:t^^^ ■' ^X-+^-X6) ; loxio-dix 
 
 /93. Howmuchare : 35—10+4 • 37— /104-7\ • qa in , o «/^ 
 
 795. How much are : ..t6-20+6 ; 47-20+8 ; 47-(37+4i -49 lo . 
 ; 62 22+10 ; 54-(34+n) ; 56-46+7 ; 17-27 + 1^4^6 1 ar+^M 
 
 796. How much are : 6X2+(2X9+3)-(3X10) • 14+114-8 ritZ 
 2X11-(10X7) J 8X16-(7X?3-f llT ? ^ ll+8-(?X4) ; 
 
 PRACTICAL PROBLEMS. 
 
 Note -When Dollars and Cents are multinlied by any 
 teger the point to separate the Dollars and Cents must 
 |hvays be worked after the lii^t two figures to the right. 
 
 798' HoT Z7 ^"' "' ?"■' '° ' '^«^ ''■''''' ^«« <=°»tail ?.47 t 
 In el "Ih r '' "" '^ "^^^' °" ^^ '^"^^^^ ^^ ^^- - « Pl«ces 
 
 »ri"?:.""'^^'.''*^ '^'^^^ ^-" fi»«^ o« i« -X hours at the rate of 
 
 |20 shots in one hour ? 
 800. A 
 
 family sj,e,id. f 1,3? a da^ ; how mucl, will it spend 
 
 inl6^ 
 
32 
 
 MtJLTirLICATION. 
 
 801. A train is composed of 27 cars each weighing 4800 pounds. What 
 is the weight of the entire train ? 
 
 802. What is the price of 490 pounds of mercury at $2.80 a pound I 
 
 803. How many hours are there in a month of 30 days? 
 
 804. How many hours are there in a year of 365 days ? 
 
 805. A man gains $45 a month ; what is his annual income t 
 806 What number is 37 times larger than 4015 ? 
 
 807. An acre of land costs $72.50 ; how much would you have to pay 
 
 for 18 acres ? , , u a'a 
 
 808. Twenty-seven children received 15 cents each, how much did 
 
 they all receive ? > i. v 
 
 809. It requires 38500 slabs to cover a street ; how much must bo 
 
 paid if each one cost 49 cents ? 
 
 Problems In Addition, Subtraction and Multiplication. 
 
 810. On a tree there are 942 apples ; how many remain if 579 are 
 
 gathered ? ., .- 4.1. j 
 
 811. How many apples on a tree, knowing that if 345 are gathered, 
 
 there remain 407 ? , j n« j 
 
 812. Bought 72 pounds of coffee at 34 cents a pound, and 95 pounds 
 of sugar at 7 cents ; how much must be paid for all ? 
 
 813. What is the number of oranges contained in two boxes if the 
 first contains 345 and the second 367 ? 
 
 814. A box of oranges contains 345 oranges ; another coutams 642 
 oranges ; if 47 be taken from the second and placed in the first, how 
 many will each box then contain 1 
 
 815. A servant receives $12.85 a month,. what are his yearly wages? 
 
 816. A box contains 476 oranges, another contains 504 ; how many 
 must be put in the fiist box so as to equal the number in the second box ? 
 
 817. A merchant receives four orders each for 450 bottles of beer; he 
 sends'on two occasions 370 bottles each time.^ How many botUes must 
 
 he still send ? ' v u 
 
 818. A man bought 12 reams of paper at 15 cents a quire, how much 
 must he pay if there are 20 quires in a ream 1 
 
 819 How many travellers can a train of three cars transport, if there 
 are in the 2nd class car 36 places, in the Ist class 40, and in the parlor; 
 
 car 20 ? , ., *u 
 
 820. How many pupils are absent in a class of 76 places, if those 
 
 presfiiit are seated on 8 tables of 9 places each ? 
 
 821. What is the number of boards iu two loads the first containing 
 240 and the second 275 'i _ 
 
MUtTIPLICATION. 33 
 
 S.'"; It, °'°* °"'" "^ '"'" '° " "■"• """"S i-fng 20 d.,. .. 
 .wfy's^l ""*"" ""'" "' ''"■■''" "<" ""!' «°»ta •"- '"king 
 
 J2«.^How many fig, a„ ,h.„ ;„ „ ^^^^^ each c..,dm.g 125 
 
 mel'LI?" " "■" '"™ '""• «'• «ee,.f9„».„ crry,„g45« 
 
 ..i"'™;™7 "^ ""' " ■"""' '» ° """"-■•"' »' «^ - •» " 
 830. Wli»t iBthe totalmiiiiberofyearsinthe.m.rfj,„.~™ • 
 
 «y. .,e «... w„g «. .He .».. '«. .,. :;^T; l\';:x„: ; 
 
 minutes iu an hour » '*°"'' '" "■ ^"^ ""^ «» 
 
 840. A basket contains U6 1 
 many ftre there in it now ? 
 
 eggs ; 17 dozen were^ added to it, how 
 
 «■-•. ; ' 
 
34 
 
 MULTIPLICATION. 
 
 
 ■*;■'! 
 
 841. What is gained by selling at 35 cents a pound, 60 pounds of. 
 goods that cost 28 cents a pound ? 
 
 842. What is the number of men in an army composed of 14700 
 iijfantrjs 3800 cavalry, 2160 artillery and 1140 huicers? 
 
 343. In thrnshing wheat with a flail a man strikes 37 times a minute ; 
 how.many limi's will he strike in a day of 10 hours I 
 
 844. If a pile of sheaves give an average of 32 gallons of wheat, 
 Kow many gallons will 95 piles give ? 
 
 845. A man earns 75 cents a day, what will he receive for the work of 
 the five, last mouths of the year allowing 25 days for Sundays and sick- 
 ness 1 
 
 8^6. A city pays annually $1345600 for butter and $5498060 for fish ; 
 by iiow much does the amount paid for fish exceed that paid for butter ? 
 
 847. The area of Prince Edward Island is 2133 square miles ; that of 
 Nova Scotia, 20907 square miles; New Brunswick, 27174 square miles; 
 Quebec, 188688 square miles; Ontario, 101733 square miles; British 
 Columbia, 341305 square miles ; Manitoba, 123200 square miles ; the 
 Territories; 2665252 square miles. What is the area of the Dominion 1 
 
 . 848. A workman saves 40 cents a day ; how much can he save in 3 
 years of 305 working-days each ? 
 
 849. Bought 12 yards of cloth at $4.30 a yard and 31 yards at $5.50 a 
 yard. I sokUhe whole at $6.80. Did I gain or lose and how much ? 
 
 850. There are 15780 slates placed on a roof ; and the slaters say that 
 they want 29 times as much to complete it ; how many slates will there 
 
 be on the roof ? 
 
 851. In a hospital containing 156 persons, they distribvte yearly 5 
 shirts and 3 pair of stockings ; how many shirts and pairs of stocking 
 will there be distributed in 4 years ? 
 
 852. How much does a man earn yearly, if he spends $212.50 and 
 
 saves $140? 
 
 853. A man was born in 1796 and died in 1882, how many months 
 
 did he live ? 
 
 854. A work ^ composed of 5 volumes, each volume contains 220 
 png«s, each page contains 32 lines and each line 11 words. How many 
 wokIh in the whole work ? 
 
 855. If a man breathes 20 times a minute ; how many times will he 
 breathe from the first of March to the first of September a i^riod of 184 
 
 days ? . 
 
 856. A merchant bought 486 dozeu pf oranges at 2 cents apiece ; ho\|r 
 
 much must he pay ? 
 
MULTIPLICATION. 
 
 s» 
 
 imes a minute ; 
 
 Ions of wheat, 
 
 867. An overseer has 20 men under liim, he pays them $1.25 a day 
 How much must he pay them for 50 days' work ? 
 
 858. How many hours are there in 11 years and 20 days? 
 
 859. What sum is required to maintain 34 sick persons during a year 
 of 365 days at an average of 3 cents each hour ? 
 
 860. A father of a family earns $2.50 a day and spends $1.60 ; how 
 much money will he have remaining at the end of a year if he abstained 
 Irom working during 52 Sundays and 9 Feast-days ? 
 
 861. How many days are there in 34 years, if 27 are of 365 and the 
 remainder of 366 dnys ? 
 
 862. In a workshop there are 33 workmen, 11 of whom earn $1.30 a 
 day ; 12 others $1.50, and the remainder $1.75 ; what sum is required to 
 pay them for a year if they did not work on Sundays and on 9 festivals « 
 
 863. Six baskets of apples contain 15 dozen each, what is the total 
 contents of these baskets ? 
 
 864. 10 baskets containing 125 dozen of figs each were bought for 2 
 cents a fig ; what was the amount paid ? 
 
 865. An army of 49854 men received reenforcemeuts after which the 
 army numbered 65878 men. What was the number of the reenforcement » 
 
 866. A man received 3690 boxes each containing 1350 pens at 2 cents 
 a lien. Require the cost. 
 
 867. Six boxes, containing 24 dozen of knives each, were boucht for 
 45 c. ,.ts a knife ; what was the total cost ? 
 
 868. A merchant sold 645 plates : he delivered 340 the first time and 
 1 ^8 the second time. How many are stUl to be delivered f 
 
 869. In 8 building there are 85 windows having 24 panes of glass each • 
 the glazier received 15 cents for each pane : how much did he receive fo^ 
 ail ! 
 
 870. What must be paid for 2 boxes of soap the first box containing 
 242 pounds and the second 191 pounds, at 6 cents a pound ? 
 
 871. In selling 30 yards of cloth for $180 I gained 90 cents on a yard 
 what did the cloth cost me ? ■ 
 
 872. What would be the gain on 50 pounds of tobacco that were sold 
 lor 40 cents and bought for 33 cents ? 
 
 873. A man bought 36 yards of silk at $2. 60 a yard, 64 pounds of salt 
 at 3 cents a pound 15 gallons of oil at 42 cents a gallon, and 26 cords of 
 wood at $3.70 a cord. How much must he pay for all ? 
 
 874. A contractor has three workmen, by the first he gains 46 cent, 
 perday. by the second 30 cents, by the third 25 cents ; what wiU be his 
 entire gain at the end of 3 weeks, omitting Sundays ? 
 
86 
 
 DIVISION. 
 
 I I 
 
 !!« 
 
 DIVISION. 
 
 44. Division is the process of finding how many times a 
 number call divisor is contained in another number called 
 dividend. 
 
 45. The result of the division is called quotient. 
 
 46. Division is indicated by the sign -v- or : which reads 
 divided by, or by a line placed between the dividend and the 
 divisor. 
 
 Thus to indicate the division of 21 by 3, it is written 21-^3 
 or V. 
 
 Note.— The quotient of a division may be obtained by subtraction. 
 Tlius, to find the quotient of 16 by 5 ; subtract 5 from 16, this gives 11 
 for remainder ; then 5 from 11 give 6 for remainder ; 5 from 6 leave 1 
 for remainder. Another subtraction being imposiiible it is seen that 16 
 contains 5 three times with 1 for remainder. 
 
 This means of fiudiug the quotient of two numbers requires too much 
 time and would not be practical in many cases ; a shorter method of 
 solving division is therefore necessary. 
 
 pivision Table. 
 
 Ex. 20-i-6=3, r. 2. Read 20 divided by 6 equal 3 remain- 
 der 2. 
 
 =1 
 
 =l,r. 1 
 =1, r. 2 
 =1, r. 3 
 =2 
 
 =2, r 1 
 =:2, r. 2 
 =:2, r. 3 
 =3 
 
 =3, r. 1 
 =3, r. 2 
 =3, r. 3 
 
 =4, r. 1 
 =4, r. 2 
 =4, f. 3 
 
 l-f-l=l 
 
 17--2=8, r. 1 
 
 15-5-3=5 
 
 4- 
 
 .4 
 
 2-^-2=1 
 
 18-=-2=9 
 
 16^3=5, r. 1 
 
 5- 
 
 —4 
 
 3-^2=1, r. 1 
 
 19-5-2=9, r. 1 
 
 17h-3=5, r. 2 
 
 6- 
 
 -4 
 
 4-r-2=2 
 
 
 18-f-3=6 
 
 7- 
 
 —4 
 
 6^-2=2, r. 1 
 
 3-5-3=1 
 
 19-5-3=6, r. 1 
 
 8- 
 
 -4 
 
 6-=-2=3 
 
 4-5-3=1, r. 1 
 
 20-5-3=6, r. 2 
 
 9- 
 
 -4 
 
 7-f-2=3, r. 1 
 
 5-5-3=1, r. 2 
 
 21^3=7 
 
 10- 
 
 -4 
 
 8-5-2=4 
 
 6-5-3=2 
 
 22-5-3=7, r. 1 
 
 11- 
 
 —4 
 
 9 .-2=4, r. 1 
 
 7h-3=2, r. ) 
 
 23-5-3=7, r. 2 
 
 12- 
 
 - 4 
 
 10-:-2=5 
 
 8-5-3=2, r. 2 
 
 24-5-3=8 
 
 13- 
 
 -4 
 
 11-8-2=5, r. 1 
 
 9--3=3 
 
 25-5-3=8, r. 1 
 
 14- 
 
 -4 
 
 12-*-2=6 
 
 10-5-3=3, r. 1 
 
 26^3=8, r. 2 
 
 15- 
 
 -4 
 
 13-h2^6, r. 1 
 
 llH-3=3, r. 2 
 
 27^3=9 
 
 16- 
 
 -4 
 
 14-!-2=7 
 
 12-1-3=4 
 
 28-f-3=9, r. 1 
 
 17-5-4 
 
 15-1-2=7, r. 1 
 
 18-5-3=4, r. 1 
 
 29-r-3=9, r. 2 
 
 IS -4 
 
 ie-f-2=8 
 
 14-5-8=4, r. 2 
 
 
 19-^ 
 
 ■-4. 
 
 6^5= 
 6-^5= 
 7-1-5= 
 8-5-5= 
 9-5-5= 
 10-5-6= 
 11-^5= 
 12-^.5= 
 13-5-6= 
 14^6= 
 15-5-6= 
 16-5-6= 
 17--6= 
 18-5-6= 
 19-5-6=; 
 20h-5= 
 21-h6=. 
 22-5-5=' 
 23-;-5=< 
 24-f-5=< 
 25-5-5=i 
 26--6=i 
 27-5-6=£ 
 28-5-5=£ 
 29-5-5=5 
 30-^6=fi 
 31-f-5=e 
 32-^5=6 
 33-5-6=6 
 34-5-5=6 
 
w many times a 
 r number called 
 
 tient. 
 
 r : which reads 
 ividend and the 
 
 is written 21-^3 
 
 led by subtraction. 
 
 n 16, this gives 11 
 
 5 from 6 leave 1 
 
 I it is seen that 16 
 
 requires too much 
 shorter method of 
 
 equal 3 remain- 
 
 DIVISION. 
 
 12- 
 
 13-r-4:: 
 14-T-4:: 
 15-4-4^ 
 
 16^4^ 
 17-4-4= 
 IS -4= 
 
 19^4= 
 
 6-7-4= 
 
 ■4= 
 
 8--4= 
 
 9h-4= 
 
 10-f-4= 
 
 11-h4= 
 
 4= 
 
 :l 
 
 :l,r. 1 
 :1, r. 2 
 :1, r. 3 
 
 :2 
 
 :2, r 1 
 :2, r. 2 
 -2, r, 3 
 
 :3 
 
 ;3, r. 1 
 ^3, r. 2 
 -Z, r. 3 
 
 ^4, r. 1 
 :4, r. 2 
 :4, f. 3 
 
 20 
 21 
 22 
 
 4 
 -f-4 
 
 -r-4^5 
 
 23-J-4: 
 24-^4: 
 
 25 
 
 26-=-4: 
 27-?-4: 
 
 28 
 
 29-f-4: 
 
 30-f-4: 
 
 31-r-4. 
 32-f-4: 
 
 33-^ 4 1 
 34- 
 
 35- 
 36^^ 
 
 37-=- 
 
 38 
 
 89 
 
 ^5 
 
 =5. r. 1 
 
 4= 
 
 4= 
 
 :5, r. 2 
 :5, r. 3 
 
 :6 
 
 :6, r. 1 
 :6, r. 2 
 :6, r. 3 
 
 :7 
 
 -7. r. 1 
 =7, r. 2 
 =7, r. 3 
 =8 
 
 -8, r. 1 
 =8, r. 2 
 =8, r. 3 
 .9 
 
 :9, r. 1 
 :9, r. 2 
 :9, r. 3 
 
 5--5 
 6-J-5 
 7--5 
 8-f-6 
 9-^5 
 10-^6 
 11h-5 
 
 12-1-6; 
 13-f-6: 
 14^6: 
 15-5-6: 
 16 4-6: 
 
 17^6= 
 l8-f-6= 
 
 l9-f-6: 
 20-i-O: 
 
 21-f-6= 
 
 22-i-5= 
 
 23^6 
 
 24-J-5 
 
 25H-5 
 
 26-^-6: 
 27-^5: 
 28-f-5: 
 29-5-6: 
 
 30-5-5= 
 
 =1, r. 1 
 :1, r. 2 
 i=l, r. 3 
 =1, r. 4 
 =2 
 
 =2, r. 1 
 =2, r. 2 
 =2, r. 3 
 =2, r. 4 
 =3 
 
 =3, r. 1 
 =3, r. 2 
 =3, r. 3 
 :3, r. 4 
 
 :4 
 
 4, r. 1 
 
 4, r. 2 
 
 =4, r. 3 
 
 =4, r. 4 
 
 =5 
 
 =5, r. 1 
 =5, r. 2 
 =5, r. 3 
 :6, r. 4 
 
 :6 
 
 31-=-5=6, r. 1 
 32h-5=6, r. 2 
 33-5-6=6, r. 3 
 34--6=6, r. 4 
 
 35-=-5=r7 
 36-5^7, r. 1 
 37-5=7, r. 2 
 38--5=7, r. 3 
 39--5=7, r, 4 
 40^5-=8 
 41-T-5=8 r. 1 
 42---5.T.8, r. 2 
 43-5-5-^8, r. 3 
 44-5-5-=:8, r. 4 
 45-5-5=9 
 46-5-5=9, r. 1 
 47-^5=9, r. 2 
 48-5-5=9, r. 3 
 49^5=9, r. 4 
 
 6h-6 
 
 7-5-6 
 
 8-5-6 
 
 9-5-6 
 
 10^-6 
 
 n--6 
 
 12-5-6 
 
 13-=-6 
 
 14-5-6 
 15^6 
 16H-6 
 17^6. 
 
 18-5-6: 
 19-H6: 
 
 20^6 
 
 21-5-6: 
 
 22-!-6. 
 
 23-H6: 
 
 24-4-6= 
 
 25-5-6= 
 
 26-T-6z 
 
 27^6= 
 
 28-H6 
 
 29-H6 
 
 30-^6 
 
 31H-6 
 
 32-f-6= 
 
 33-4-6= 
 
 34-4-6= 
 
 35-4-6= 
 
 38-5-6 
 
 =1 
 
 --1, r. 1 
 
 i=l, r. 2 
 
 ■ :1, r. 3 
 
 :1. r. 4 
 
 i=l, r. 5 
 
 't 
 -2, r. 1 
 =2, r. 2 
 =2, r. 3 
 =2, r. 4 
 =2. r. 5 
 -.A 
 
 .3, r. 1 
 =3, r, 2 
 :3, r. 3 
 :3, r. 4 
 :3, r. 6 
 
 :4 
 :4 
 
 =4, 
 
 r. 1 
 :4, r. 2 
 :4, r. 3 
 
 i, r. 4 
 :4, r. 5 
 
 :5 
 
 :5, r. 1 
 :5, r. 2 
 6, r. 3 
 5, r. 4 
 :6, r. 6 
 
 :6 
 
 37-4-6=6, r. 1 
 38H-6=6, r. 2 
 39-4-6=6, r. 8 
 
 •11 ; 6 
 4 2 --6 
 
 43-f-6: 
 44-5-6: 
 45-5-6; 
 46^6: 
 47H-6: 
 
 48^-6= 
 
 49-5-6r 
 
 50-5-6= 
 51-5-6= 
 52h-6= 
 63-^6^ 
 54-5-6= 
 55 .-6 = 
 56-5-6= 
 57^6 = 
 58 5-6 = 
 59-5-6= 
 
 =6, r. 5 
 =7 
 
 =7, r. 1 
 =7, r. 2 
 '-'~7, r. 3 
 =7, r. 4 
 =7, r. 5 
 =8 
 
 =8, r. 1 
 :8, r. 2 
 :8, r. 3 
 :8, r. 4 
 
 8, r. 5 
 
 :9 
 
 9, r. ] 
 9, r. 2 
 9, r. 3 
 9, r. 4 
 9, r. 5 
 
 7-5-7 
 8-5-7 
 9-=-7 
 
 lO-r-7 
 
 11^7 
 12-5-7 
 13-7 
 14--7 
 154-7 
 16-5-7 
 17^7 
 18-5-7^ 
 
 19 4-7: 
 20-5-7: 
 21-5-7: 
 
 22-5-7= 
 
 23-5-7= 
 
 24-5-7= 
 
 25-4-7= 
 
 26-5-7= 
 
 27-5-7= 
 
 23-5-7= 
 
 29-5-7= 
 
 30-5-7= 
 
 31-4-7= 
 
 32-5-7= 
 
 33 
 
 '=1 
 
 =1. r. 1 
 
 :], r. 2 
 
 1, r. 3 
 
 =1, r. 4 
 
 =1, r. 5 
 
 =1,4. 6 
 
 =2 
 
 =2, r. ] 
 =2, r. 2 
 =2, r. 3 
 =2, r. 4 
 =2, r. 6 
 =2, r. 6 
 =3 
 
 =3, r. 1 
 =3, r. 2 
 =3, r. 3 
 =3, r. 4 
 =3, r. 5 
 i3, r. 6 
 
 :4 
 
 :4, r. 1 
 :4, r. 2 
 :4, r. 3 
 4, r. 4 
 
 7=4, r. 5 
 34-5-7=4, r. 6 
 35--7=5 
 36-5-7=6, r. 1 
 
 38-5-7 
 39-f-7 
 40-5-7 
 41-5-7 
 42-5-7 
 43-5-7 
 44-4-7. 
 
 45-5-7: 
 46--7: 
 47--7: 
 48-7: 
 
 49-5-7 
 
 504-7: 
 51-5-7: 
 
 52--7= 
 
 53-^7: 
 
 64-7= 
 
 55-4-7= 
 
 56h-7= 
 
 57-5-7= 
 
 58-7= 
 
 59-5-7= 
 
 60-4-7= 
 
 61h-7= 
 
 62-4-7= 
 
 634-7= 
 
 644-7= 
 
 60 4-7= 
 
 66-5-7= 
 
 67-5-7= 
 
 684-7= 
 
 69-5-7=1 
 
 37 
 
 :5, r. 3 
 
 :5, r. 4 
 
 =5, r. 5 
 
 =.5, r. 6 
 
 =6 
 
 =6, r. 1 
 =6, r. 2 
 =6, r. 3 
 =6, r. 4 
 =6, r. 5 
 =6, r. 6 
 =7 
 
 =7, r. 1 
 =7. r. 2 
 =7, r. 3 
 =7, r. 4 
 =7, r. 5 
 =7, r. 6 
 =8 
 
 =8, r. 1 
 =8, r. 2 
 =8, r. 3 
 :8, r. 4 
 :8, r. 5 
 :8, r. 6 
 
 :9 
 
 :9, r. 1 
 :9, r. 2 
 :9, r. 3 
 :9, r. 4 
 :9, r. 5 
 :9, r, 6 
 
 8-5-8=1 
 
 9-8=1, r. 1 
 
 10-8=1, r. 2 
 
 11-4-8=1, r. 3 
 
 12-5-8=1, r. 4 
 
 13-5-8=1, r. 5 
 
 14 4-8=1, r. 6 
 
 15-8=1, r. 7 
 
 16-5-8=-^2 
 
 17-5-8=2, r. 1 
 
 18-5-8=2, r. 2 
 
 19-5-8=2, r, 8 
 
 20-4-8=2, r. 4 
 
 21-5-8=2, r. 5 
 
 22-5-8=2, r. 6 
 
 23-4-8=2, r. 7 
 
 24-4-8=3 
 
 40^6=6, r. 4 | 37-5-7=6, t. 2 | 26-1-8=3, r. 1 
 
;/ 
 
 m Hi 1 
 
 i; ri^ 
 
 88 
 
 DIVISION. 
 
 26 
 27 
 28 
 
 29-f-8 
 
 30 
 
 31^8 
 
 32 
 33 
 34 
 
 35^8 
 
 36 
 
 37---8. 
 
 38-V-8: 
 
 39h-8= 
 
 .8= 
 8= 
 
 40. 
 
 41- 
 
 42-f-8= 
 
 43h-8. 
 
 44-h8= 
 
 45^-8= 
 
 46- 
 47- 
 
 48.^8 
 
 49-^8 
 
 50-5-8 
 
 51-^8= 
 
 52-f-8. 
 
 53h-8. 
 
 54^8= 
 
 55^8= 
 
 56 
 
 58 
 59 
 
 8- 
 
 8_ 
 
 57-r-8 = 
 
 :3, r. 2 
 
 -3, r. 3 
 
 -3, r. 4 
 
 :3, r. r. 
 
 -3, r. 
 
 =3, r. 7 
 .4 
 
 :4. r. 1 
 
 :4, r. 2 
 
 .4, r. 3 
 
 :4, r. 4 
 
 -A, r. 5 
 
 ■4, r. 6 
 
 :4, r. 7 
 
 :5 
 
 :5, r. 1 
 
 :5, r. 2 
 
 :5, r. 3 
 
 :5, V. 4 
 
 :5, r. 5 
 
 :5, r, 6 
 
 :5, r: 7 
 
 :6 
 
 =6, r. 1 
 
 :6, r. 2 
 
 :6, r. 3 
 
 :6, r. 4 
 
 :6, r. 5 
 
 :6, r. 6 
 
 :6, r. 7 
 
 :7 
 
 :7, r. 1 
 
 :7, r. 2 
 
 :7, r. 3 
 
 8= 
 
 60-4-8 
 61-f-8 
 62-f-8 
 63-4-8 
 64-f-8 
 
 66-r-8 
 
 66 --8 
 67-^8 
 68--8 
 
 69-r-8 
 
 70^8 
 
 71-r-8 
 
 72-^-8 
 73 --8 
 74f-8 
 75-5-8 
 76-=-8 
 77^8 
 78^-8 
 79-5-8 
 
 ^7, r. 4 
 =7, r. 5 
 =7, r. 6 
 =7, r. 7 
 =8 
 
 =8, r. 1 
 =8, r. 2 
 =8, r, 3 
 =8, r. 4 
 =8. r. 5 
 =8, r. 6 
 =8, r. 7 
 -^9 
 
 =9, r. 1 
 ^9, r. 2 
 =9, r. 3 
 =9, r. 4 
 =9, r. 5 
 =9, r. 6 
 =9, r. 7 
 
 9-5-9.^1 
 10-5-9^=1, r. 1 
 11-5-9=1, r. 2 
 12^9=1, r. 3 
 13-5-9=1, r. 4 
 14-5-9=1, r. 5 
 16^9=1, r. 6 
 16-5-9=1, r. 7 
 17-^9=1, r. 8 
 18-5-9=2 
 19^9=2, r. 1 
 20-5-9=2, r, 2 
 21-5-9=2, r. 3 
 
 22^9= 
 
 23. 
 
 24_:-9 
 
 25. 
 26. 
 
 27^9= 
 
 28-^9: 
 
 29-^9= 
 30^9^ 
 31^9= 
 32^9- 
 
 33 
 
 34-1-9=: 
 
 35 
 
 36-f-9.^ 
 37-5-9^ 
 
 38. 
 
 42 
 
 44. 
 
 45-5-9 
 
 46 
 
 48 
 49 
 
 50-5-9: 
 61-f-9r 
 52-5-9; 
 
 53-5-9. 
 
 54^-9 
 
 554-9 
 
 .9= 
 
 .9= 
 
 .9^ 
 
 39--9= 
 40--9. 
 41^9= 
 
 43--9= 
 
 ■9. 
 
 47--9=i 
 
 :2, r. 4 
 
 -2, r. 5 
 
 :2, r. 6 
 
 ^2. r. 7 
 
 =2, r. 8 
 =3 
 
 :3, r. 1 
 
 :3, r. 2 
 
 :3, r. 3 
 
 -3, r. 4 
 
 :3, r. 6 
 
 :3, r, 6 
 
 :3, r. 7 
 
 :3, r. 8 
 -A 
 
 A, r. 1 
 
 :4, r. 2 
 
 ■A, r. 3 
 
 :4, r. 4 
 
 :4, r. 5 
 
 :4, r. 6 
 
 :4, r. 7 
 
 :4, r. 8 
 
 :5 
 
 :5, r. 1 
 
 :5, r. 2 
 
 :5, r. 3 
 
 :5, r. 4 
 
 .5, r. 5 
 
 -.5, r. 6 
 
 :5, r. 7 
 
 :5, r. 8 
 
 :6 
 
 =6, r. 1 
 
 •9= 
 
 9= 
 
 9= 
 
 Difi'erent Gases of Division. 
 
 56-5-9= 
 
 67-4-9 
 
 58-5-9 
 
 59-=-9 
 
 60-4-9 
 
 61-5-9 
 
 62-5-9 
 
 63H-9 
 
 64^9 
 
 65-r-9 
 
 66-5-9 
 67-4-9 
 68-4-9 
 69H-9 
 70-4-9: 
 71H-9: 
 72-5-9 
 73-H9: 
 74-5-9^ 
 76-^-9 
 76^9: 
 77-4-9 
 78-5-9: 
 79^9 
 
 80-t-9: 
 
 81-^-9: 
 
 82^9: 
 
 834-9: 
 844-9 
 85-5-9 
 86 5-9 
 87-5-9 
 884-9 
 89^9 
 
 =6, r. 2 
 
 -6, r. 3 
 
 :6, r. 4 
 
 '.Q, r. 5 
 
 :6, r. 6 
 
 =6, r. 7 
 
 =6, r. 8 
 =7 
 -7, 
 
 r. 1 
 —7. r." 2 
 
 =7, r. 3 
 =7, r. 4 
 =7. r. 5 
 
 =7, r. 
 =7. r. 
 =7, r. 
 7, r. 
 
 =7, r. 6 
 
 =7, r.: 7 
 
 =7, r. 8 
 =8 
 
 =8, r. 1 
 
 =8, r. 2 
 
 =8, r. 3 
 
 =8, r. 4 
 
 =8, r. 5 
 
 =8, r. 6 
 
 =8, r. 7 
 
 =8, r. 8 
 
 :9 ■ 
 
 :9, r. 1 I 
 
 :9, r. 2 \ 
 
 -.9, r. 3 ^ 
 
 =9, r. 4 
 
 :9, r. r. 
 
 :9, r. 6 
 
 =9, r. 7 
 
 :9, r. 8 
 
 48. Case I. — The divisor in let's than 10. In this case the, 
 qiiotient may be easily fouud by the nmltiplication table. 
 
 Ex.\MPLE. — Divide 51 by 6. 
 
 Ill the multiplication table it is seen that 51 is greater OPEiiATloy,; 
 
 than 6X8, and smaller than 6X9 ; therefore 8 is the 6) 51 
 
 quotient with a lemainder of 3. 8 R. Sl 
 
 Example 2.— Divide 8754 by 8. 
 
 Solution. — 8 is contained in 8 thousands 1 OPKitATioyr 
 
 thousand times, with uo remainder ; 8 into 7 8 )8754 
 
 hundred is contained hundred times. Annex 1094 — 2 
 
 5 tens, ' 
 9 for qu( 
 34 units 
 The quol 
 
 49. ( 
 
 figure. 
 Find 
 
 Solut 
 
 with a 1 
 
 horizouta 
 
 42 is 1 
 
 there are 
 
 tliousand 
 
 thousand 
 
 thousands 
 
 hundreds 
 
 liuodred 1 
 
 3 hundred 
 
 tens, a cip 
 
 units. 42 
 
 which sub 
 
 The quo 
 
 50. N 
 [the subti 
 divisor is 
 [Thus 3 tin 
 3 tin 
 
 Kemaind 
 
 51. Ri 
 
 same line. 
 ]/iorizuntai 
 II. Fir. 
 
 iffures Oj 
 \lii:isor ; f 
 
 ill M 
 
 roductfr 
 \he follow. 
 
56-i-9= 
 
 67-5-9: 
 68H-9: 
 59-^-9: 
 60-^-9: 
 
 61-4-9: 
 
 62-4-9: 
 63-=-9: 
 
 64^9 
 65^9 
 66-4-9^ 
 
 67-r-9 
 68-4-9: 
 
 69-4-9^ 
 
 70-4-9: 
 
 71-4-9= 
 72-4-9 
 73-h9= 
 74-4-9= 
 
 76-4-9: 
 
 76-4-9= 
 77-4-9= 
 78-4-9= 
 79-5-9= 
 80-4-9= 
 
 81-5-9: 
 
 82-4-9= 
 834-9: 
 84^9: 
 85-4-9; 
 
 86 4-9: 
 87^9: 
 88-4-9: 
 89 4-9: 
 
 =6, r. 2 
 -:6, r. 3 
 :6, r. 4 
 -Q, r. 5 
 :6, r, 6 
 =6, r. 7 
 :6, r.' 8 
 =7 
 
 -7, r. 1 
 =7, r: 2 
 =7, r. 3 
 =7, r. 4 
 =7, r. 5 
 -7, r. 6 
 =7, r.: 7 
 =7, r. 8 
 =8 
 
 =8, r. 1 
 =8, r. 2 
 =8, r. 3 
 =8, r. 4 
 =8. r. 5 
 =8, r. 6 
 =8, r. 7 
 =8, r. 8 
 
 :9 ' 
 
 =9, r. 1 
 
 =9, r. 2 
 
 =9, r. 3 
 
 =9, r. 4 
 
 =9, r. r. 
 
 =9, r. « 
 
 =9, r. 7 
 
 =9, r. 8 
 
 DIVISION. 
 
 39 
 
 Opkkation. 
 12945 |42 
 ^26 3U8 
 
 345 
 
 336 
 9— Rem. 
 
 n. 
 
 In this case the 
 [cation table. 
 
 reater Opeuation, 
 is the 6) 5 1 
 
 8 JR. S| 
 
 OPERATTOJf, 
 8 )8764 
 1094—2 
 
 5 tens, 7 hundreds and 5 tens are 75 tens, which divided bv 8 gives 
 9 for quotient and a remainder of 3 tens. 3 tens annexed to 4 unit^ are 
 34 units which divided by 8 gives a quotient of 4 and a remainder of 2 
 Ihe quotient then is 1094 and a remainder of 2 units. 
 
 49. Case II. — When the divisor contains more than one 
 figure. 
 
 Find how many times 42 is contained in 12945. 
 
 Solution. -V/rite tlie dividend and the divisor on the same line 
 with a vertical line between them and draw a 
 horizontal line beneath the divisor. 
 
 42 is not contained in 1 ten-thousand hence 
 there are no ten-thousands in the quotient ; 1 ten- 
 thousand and 2 thousands are 12 thousands ; 12 
 thousand does not contain 42, hence there are no 
 thousands in tiie quotient ; 12 thousands and 9 
 
 hnndreds are 129 hundreds. 41 is contained 3 hundred times in 129 3 
 hundred times 42 are 126 hundreds, which subtracted from 129 leave 
 3 hundreds which with 4 tens are 34 tens. 42 is not contained in 34 
 tens, a cipher is written in the quotient. 34 tens with 5 units are 345 
 units 42 is contained 8 units times in 345. 8 units times 42 are 336 
 which subtracted from 345 leave a remainder of 9 units. 
 The quotient then is 308 with a remainder of 9. 
 
 50. Note I.— It ia not necessary to write the number 12G 
 the subtraction may be made mentally after the figure of the 
 divisor IS multiplied by the quotient : - . . 
 Thus 3 times 2.... 6 from 9 leave 3 • 
 
 3 times 4. . .. 12 from 12 leave 
 Remainder 3 hundreds, add 4 tens .... 34. Proceed as above. 
 
 51. Rule.—/. Write the dividend and the divisor on the 
 same line, separating them bi:] a vertical line and drawing a 
 horizontal line under the divisor. . , 
 
 //. Find hoxo many times the number expressed by thd first 
 'guns of the dividend contmns the highest units of the 
 tlivtsor; place this figure in the quotient. 
 
 Ill Multiply the divisor by this figure, and subtract the 
 •oductfrom the partial dividend. To the remainder anr^x 
 nefollowtug figure of the dividend. 
 
i/ 
 
 . i 
 
 % i 
 
 ! 
 
 11 
 
 I 
 
 11" 
 
 40 
 
 DIVISION. 
 
 Example. 
 
 6|00 ) 97180 
 16—180 B. 
 
 IV. Proceed as be/ore till all the terms of the dividend 
 have been used. 
 
 V. If any partial dividend will not comain the divisor 
 plate a cipher in the quotient and annex the following figure 
 of the dividend and proceed as above. 
 
 52. Note. — I. When the divisor has but one figure. The 
 quotient is written under the dividend without writing down 
 the remainder as shown in Case I. 
 
 II. When there are ciphers to the right 
 of the divisor, they are cut off from the di- 
 visor and as many figures from the right of 
 the dividend. Then divide the remaining 
 figures as usual ; prefix the remainder to 
 the figures «ut off. 
 
 III. To divide by 10, 100, 1000 it suffices to cut off one, 
 
 two, three figures to the right of the dividend. 
 
 63. Proof. — Multiply the quotient by the divisor and add 
 the remainder, if any, to the product; if the work is correct the 
 result will equal the dividend. 
 
 54. Proof of multiplication.— Divide the product by 
 the multiplier ; the c^uotient will equal the multiplicand if the 
 work is correct. There should be no remainder. 
 
 Examples for Fraotioe. 
 Divide 
 
 87S. 
 870. 
 877. 
 878. 
 879. 
 880. 
 881. 
 882. 
 883. 
 834. 
 885. 
 886. 
 887. 
 
 889. 
 
 468-r-2 
 963-i-3 
 624-f-4 
 970-i-6 
 672-r-6 
 434H-7 
 ■ 672-H8 
 405-5-9 
 
 621-r-9 
 
 207-V-9 
 42047-.-5-2 
 407630^5 
 342009-f-9 
 492630-^6 
 644013-^3 
 
 890. 
 891. 
 892. 
 898. 
 894. 
 895. 
 S96. 
 897. 
 898. 
 899. 
 900. 
 901. 
 902. 
 903. 
 904. 
 
 333006-i-6 
 870120-5-9 
 540764-5-4 
 761002-5-7 
 432536-5-8 
 478353-5-3 
 981006H-6 
 453607-5-7 
 600702-5-8 
 604430-5-5 
 650016-5-8 
 450U09-5-9 
 674108^4 
 894609^-7 
 874224-5-4 
 
 905. 
 
 906' 
 
 907. 
 
 908. 
 
 909. 
 
 910. 
 
 911. 
 
 912. 
 
 91 J. 
 
 914. 
 
 915. 
 
 916. 
 
 917. 
 
 918. 
 
 919. 
 
 920. 
 
 921. 
 
 922. 
 
 923. 
 
 924. 
 
 92.'i. 
 
 926. 
 
 927. 
 
 928. 
 
 929. 
 
 930. 
 
 931. 
 
 932. 
 
 933. 
 
 934. 
 
 935. 
 
 936. 
 
 937. 
 
 938. 
 
 939. 
 
 940. 
 
 941. 
 
 942. 
 
 943. 
 
 944. 
 
 945. 
 
 946. 
 
 947. 
 
 948. 
 
 949. 
 
 960.* 
 
 951. 
 
 952. 
 
 963. 
 
 954. 
 
 955. 
 
DIVISION. 
 
 of the dividend 
 
 cain the divisor 
 following figure 
 
 lue figure. The 
 It writing down 
 
 EXAMPLK. 
 
 i|00 ) 97180 
 16—180 R. 
 
 ces to out off one, 
 lend. 
 
 divisor and add 
 )rk is correct the 
 
 the product by 
 ultiplicand if the 
 ler. 
 
 833006-H6 
 870120-5-9 
 640764-^4 
 761002-i-7 
 432536-f-8 
 478353-5-3 
 981006-^6 
 453607^7 
 600702-^3 
 604430-r-5 
 650016-(-8 
 460U09h-V> 
 674108-4-4 
 894509H-7 
 874224-!-4> 
 
 905. 
 
 906' 
 
 907. 
 
 908. 
 
 909. 
 
 910. 
 
 911, 
 
 912. 
 
 91 J. 
 
 911. 
 
 915. 
 
 916. 
 
 917. 
 
 918. 
 
 919. 
 
 920. 
 
 921. 
 
 922. 
 
 923. 
 
 924. 
 
 92.'5. 
 
 926. 
 
 927. 
 
 928. 
 
 929. 
 
 930. 
 
 931. 
 
 932. 
 
 933. 
 
 934. 
 
 935. 
 
 936. 
 
 937. 
 
 938. 
 
 939. 
 
 940. 
 
 941. 
 
 942. 
 
 943. 
 
 944. 
 
 945. 
 
 946. 
 
 947. 
 
 948. 
 
 949. 
 
 950.* 
 
 951. 
 
 952. 
 
 963. 
 
 954. 
 
 965. 
 
 41 
 
 4596ri5^:- 9 
 354-f-ll 
 407--12 
 984-f-14 
 649--2() 
 895 ^--J.J 
 780^25 
 354--2fi 
 197 -T 28 
 425 -:-33 
 407-34 
 654 f ;i5 
 954 - ;J9 
 201 ^43 
 426^46 
 999^46 
 864 --50 
 9G4 V 63 
 975-r-54 
 5^3288-f-12 
 90,-)765-r-17 
 405680-t-20 
 652.';47-=-23 
 743240 ■?- 25 
 793751-5-26 
 704900-5-29 
 805909-5-33 
 847216-5-36 
 487804-5-38 
 497999-5-40 
 659415-5-43 
 710756^46 
 926404-5-49 
 845001-5-53 
 858415-5-67 
 867010-5-69 
 984824-5-Gl 
 694115-5-64 
 699999-5-66 
 840026-5-68 
 600010-5-72 
 430074-5-76 
 605407-f-78 
 604905-5-81 
 806404-5-85 
 676477-H86 
 934376^89 
 297049-5-91 
 977046-5-93 
 674246 -=-96 
 306423-5-99 
 
 9.')6. 
 9.^7. 
 953. 
 959. 
 !<(J0. 
 961. 
 902. 
 9«3. 
 9'i4. 
 9fi5. 
 960. 
 967. 
 968. 
 969. 
 970. 
 971. 
 972. 
 973. 
 974. 
 975. 
 970. 
 977. 
 978. 
 979. 
 980. 
 981. 
 982. 
 983. 
 984. 
 985. 
 986. 
 987. 
 988. 
 989. 
 990. 
 991. 
 992. 
 993. 
 994. 
 995. 
 996. 
 997. 
 998. 
 999. 
 1000. 
 1001. 
 1002. 
 1003. 
 1004. 
 1005. 
 1006. 
 
 800715-i- 36 
 640072-5- 69 
 695425-5- 97 
 78!)(»16h- 84 
 42b'432-5- 67 
 6941 20-T- 68 
 94327 4 -r- 62 
 796425-5- 75 
 843255-5- 87 
 169400 5- 78 
 345895 ^ 85 
 474050-T- 470 
 654207-^ 147 
 674604-^ 341 
 805940-5- 276 
 606825-5- 376 
 646079H- 346 
 654054-H 897 
 907850-i- 307 
 612904-f- 761 
 576452-i- 384 
 764805-T- 359 
 975450-+- 970 
 389807-*- 778 
 676402-*- 876 
 672070-H 462 
 908406-*- 607 
 454026-f- 247 
 430020-*- 7£9 
 874984-*- 789 
 678761-*- 290 
 904868-*- 207 
 767766-*- 461 
 896876-*- 675 
 845790-*- 475 
 664327-*- 147 
 842364-*- 915 
 846618-*- 964 
 846618-*- 854 
 809456-i- 942 
 654827-*- 835 
 676464-*- 807 
 466872-*- 867 
 660017-5- 466 
 976460-5- 749 
 845872-5- 948 
 470878-5- 548 
 765484-»- 654 
 452878-*- 874 
 829742-»- 764 
 840742-5- 842 
 
42 
 
 DIVISION. 
 
 t li 
 
 'M 
 
 ll' I 
 
 1007. 
 1008. 
 1009. 
 1010. 
 1011. 
 1012. 
 1013. 
 1014. 
 .1015. 
 1016. 
 1017. 
 1018. 
 1019. 
 1020. 
 1021. 
 1022. 
 1023. 
 1024. 
 1025. 
 1026. 
 1027. 
 1028. 
 1029. 
 
 ao3o, 
 
 1031. 
 1032. 
 3033. 
 1034. 
 1035. 
 1Q36. 
 1037. 
 
 ao3P.. 
 
 1039. 
 
 1040. 
 
 1041. 
 
 1042.- 
 
 1043. 
 
 1044. 
 
 1045^ 
 
 1046; 
 
 1047. 
 1048. 
 1049. 
 1060. 
 1061. 
 106?. 
 1053. 
 1054. 
 1055. 
 1066. 
 1057. 
 
 459066+ 
 739874+ 
 605427+ 
 605207-; 
 437878 + 
 859049 + 
 754754301+ 
 178935421+ 
 351978432+ 
 794325069+ 
 459457853+ 
 373765007+ 
 394756809+ 
 947450207+ 
 517486809+ 
 929452907+ 
 465027897+ 
 167047096+ 
 757807953+ 
 847695876+ 
 954761827+ 
 807436587+ 
 604876554+ 
 874256084+ 
 749657822+ 
 397458701+ 
 907009471+ 
 642324529+ 
 453873201+ 
 940079009+, 
 675423804+. 
 fl432l7876+ 
 987745878+ 
 876495688+ 
 347006921+ 
 740080008+ 
 942367460+ 
 547084372+ 
 827453671+ 
 467009840+ 
 254866763+ 
 176870009+ 
 784256862+ 
 67007 "407+ 
 496807904+ 
 696807904+ 
 • 104856009+ 
 647607007+ 
 664600070+ 
 794827954+ 
 607824087+ 
 
 774 
 819 
 742 
 78!) 
 871' 
 847 
 247 
 247 
 668 
 895 
 704 
 405 
 749 
 345 
 621 
 347 
 634 
 296 
 196 
 341 
 684 
 659 
 896 
 647 
 346 
 499 
 742 
 674 
 642 
 ,679 
 .779 
 476 
 740 
 677 
 846 
 540 
 875 
 976 
 197 
 742 
 475 
 497 
 746 
 857 
 357 
 678 
 595 
 457 
 .598 
 547 
 .679 
 
 10.^8. 
 1059. 
 1060. 
 
 lo^a. 
 
 1002. 
 
 1063. 
 
 1064. 
 
 1065. 
 
 1066. 
 
 1067. 
 
 1068. 
 
 1069. 
 
 1070. 
 
 1071. 
 
 1072. 
 
 107S. 
 
 1074. 
 
 1075. 
 
 1076. 
 
 1077. 
 
 1078. 
 
 10". 9. 
 
 1080. 
 
 1081. 
 
 1082. 
 
 1083. 
 
 1084. 
 
 1085. 
 
 1086. 
 
 1087. 
 
 1088. 
 
 1089. 
 
 1090. 
 
 1091. 
 
 1092. 
 
 1093. 
 
 1094. 
 
 1095. 
 
 1096. 
 
 1097. 
 
 1098. 
 
 1089. 
 
 1100. 
 
 1101. 
 
 1102. 
 
 1103. 
 
 1104. 
 
 1105. 
 
 1106. 
 
 1107. 
 
 1108. 
 
 345676407+ 287 
 
 809596433+ 876 
 
 576827462+ 634 
 
 852025044+- 297 
 
 654307854+ 387 
 
 745653842+ 977 
 
 300457089+.897 
 
 534875706+ 676 
 
 679854374+ 447 
 
 546894325+ 470 
 
 746876381+ 279 
 
 674237452+8907 
 
 743215908+3427 
 
 678332572+4086 
 
 674834207+6954 
 
 543207509+4987 
 
 743207008+2076 
 
 642396987+6430 
 
 453837954+6534 
 
 898754321+9784 
 
 47'940815+4110 
 
 907008752+1941 
 
 547927952+8432 
 
 764106347+B043 
 
 684124206+5398 
 
 541307650+4766 
 
 673454807+7,964 
 
 470075334+8107 
 
 807077927+9067 
 
 456374204+6760 
 
 ■407854274+1749 
 
 742960864+0765 
 
 ,674075847+2471 
 
 746820049+1986 
 
 787455654+9876 
 
 537658470+7407 
 
 876432574+1784 
 
 345653027+'4864 
 
 476845904+1664 
 
 875454807+2769 
 
 307452806+8745 
 
 746854954+2975 
 
 453347907+2794 
 
 787654927+4789 
 
 874642874+1743 
 
 546874957+2987 
 
 174854957^4789 
 
 678907854+0875 
 
 847942671+7421 
 
 742626834+1466 j 
 
 874089458+2989 1 
 
 1100. 
 1110. 
 
 nil. 
 
 1112. 
 1113. 
 1114. 
 ]!15. 
 IIIU. 
 1117. 
 
 ni8. 
 
 1119. 
 
 1120. 
 
 1121. 
 
 1122. 
 
 1123. 
 
 1124. 
 
 1125. 
 
 1126. 
 
 1127, 
 
 1128. 
 
 1129. 
 
 1130. 
 
 1131. 
 
346676407-f- 287 
 
 809596433H- 876 
 
 676827462-!- 634 
 
 862025044-+- 297 
 
 654307854-r- 387 
 
 745653842-f- 977 
 
 300457089-f-.897 
 
 634875706->- 676 
 
 679854374-^- 447 
 
 546894325-f- 470 
 
 746876381-!- 279 
 
 674237452--8907 
 
 743215908 -;-3427 
 
 578332572-r-4086 
 
 674834207-r-6964 
 
 543207509-r-4987 
 
 743207008-7-2076 
 
 542396987-^6430 
 
 453837954-!-6534 
 
 898754321-4-9784 
 
 47' 940815-4-4110 
 
 907008752-4-1941 
 
 547927952-4-8432 
 
 764106347-4-B943 
 
 684124206-4-6398 
 
 541307650-4-4765 
 
 673464807-4-7,964 
 
 470075334-4.SI07 
 
 807077927-4-9067 
 
 466374204-4.6760 
 
 407864274^1749 
 
 742960854-4.0766 
 
 .674075847-S-2471 
 
 746820049-4*1985 
 
 787455654^-9876 
 
 537658470-4.7407 
 
 876432574-4-1784 
 
 345653027-4-.4854 
 
 476846904-4-1664 
 
 876454807-4.2769 
 
 307462805-H8745 
 
 746854954-4.2975 
 
 453347907-4-2794 
 
 787664927-4.4789 
 
 874642874-4-1743 
 
 546874957-4-2987 
 
 174854957^4789 
 
 678907854-4-8875 
 
 347942671^7421 
 
 742525834-*.1466 
 
 374089458^2989 
 
 DIVISION. 
 
 1109. 
 1110. 
 
 nil. 
 
 1112. 
 
 1113. 
 
 1114. 
 
 1115. 
 
 1116. 
 
 1117. 
 
 1118. 
 
 1119. 
 
 1120. 
 
 1121. 
 
 1122. 
 
 1123. 
 
 1124. 
 
 1125. 
 
 1126. 
 
 1127. 
 
 1128 
 
 1129. 
 
 1130. 
 
 1131. 
 
 004087605-=-2984 
 741233479-!-4876 
 476807462-4-1627 
 600109729^6079 
 370230510-4-2798 
 874337452-4-2663 
 761045817-4-2352 
 216116076-!-8234 
 742676207-;-2694 
 904007369-4-2747 
 709478927^9079 
 294076927-4-7609 
 660076927-4-2476 
 346074837-4-1074 
 745674854.4-8790 
 174800976-5-1009 
 6524 75856-!- 78 46 
 895405974-4-8495 
 . 170079450-4-4560 
 900076466-!-3217 
 650074605-4-6541 
 654800077-4-7045 
 964757754-4-8794 
 
 43 
 
 1132. 
 
 1133. 
 
 1134. 
 
 1136. 
 
 1136. 
 
 1137. 
 
 1138. 
 
 1139. 
 
 1140. 
 
 1141. 
 
 1142. 
 
 1143. 
 1144. 
 1145. 
 1146. 
 1147. 
 1148. 
 1149. 
 11. 10. 
 1151. 
 11.52. 
 1153. 
 1154. 
 
 790078456 
 
 653070089 
 
 487094070 
 
 701874417 
 
 794854376- 
 
 230456876- 
 
 347606854 
 
 806423135- 
 
 636426976- 
 
 560079452- 
 
 766876342- 
 
 907880077-f 
 
 560079076-f 
 
 340058952-4- 
 
 646068095-4 
 
 647610023-4 
 
 647607432-i- 
 
 604653752^ 
 
 243072654-4- 
 
 604224012-H 
 
 894007965-4- 
 
 654006795-^ 
 
 670074027-!-, 
 
 4-2347 
 -4-6097 
 -4-6076 
 
 -4-1011 
 
 -4-4561 
 
 4-8741 
 
 -4-8479 
 
 4-4689 
 
 4-8941 
 
 4-8974 
 
 ^9784 
 
 f-2769 
 
 -4985 
 
 -4794 
 
 9765 
 
 4706 
 
 8423 
 
 8423 
 
 7981 
 
 7654 
 
 1765 
 
 9871 
 
 3799 
 
 E«l»r*« the rollowlnir nnmber. in llsares and «,ive Ihe 
 
 Problems. 
 
 1- 56. What 18 the quotient of one hundred and twenty-one thousand 
 |uo Jiuudrcd and forty-seven by seven ? mousana 
 
 I 1156. The product of a multiplication is two hundred and thirty-eight • 
 nd the .^.Itiplier is twelve. What is the multiplicand ? ' ^ ' 
 
 ],,"/■ ^''' """^ ''°''' '" *'""y =<'«t'^i'»ed iu twenty thousand and 
 
 1158 How many times is three hundred and twelve contained in 
 
 ven tlionsand four hundred and eighty-eight T 
 1 1169. If four thousand one hundred and sizty-six be multiplied by an 
 
 .known number, and if the product be fifty thousand and forty what 
 I the unknown number ? «»"'iy, wnat 
 
 t!'Jl!^ *'""'"''' """ ''*'°""*' ^'' hundred and forty, tea 
 
 11161. What will be the resujt of twenty-five thousand made one 
 lousand times smaller J maae one 
 
 Tfit^rtT^' f""'" '*" '^' °"'^^^' ""« thousand eight hundred 
 
r^ 
 
 44 
 
 DIVISIOK. 
 
 1165 hZ ^ ''""'••••^'•« are there in 8602 units ? 
 
 1170. When is the nuotipnf • i 
 greater than the divided 3 •r/'"f'^^ ^^"^ *•»•" dividend ; 2.- 
 
 , nn. Having divide^Vn^-ierb; r^: "^ = ^--^^^^ 
 dcnd contain the quotient ? ^ ' """"^ "'"'"' d«°» the divi- 
 
 1172. In dividing a number hv o u 
 
 contain the dividend ? ^ ' ^""^ '"'"^ ""^«« does the quotient 
 
 1173. How many times are • l k i o 
 
 «+4. in 60. in 70 ; 3.- 94-2 in flT- t; '°"*"'»^'i i" 21, i„ 35 ; 2.- 
 
 1174. Howman;arc: .- " 1^1 ' ^T/' "'^^ ^^' - ^ 
 
 .-3^!?rT'^:r^3^iv^;rrf"-^^ 
 
 30; 6.--29-4inl3r-12- 6-26 « f.r'' *- 18-12 in 9oJ 
 119A w ' — ■'o— 8 lu 140— 32? 
 
 J 176. How many times aw 1 le "* > 
 
 J5X7; 3.- 21. in 12X7 ; r.'lr'''"^^ '" 'X^' 2.- 5. in 
 (10-6)1 '^'' ^-».'"3X(21+9); 6.- 5. i„ 7^1' ^^ 
 
 1177. What is the .luotieut • 1 „«• r , « 
 
 .178. H.„ „„„, „ T,._ ^8 ,;*.„, +8-3X5^10 , 
 
 -3X^-^6; 4.— 
 
 1 
 I 
 
 ol t)-|-i5-jlxi2-M0 ?■ 
 
 1190. H 
 
 1191. W 
 • nst 1138 ? 
 
 1192. B} 
 
 1193. A 
 many montl 
 
 1194. W] 
 348X60 T 
 
 1195. A c 
 lt)« the value 
 
 1196. A SI 
 was the valu 
 
 1197. In ! 
 wnounted to 
 
DIVISIOK. 
 
 10" six hundred and 
 iiltiplioand u twen- 
 ier ? 
 ? 
 
 !•; 2.— of the 6th 
 
 the same number, 
 
 ^t, what change is 
 
 iplicand ; 2.— the 
 
 ■ 1. —having the 
 2 — having the 
 
 dividend ; 2 
 
 less than one T 
 '8 does the divj. 
 
 B8 the quotient 
 
 21, in 35 ; 2 
 
 >+9, in 63-f9f 
 
 15X12-1 (20X 
 
 -S, iu 107—7; 
 18-12 in 80- 
 
 15 
 
 2; 2 — 5, in 
 5. in 7X154- 
 
 ; 2.^ of4-f. 
 :5-h10 ? 
 
 l«X9-(13X 
 
 - of 9-f-7_ 
 -7 ? 
 
 2.-of9-f 
 <12--10?" 
 
 I 
 I 
 
 result ? ^ ' ^^ ^" ^'^ **»« remainder ; what is the 
 
 «l..t i. the ,L' " ' """'""' "' «• «"' 20 .0 .he product , 
 product ! ' ■ ^ ''' ""' ""'"P'S »y 11 i what „ th, 
 
 Vraolcal Problcma in MKIUw 
 
 •..t 11881 "^ ^"''' " °'"'« »''. <"""■ 3(5 bottiM 
 
 z. i'z'rz:'zit z::^ '»»''-»3.„,u,t.„., 
 
 ■nauy nouth. „«, he paid ! ' '"' '"' "«""' '''C f" how 
 
 1194. What number multinlv hw 0-7 • 
 348X60 ? P^ ^y "' S'^«' the same product a, 
 
 1196. A city of 43872 inhabitants uaid SR-^rma ,•„ * . 
 
 be the value paid by each, if in equal'plmf ""'' ' "'''* "^^^*» 
 
 11 W. A sum of $7300 is made nn nf q«k • . 
 
 was the value of a piece f ^ ^''°''' °^ ^'^'''^ ^*I«« J what 
 
 J 197. In a nrnvinna *!,» - - .""■' 
 
 -»«.ed .0 f ua.;;ioT ;sr,r;,s;;:* :;t' '"''°* " '•"- 
 
T'f"'*i-fiiifcVi" '■'-^■^•■^^ >'^^'H 
 
 h 
 III 
 
 46 
 
 DIVISION. 
 
 1198. How many 5 cent-pieces must I give in exchange for 45790 
 fifty cent-pieces ? 
 
 1199. How many days would be required for a writer to copy a book 
 of 720 pages if he copies 3 pages an hour and works 12 hours a day ? 
 
 1200. A horse-dealer bought horses for ?7990 and iu selling them for 
 $8466 he gains $28.00 on each horse. How many horses did he buy t 
 
 REVIEW PROBLEMS. 
 
 he pays $380.00, how much does he 
 
 1201. A debtor owes $4,050 
 still owe ? 
 
 . 1202. A person has in his safe $9260.00, if he deposits $750.00 more 
 at one time and then $250.00 ; what sum has he in his safe ? 
 
 1203. In an arsenal there are 92 piles of shot, each pile contains 
 3400 bullets ; what is the number of bullets ? 
 
 1204. The Carlovingian dynasty commenced in 752 and occupied the 
 throne 235 years. In what year did it end ? 
 
 1205. A decorator received $25.20 for his salary of six days' work of 12 
 hours each ; What did he gain each hour ? 
 
 1206. A printer bought paper at $2.50, $2.75 and $3.00 a ream ; he 
 had the same number of reams of each quality and he spent $330.00. 
 How many reams of each sort has he ? 
 
 • 1207. On the eve of a battle an army consisted of 80,000 men, on the 
 next day it had but 60785 ; how many men did the army lose ? 
 
 1208. I bought 75 yards of velvet at $9.20 a yard. In payment I gave an 
 equal number of pieces of $5, of 50 cents and 25 cents. How many did I 
 give of each 1 
 
 , 1209. I bought 96 reams of paper for the sum of $124.80. What is 
 the cost of each sheet knowing that a ream contains 20 quires and each 
 quire 25 sheets ? 
 
 1210. How many vessels will be required to carry 6840 men, if one 
 vessel carries 1368 men ? 
 
 , 1211. If 6 horses cost $1500, what will 16 cost ? 
 
 1212. I pay 75 cents for 25 steel pens, how many can I buy for $30 ? 
 
 , 1213. Patrick was 7 years old when he went to school, if he remains 2 
 
 years in the 3rd class, one year in the 2nd class, and 4 years in the 1st ; 
 
 at what age will he leave school ? * 
 
 1214. A man earns $25.20 in 9 days. What will he earn in 40 days ? 
 
 ,1215. From a certain sum 172 persons received $18 each and there are 
 
 $16 remaining ; what was the sum ? ^ 
 
 1216. If 90 dozen of eggs cost $4.50 j feow many eggs can be bad 
 for $12.50? ^ 99 . ^ 
 
DIVISION. 
 
 47 
 
 change for 45790 
 
 V much does he 
 
 40 men, if one 
 
 1217. A father was 35 years old at the birth of his son ; how old will 
 the son be when the father is 77 ? 
 
 1218. Nicholas was 23 years old in 1860 ; how old was he in 1851 f * 
 
 1219. A man spent 8260 in 6 months ; at that rate what would he 
 spend in 3 years ? 
 
 1220. A person has an annual revenue of $2021, how much can he 
 spend a day after placing $743.60 in bank ? 
 
 1221. Owen Kearney was born in 1870, how many years after 1892 
 will he be 47 years old ? 
 
 1222. A grocer received 308 pounds of sugar for $21 ,56 ; he wishes to 
 gam $6.16, What price will he ask for a pound ? 
 
 1223. The deluge took place 3308 years before Christ ; how many years 
 elap.sed from that event to the death of Champlain 1635 after Christ ? 
 
 1224. The siege of a city lasted 45 days, and the besiegers fired 13365 
 bombs into the city, how many bombs did they fire on an average per day t 
 
 1225. What number multiplied by 341 gives 443641 for product ? 
 
 1226. How many years in 10512000 minutes ? (365 days to the year) 
 
 1227. A bookbinder had 640 volumes to bind at the rate of 16 cents 
 per book ; if he completes the work in 41 days, what will he earn a day ? 
 
 1228. A general distributes 116000 cartridges among 5 batallions each 
 comprising 650 men ; how many cartridges will each soldier receive ? 
 
 1229. A vestibule is paved with marble tiles and is divided into 44 
 parts the whole number of squares is 148852, how many squares in 
 each part t 
 
 1230. Peter owes $168, he pays $62. then $63 ; how much remains due f 
 
 1231. A butcher buys 28 oxen for $1200 ; he sells them and gains $10 
 on each ox. What is his entire gain ? 
 
 1232. A grocer receives 6 cases containing 1500 pounds of cheese • 
 what did each case contain, and what will be the cost of a pound know' 
 ing that he 'aid $189 for the 6 cases ? 
 
 1233. Ernest received 40 cents to buy 6 pounds of bread at 4 cents a 
 pound and 2 candles at 3 cents apiece. How much money did he spend ? 
 
 1234. What is the weight of a case which contains 85 packages of 
 • aiidles each package containing 4 pounds, knowing that the case when 
 empty weighs 24 pounds f 
 
 1235. A hundred volumes cost $75.00, what will be the cost of one 
 volume, and for what will I have to sell them to gain $5.00 on all ? 
 
 1236. A contractor engaged 10 workmen at $1.20 ; 15, at $1 00 • 20 
 ai 80 ots., and 25 at 60 cts. What 8um ot money will he require each 
 week to pay th« workmen f 
 
48 
 
 sivieiov. 
 
 ;!l!. 
 
 li 
 
 1287. A father when dying left §3500 to each of his 4 sons and |6600 
 to each of his 2 daughters. What was his fortune ? 
 ' 1238. A hundred eggs cost f2.00, how many can you purchase for 
 $15.00? ; 
 
 1239. 135 pages of 15 lines each were written by 46 pupils ; how 
 many lines did each pupil write ? 
 
 1240. How many pages can be written by 55 pupils, if each pupil 
 writei 4 pages of 18 lines each I 
 
 1241. A remnant of cloth cost $126.00 and in selling it for $155.25 I 
 gain $2.25 a yard ; how many yards were contained in the remnant f 
 
 1242. A man said that in 16 years he would be 49 years old and his 
 son would be 23 ; what are the ages of father and sou I 
 
 1243. A rosary contains 70 grains ; how many grains will be wquired 
 for 3 docen of rosaries t 
 
 1244. A hone and harness cost $170.00, the horse without the harness 
 cost $76.00 ; how much does the price of the bMmess exceed that of the 
 horse t 
 
 1245 George's overcoat cost 3 times as much is Andrew's shoes which 
 cost $6.50 ; what is th« cost of the overcoat ? 
 
 1246. A work lasted 18 days; on what day was it begun if it was 
 finished on the 23rd of May and there were two Sundays in that time ! 
 
 1247. A person says that with $72.46 more he would double his 
 money and have $24.46 over ; how much has he ? 
 
 1248. A workman started his day at 4 o'clock A. M. and left work 10 
 hours after ; what o'clock was it ? " 
 
 1249. A servant receives $182.60 » year ; if he loses 78 days how 
 much less will h» receive I 
 
 1260. A man spends $1.35 a day ; how much does he save a day if he 
 gets a salary of $7.80 ? 
 
 1251. I am to receive $7424 in three payments: thvinrstwill be 
 $1 704, the second $4026 ; what will be the amount of the third T 
 
 1252. A miller wants $84 in order to pay for 125 barrels of flour at $4 
 a barrel. How much has he ! 
 
 1268. Along a road trees are planted every 12 yards ; how many trees 
 will there be in a distance of 3660 yards i 
 
 1264. A subscription was taken up in a church on different occasions : 
 the first collection realized $37.00, the second $9 mora than the fint, the 
 third $52.00, and the fourth as much as the 1st and the 2nd ; what was 
 the amount of the subscription ? 
 
 1265. I pay $4.60 a yard for a certain work ; how many yards should 
 a workman do to receive $90.00 ? 
 
DivisroN. 
 
 49 
 
 drew's shoes which 
 
 ; how many trees 
 
 How many days 
 
 
 nauy yards should 
 
 1256. A workman received 342.50 for 17 days work, 
 will he work for ?1487.50 ? 
 
 1257. A house has 28 windows each containing 12 panes ; how much 
 will the glazier be paid at 15 cents a pane ? 
 
 1258. Peter has ^570, Paul has $60.00 more than Peter, and John 
 has as much as the other two together less $45.00. How much have 
 Paul and John ? 
 
 1259. A tailor has a piece of cloth worth $189.00. he made 4 pairs of 
 pants at $3.50 and 8 coats at $35.00 ; how much did he receive for it? 
 
 1260. A man having $12300 gave $8900 to an hospital and divided 
 the remainder among his 5 sons, what did each receive ? 
 
 1261. 1 bought 12 books at 52 cents each and I received 13 books free • 
 how much did each book actuully cost me ? 
 
 1262. A scholar had to recite 250 lines ; but having recited only 125 
 hnes, he has to write 2 lines for every line not recited ; how many pages 
 has he to write, if each page c ^ ;os 25 lines ? 
 
 1263. A squadron is coir < ,( 6 corvettes and 2 frigates. The 
 vessels carry each 400 me. and the frigates 350 men ; what is the 
 number of mm in the squadron ? 
 
 1264. A man spends 65 cents on Monday, 90 cents on Tuesday, 65 
 cents on Wednesday, $1.04 on Thui-sday. 75 cents on Friday and $1.64 
 on Saturday ; how much has he left if he had $4.00 on Sunday ? 
 
 1265. Three gamblers made a common purse, John gained $76.00 but 
 1 eter and Charley lost each $27.00. What is their gain ? 
 
 1260. A gentleman having an annual revenue of $3560, pays $56 00 
 for tajces and other expenses ; what can he spend daily after paying 
 
 1267. The city of Constantinople was 2540 years in existence in 1882 • 
 what 18 the date of Its foundation, and how many years after the creation 
 was It built ? 
 
 1268. Four gambler., have a common purse ; the 1st loses $40.00 ; the 
 2nd, $7.00 .ess than the first : and the 3rd gains $15.00 and the 4th 
 «25.00 ; what is their net loss ? 
 
 1269. A boatman made 4 voyages a day, he carried 80 persons each 
 time at 30 cents each ; what does he gain eveiy day, his daily expenses 
 oouig $33.00 I 
 
 1270. A man having no children ; left half of his goods to his four 
 nephews and the other half to his six cousins ; how much does each 
 receive, the fortune beiug $20640 ! 
 
,v.i»'«»'W.<n<0'.j,H' 
 
 t''\ 
 
 A"' ,1 
 
 00 
 
 nivrsioN. 
 
 1271. I bought a certtin auiouut of goods for $620 ; if I had sold them 
 for $56 moip 1 would Imve gained half the cost price ; how much should 
 I hnve sold 'lem for ? 
 
 1272. Fred had $1500 before borrowing $850, if he pays a debt of $1860, 
 how much money has he left ? 
 
 1278. A workman gains $730 a year ; and spends $1.25 a day ; what 
 sum does he possess at the end of the year I 
 
 1274. A merchant has a revenue of $6935 ; what can he spend daily ; 
 
 1275. St Louis reigned from 1226 to 1270 and Louis XII from 1498 to 
 1615, how many years more did St Louis i-cign than Louis XII? 
 
 1276. A sailor buys silk for 30 cents, thread for 25 cents, needles for 
 8 cents and cotton for 6 cents, after paying these amounts he had 55tts. 
 remaining, 'iow much had he at fii-st ? 
 
 1277. Of three individuals ; the first receives twice as much as the 
 second plus $55, and the third as much as the other two minus $120 ; 
 how much has the third knowing that the first had 66 times $2.50 ? 
 
 1278. Thornl'ey went out with $1.30 ; how much money should he 
 bring back to his mother after paying . 40 cents for sugar, 26 cents 
 for coffee, 18 cents for butter and 8 cents for milk ? 
 
 1279. On an avenue there are 36 trees 15 yards from each other ; if 5 
 trees more were added ; what would be the distance between the fii-st and 
 the lost tr^ t 
 
 1280. Frank walks from the city to the village twice a day during I 
 three years, knowing that the village is 5800 yards from the city, how 
 many y^rds did jie cover ? 
 
 1281. How many seconds in 15 hours and 6 minutes ? 
 
 1282. With $540 more than I have, 1 could pay $1800 and have $28 j 
 remaining ; how much money have I ? 
 
 1283. Twenty-five men worked 60 days at $1.25 a day ; what surnj 
 will they receive ? 
 
 1284. A postman has 60 unpaid letters to distribute, among the 
 number thei-e are 23 at 3 cents and the remainder at 6 cents ; how mucli 
 will he collect in all ? 
 
 1285. A merchant has $12000 cash, he gains 3 times $580, and 5 times! 
 9805 ; how much money has he ? 
 
 1286. A man gains 1 cent on every pencil sold ; how many pencils did 
 he sell knowing that he received $13.80 for what cost him $11.04 ? 
 
 1.287. A dozen of omnges cost 60 cents ; what will 36 oranges cost f 
 
DIVI8I0X. 
 
 61 
 
 ys a debt of SI 860, 
 
 1.25a day ; whnt 
 
 $580, and 5 times I 
 
 llft;.lLlti\'' T' *''*" ^^'^ ^«*'*'^« third half of the first 4«^ 
 i9«i aV ^'"^ *^"" ^^"^ ^^'^ ' ^'•^^ ^"^ »1^« ««» divided f 
 1289^ A dozen of copies cost 42 cents ; how much would a person 
 
 ga.n who would sell 108 of these copies, at the ^te of 4 cents a coj" 
 
 .o.rgafnrorthrw:o;:r ''' ' '- --' -'^-^^^ ^ 
 ini'jL'td rZthsf *^ '' '' -'-' ^" "^""^^ '' ^^^* -'' ^« -- 
 
 1292. I have bought 48 dozen of pencils for the sum of $11.52. I wish 
 S Tr* "" '"'\ ^""' • '" ^^^* '^"^* ' ««" them a dozen 1 
 9 < Af TT "°^7' ^^ ^'''"'""' ''^ '^' '^^' °f 80 cents a day for 
 
 1294. Howmany hours in a journey which begins Monday at 7 o'clock 
 A. M. and finishes on Wednesday at 8 o'clock P. M.? 
 
 1295. A man having an income of $1328.25, has .saved $3225.00 in 15 
 years ; how much did he spend a day ? 
 
 1296 The quotient of a division is 102215. the divisor 342 and the 
 remainder is 341 ; what is the dividend ? • 
 
 tK.T^* "^IW^^T ^"^"'^ """'^'^ ^'"' ^« ^''y' "°«'^«<1 »« ; one of 
 amount did each receive ? 
 
 J^lL^'^f ^\ ^^l f ** ^**"' that a journey began knowing it took 
 86 hours and was finished on Saturday at 11 o'clock AMI 
 
 1299. A workman from whom $7.50 were retained, received $42 as his 
 I salary for 18 days' work ; how much did he gain a day ? 
 i ^r°" J° t ^r"^ **"' '"*^" eains $56 a month, the mother $2 70 a 
 yeaM * * "" **"-^' " ^'" ' ^°^ '""'^^ '^'•^ they all gain I 
 
 h ^^??-i/T"^*'*"''P''^2^^*^^»"<^^«««fhayfrom4acre8, which 
 I he sells $30 a hundred. How much did he get from each acre » 
 
 13U2 A child being sick the doctor came to see him 15 times. The first 
 
 tranh?H*\'"* *'•''; f ' *'^ ^'"^ ''''"''' °^*^« ''t^- visits knorg. 
 I that the doctor received $9.25 in all ? ""i"B 
 
 1303. If I had 25 $5-bills, 45 $2.bills and sixty 50.cent pieces, I could 
 pay my debts and have $7.60 remaining ; what do I owe ? 
 
1': 
 
 j'i'i 
 
 ill 
 
 ! i 
 
 r i 
 
 62 
 
 MENTibl. ABITHMETIO. 
 
 MENTAL ARITHMETIC. 
 
 55. Mental Arithmetic is the art of calculating with- 
 out writing the numbers. A pupil acquainted with writtenwork 
 only, will not readily detect an error by the absurdity of the 
 result obtained. He, who is in the habit of calculating men- 
 tally, will, on the contrary, immediately detect such errors, 
 and will seek to correct his work. 
 
 Rules for Addition. 
 
 56. To add a small number add the tern successively and 
 then the units. 
 
 Example.— To add 37 to 44, first add 3 tens to 44, thus : 54, 64, 
 
 74 ; tbeu add 7 units and the result gives : 74-j-7=81. 
 
 57. To add, a number^ it may be decomposed into parts and 
 then added successirelij. 
 
 Example.— To add 324 to 475 ; decompose it into parts as : 300-f 
 20+4, then 475+300=776 ; 776+20=795 ; 795+4=Au8. 799. 
 
 58. It is sometimes more advantageous to add a larger 
 number than that given, and then subtract the difference. 
 
 Example.— To add 92 to 446, first add 100 and then subtract 8, 
 since 92=100—8 ; thus 446+100=546 ; 546— 8=An8. 638. 
 
 59. When the numbers to be added end «» the same number 
 of ciphers, add the aignificant figures, and annex the number 
 of ciphers in either number. 
 
 Example.— To add 1200, 600 and 900, first add 12, 6 and 9 : 12+ 
 6=18+9=27 ; then annex two ciphers, 2700. 
 
 Problems in Addition. 
 
 1304. I bought $7 worth of bread, $4 of butter and $6 of wheat ; how 
 much did I spend t 
 
 1305. A piece of clcth cost J70, another $80 ; find the total cost ! 
 
 1306. A school consists of two classes : in the 1st there are 30 pupils, 
 in the 2nd 45 ; how many pupils in the school ? 
 
 1307. How many minutes in one hour and a hi\lf t 
 
 1308. Paul was born in 1874 ; in what year was he 11 years old ! 
 1809. What is the perimeter of a room 9 yards long and ? yards wide? 
 
 (There are 2 lengths and 2 breadths in the perimeter.) 
 
MENTAL ARITHMETIC. 
 
 «8 
 
 J of wheat ; how 
 
 To pay he offers 
 
 Biiles for Subtraction. 
 
 60. Two processes are us 1 to solve questions in subtmction : 
 Tim first process w to subtract successively the mils of the 
 
 smaller number from the iarger. 
 T1»U8 to snbtrnct 3 from 15, say : 15—1=14 • H-l=]3 • l3_i=3 
 
 12 Ans. Or, 15-1=14 ; 15-2=13 ; 15-3=12. 
 
 The second method is to add to the smaller number the units 
 required to equal the larger number. 
 
 Example.— To subtract 4 from 9. 
 
 4 ami 1 make 5 and 1 make 6 and 1 make 7 and 1 make 8 and 1 make 
 9. Tints 5 units are required to have 4 equal 9. The practice of addi- 
 tion enables the pupil to resume these operations in a si-jgle one. Thus 
 4 and 6 make 9. The answer is 5 units. 
 
 Problems In Subtraction. 
 
 1310. A person buys meat for |4, vegetable for |2. 
 I n $10 bill ; what change will he receive ? 
 
 1311. I sold goods for $75 and gained $12 ; how much did I 
 pay for it ? 
 
 1312. I'eter is 15 years old and Paul 29. How many years older is 
 Paul ? 
 
 1313. A man was 30 years at the birth of his son. How old is the 
 I son now the father being 77 ? 
 
 1314. One traveller walked 47 miles and a second 22 miles. How 
 I many miles did the first one walk more than the second * 
 
 Rules for Multiplication. 
 
 61. When the multiplier is n or U, the multljjUcation can 
 I he solved as by one number. 
 
 Example. — 97085 
 
 12 
 
 1165020 
 
 I Thus : 12 times 5«60, write and cany 6 ; 12 times 8=96 and 6 
 make 102, write 2 and carry 10 ; 12 times 0=0 and 10 make 10, write 
 and carry one ; 12 times 7 are 84 and 1 are 85, write 5 and cany 8 • 12 
 times 9 are 108 and 8 make 116. Write 116 ; the product U 1166020. 
 
64 
 
 MENTAL ARITHMETIC. 
 
 62. The product does not change if one factor is multiplied 
 and the other factor divided by the aame number. 
 
 Example.— Multiply 24 by 5. * 
 
 Multiply 5 by 2 to have the factor 10 and divide 24 by 2 this gives 12 
 which multiplied by 10 will give 120. 
 
 63. To multiidy a number by 20 it can be doubled and then 
 multiplied by 10. 
 
 Example.— Multiply 42X20 
 42X2=84 ; 84X10=840. 
 
 64. To multiply a number by 50 it can be multipliec^ by 100 
 and then half of the product talen. 
 
 Example.— Multiply 36x50 
 
 36X100=36 hundreds ; 36 hundreds -4- 2=1800. 
 
 65. To multiply a number by 25 we can multiply it by 
 100 and divide the product by 4. 
 
 Example.— Multiply 56X25 
 
 56X100=56 hi^dieds ; 56-r-4=14 hundreds =1400. 
 
 Problens In Bfnltlplicatlon. 
 
 1315. I bought 40 yards of cloth at $4 a yard. How much did I pay t 
 
 1316. What will be the cost of 100 yards of cloth at $5.50 a yard t 
 
 1317. What will 40 registers cost at 50 cents apiece t 
 
 1318. What is the price of 50 chairs at 60 cents each ! 
 
 ^ Rules for Division. 
 
 66. To divide a number by 10, by 100, etc., make the number 
 10 times, 100 times smaller by cutting off one, two or more 
 figures. 
 
 1st Example.— 275-5-100=2.75 or 2 with a remainder of 75. 
 2nd «« 12451-7-000=1.245 or 1 and a remainder of 245. 
 
 \ Problema in Division. 
 
 1319. Six persons share $54 ; what part does each receive f 
 
 1320. If you divide $130 among 5 persons what will be the share 
 of each ? 
 
 1321. I bought 5 dozen of eggs for 60 cents. What is the price of a 
 dozen ? 
 
 1322. Divide $5 among 20 children. What is each one's share T 
 
 1323. Twenty men earn $46. What is one man's wages t 
 
MENTAL AniTHMEriC. 
 
 65 
 
 the price of a 
 
 " Problems In Mental Arithmetle. 
 
 H«w"* ^"f ^u\^ """* °^ ^"''"^ *«» ^' ' »»• •>«» « ™"« to ftnUh. 
 How many has he done f 
 
 now f * '^°**"'' ^"^ ^* '°'"'^''' ' ?' ''°" ^ ™°"- "'*' °^^y »»«« he 
 
 1326. Owen hud 25 pens in a box ; he lost 7 of them. How many 
 had he remaining T ' 
 
 1327 James had 60 cents, his father gave him 40 cents and his aunt 
 60 cents. How much has he now ? 
 
 1328. Louis had |80 in bank, his uncle gave him $15. How much 
 has he not? ! •»•»«" 
 
 1329. Add 260 to 150. 
 
 1330. What is the sum of 360 and 140 ? 
 
 1331. My uuclo had 15 hens; he bought 2 others and gave me 4. 
 How many has he remaining ? o « ». 
 
 1332. Alfred had 15 cents ; he buys a pen for 1 cent and 2 copy-books 
 at 3 cents each. How much has he remaining 1 
 
 1833. How many hats must I sell at §3,00 ench to recoive «30 ? 
 
 1334. Walter received 18 pieces of candy ; he gives 3 to each of hi, 
 companions and keeps 8 for him.self. What was the number of his 
 companions ? 
 
 1835. Louis gains 60 cents a day ; how many days will it take him to 
 gam 90 I 
 
 1336. Philip has arranged his pens in several piles ; the Ist contains 
 25 the 2nd 35. the 3rd 40, and the 4th 70. How ma'ny pens h^t T 
 
 1337. John buys oil for 12 cents, ink for 15 cents and coffee for 6 
 cents. What sum did he spend ? 
 
 1338. A merchant sold 150 newspapers in the morning and 130 at 
 night. How many has he sold in his day ? 
 
 1339. What is the product of 4 by 7 ? 
 
 1340. Henry has 35 apples, his brother 25 and his sister 40. How 
 many have they together ? 
 
 1341. A man owes $15 to the grocer. $25 to the baker and $20 to the 
 butcher. How much does he owe them all ? 
 
 1342. Leo had 37 apples ; he gave 4 of them to each of his four 
 comiMuions. How many has he rtmaining ? 
 
 1343. A husband earns 80 cents a day, his wife 40 cents, his son 60 
 cents and his daughter 20 cents. How much do they save if thev 
 spend 11.40? ' 
 
M 
 
 MKNTAL AHITUME'l'lC. 
 
 184«. Joseph received 60 cents from his father, 40 cents from his 
 nude nnd $2 from his god-mother. How much did he receive in all t 
 
 1345. James bought a horse for 9450 and sold it for $200. How 
 much did he lose T 
 
 1346. If I hod $4 more I would hnve |29. What is my fortune T 
 
 1347. Charles bought a cupboard for |50 and sold it for |68. Hdt^ 
 much has he giiined ? 
 
 1348. If Peter had 7 cents less, he would have 27 cents. How much 
 has he ? 
 
 1349. A barrel contains 220 qunrts of wine ; 4 quarts are dn^wn every 
 day during 20 days. How many quarU reinniti in the barrel ? 
 
 1350. Paul obtained 7 goyl notes a day d^'riag 4 days. How many 
 has he now knowing that he had 14 olready ? 
 
 1861. How many pair of boots at $1.50 » pair can be bouglit for f 6 ? 
 
 1352. If a boy drawd 4 quarts of oil out of a barrel that contains 32 
 quarts, how many will be remaining at the end of 8 days f 
 
 1353. I had $75 t I have given |5 to the poor and placed $50 in 
 the Savings Bank. How much have I remaining 1 
 
 1354. Alphonsis had 45 marbles ; he lost 15 and gained 20 ; how 
 many has he now ? 
 
 1355. A flock is composed of 730 sheep ; 1 00 are sold every day during 
 7 days. How many sheep remain ? 
 
 1866. Felix's father spends 4 cents a day for tobacco. How much dees 
 he spend weekly T 
 ,J^1367. A family eats 8 pounds of brtad a day. How long will it take 
 to eat 72 pounds T 
 
 1858. Leo gained 8 good notes a day during 5 days ; how many has 
 he now knowing that he had 14 to start with t 
 
 1359. Thomas had 24 apples ; he ate 8 a day. How long did his 
 provisions last f 
 
 1860. A fruit-seller offers me 9 plums for a cent. I bought some and 
 ho gave me only 50 for 6 cents. How many are missing ? 
 * 1361. How many 10 cent-pieces will it take to pay $1.20 t 
 
 1362. A gardener plants 144 cabbages in a piece of land in which only 
 12 can be planted on the width. How many rows will he be obliged to 
 make t 
 
 1868. How many months in 15 years t 
 
 1364. Eugene is 12 years old, his younger sister is 7, his father 85 aad 
 his mother 29. What will be their agci in 12 years f 
 
MBMTAt ABITHMITIO. 
 
 W 
 
 1M5. A 1MB booght 100 egg, on the market. He broke 4 In couiln^ 
 home. How many dozen ha. he remaining to sell T ^ 
 
 6^1\ll "^fT"" P™'^""'" ^^^ "PP^""- The proprietor gives 8 
 dc^en away and keep, the «„t for himself. How ma'y do«n'did h! 
 
 ^«7.^At 18 cent, a dozen for eggs, how many eggs could I buy for 
 
 oe„\?!' t ^^ij""*"" "'^'^"' " ^"'°'»- 'J^i^J* »>« «e"B at « gain of 15 
 cents each. How much did he gain ? ^ 
 
 per' doL^fr" '''""^^* "^ '«»' *" "**"* •"'^ "''"- them for 20 cents 
 870 ir/ "'' '"'" f *'•'"*' ''«- ^'^"^ •"»«* he receive » 
 
 Jr AvVr//"*" "•"'"'^ • "'I"*" K*''^^" *ho«e side is 13 yards 
 long. What distance did he go ? uo ib lo yaras 
 
 o J"^'u'? * ^'''"*** containing 25 needles, 3 are broken, 5 are rustv 3 
 
 18^ Ho:l' m "^ ""'• ""^^' ™^»^ -^'- «- '-old?' 
 
 1372. How much do I owe for 8 umbrellas bought for »1.40 each f 
 
 1373. How many buttons are ther« in 15 dozen ? 
 
 money ha'e I J ' """ ' ""^^ '''' * ^''^^ ^"'^^ *2«- How much 
 
 Jef-H?kr.i'l8''f''f •"":;• "• ^^" " *" *-h ofh--- 
 com^de. , "^ " '" ''""^'- «°^ -»y •'•^ »>« «- to hi. 
 
 8o'c'ent« f"^ "^' """"^ **' "•"**" '* " «"**• * ^«^«-' ««H ^e had for 
 
 the ™t oT,^*.*2^;r1a^r ""^^^ "^ '^^"-^ *° ^^ ^« -^- «* 
 
 1379. Maurice was 16 years old when his sistor was born Wh.t „ni 
 
 1385. Andrew disuosed .Ifln fr«»men*s Af -^n« • -c - 
 
 -__ .V . * . : o'"eB,s 01 =ionc ui iS pues. How 
 
 father 86 and | '*""* *«" there in each pile ? 
 1^6. I bought 18 eggs at 
 
 many 
 
 themt 
 
 eggs at 18 cent, per do,en. What must I give for 
 
M 
 
 MBMTAL ARITHMETIC. 
 
 1887. Eugene will be 18 yean old in 11 yearn. How old is he now t 
 
 1388. John's father receive); $9 for 4 days work. What will he get for 
 20 xya work, t 
 
 1389. ^Vilfrid changed forty-five 5 cent-pieces for twenty -five cent- 
 pieces. How many did he receiv'< ? 
 
 1890. A ream of paper contains 20 quires and each quire 24 sheets. 
 How many sheets in a half quire T 
 
 1391. Charles gains $15 per month. What is his annual gain t 
 1892. Adolphus was born in 1864. How old was he in 1885 f 
 
 1393. In adding $3 to what I have ac^iallyt aud in doubling the sum 
 obtained, I find I have |14. What is my money ? 
 
 1394. Joseph's mother paid f21 for three pair of sheets. What ab the 
 price of one pairt 
 
 1895. Stanislas was 8 years old the first of March 1893 in what year 
 was he half this age T 
 
 1398. If the sum of money I have were tripled I would have |46, 
 what is this sum ? , 
 
 1397. I had 50 plums. I gave 32 to my brother ; iind after eating a 
 part I fined that I have 18 remaining. How many plums did I eat 1 
 
 1393. I met three poor persons and to the first I gave two cents. How 
 much did I give in all knowing that to the others I tripled the amount 
 given the first t 
 
 1899. Edgar bought 45 yards of cloth for $27. He sold 15 yards at 
 eost price. JIow many yards remain and what is he to receive for the 
 part sold f 
 
 1400. I give $14.60 to my baker and this sum is only half of what I 
 owe. What credit did he give me f 
 
 1401. If the sum I had were four times greater I would have |32. 
 What is the sum T 
 
 1402. Four brothers have each 25 marbles : The 3 older give what 
 they have to their youngest brother. How many marbles has the 
 youngest brother ? 
 
 1403. Ferdinand divides his pictures he has into 4 parts and gives 
 one of these parts to «ach of his companions. Counting those that 
 remain he has 35. How many had he at first t . 
 
 1404.^ If James's pictures were multiplied by five he j^;Quld rh^ve 7& ; 
 how many has he ! 
 
 1 405. Andrew's father received $35 for tan (^ays* work. How much 
 would he have received had he worked only 7 days ? 
 
 1406. Seven times my money would be sufficient to purchase 6 yard* 
 of silk at $7 a yard. How much have I ! 
 
MENTAL AniTHMETIC. 
 
 59 
 
 forT? '' ""**" °' "'''"" '""' ^'•''- ""^^' '"'"'^ y"'^^ ^"^ ^ «-i^« 
 
 1409 Louis gave one-half Lis money to th« poor and hi, father multi- 
 centi now , ' " '' *"•"• "•"•' ™"«'» '^^ ''« "^^ ^-t if he has 24 
 
 1410. Half a certain sum equals 24. What is four times this sum ? 
 
 1411 I received three tunes a certain amount wheu T H.„;rht 1 would 
 receive four times the amount. How much did I .c ei. t,^ Z J 
 a., .cpated. if the double of what 1 received equah. $n7 " ' 
 
 1412. Alfred's money was doubled three time . a., he nov has SI40 
 How much had he at first ? *^"* 
 
 1413. William arrived home on the 28 of Februarv .r »., oK 
 
 15 days. When did he leave home f " "'^^^'^^'^^ '"»» "I'^^nceof 
 
 1«4. My mother is 5 yeara younger than my father. What is th,. «„« 
 1«8 A grocer .old a tub of butter for «I0, and a box of chee» tor «li 
 
 ""bT;:;™'" '»'""■""»- «'«»»• »»«-; »«. h^ ^ri^S; 
 
 "19. If • iKwnd of coffee coets 31 cent.. How much will ■ 1 . 
 l«n«d. coat J s._ 7 pounds : 3.- 8 pound, I ' " ' 
 
 U20. How much will be paid for 6 pounds of boiler., i-i™. 
 l«.u»d, and 4 i»nnda of sugar at 8 cent, a jound ! ""'' * 
 
 u.uoMid ill*'," '° ""•* "* •= " "'•■^ '"^ -" '"- '» »»»• How 
 
 lioq A 1 , ^''^"" ' 2— 72 cents ; 3.-^ 90 cents ? 
 
 *m H Z T ^''"'^^ ^°'' *^« ''' «»« t™« ; '^ second time for 
 
 $130 Having sold them for «2. how much did he gain ? 
 
 1424. A man having been married 49 years dies at theaaeof 77 
 What age was he when he was married ? * "* 
 
 1425 At 18 cents a yaid what cost : 1.- 6 yards of calico • 2 7 
 yards ; 8.— 9 yards ? "'^ ' * — ^ 
 
 i 
 
 I 
 
 4 
 
 \ 
 
 \ 
 
60 
 
 MENTAL ABITHMKTIO. 
 
 1426. A farmer sells 14 sheep at $4 each and 10 lambs at |2 each. 
 How much did bo receive for all t \ 
 
 1427. What is the sum of: 1.-9+12+6—7 ; 2.-36410—12; 
 3.— 14+10+12—24 ? 
 
 1428. A mau walks 25 miles per day : how many miles will he walk : 
 1. — in 10 days ; 2. — in 12 days ; 3. — in 15 days ? 
 
 1 42d. John has 1 6 marbles, and Leo has 4 times as ma;iy as John. 
 How many have both together ? 
 
 1430. What is the result of the following combinations : 1. — 43+ 
 37—20 ; 2.— 9+12+15—26 ; 3.— 26+15+7—18 ; 4.— 27+23— 
 20—2 ; 5.— 33+28+9—30+15 ; 6.— 16+12+9+6—34+7 ; 7— 
 44—20+11-12 ; 8.— 16+26—30+15 ? 
 
 1431. By how many does the number 58 exceed 31+19 f 
 
 1432. What cost 12 pounds of butter : 1. — at 15 cents per pound ; 
 2.— at 18 cents ; 3.— at 20 cents ? 
 
 1433. I have ^Ol 1 buy a coat for $15 a veat for $5 and a bat for $4. 
 How mnch will I have remaining t 
 
 1434. Joseph bought 12 oranges for 3 cents each ; 8 melons for 4 cents 
 each aud five pen holders at 2 cents. How much did he spend t 
 
 1435. A child bought 16 apples from one stand, 18 from another ; he 
 at)! 6 and lost 5. How many has he remaining T 
 
 1436. At 66 cents a pound for tea what will be paid for: 1. — 9 pounds ; 
 2. — 7 pounds ; 3. — 10 pounds ; 4.-8 pounds ; 5. — 12 pounds ? 
 
 1437. Henry has 48 cents in 3 boxes : the first contains 16 cents, the 
 second 19 ; how many arc in the third ? 
 
 1438. A merchant employs a mau and his son, he pays the father $1.80 
 a day and the son 80 cents. How much will he owe them : 1. — in 7 days ; 
 2.— in 10 days ; 8 in 12 days ? 
 
 14R9. Jack had 12 marblc!*: one of his comrades gave 
 10 ; a third comrade gave him enough marbles to mi 
 did the third give him ? 
 
 1440. If a railroad train runs at !ie rate of 24 mi 
 will it run : 1.— in 7 hours ; 2.— in 9 hours ; 8.— i 
 hours ; 6.— in 16 hours ? 
 
 1441. Francis who is 17 years old is 8 yean older 
 12 yean younger ilxan Leander. What are the 
 Leander f 
 
 1442. At the ra* ■ of 30 eenta a hushil, what cost 
 potatoes ; 2.— 7 bushels ; 3.— 9 bushels ! 
 
 im 8, another 
 how many 
 
 hour, how far 
 lun ; 4.— in 12 
 
 Louis, who is 
 of Louis and 
 
 5 bushcla of 
 
 
)s at |2 each. 
 
 6 bnshcla of 
 
 MENTAL ARITHMETIC. *gi 
 
 Of IJll'lJt'^'T "'"" •ndahalfofegg,for20ce«t.; one bushel 
 
 the ::t o'AragLf '"" ^^' ^"^^ ^^"^^ ^^ *^- ^^ ^- ^^^^ i- 
 
 Klivef fot r"^ T ^"^' ' ^"* ^°' *^' '^ P"' of ^oot'* for $8, a pair of 
 gloves lor «2, and an umbrella for Si H« .mV *u i 
 
 ...;:^-.u'';4" niX'; '"^ °""°' "'" "'^ «"" '-'» * 
 
 Michael ? '"'''^ ^'^ •^«''«"^e tjained than 
 
 at $16 each, for 8 calves at $9 each ? ^ *^ 
 
 les^'foua'rr'H*''' ' 'T?/ '*'"^'-' ^"""^ ^''''^S times as many 
 lesa quarts. How many did Frank pick ? 
 
 ceT'.'^tZ'^'"T^r''^'"'^''''^ ' '^'^'»''^y»'' '^ have 82 ' 
 Lt^Jha. th^tlirb;? " '"*' "'^^" ^'^^^^^ ^- ^« --." How 
 
 the'^ki^irh-r^;^^^^^^^^^^ .t r • ""-"^" '^-^^ ^ ^^^' - 
 
 I ?if^]f ^"^ ^'^ " ^ '""'' * PO""*^ *»d pork 9 cents : what will 
 b. the difference in cost of 9 pounds of each ? " 
 
 J«6. What is the difference between 7 times 18. and 8 
 wii^bl?" ^ * *'"" ^ P'"""' •'^'^ H-'^'y 8 «»- 8. How many 
 
 1469. What wiU 6 lemons cost at 3 for 12 oents f 
 
 timfts Or, 
 
 'S 
 
62 
 
 MEKTAL ARITHMETIC. 
 
 m ! 
 
 1460. If 4 peaches are worth 8 cents, what will be the cdstof 8 
 jwachcs ; of 18 peaches ; of 27 ^waches ? 
 
 1461. If 7 pounds of meat cost 42 cents what will be the cost of 9 
 pounds ; of 13 pounds ; 17 pounds ? 
 
 1462. What will 11 barrels of flour cost at the rate of 5 ',rTrelsfor$30 ? 
 
 1463. A man walks a distance of 36 miles in 4 days. What distance 
 will lie wnliv in 12 ; in 15 days ; in 20 days ? 
 
 1464. What will be paid for 5 turkeys at the rate of 120 cents for 3 
 turkeys ! 
 
 1465. William gave 10 cents for apples at the rate of 3 apples for 9 
 cents ; how many did he get ? 
 
 1466. If 6 men can mow 12 acres of land in one day. How much will 
 15 men do ? 
 
 1467. Six cooks use a chest cf laa in 12 days ; what time will 4 chests 
 last T 
 
 1468. If 5 workmen can do a certain amount of work io 16 days. In 
 wliat time would 20 men do the same work '( 
 
 1469. How many men would be required to build a yacht in 6 days, if 
 3 men can build it in 12 days ! 
 
 1470. Maurice paid 8 cents for a ball. How many balls of the Lame 
 kind can he buy for 32 cents ; 56 cents ; 80 cents ; 96 cents ; 104 cents t 
 
 1471. If 4 pounds of butter cost 60 cents, what will 6 pounds cost f 
 
 1472. If 9 dozen of eggs cost 81 cents ; what will 1 dozen cost ? 
 
 1473. If 6 pen holdei-s cost 12 cents ; what will be the cost of 7 pen 
 holders ; 10 pen holders ? 
 
 1474. When beefsteak cost 10 cents a pound, how many pounds can 
 be had for 70 cents ; 90 cents ; |1.20 ; |3.00 ; $5.50 I 
 
 1475. If a child reads 7 pages per day, how many days will he require 
 to read 49 pages ; 77 pages ; 98 pages ? 
 
 1476. If a horse goes 42 miles in 7 hours ; what distance will he go 
 in 11 hours ? 
 
 1477. What will 9 pon Is of coffee cost if 3 pound*-«o8t 27 cents ? 
 1.478. If 6 barrels of flour cost $54 ; how much will 8 barrels cost ? 
 
 1479. If 15 yards of cloth cost $75. What will be the cost of 12 
 yards ; 16 yards ? 
 
 1480. When melons are sold at the rate of 3 for 60 cents, how many 
 can I buy : l.-for$1.20 ; 2. -for $1.60 ; 8.— for $2.40 f 
 
 1481. If 9 yards of muslin cost $1.08, what will be the cost : l.-of 
 5 yards ; 2. —8 yards ; 3,-10 yards ; 4. =18 y-wds ? 
 
 1482. A fruit-dealer gives 3 apples for 4 ceuts, how many will he give 
 for: 1.-24 cents ; 2. -40 cents : 3.-56 ceotr '. 
 
MENTAL ARITHMETIC. gg 
 
 .•.".■-63*;., V 45°'"?" f .' """^ '■°' "■"' -" ^<"' ""J' 
 oo cenis , 2.-45 cents ; 3. -$1.08 ? 
 
 »,«r! Jte ir ;i ;err "'°"'" '° "^ '- ' "»»«"■ «- 
 ..." r!; :''..iirrir.' i "r :• ^t "-^ °"*' -'^ ^"" 
 
 1491 I h.»ll " ' • 2— 3b chestnuts ; 3.- 48 chestnuts ? 
 
 Howich S'j: r '' ' '-' '' -' ^"^ ' -'' *^- ^* « ^o'«7. 
 
 .uuiris Iff 'J.*'''' 'l^'""^' °^ ^"S^^ ^'' ' P""""^'' of butter ; how 
 
 UOi w. ^? ^'''*^- ^''^^ 's the price of 1 yard of the cloth ? 
 1 494. When wheat is worth $1 for 5 bushels Hnw .«„ V , , 
 would be required to buv s .n J "r o ousnels. How many bushels 
 1 iQK IP ; 1 , , ^ °'^'^^ °*^ '''°°'* "t ^^ a cord ? 
 
 buheL/r^^'^^*^''' '*'•'' ^^^"'^l^ bushels of corn; how many 
 bushels of corn equal 10 bushels of wheat ? ^ 
 
 1497. A man bought 14 barrels of cider for $56 ; he dvel 5 barrel, 
 for a certain number of yards of clofh at ao . 7 « * "^®" 
 
 1498. Five men buy a mowing machine for 8120 Th.„ u a -. , ■ 
 
 ^^ ,. per „ee. .„d .,Ua. .u'r j:;v:?r2 
 
 Srf for 7« aato ! ' ■ ■" '"' *' 'PP'"' i 2nd for 60 .ppl„ j 
 
; *ll1: 
 
 64 
 
 COMMON VRACTIOKS. 
 
 1501. If one bushel of corn equals 2 bushels of oats, and one bushel 
 of wheat equals 2 of corn, how many bushels of wlieat will equal 20 
 bashels of oats ? 
 
 IBOi,. Jf it require 8 days for 10 men to build a wall. How many men 
 would it take to build it in 5 days ? 
 
 1503. Justin gave 7 aiyples for 21 chestnuts ; at this rate how many 
 chestnuts can he have for 8 apples ? 
 
 1504. 1 gave 8 yards of merino for 6 pints of syrup : what will a pint 
 of syrup cost, if 4 yards of merino cost 48 cents ? 
 
 1505. Felix bought 7 yards of cloth for $21, and he gave 4 yards of 
 this cloth in exchange for apples worth $2 a barrel. How many barrels 
 of apples did he receive ? 
 
 ^ COMMON FRACTIONS. 
 
 67. A fraotiidn is ono or more of the equal parts of a unit; 
 as, one-ha^ff tvco'thirds, 
 
 If we divide a unit into 5 equal parts, we can take one of these 
 parts and have one-fifth. If three parts were teken then the 
 part would be three-fifths ; one-fifth and three-fift} - are 
 fractions. 
 
 68. A fraction is represented by means of two nuvabers 
 placed one over the other and separated by a dash. For 
 example the fraction three-fifths is written |. 
 
 The number above the line is called numerator. It denote^ 
 the number of equal parts which is taken. 
 
 The number below the line is called denominator. It 
 denotes the number of parts into which the unit is divided. 
 
 69. To read a fraction the numerator is called first, then the 
 denominator. Example : f is read three-fourths. 
 
 The fractions J, §, |, |, |^, are read, one-half, two-thirds^ 
 three-fourths, four-fifths, five-sixths. 
 
 70. The numerator can be greater or less than the deno* . 
 nator, or it can be equal to it. 
 
 When the numerator is smaller than the denominacot a 
 have a proper fraction, that is to say, a value less than Sk 
 unit. Ex. : ^. 
 
 4 
 
 i 
 
i 
 
 COMMON FRACTIONS. ^ 
 
 When the numerator is greater than the denominator it is 
 unitT^Ex^T *°'^' *^'' '' *° '^y * ^^^"« S^«^t«^ t^a^i 
 
 When the numerator is equal to the denominator the fraction 
 equals unity. Ex : f , |, |g.. "<»cuon 
 
 bv'^?vfd1^°^®''® • v^'"''' '^'" ^'^^^ °^ ^^^<^t^"°«« to the pupils 
 
 board n/ T'."'^'' ''''^"^ *^"" ' ^^'^^^« ^^ ^he Mack- 
 Doard, an apple, etc. 
 
 EXBROISES. 
 1. Bead the rollowinjr fraction* 
 
 § 
 i 
 
 i 
 
 
 
 I* 
 
 fi 
 
 I? 
 It 
 
 II. Write in fflgnreB the f»lIowln9 fraction* 
 
 nZ^TJ" ^^T :?r'°"^''^"*^ Thirtee^-fourteenth, 
 oLe hif j!^«-t«°ths Th«e.fifteenth8 Seven-eighteenths 
 
 Jwj'Srds Sr T^ Four-sevenths Ninteen-Lntieths 
 iwo thirds Eight-nmths Four-twentiethi "-ven-twenty-filths 
 Seven.e.ghts Four-elevenths Six-ninteenths . - ..ty-seve'-Seths 
 III. What fraction is obtained by dlTldinff a unit 
 
 Ans..J 
 
 1.— Into 2 equal parts 
 4 
 8 
 12 
 16 
 20 
 24 
 2d 
 
 1.— Into 5 equal parts 
 7 
 
 AUS...J 
 
 11 
 15 
 19 
 23 
 27 
 81 
 
 II 
 II 
 II 
 II 
 II 
 II 
 
 IT. int. how many e,nal part, mnst a nnlt be divided to obtain : 
 
 I tia1«*An a 
 
 1 — halves 
 fourths 
 sixths 
 tenths 
 
 Ans. into 2 
 
 fifteenths 
 eighteenths 
 twentieths 
 twentjr.fiftbs 
 
 f • • • f . 
 
 . • * . f n 
 • f f ft 
 
 '• ; i i 
 
 [Hi 
 UK 
 
 'ili 
 
m 
 
 66 
 
 2.— thirds 
 fifths 
 sevenths 
 elevenths 
 
 COMMON iT.ACTIONS. 
 
 Ans. into 3 
 
 seventeenths 
 thirteenths 
 eighteenths 
 thirtieths 
 
 ^V. lExiirei** In the form of a fractlCMs 
 
 1 . Five numbers smaller than xtnity. 
 
 2. Five numbers greater than unity. 
 ?,. Five numbsvs pqwal to ur.ity. 
 
 VI. Willi* arc . 2se r«»f !'»wii!jg expressloiiia In relation to a maiiSt 
 
 9 
 
 I 
 i 
 
 I 
 i 
 tV 
 
 H 
 H 
 
 
 REDUCTION OP FRACTIONS. 
 
 71. Reduction of fractions is the several operations 
 to 'vhich the terms of a fraction may he suhmitted without 
 chan^in" or altering the value of the fraction. 
 
 There arc four principal reductions of fractions, 
 
 72. To reduce a whole or mixed number to an 
 improper fraction. 
 
 1 .— Let it be required to reduce 4 to fifths. 
 
 A unit equals 5 fifths = |, 4 units will equal 4 times f or ^«. 
 2.— Let it be required lo reduce 6 units § to an improper fraction. 
 
 A unit equals 3 thirds= |, 6 units will equal ^ : adding f we have 
 Y4-i=V- Therefore 6-|-i=or ^=^°-. 
 
 73. Rule.— To reduce a whole or mixed number . v.. 
 improper fraction, m.l Ay the given denomin.. i" the 
 whole number and add ;..; numerator of the /rac * > cny. 
 
 I. Red 
 
 130vS. 
 J509. 
 » h-jlO 
 1511. I 
 
 II. RC4 
 
 1518. 
 1519. 
 1520. 
 15'21. 
 1522. 
 1523. 
 
 74. Ti 
 ormiz< 
 
 1.— Le 
 
 expressio 
 
 One u 
 the fractio 
 therefore ^ 
 
 2.— Lei 
 ex] issioi 
 
 Oneun 
 the remaiud 
 
 75. Ru 
 
 improper i 
 the quotiei 
 
COMMON FIIAOIJONS. 
 
 67 
 
 I 
 
 u 
 
 il operations 
 tted without 
 
 ber to an 
 
 jer fraction, 
 iiug f we have 
 
 imber . ,-/ 
 ti.:;" ' the 
 '^iuya i^ any. 
 
 EXERCISES. 
 I. Redncetoan ImproiMr rracllon 
 
 1506. 
 
 1507. 
 
 130S. 
 
 1509. 
 
 1510 
 
 1511. 
 
 units to halves Ans, § 
 " thirds 
 " halves 
 " fourths 
 " thirds 
 " fourths 
 
 1512. 6 
 
 1513. 8 
 
 1514. 9 
 
 1515. 10 
 
 1516. 11 
 
 1517. 12 
 
 units to fifths 
 sixths 
 
 Ans. ^jO- 
 
 sevenths 
 eights 
 sixths 
 ninths 
 
 II. Beduoe .he following numbers to Improper fraction. 
 
 1518. 4^ 
 
 1519. 5^ 
 
 1520. 8 J 
 
 1521. 9^ 
 
 1522. 6^ 
 
 1523. 9g 
 
 s. 8 
 
 1524. 
 
 24 
 
 1525. 
 
 n 
 
 1526. 
 
 6| 
 
 1527. 
 
 n 
 
 1528. 
 
 H 
 
 1529. 
 
 8s 
 
 Ans. >^ 
 
 1530. 7f 
 
 1531. 4g 
 
 1532. lot 
 
 1533. 141 
 
 1534. 17i 
 
 1535. 21| 
 
 Ans. Jyi 
 
 74. Ta reduce an improper fraction to a whole 
 or mixed number. 
 
 l.-Let it be required to find the units contained in the 
 expression V. 
 
 th. ,°";.""'';f'l"''I^ ^ f°"rths or |. As often as 4 is contained in 12, 
 the fraction then contains one unit. The quotient of 12 by 4 is 3' 
 therefore ^=3 units. * "j' » is o , 
 
 2.-Let it be required to find the units contained in the 
 ex] ssion HK • 
 
 One units contains 8 eights = |. The quotient of 1 47 by 8 in 18 and 
 the remainder is 3, thefore A|i=18+| or ISf. ■ 
 
 75. Rule.— To find the number of units containfld m an 
 improper fraction divide the numerator by the denominator • 
 the quotient is ihe number of units. 
 
 \y-4 
 
C8 
 
 COMUON FRACTIONS. 
 
 EXERCISES. 
 Find the nnlta contained In the followlnfr nninbera 
 
 1636. 
 
 s 
 
 Ans. 3 
 
 1542. 
 
 ¥- 
 
 Ans. 3i 
 
 1548. 
 
 ¥ 
 
 1537. 
 
 ^4* 
 
 • • • • 
 
 1543. 
 
 •V"- 
 
 
 1549. 
 
 V 
 
 1538. 
 
 V- 
 
 • • > • 
 
 1544. 
 
 ■V- 
 
 
 1650. 
 
 -V 
 
 1639. 
 
 ¥ 
 
 
 1545. 
 
 V 
 
 
 1551. 
 
 
 1640. 
 
 ¥ 
 
 • • ■ * 
 
 1546. 
 
 ¥ 
 
 
 l.')52. 
 
 ¥ 
 
 1541. 
 
 V 
 
 . • . • 
 
 1547. 
 
 V 
 
 .... 
 
 15.'i3. 
 
 ¥ 
 
 Ans. 3^ 
 
 To reduce a fraction to its lowest terms. 
 
 76. To simplify a fraction is to represent it by its lowest 
 terms. The fraction || simpliiied could be written ^ or |. These 
 are obtained by dividing by 2 and then by 3. 
 
 To reduce a fniction to its lowest terms is to represent 
 it by the smallest numbers possible. 
 
 1. — Let it be required to reduce to its lowest terms the 
 fraction U. 
 
 Divide both terms by 2 and we have ^^ ; divide again both terms of 
 the new fraction by 2 and we have |, of which both terms may be 
 divided by 3 and the quotient=i. } is the lowest term of '^J. 
 
 2. — Let it be required to reduce to its lowest terms the 
 fraction IB. 
 
 Divide saccessively both terms by 10 and by 6 and we have § as the 
 lowest terms of ^f ^. 
 
 76. Rule. — To reduce a fraction to its lowest terms, divide 
 both terms of the fraction by the same number, and repeat 
 this operation with each new fraction until a fraction is 
 obtained whose terms will contain no common factor. 
 
 EXERCISES. 
 Bcdnce the foUowlns fmetlona to their lowest terms 
 
 1654. 
 
 t 
 
 Ans. § 
 
 1560. 
 
 if 
 
 Ans. 1 
 
 1566. 
 
 M 
 
 Ans. H 
 
 1566. 
 
 i 
 
 t • • • 
 
 1561. 
 
 H 
 
 
 1567. 
 
 fi 
 
 
 1556. 
 
 Xi. 
 
 
 1562. 
 
 ii 
 
 
 1568. 
 
 13 cj?r 
 
 
 1667. 
 
 H 
 
 • • • • 
 
 1563. 
 
 iS 
 
 
 1569. 
 
 m 
 
 
 1658. 
 1669. 
 
 A 
 « 
 
 • • • • 
 t • • • 
 
 1664. 
 1666. 
 
 
 
 1670. 
 1671. 
 
 1444 
 
 
 
COMMON FnACTIOVS. 
 
 99 
 
 To reduce fractions to a common denominator. 
 
 Fractions have a common denominator when both 
 have the same number for denominator. 
 
 1 — To reduce two fractions | and ^ to a common denomi- 
 nator. 
 
 
 Ol'KUATION. 
 
 
 3 
 
 3X8 
 
 24 
 
 — 
 
 
 :=! 
 
 5 
 
 5 X 8 
 
 40 
 
 7 
 
 7 X 5 
 
 35 
 
 8 
 
 8 X 5 
 
 40 
 
 Multiply both terms of the first 
 by 8, and both terms of the second 
 by 5, and we obtain J^, JJ. 
 
 
 77. Rule. — To reduce two fractions to a common denomi- 
 nator muUiply both terms of each by the denominator of the 
 other. 
 
 2.— To reduce more than two fractions to a common denom^ 
 nator. Ex.--J,|andf 
 
 Oi'EnATioy. 
 2_2 X 6X7 70 
 
 3 3X6X7~105 
 *_* X 8 X 7 84 
 
 6 6 X 3 X 7 ~ 105 
 « « X 8 X 5 90 
 
 7 7X8X6 105 
 
 Multiply both terms of the first 
 by 5 and 7, then both terms of the 
 second by 3 and 7, and both terns 
 of the tKird by 3 and 6. We 
 thu8obtain^j,^5^,^^V 
 
 78. Rule.— To reduce more t jrn two fractions to a common 
 denominator, multiply both i,,ma of each fraction by the 
 product of the denominators of the other fractions. 
 
70 
 
 ABDiTioa OF r V A . IONS. 
 
 BXBBOISES. 
 Bednce the followliiit rrnetioiM to n cnminon denominator 
 
 1672. 
 
 i i. 
 
 1673. 
 
 i. h 
 
 1674. 
 
 hh 
 
 1676. 
 
 ?. h 
 
 1676. 
 
 i h 
 
 1677. 
 
 ^ 3- 
 
 1678. 
 
 <i. i'. h 
 
 1679. 
 
 i. h a. 
 
 1680. 
 
 ^ h h 
 
 Ans. f, §. 
 
 1581. §, ^ i. Aad. tii:;,18S. ^. 
 
 1682. f, ^, f ; 
 
 1683. -8, S, 4 
 
 1584. S, i f 
 
 1585. f, i, f 
 
 1586. il, I, f 
 
 1587. i, t, A 
 
 1688. I, i, T?, 
 
 1689. i, fi, T>, 
 
 ADDITION OF FRACTIONS. 
 
 79. Addition of fractions is the process of finding the 
 sum of two 01* more fractious. 
 
 . Example. What is the sum of f and H 
 
 Solution. Reduce the fractions 
 to a common denominator. ^ = }J. 
 andi = ^;; 20 twenty-eight' .md 
 7 twenty-eights are 27 tweiiiy- 
 eights. 
 
 OPKBATION. 
 
 f < i = U 
 M + A =11 
 
 80. Rule. /. — Reduce tiiii fractions to a .ommon denomin- 
 ator, add the numeratora and place the sum over the common 
 denominator. 
 
 II' — If the numerator is greater an f'e denominator 
 divide to find the units and annex the Mi r as a fractio, 
 If thereare units add them and annex t. fraciton to the result. 
 
 Note. — Before reducing to a common denominator, reduce 
 each fraction to its lowest terms, and also the result after 
 addition. 
 
 
Inator 
 
 ading the 
 
 --n 
 
 denomin- 
 e common 
 
 \ominaior 
 I fractioi: 
 he result. 
 
 ir, reduce 
 lult after 
 
 SCBTRACilON OF FRACTIONS. 
 
 What ' i the Muin of the followlnv rrnctlona 
 
 71 
 
 1690. 
 1691. 
 1692. 
 1693. 
 1694. 
 1696. 
 1696. 
 1697. 
 1698. 
 
 i and f 
 
 « and i 
 
 i and f 
 
 f and jPy 
 
 » and ^ 
 
 2> and 3* 
 
 3.^ and 2^ 
 
 h i n»d § 
 
 h i and I 
 
 1699. 
 1600. 
 1601. 
 1602. 
 1603. 
 1604. 
 1 '^>06. 
 1606. 
 
 
 s 
 
 8 I. 
 18 §, 
 
 1607. 31^, 
 
 I 
 
 6i 
 
 lOj'^ 
 40 
 
 1 M 
 
 and 
 and 
 and 
 and 
 and 
 and 
 and 
 and 
 and 
 
 i 
 
 10 J 
 
 "A 
 
 1608. John ha.) § of a fam and bought i more ; how much has he now f 
 
 1609. Louw had „ of a ton of coal, he buys i more ; how much has he 
 at present? 
 
 1610. Martin had |2i, he receives |5.1, how much has he ? 
 
 nil' o'^J""" ^"^ lOi acres and buys llj acre8,how many acres has he ? 
 
 1612. Prude- I receives 16i bushels from one farmer. 10^ from another, 
 IH from anothe • bow much has he in all ? 
 
 1613. A merch. had 107§ yards of cloth and buys 146J yards, how 
 many yards has he » .r g j , «« 
 
 1614. RogatiansoV 4| yards of silk and has 49i yards remaining, 
 how many yords ha he ? * 
 
 1616. Bernard sold 671 pr N of honey to Jack Shallow, 351 to Dan 
 Dufly and has 17f remaining ; . av many pounds had he at first I 
 
 CUBTRACTIOX. 
 
 ■ 81. Subtraction effractions is the process of finding 
 the diflference b itween two fractions. 
 
 Example.— Subtract f from f 
 
 S>lution.— Reduce the fractious to a common 
 denominator f = f J and ^ = |f ; then 27 thi. ty. 
 sixths from 28 thirty-sixths leove ^. This gives 
 the following 
 
 OrKRATION. 
 
 I - i = 
 
 *J - H = ^f 
 
 82. Rme— Reduce the fractions to a com?non denominator 
 and subtract the numerators, and jplac. th^ result over the 
 common denominator. 
 
72 
 
 SUHTIIACTION OF ri!A< TIONM. 
 
 // there are units avUra t the fractioiM and then auhtraet 
 the whole mtmbert'. 
 
 Note.— Keduce both the frnctinns, and the diflVreuce to their lowe«t 
 terms. 
 
 Mnlttrnct 
 
 1616. 
 
 
 from 
 
 f 
 
 1623. 
 
 f 
 
 from 
 
 1 
 
 1617. 
 
 
 from 
 
 i 
 
 1624. 
 
 /ff 
 
 from 
 
 H 
 
 1618. 
 
 
 from 
 
 1 
 
 1626. 
 
 «J 
 
 from 
 
 m 
 
 1619. 
 
 
 from 
 
 i 
 
 1626. 
 
 lou 
 
 from 
 
 nn 
 
 1620. 
 
 
 from 
 
 ^2 
 
 1627. 
 
 2J 
 
 from 
 
 6J 
 
 1621. 
 
 
 from 
 
 
 1628. 
 
 13 J 
 
 from 
 
 21 t 
 
 162i2. 
 
 
 from 
 
 l^ 
 
 1629. 
 
 14i 
 
 from 
 
 18 i 
 
 1630. John has | of a dollar and he gave James | of a dollar ; what 
 had he remaiDing ! 
 
 1631. Mary has } of a pie, she gave her sister | of it ; how much 
 how much had she ? 
 
 1632. From I of a ton of hay a farmer sold } of a ton ; what has he 
 remaining ? 
 
 1633. A merchant has ^ of a ship, he then bonght \ of the ship and 
 afterwards sold \ of the ship ; what has hs on hand f 
 
 1684. The suui of two fractious is {, one of the fractions is f, what is 
 the other t 
 
 1686. Three fractions make together ^, one is \ and snother \, what 
 is the third t 
 
 1636. A man has ^ of a dollar he owes John \ of a dollar and Peter | ; 
 what will he have after paying his debts ? 
 
 1637. From 42^ pounds of butter, a man sells 10^ and 14^ pounds ; 
 how much has he on hand still } 
 
 1638. Joseph had 45} cords of wood, he buys 80^ cords and then sells 
 40^ cords ; how many cords has he now ? 
 
 1639. John has ?20 and pays $9} for a coat, $2} for a hat, and |4^ for 
 shoes ; how much has he remaining f 
 
t subtract 
 lieir lowest 
 
 i 
 
 18 i 
 liar ; what 
 
 how much 
 
 lat has he 
 
 lie ship and 
 
 I ^, what is 
 
 tier \, what 
 
 ad Peter ^ ; 
 
 1} pounds ; 
 
 L then sells 
 
 and |4^ for 
 
 MUI/ni'I.tCATION or FUACTI0N8. 
 
 MULTIPLICATION OF FRACTIONS. 
 
 71 
 
 Multiplication effractions is tlio process of multi- 
 plying wlieu one or both tc-nn.s are fractions. 
 
 Case L—To mnlHplu a /ruction by a whole number. 
 
 Exainple._Miiltii)ly g by 6. 
 
 Solution.— 6 times %=,^, which reduced to 
 its lowest terms equals ',". 
 
 QPEHATION. 
 
 84. R\iie.—Mul{i/,h/ the numerator by the whole number 
 and reduce the remit to its lowed terms. 
 
 Unit I ply 
 
 1640. 
 1641. 
 1642. 
 1643. 
 
 ^s X 7 
 
 I X 6 
 
 « X 10 
 
 if X 12 
 
 1044. 
 1645. 
 1646. 
 1647. 
 
 if X 22 
 
 § X 18 
 
 i X 86 
 
 * X H 
 
 1648. John has | of an acre aud Louis has 10 tim.s as much ; how 
 many acres has Louis ? 
 
 Case II.— 7*0 multiply a fraction by a fraction. 
 Example-Multiply j by f. OPEiiATioy. 
 
 Solution.— Multiply the numerators together i X J == H 
 for a new numerator, and the denominators for a iJ = | 
 
 new denominator. Keduce the result to its lowest terms. 
 
 86. Rule.— Multiply the numerators together for the numer- 
 ator, and the denominators together for tho, denominator of 
 the product. 
 
 NotC—l. If there are units in one of the factors reduce to an 
 
 improper fraction before multiplying. Ex. 2i multiplied by 81. 24— 
 
 i and Z\=x^ • iX¥=!i=7/^. y i i- 
 
 2. Reduce the result to its lowest terms. 
 
 »■•■ 
 
74 
 
 DIVISION OF FKACriONS. 
 
 What is the proflnct or 
 
 1649. 
 
 1660. 
 
 1651.. 
 
 1652. 
 
 1653. 
 
 f by ^ ? 
 f by n 
 
 ^ by 
 by 
 
 T5 
 
 ? 
 
 T? 
 
 if by 
 
 3. 7 
 
 1664. i? by ft 
 
 1655. 2\ by 3i ? 
 
 1656. 7 J by lOf ? 
 
 1657. 18 1 by | I 
 
 1658. 40^ by sj? 
 
 165&. John has f of f tons of hay, Peter has 4J tons more ; how many 
 tons has Peter ? 
 
 1660. "What remains after selling the | of 10 J pounds of honey ? 
 
 1661. Find the cost of 9| yards of cotton at 11 J cents a yard ? 
 
 1662. John pays for 14| pounds of coffee at 15^ cents a pound, how 
 much did he spend ? 
 
 1663. What will 9 tons of coal cost at $6| a ton ? 
 
 ' 1664. A fanner sells 14| pounds of butter at 21 1 cents a pound ; what 
 does he receive ? 
 
 1665. Martin has | of a load of hay, Tobias has ^ as much plus 3} 
 tons ; how much has Tobias ? 
 
 1666. I have $25, I buy 6^ pounds of tea at 60 cents a pound, and 4 
 teapots at $3| apiece ; what have I remaining ? 
 
 1667. At $3J a yard what will 9| yards of cloth cost ? 
 
 1668. A man pays $10^ for a coat and | as much for a rest ; what 
 will both cost ? 
 
 1669. In a room containing 56 persons, ^ are boys, g are girls, how many 
 remain ? 
 
 1670. A dozen of eggs cost $^ ; what will 25 dozen cost ? 
 
 1671. Find the cost of 20J^ pounds of cheese at llf cents a pound. 
 
 DIVISION OF FRACTIONS. 
 
 86. Division of fractions is the process of dividing 
 when one or both of the terras are fractions. 
 
 Case I. — To divide when the dividend is a fraction. 
 
 Example.— Divide || by 4. 
 
 Solution. — {} divided by 4=^^. When the numer- Operation 
 ator will not contain the divisor, multiply the deuomin* 
 ator by that numlii . , {^ -j- 4=/^ 
 
 87. Rule- — Divide the numerator or multiply the denomi- 
 nator by the divisor. 
 
MENTAL EXKliCIsnS IN REDUCTION. 
 
 75 
 
 i? 
 
 V 
 
 f ? 
 
 how many 
 
 ney ? 
 
 i? 
 
 ound, how 
 
 md ; what 
 ich plus 3 1 
 ind, aud 4 
 
 est ; what 
 how many 
 
 Mund. 
 
 Divide. 
 
 1672. 
 1673. 
 1674. 
 1675. 
 
 t% 
 
 I 
 
 by 
 
 by 
 by 
 by 
 
 3 
 
 6 
 12 
 11 
 
 1676. 
 1677. 
 1678. 
 1679. 
 
 HI 
 
 V- 
 
 by 
 by 
 by 
 by 
 
 6 
 
 9 
 
 10 
 
 12 
 
 1680. 1 gave $5^ to 8 little boys, what did each receive ? 
 Case n. — To divide lohen the divisor is a fraction. 
 
 Solution, f divided by 1 equals «. Hence f di- Opkkation. 
 vided by i equals 4 times f, and f divided by | equal 4^3^ 
 4 of 4 times f or f times § which give ^ or V. Hence 5 v i-*" nr .1 a 
 we see that the divisor becomes inverted. » A *— r s or 5 
 
 88. BmIq.— Invert the divisor and multiply the dividend 
 by the restdting fraction. 
 
 Divide. 
 
 1681. 
 1682. 
 1683. 
 
 1684. 
 1685. 
 
 I 
 
 i 
 
 if 
 
 by 
 by 
 by 
 by 
 by 
 
 I 
 
 * 
 
 12 
 11 
 
 1686. fl 
 
 1687. 4 J 
 
 1688. 7^ 
 
 1689. 12| 
 
 1690. 15| 
 
 by 
 by 
 by 
 by 
 by 
 
 i 
 I 
 
 1691. How many pounds of butter at ^ can b" had for |2.i ? 
 
 1692. At .$7 1 per ton how much coal can be had for$5o ? 
 
 1693. Oiviue ?;156 among a group giving each $10^ ; how mai.v persons 
 can be paid ? - i 
 
 1694. I had 1200 and spent $96>, how many acres of land can 1 buy 
 with the remainder at |15§ an acre ? 
 
 
 dividing 
 
 on. 
 
 RATION 
 
 ^4=^ 
 
 denomi- 
 
 MENTAL EXERCISES IN REDUCTION. 
 
 1695. If an apple is divided into two equal parts, what do you call : 
 1 — One of these pnrts ; 2.— Two of these parts ? 
 
 1696. What is the half: of 8 ; of 12 ; of 16 ; of 28 ? 
 
 1697. If a pound of butter cost 18 cents ; how mnch will half a 
 pound cost ? 
 
 1698. Thomas bought 24 sheep ; in selling half of them, how many 
 does he sell? , ' / 
 
76 
 
 UEXTAIi EXERCISES IN SEDUCTION. 
 
 m 
 
 1699. If I divide an apple into three equal parts, how do you call : 
 1. — One of these parts, 2. — 2, and 3 of these purts. 
 
 1700. What is the third : of 6 ; of 12 ; of 18 ; of 21 ? 
 
 1701. Henry had 30 cents, and he lost the third ; how many cents 
 did he lose t 
 
 1702. How many thirds are there in : 3 units ; 5 units; 8 units ? 
 
 1703. Louis having 42 marbles, gave the third of them to Edwnrd ; 
 how nuny had he remaining ? 
 
 1704. What are the two-thirds ; of 9 ; of 15 ; of 24 ; of 30 ; of 27 ; 
 of 33 ? 
 
 1705. How many thirds in : 1.— 4S ; 2.— SJ ; 3.— 2f ; 4.— 6§ ? 
 
 1706. Joseph had 21 cents ; he gave § of them to his sister. How 
 many cents did she receive ? 
 
 1707. John lost the § of $36 ; how much has he remaining 1 
 
 1708. How many units in : 1— f ; 2.— \o ; 3.— ^ ; 4.— J/ ^ 
 
 1709. If an apple is divided into four equal parts, what do you call : 
 1.— One of these parts ; 2. — Two of these parts ; 3.— Three of these 
 parts? 
 
 nir^. What is the fourth : of 12 ; of 20 ; of 32 ; of 48 ? 
 
 1711. What are the two-fourths : of 16 ; of 40 ; of 24 ; of 36 ? 
 
 1712. What are the three-fourths . of 20 ; of 24 ; of 16 ; of 12 ? 
 
 1713. If a yard of cloth cost $16, how much will the | of a yard cost ? 
 
 1714. James gave his brother the | and his sister the £ of 28 oranges ; 
 how many did each receive ? 
 
 1715. How many fourths : in 5 ; in 7 ; in 4| ? 
 
 1716. How many units : in f ; in ^^ ; in \^ ; in \* t 
 
 1717. Victor is 24 years old and Alfred is f as old ; what is Alfred's age 1 
 
 1718. If you divide an orange into 5 equal parts, what do you call 1, 
 2, 3 and 4 of these parts I ' 
 
 1719. What is a fifth? 
 
 1720. What isthelifth: of 25; of 10; of 15: 
 J721 . What are the two-fiftl. : of 15 ; of 30 ; of 45 ; of 50 ? 
 J722. What are the three-fifths : of 10 ; of 30 ; of 25 ; of 65 ! 
 J 723. What are th.- four-fifths ; of 55 ; of 35 ; of 40 ; of 50 ? 
 
 1724. James has 15 oranges and Maurus has g of this number; how 
 many oranges has Maurus ? 
 
 1726. Julia it. 25 years old and her sister is | of her age ; how old is 
 her sister ? 
 
 ImV. M-Vvt luauy 1111,113 : ;u u ; n. a ; :u 'ig ; Uj : 
 
 1727. Andrew is 86 years old and his wife is ^ of his age ; what i> her 
 age? 
 
 of 30*? 
 
 1728, 
 3, 4 and 
 1729. 
 1730. 
 1731. 
 1732. 
 1733. 
 1734. 
 less 4 ; i 
 1735. 
 the I ; 1 
 1736. 
 bought f 
 1737. 
 iu 23 ? 
 1738. 
 1739. 
 1740. 
 
 1741. : 
 
 4, 5 and 
 1742. 
 
 1743. ' 
 
 1744. ' 
 1745. 
 1746. 
 1747. 
 1748. 
 1749. 
 1760. 
 
 in If? 
 
 1751. i 
 
 1752. B 
 1763. A 
 
 was the loi 
 1754. If 
 yards cost 
 
 1765. If 
 fif these pa 
 
 1766. Vi 
 J767. W 
 
MENTAL EXEnciSES IN KEDUCTION 
 
 1728. If you divide a melon into 6 equal parts, what do you rail 
 3, 4 and 5 of these parts ? 
 
 1729. What are the two-sixths ; of 24 ; of 18 ; of 36 ; of 60 ? 
 
 1730. What are the five-sixths : of 18 ; of 54 ; of 24 ; of 72 ; of 
 
 77 
 
 1.2. 
 
 36? 
 
 '■ rate( 
 
 laya 
 
 1731. What will the f of 36 yards of cloth cost, at 
 1/32. How many sixths : in 5 ; in 2J ; in 4J ? 
 
 1733. How many units : in V ; in ^ ; iu V ; in J ? 
 
 1734. Alfred had 12 tops, and Louis had only the § of this number 
 less 4 ; how many tops had Louis ? 
 
 ♦.,^?V'^"'' ^"""^ ^^ plums; he gave Jane J of them, and Charles 
 tne f ; how many had he remaining ? 
 
 1736. If a yard of cloth cost ^ of 50 cents ; ho^v many yards can be 
 bought for 60 cents ? 
 
 • o?I' ""'"^ ""^"^ '' ^—fourths in 21 ; 2.- Fifths in 24 ; 3.-Sixths 
 111 Zo f 
 
 1738. How many dollars in $ ?/ ! 
 
 1739. Express in whole numbers : 1.— 2fi ; 2.— f f ; 3.— "5 ■? 
 
 1740. What are the relation of the following fractious to unity • 1 -4 • 
 2— i%;3.-|; 4.-J;5.-9? , ^' ' *' 
 
 1741. If you divide a melon into 7 equal parts, how do you call 1 o 3 
 4, 5 and 6 of these parts ? - f . » 
 
 1 742. What is the seventh : of 21 
 
 1743. What are the two-sevenths : 
 
 1744. What are the three-sevenths , 
 
 1745. What are the four-sevenths : of 70 
 
 1746. What are the five-sevenths : of 77 ; 
 
 1747. What are the six-sevenths : of 35 ; of 42 ; of 49 
 
 1748. How many sevenths in 9^ pounds I 
 
 1749. What are the lowest terms : of f f ; of f J ; of || ? 
 What is required to complete the unity' : in i ; in f ; in | ; 
 
 of 28 ; 
 
 of 28; 
 
 of 14 
 
 of 42 ; of 56 ? 
 
 of 49 ; of 63 ; of 70 ? 
 ; of 49 ; of 49 ? 
 of 63 ; of 84' 
 of 42 ; of 28 ? 
 of 140? 
 
 ; of 35 
 of 77; 
 of 91; 
 
 1750. 
 inH? 
 1751. 
 1752. 
 1753. 
 
 Express in cents : 1.- the | of a dollar ; 2— the f of $1.50. 
 How roiny bushels of potatoes in Sj^ of a bushel ? 
 A watch which cost $70 was sold for the f of its cost. What 
 was the loss ? 
 
 1754. If the half of 10 yards of cloth cost $10, what will l of 6 
 yards cost ? a "■ « 
 
 ^ 1755. If you div. i. . aything into 8 equal parts, how do you call one 
 fii ihese parts ? 
 
 1766. What is th. >-vhth : of 24 ; of 48 ; of 72 ; of 88 ? 
 J767. What are the three-eights : of 16 ; of ^ j of 80 ; of 96 f 
 
 1 2 
 
78 
 
 MENTAL EXERCISES IN REDUCTION. 
 
 1768. What are the fivo-eights : of 8 ; of 24 ; of 48 ; of 64? 
 
 1759. How many times : Three in § of 24 ; 5 in § of 40 ; 8 in | of 80 ; 
 7 in § of 56 ; 12 in f of 64 ; 3 in i of 72 ? 
 
 1760. How many fourths : in 2i ; in 7| ? 
 
 1761. How many sevenths: in 5j ; in 3^? 
 1762 How many sixths : in 7f ; in 3| ? 
 176?-. How many eighths : in 7| ; in 5| ? 
 
 1764. Reduce § to 12ths. | to 30ths. 
 
 1765. " i tol6ths. ji to 36 ths. 
 
 1766. '« ^% to 20ths. I to Slsts. 
 
 1767. How many units : in -'5* ; in J| ; in '5* ; m 'j* ; in Y ; in V > 
 in V; V? 
 
 1768. What must be added to the following fractious to complete 2 
 units: 1.-^; 2.-| ; 3.-^; 4.-3 ? 
 
 1769. If you divide an orange into 9 equal parts what part of the 
 orange would you obtain if you take 1, 2, 3, 4, 5, 6, 7, 8, and 9 of these 
 parts ? 
 
 1770. What are the | : of 18 ; of 27 ; of 45 ; of 36 ? 
 of 9 ; of 36; of 54 ; of 81? 
 of 54 ; of 72; of 63 ; of27 1 
 of 18; of 99 ; of 27 ; of 108? 
 
 1774. What are the lowest terms: of }S ; of j^V of \^ ; o( ^^ ; 
 of|§; Hiofll; H? 
 
 1775. What is the sum of: 1.— 8 times 6 and § of 6 ; 2.— 4 times 12 
 and I of 12 ; 3.— 5 times 10 and ? of 10 ; 4.— 5 times 7 and 4 of 7 ; 5. 
 — 9 times 8 and J of 8 ? 
 
 1776. Louis bought 15 horses and after selling 6, found that he 
 required 4 to have 20. How many had he at first ? 
 
 1777. How much should you pay for a case of soap, if the J of a case 
 cost $15 ? 
 
 1778. If the I of a yard of cloth cost $6, what will a yard cost? 
 
 1779. If 5 yards of cloth cost $2.50, how miichwill 6 yards cost ? 
 
 1780. What must you pay for 10 peaches, if 3 peaches cost 4J cents ? 
 
 1781. 2 apples cost f cents, what will 5 apples cost ? 
 
 1782. What is the cost of 9 lamps, if 5 lamps cost $ -'^ ? 
 
 1783. Of what number is ; 1 . — 6, three times its J ; 2. — 8, twice its ^ ; 
 3.-16, four times its ^ ; 4.-9, three times its J ? 
 
 1784. Frank's coat cost $10 which sum equals J of 6 times the price of 
 
 1771. WHatarethe* 
 
 1772. What are the ^ 
 
 1773. What are the I : 
 
 J785, Of what nul^ber is : 9 the f ; 6 the |, 10 the f ; 12 the ^? 
 
WRITTEN EXERCISES 79 
 
 nil' T"* r"i ^ ^,r° '^ •'^^^ "^^ ''^ 18^ ''^'^ « dozen ? 
 1 7R0* T r f ''"^ '"'* * ^' ^^''* ^'» 6 '°*ds cost ? 
 
 ^^789, Tobias purchased 6 pair of shoes for J18|. what did they cost a 
 
 for'eSluL?"' '' '''°'' '''* ^ '' '' "°*^' '^"^^ ""^"y y"d« -» be had 
 
 1791. How often do the | of 32 contain the J of 12 f 
 
 1792. How often do the | of 56 contain the ^ of 42 ? 
 1/3. How often do the § of 27 contain the | of 12 ? 
 
 tulst !t '"'"■'°" ''*'''"« '^P'*^ ^^ b"«h«l «f °«ts, sells J to Michael and 
 th I of the remainder to Bernard, how niany bu. '.els hat he S 
 
 Jch did's"Cveray't '' '''''^" '' " ^^'^ ^^ « ^ *« «- ' ^o^ 
 
 Im 7T IV/'J^'. '' '''''' •="'*' ^^ * «f •* y"d cost «6 » 
 bleu ,^ '''"'"'' *''P^'^^^''"'«2'^- -"^'^ -^' ^' paid for 3 
 
 JyJJ" M ?' * "-^ V*"^' ''^ '^''^^'°'' «3^' ^°^ """ch will 9 yards cost ? 
 
 WRITTEN EXERCISES. 
 
 1800. Reduce f and ^ to tlie same deuomi.mtor ? ' 
 
 1801. Which is the greater of tl>€ two fractions § and A ? 
 
 1802. Joseph empties f of a tun in 8 hours; Louis empties the U in 
 tlie same iime. Which is the more active ? ^^ 
 
 1803. How many sixths : in J ; in | ; S ? 
 
 1804. How many eighths : in i ; in ^ ; f ? 
 
 1805. How many twelfths ; in f ; in | • ai I. 
 
 1806. Reduce §, f, and | tc twelfths. 
 
 1807. Reduce i and | to a common deno^iriai ^r 
 
 1808. If 2i y.rds of lace ..ost 13 cents wh t will 3 yar-ls cost? 
 
 1809. Low many fourths in J, |, ^j, iq, 
 
 1810. Whatmustyouaddtoorsubstract /:om the followin<r 
 
 ainiiH i-n Imiro 1 i. 
 .J 
 
 3 
 
 V'» 6 
 
 expres- 
 
 Mil. How many fifteenths : in § , iu ^ ; in | ; in f f 
 
 
80 
 
 WaiTTRN EXEBCI8E8. 
 
 'I': 
 
 1812. Seduce the following fractions to a common denominator : ^, §, 
 
 1818. Eugene lost 20 roses which were | of all his number. How 
 many had he ? 
 
 1814. Write in order of their value §, f, f, J. 
 1816. How many sixths : in |§ ; ^j ; in § ; in ^Sj t 
 
 1816. Reduce: ^% to fifths; ^ to fourths ; ^^ to halves; ^j to 
 foiirUis ; f to thirds ; ^^ to sixths ; ^j to sevenths ; || to nineths. 
 
 1817. If 8 is I of a number, what is the J of twice that number ? 
 1318. Two boys buy coffee at 30 cents a pound, one buys 3^ pounds 
 
 the second ^i pounds. Who spends the more ? 
 
 1819. Reduce to a common denominator : 1. — § and |, 2. — i and ^ 
 3.— i and ^ ; 4.— § and | ; 5.— f and f ; 6 | and ^g. 
 
 1820. Reduce to a common denominator ; 1.— J, i, i ; 2.— f, i, i 
 
 3.-*, i, i; 4.-ia.i»5- 
 
 1821. Joseph found 60 cents which equals f of i of what he then had 
 how much had he at first ? 
 
 1822. Paul said to Arthur ; " Would you prefer to receive the | or the 
 § of my money and why " ? 
 
 1823. Reduce the following fractions to their lowest terms : ^f ; |J ; 
 
 1824. Four times 50 years is 10 years less than 10 times Philip's age. 
 What is Philip's age ? 
 
 1825. How many lemons would be required to pay 7 oranges, if 6 
 lemons equal 4| oranges. 
 
 1826. Which is the smallest of the following fractions : i, f, ^Sj, f ? 
 
 1827. What will 3 J pounds of sugar cost if 2i pounds cost 25 cents? 
 
 1828. A horseman can travel 21 miles in 3^ hours, how fat will he 
 travel in 5^ hours ? 
 
 1829. Henry gives 16 conts to a beggar and John gives ^ of a dollar. 
 Who was the more generous and by how much ? 
 
 1830. Reduce to their lowest terms : ^Sj, ^j and |f ; and then reduce 
 to a common denominator. 
 
 1831. if it requires 83 yards of cloth for 2 coats, how many yards will 
 9 coats require f 
 
 1832. f of 48 oranges cost 40 cents, what will | of 12 oranges cost ? 
 
 1833. It requires ^ days for 6 men to build a boat ; how loiig will it 
 take 3 men to build it ! 
 
 1834. Reduce to an improper fraction :— 2| ; 5J ; 6)^ ; 4J ; 5J ; 2i ; 
 8f 5 8| ; 4i ; 6} ; 5J ; 9* ; 7|; Si , eg , 9J ; 7f ; 8i; 6| j 91- 
 
 1835. A 
 
 1836. ^\ 
 
 1837. H 
 nineths in 
 
 1838. A] 
 in the othe 
 
 1839. Lo 
 Louis still ] 
 
 1840. W 
 X1841. Wl 
 
 1842. Ap 
 
 1843. A) 
 \1844. At 
 .1845. At 
 
 1846. A f 
 
 1847. As 
 how many y 
 
 1848. Tw( 
 T849. Ah 
 
 is 6 mouths I 
 
 1850. Johi 
 how many pi 
 
 1851. Am 
 many bushels 
 
 1862. Hon 
 for $18|. 
 ^ 1853. I sol 
 much is due j 
 
 1854. How 
 
 1855. 1 spe 
 did I buy ? 
 
 1866, Thej 
 other ? 
 
 1857. Theq 
 dividend ? 
 
 1858. Byw 
 
 1859. Byw 
 
 1860. If^o 
 
 1861. What 
 taace is 108 mi 
 
1835. A man 
 
 WRITTEN EXERCIHE8. 
 
 81 
 
 1836. mat sS''^'"'"^^'''"^^'""^^-"''^ 
 
 1837. How many : eights iu A, U 
 
 earn in 5 days ? 
 a man pay for 8 barrels of apples at $3 J a barrel T 
 
 fifth 
 
 nineths in H, |^ rtent^L'i/^^^^/'^n '" "' ^' ' ^"^"^^^ *?' ^ ' 
 
 Lors;iJrr:;t-\^r^^ 
 
 u'a!?' wk'! '°n '' °'""S'' ^'^ °^* ^«"t «««h » 
 1849 , f ^"'"y°" P*y f«r 16| yards of calico at 9* cents a yard ? 
 
 8 3 a'' ""?.'* ^^•' '"^^^ ' ^^'^''^ -•" b« P-<i for Srbarrels t 
 
 .845. A bntcher buys sheep at |8 a he.ul. how many will he get for m ? 
 846. A farmer has 14| tons of hay and sells 9J tons, whaf remls 
 
 how i^Shiri!:^ "^^ -^^ "'• ^'-' ^« ^"- -i --=; 
 
 1848. Two fractions together ffivp a eiimnf 18 «« • < , . 
 ^ 1849. A bov earn, «i of! I T ^^'°°^ '* ^' ''*>''* '« ^^^ °"»er ? 
 is 6 months ? ^ ^ '"'"*'' '"'^ 'P^"*^' «^2|. what will h. have 
 
 how ly;t?r„dtr ' ''' ^^"""^ '"'^^^ -' '- ^^1 --^'^"«. 
 manyL1;er::m:i:r'"""^*'^'^*'^*^ bushels of oata ; how 
 for «18|."" ""' '"'^ "' ^"""^ ^* ^ «^ « '^°"- a y,rd can be bought 
 
 jrisdrf '''^"""'^"^-^^r^^^^i-*-"^ -ived ,5. how 
 
 1854. How many sheep at 08* per head can a man buy for $200^ ] 
 did I buy r* ''■''' '" "^^* '' ''' ''^'^ ^ P-"'^' ^- many pounds 
 otJeM ' '''' ''°'"'^' '' *"° ''"""^^ ^« «' -« °f ^^- - i. what is the 
 
 divMend?' '"""' °' *"' ^""'^'•^ " * ^ *^« <^-- » i -hat is the 
 
 1858. By what number must you multiply J to got 13i ? 
 
 1859. By what number must 3^ be divided to get | ? 
 
 1860. If ^ of an arrp nf ^anA ^r^*^ ooa „.i. . .,, _ 
 
 --_.„...., .. ^._..j-^ uiiUv vviii o &ci*cs cost? 
 
82 
 
 DKKOMINATK MUMBKR8. 
 
 1862. If } of a farm cost $120, what would 8 similar farms cost I 
 
 1863. A barrel of flour costs J18, what will § of a barrel cost ? 
 1664. If j of a barrel of flour cost |12, what will f of n bairel cost t 
 1865. Louis had $1240 he spends f of it and then 2 of the remainder, 
 
 how much has he now ? 
 
 DENOMINATE NUMBERS. 
 
 104. A Denominate number is a concrete number in which 
 the unit is a measure ; as, 5 pounds, 6 yards, 3 minutes. 
 
 105; Reduction is the process of changing a number from 
 one denomination to another, without changing its value. 
 
 It may be either ascending or descending. 
 
 CURRENCY. 
 
 106. Money is the measure by which we estimate the 
 value of thingd. 
 
 Gurrency is money used ab a circulatinj^ medium. 
 
 Table. 
 
 (m) equal 
 
 10 
 10 
 10 
 
 mills 
 cents 
 dimes 
 
 « 
 
 1 
 1 
 1 
 
 cent 
 dime 
 dollar 
 
 et. 
 d. 
 $. 
 
 107. Coins are made either of copper, silver or gold : 
 The 60 cts, 25 cts, 10 cts, and 5 cts, are made of silver. 
 The 1 ct, and 2 cts, of copper. 
 
 Exercises. 
 
 1866. How many cents in $3^ ? 
 
 1866. How many 10 cent-pieces : 1. — in 50 cts ; 2.— in §1 ; 3.- 
 12.30 ; 4.— in $3.80 ? 
 
 1867. How many 5 cent-pieces would be required for : 1. — 65 cts ; 
 2.— 90 cts ; 3.— $1.70 ; 4.— $5.25 ? 
 
 1868. How many 26 cent-pieces : 1.— in $4.25 ; 2. — in |6.50 ; 8.— 
 in 17.75 ? 
 
 1869. I owed Henry $4.20 ; I gave him 60 five-cent pieces. How 
 much do I still owe him ? 
 
 in 
 
 1870. I 
 many dolli 
 
 1871. H 
 5.-$i; ( 
 
 1872. V 
 
 108. E 
 
 4 fart 
 
 12 
 
 pen 
 
 20 shil 
 
 21 
 
 shil 
 
 Note.- 
 
 5 shillings. 
 
 1873. 
 
 Ho 
 
 1874. 
 
 Ho 
 
 1876. 
 
 Ho^ 
 
 1876. 
 
 Ho^ 
 
 187^ 
 
 Bed 
 
 lP/8. 
 
 In) 
 
 109. Tr( 
 jewels, &c. 
 
 24 graini 
 20 })enn] 
 12 ouQoe 
 
COBtt 
 
 stT 
 
 rel cost T 
 remainder, 
 
 ir in which 
 
 les. 
 
 Bber from 
 
 ralue. 
 
 bimate the 
 
 n. 
 
 Id: 
 iilver. 
 
 DENOMIHATB NDMBERB. (g 
 
 Jnl'^; n ^^"^ I ^''''' °^ ^^ ''"*'• ""^ 3 piece, of 26 cents. How 
 many dollars and cents have I? 
 
 1871. How many cents in : 1— «i : 2.— «i • 8 _ «a • i •! 
 
 1872. What port of 8 cents is the f of 10 cents! 
 
 ENGLISH MONEY. 
 
 108. English money ia the money of Great Britain. 
 
 Table. 
 
 equal 
 i< 
 
 M 
 <« 
 
 1 penny ^^ 
 
 1 shilling g^ 
 
 1 pound or sovereign jg. 
 
 1 guinea ^ 
 
 4 farthings (/ar.) 
 12 pence 
 
 20 shillings 
 
 21 shillings 
 
 5 sWUin^'s""^^^ ^°"°*^ " sovereign is worth «4.866. A crown is worth 
 
 Exerelaea. 
 
 1873. How many farthings in 10 d. and 3 far. f 
 
 1874. How many pence in 16s. and 9 d. ? 
 1876. How many farthings in ^ 16 6s. 3d. I 
 1876. How many shillings in 900 far. t 
 187^ Reduce 3178 pence to pounds ? 
 
 lP/8. In 9760 farthings, how many lounds I 
 
 51 ; 3.— in 
 . — 65 cts ; 
 16.60 ; 8.— 
 ieces. How 
 
 MEASURES OF WEICJHT. 
 Troy. 
 
 109. Troy weight k used in weighing gold, silver, 
 jewels, &c. * 
 
 24 grains (gr.) 
 20 jH'nnyweights 
 12 ounces 
 
 Table. 
 
 equal 
 
 M 
 
 1 pennyweight pwt. 
 : I oniice ox. 
 
 |po\iBd lb. 
 
 r 
 
84 
 
 DEI^OlilKATB kCMDERS. 
 
 Exercises. 
 
 How many : 
 
 1879. Grains in 4 oz. 5 pwt f 1882. Pennyweights in 2 lb. 3 oz ? 
 
 1880. Pounds in 7365 grs ? 1883. Oz., and pwt., in 4170 grs ? 
 
 1881. Grains in 3 lb. 4 oz. 6 pwt? 1884. lb.,oz., and pwt. in 10302 grs? 
 
 Apothecaries*. 
 
 110. Apothecaries' weight is used in measuring 
 medecines. 
 
 Table. 
 
 20 grains (gr.) 
 
 equal 
 
 1 scruple 
 
 ser. 
 
 8 scruples 
 
 II 
 
 1 dram 
 
 dr. 
 
 8 drams 
 
 It 
 
 1 ounce 
 
 oz^ 
 
 12 ounces 
 
 Exerclsrs. 
 
 1 pound 
 
 lb. 
 
 How many : 
 
 1886. Grains in 3 oz, i <■! 
 
 1888. Pounds and oz. in 239 drams ? 
 
 1886. Drams in 2 lb. ,..i? , £ ds" ? 1889, Oz. in 4800 grains ? 
 
 1887. Drams in 960 gr i 1890. Pounds, &c., in 91304 gr I 
 
 AVOIRDUPOIS WEIGHT. 
 
 111. Avoirdupois weight is used in weighing all 
 tfAxnmon goods. 
 
 table. 
 
 16 ounces (pz.) 
 100 pounds 
 20 hundred-weight 
 
 equal 
 
 II 
 II 
 
 1 pound n, 
 
 1 hundred- weight ewt. 
 1 ton T, 
 
 ■fiTote. A quarter is one-fourth of a hundred-weight. 
 
 Exercises. 
 
 How many : 
 
 1891. Oz, in 3cwt! 
 
 1892. Pounds in 6 T 10 ewt I 
 
 1893. Pounds in 976 ozt 
 
 1894, Cwtin 1000 oz'. 
 
 1895, T in 15630 oz f 
 
 1896, Ounces in 20 owt 16 lbs 6 oz? 
 
DENOMINATE NUMBEHS. 
 
 85 
 
 1897. How inniiy ounces in : 1.— 3 lbs ; 2.— 6 lbs ; 8.— 8^ f 
 
 1898. If I pay 33 ceuts for 6 ounces of soda, how much will I nov 
 for : 1.- 2 lbs j 2.- 6 lbs ; 3.- 6 lbs j 4.- 7i lbs ? 
 
 1899. For 4 ounces of camphor I pay 14 cents ; how rany ounces 
 cnu bo bought for : 1.- 21 cents ; 2.- 36 cents ; 3.- 42 cents ? 
 
 icr. 
 
 dr. 
 
 oz. 
 
 lb. 
 
 39 drams ? 
 
 34 gr? 
 
 MEASURE OF LENGTH. 
 
 112. Measure of length or long measure ia used 
 in measuring length, breadth, depth, etc. 
 
 Table. 
 
 12 inches (in.) 
 
 8 feet 
 • 6 J yards or 16 J ft 
 320 rods 
 
 8 miles 
 
 equal 
 
 foot 
 
 yard 
 
 rod 
 
 mile 
 
 league 
 
 yd. 
 
 rd. 
 
 mi. 
 
 I. 
 
 Xote.— lu the old tables 40 rod8=l furlong and 8 furlong8=l mile. 
 I KxerolBes. 
 
 1900. How many inches in : 1 3 ft.; 2.— 4 yds 6 ft ? 
 
 1901. How many inches in : 1.— 4 rd. 5 yds. ; 2. - 6 yds. 2 ft. 4 in.l 
 
 1902. How many miles in ; 1.- 13720 feet ; 2.— 870 rods ? 
 
 1903. How many yards in : 1.— 376 inches ; 2.— 97 ft. 5 in.? 
 
 1904. How many inches between Mont al and Quebec if the distance 
 is 180 miles? 
 
 II. 
 
 SURFACE OR SQUARE MEASURE. 
 
 113. Surface or Square measure is used in measur- 
 ing purfaces; as, loards, lands, etc. 
 
 Table. 
 
 144 square inches (sg'. in.) equal 1 square foot ^q./t. 
 
 9 square feet ^ « i Bquare yard ya 
 
 m square yards ^ « , i perch or square rod P. 
 
 160 perches «« i ac^e j 
 
 •*^ «wrei I. I square mUo tq. mi. 
 
 M 
 
^ 
 
 .^^> 
 
 
 IMAGE EVALUATION 
 TEST TARGET (MT-3) 
 
 
 fe 
 
 1.0 
 
 I.I 
 
 11.25 
 
 2.5 
 
 lii|2B 
 
 US 
 
 ja |2|2 12.2 
 
 I li& |2.0 
 
 U |K6 
 
 Hiotogiaphic 
 
 ^Sciences 
 
 Corporation 
 
 « 
 
 23 WfST MAIN STRKT 
 
 WfBSTIR.N.Y. I4SM 
 
 (716) •73-4S03 
 
 ^^ a\. ^rS 
 
? 
 
 „v 
 
 A 
 
 
 ^\5^ 
 
86 
 
 DKKOMINATR KI7MBKU*. 
 
 ExerclMM. 
 
 How many : 
 
 Square in. in 3 sq. yds. 
 
 1905. 
 
 7 sq. ft ? 
 
 t sq. It i 
 
 1906. Perches in 9760 sq. tt t 
 
 1907. Square feet in 3 ' 
 
 6 sq. yds I 
 
 A 4 P. 
 
 1908. Square ft. in 3 P. 8 sq. yds. 
 
 3 sq. ft ? 
 
 1909. Acres in 120460 sq. ft f 
 
 1910. Acres in 35670 squars 
 
 yards T 
 
 CUBIC OR SOLID MEASURE. 
 
 lU. Cubic or Solid measure is used in measuring 
 things which have length, breadth and thickness. 
 
 
 
 Talile. 
 
 
 1728 
 
 cubic inches (cu. in. 
 
 equal 1 cubic foot 
 
 cu.ft. 
 
 27 
 
 cubic feet 
 
 *• 1 cubic yard 
 
 eu, yd. 
 
 16 
 
 cubic feet 
 
 " 1 cord foot 
 
 ed. it. 
 
 8 
 128 
 
 cord feet or 
 cubic feet 
 
 " 1 cord of wood 
 
 ed. 
 
 Sxerelmes. 
 
 How many : 
 
 1911. Cu. in. in 6 cu. yds. 6 cu. 1913. Cu. ft. iu 9 cords of wood T 
 
 ft. 4 cu. in } 
 
 1912. Cubic yardsin 24560 cu. in.T 1914 Cords in 8766 oo. ft.t 
 
 LIQUID MEASURE. 
 
 115. Liquid measure is used in measuring nearly all 
 kinds of liquids. 
 
 Tabl«. 
 
 equal 
 
 4 gills (i/O 
 2 pints 
 4 quarts 
 31 i gallons 
 63 gallons 
 
 1 pint 
 1 quart 
 1 gallon 
 1 barrel 
 
 ft. 
 
 qt. 
 
 gal. 
 bbl. 
 
 1 hogshead hhd. 
 
 Exercises. 
 
 Ho\V many : 
 
 10]S, Gills in 6 quarts 4 pints ; in 5 gals ; in 4 qu.irt9 ! 
 
 Idld. Quarts, in 1 barrel ; in 16 gals ; in 2 hhds t 
 
 1917. Gallons in 56D pints ; Hhds iu 1000 quarts ; bbla. in 760 giJi t 
 
'. 8 sq. yds. 
 
 Kq. ft T 
 ro squaro 
 
 noasurmg 
 
 eu.fl. 
 «. yd. 
 cd. Jt. 
 
 ed. 
 
 a of wood ? 
 , ft.t 
 
 learly all 
 
 pt. 
 
 It. 
 il. 
 I. 
 \d. 
 
 DEKOKiyATE MUUBEU, 
 
 DRY MEASURE. 
 
 87 
 
 116. Dry measure is used in measuring dry substances : 
 as, grain, fruit, salt, &c. 
 
 Tnble. 
 
 2 pints (pt) 
 8 quarts 
 4 jiecks 
 
 eqnal 
 
 It 
 « 
 
 1 qaart. 
 1 peck. 
 1 busheV 
 
 qt. 
 pk. 
 bu. 
 
 Kxerelaes. 
 
 1918. In 170 pints how many pecks ; how many bushels in 200 qnartst 
 
 1919. How many pints in 2 bushels ; in S pecks 2 quarts t 
 
 1920. What part of 3 pecks ».re 6 pinto t 
 
 1921. At ]0 cents a peck, how many bushels of com can I bay for |8 I 
 1922 I gave 5 quarts of s^lt at 15 cento a pint, for potatoes at 60 cento 
 
 » bushel ; how many bushels of potatoes will I receive I 
 
 MEASURE OP TIME. 
 
 117. Measures of time are those used to maasore 
 periods of duration. 
 The unit of the measura of time is the day. 
 
 Minor diTlslona of the liny and year. 
 
 1 minute. 
 1 hour. 
 1 day.. 
 1 week. 
 1 month. 
 
 60 seconds (see.) 
 60 minutes 
 24 hours 
 
 7 days 
 
 4 weeks 
 
 equal 
 
 «( 
 
 1 year, 
 
 1 common year. 
 
 m. 
 
 rtr. 
 da. 
 ick. 
 mo. 
 
 12 month or 52 weeks << 
 865 days « 
 
 Wa«e.'»rtt,«tw«lTe months or «!.• yew With tbelr r«^.«cfivo 
 
 number of days. 
 
 July 31 days. 
 
 760 Ids t 
 
 January 31 days. 
 Feoruary 28 " (29) 
 Harch 31 << 
 April SQ " 
 May 31 
 
 June 80 
 
 « 
 
 August 31 
 
 S<'pteinber 30 " 
 
 October 31 M 
 
 November 30 •• 
 
 December 31 <« 
 
/ . ' 
 
 88 DECIMAL FRACTIONf. 
 
 Exerciseii. 
 
 1923. How many seconds in : 1.— 2 minutes ; 2.— 3 minutes } 8— 
 6 minutes ; 4.— 1 day ? 
 
 1924. How many minutes in : 1.— 3 hours ; 2.— 4 days ; 3.— 120 
 seconds ? 
 
 1925. How many houra in : 1.— 2 days; 2.— 240 seconds; 3.— 1 
 year ? 
 
 1926. How many days in : 1.— 3 weeks ; 2.— 8 weeks ; 3.— 48 iiours ? 
 
 1927. How many minutes : in 1 year ; 2.— hours in 63,780 seconds ? 
 
 CIRCULAR MEASURE. 
 
 118. Circular measure is used to measme angles. 
 
 Table. 
 
 60 seconds (") equal 
 
 60 minutes << 
 
 30 degrees " 
 
 12 Signs, or 360 degrees <* 
 
 ,, Exereiaefi. 
 
 How many : 
 
 1928. Seconds in 5 minutes ? 
 
 1929. Alinutes in 8 degrees T 
 
 1930. Seconds in 4" 3' 2" I 
 
 1 minute. 
 1 degree. 
 1 sign. 
 1 circle 
 
 S 
 
 
 1931. Minutes in 500 seconds? 
 
 1932. Degrees in 175'' ^sconds ? 
 
 1933. Minutes in 15 .' 
 
 a 
 o 
 
 
 5 
 
 00 
 
 DECIMAL. FRACTiONS. 
 
 119. A Decimal Fraction, or simply a decimal, is a 
 number of the decimal divisions of a number ; that is, a 
 number divided into <cm, a hundred, etc. equal parts. 
 
 120. When the unit is divided into ten parts each part is a 
 tcuth ; if into a hundred parts, hundredths, etc. 
 
 If a line be divided into ten parts, each part will be one 
 tenth of the unit which is here the line, two parts will be two 
 tenths, etc. 
 
 :l iinii 
 
 
 10 
 
nutes ; 3. — 
 
 «; 3.— 120 
 
 mds ; 3. — 1 
 
 — 48 hours ? 
 80 seconds ? 
 
 gles. 
 
 S 
 
 
 seconds ? 
 "yconds ? 
 
 DECIMAL FRACTIONS. 
 
 89 
 
 Should one tenth be divided into ten equal partsi each of 
 these parts would be a hundredth; if one hundredth be 
 divided into ten equal parts, each one will be a thousandth,.. 
 
 Tenths are then ten times less than unity, the hundredths 
 ten times less than tenths, thousandths ten times less than 
 hundredths, 
 
 121. A decimal fraction is generally expressed by placing a 
 point before the numerator and omitting the denominator. 
 Thus, .6 represents ^n ; .06 represents jh. 
 
 The point is called th 3 decmaZjsojw/.. . .. , 
 
 Nameratlon and notation Table. 
 
 
 a 
 o 
 
 1 I 
 
 a S 
 6 6 
 
 5 
 
 00 
 
 •3 
 
 o 
 
 2! 
 
 a 
 
 9 
 M 
 
 •3 
 
 a 
 
 p 
 o 
 
 a 
 H 
 
 -3 
 
 a 
 
 9! 
 
 a 
 o 
 
 H 
 6 
 
 i I 
 
 
 4 
 
 a 
 
 a • -S 
 ►r J ^ 
 
 S Eh t3 
 
 66666666 
 
 
 , a 
 S 
 § 
 
 Eh 
 
 a 
 
 o 
 
 & 
 
 a 
 a 
 
 n 
 
 CO 
 
 2 ■" 
 
 &« CO 
 
 
 
 a 
 
 09 a 
 
 a •- 
 
 .2 a 
 
 S • H 
 
 6 6 
 
 -5 -« 
 
 t» 00 
 
 I 
 
 -■■■'.;. fii* 
 
 mal, is a 
 that is, a 
 
 part is a 
 
 I be one 
 ill be two 
 
 10 
 
 EXERCISES IN NUMERATION; 
 
 Example. Read the decimal .47. 
 
 Solution. This expresses 4 tenths and? hundredths, 4 tenths equal 
 40 hundredths and 40 hundredths plus 7 hundredths equal 47 
 hundredths. Hence 
 
 122. Rule. Head the decimal as a whole number and give 
 it the denominator of the last term on the right ; numerate 
 towards the point to determine the numerator, and from the 
 point for the denominator. 
 
 To read a decimal number, read the wbola number and then 
 the decimal part to which the name of the decimal unity of the 
 last figure is given. 
 
»0 
 
 VICIMAL FRACTIONS. 
 
 Thus .8 
 .76 
 
 .004 " 
 
 .0705 " 
 
 26.4 « 
 
 24.07 " 
 
 11.017 " 
 
 108.00012 " 
 
 is read eight Unt?u. 
 •• seventy-fire hundredlht. 
 " four thousandths. 
 
 " seven hundred and five ttn-thousandtha. 
 " twenty-six and four tenths. 
 " twenty-four and seven hundredths. 
 " eleven and seventeen thousandths. 
 
 one hundred and eight and twelve hutdred-thou- 
 tandths. 
 
 EXEBOISES. 
 I. Bead the rollowlng declmnl nnmbere i 
 
 1084. 
 
 .01 
 
 .001 .0001 
 
 .00001 
 
 .000001 
 
 1985. 
 
 .02 
 
 .020 .200 
 
 .0200 
 
 .002 
 
 1936. 
 
 .025 
 
 .205 .25 
 
 .250 
 
 .2005 
 
 1937. 
 
 .20050 
 
 .3008 .803 
 
 .8300 
 
 .80030 
 
 1938. 
 
 .80003 
 
 .027 .4006 
 
 .3010 
 
 .30607 
 
 1939. 
 
 .123456 
 
 .500 .00500 
 
 .00005 
 
 .10407 
 
 1940. 
 
 .36092 
 
 vii7(i .0051 
 
 .00061 
 
 .60001 
 
 1941. 
 
 .64321 
 
 .908006 .9864 
 
 .100200 
 
 .00605 
 
 1942. 
 
 .10065 
 
 .00705 .003281 .004682 
 
 .1067890 
 
 1948. 
 
 .015 
 
 .2004 .1206007 .06987 
 
 .698765 
 
 1944. 
 
 1.5 
 
 2.21 
 
 8.60 
 
 25.05 
 
 1945. 
 
 60.70 
 
 76.07 
 
 320.32 
 
 10.09 
 
 1946. 
 
 96.006 
 
 309.0870 
 
 123.987 
 
 56.6543 
 
 1947. 
 
 6701.4 
 
 6642.004 
 
 8.01045 
 
 6070.006 
 
 1948. 
 
 8965.00009 104.00186 
 
 87.010849 
 
 186.0678 
 
 1949. 
 
 12345.07 
 
 2083.0102 
 
 105.102343 
 
 24.00966 
 
 1950. 
 
 4005.005 
 
 17.0306 
 
 9.30051 
 
 8.05063 
 
 1951. 
 
 16073.2 
 
 1061,075 
 
 34.00703 
 
 145.7 
 
 1952. 
 
 231.0061 
 
 I 24.0208 
 
 439.115 
 
 5402.509 
 
 1953. 
 
 7.00075 10.01023 
 
 25.6403 
 
 198.2047 
 
DECIMAL FRACTIONS. 
 
 ft 
 
 EXERCISES IN NOTATION. 
 
 Example. - Express 30 hundredths in the form of a decimal. 
 Soliitiou.d) 36 hundredths equnl 3 tentiis ni,d 6 hundreds, and this 
 is expressed by writing a decimal point before 36, thus .36. 
 
 Rule. Write the decimal as you iconld a whole number, 
 placiny the decimal point so as to give each figure its proper 
 place, using ciphers after the decimal point i/ necessary. 
 
 III. Express the rollnwinff decimal fractions In Hcnres. 
 
 1954. Three tenths, four hundredths, seven thoxtsandths. 
 
 1955. Six len-thoutandtlis, twelve hundred'hs, thirteen thousandth*, 
 
 1956. Seven hnndred-thousandths, eight millionths. 
 
 1957. Nine ten-milUoiUhs, fourteen ten-thousandths. 
 
 1958. Fifteen hundred-thousandths, cue hundred and twenty-four ttm- 
 thousandths. 
 
 1950. Two hundred and twenty-eight hundred-millionths. 
 
 1960. Four thousand four hundred ten-thotisandths. 
 
 1961. Kight hundred and fifty-six hundred-thousandths. 
 
 1962. Twenty-three thousand nine hundred millionths, 
 
 1968. One hundred and seven thousand and eighteen <«n-OTi7Wo7i/A*. 
 
 1964. Thirty thousand four hundred and seventy-two hundred- 
 thousandths. 
 
 1965. Seven hundred and ninety billionths. 
 
 1966. Thirty-four tenths, two thousand and thirty-five hundredths. 
 
 1967. Four hundred and twenty-seven thousand and eighteen 
 thousandths. 
 
 1968. Fifteen thousand three hundred and thirty-four hundredths. 
 
 1969. Three hundred and forty and five tenths. 
 
 1970. Fifty-six and sixty-five hundredths. 
 
 1971. One hundred and twenty-three and forty-eight thousandth's. 
 
 1972. Eight hundred and fifty-two dollars and fifteen cents. 
 
 1978. Sixteen and two thousand four hundred and twenty ten- 
 thousandths. 
 1974. Nine thousand eight hundred and twelve dollars and three cents. 
 1976. Seventy-five and thirty-two millionths. 
 1976. Six hundred and twenty-four dollars and ninety cents. 
 
 , n) Young pupils are sometimes helped to seize the method of writipg decimals. 
 Djrfacing told to call the point « unU of the m-der of the denmal num^tobi 
 jmMjn. Thus seven thousandths are written as one thoussDdsndflevtn-^oSr 
 in like manner four thousand and one millionths. wonld bs writfam aa aam 
 miUion four thoassnd and one=.0W001. """'""""• ^«'"'* ■• wnttwi as om 
 
 4 
 
9i 
 
 DKCIMAt FHACTIOys. 
 
 (it 
 If 
 
 1977. Five hundred thousuiul and six teu-milliouths. 
 
 1978. One thonsand and four and twenty five ten-thousandths. 
 
 1979. Five cents, one hundred dollars and ten cents. "^ 
 
 1980. Ninety three and fifty thousandths. 
 
 123. Principles.— 1. Chantjing the decimal jooint oneplace 
 towards the right multiiMes the number by \0; two places, 
 hy 100, etc. 
 
 2. Changing the decimal point one place towards the left 
 divides th& number by 10; two places, by 100, etc. 
 
 3. Placing a cipher between the decimal point and a 
 decimal divides the decimal by 10 ; placing tico, by 100, etc. 
 
 Thus : To multiply 67 by 10 we would write 670 ; by 100, 6700. In 
 like manner to divide 67 by 10 we would write 6.7 ; by 100, .67 ; adding a 
 cipher to .0175, changes the number to .00176 which is ten times smaller 
 than .0176. 
 
 124. The value of a decimal is not changed when one, two, 
 three, etc., zeros are written to the right of it, because after this 
 operation the number obtained contains ten times, one 
 hundred times, etc., more parts, but these parts are ten, a 
 hundred or a thousand times smaller than the first. 
 
 Exercises on the Method ased to make a nnmber 10, 100, 1000> 
 etc., times vreater or less. 
 
 1981. 
 
 Make the numbei 
 
 1982. 
 
 Make the numbei 
 
 1983. 
 
 Make the number 
 
 
 25 
 
 
 4.75 
 
 
 0.06 
 
 1. 
 
 10> 
 
 c 
 
 1. 
 
 10" 
 
 ) ,: 
 
 1. 
 
 10^ .. 
 
 2. 
 
 100 
 
 
 2. 
 
 100 
 
 s 
 ■s 
 
 2. 
 
 100 
 
 
 3. 
 
 ^ 1000 
 
 . 1, 
 
 3. 
 
 1000 
 
 2 
 
 3. 
 
 1000 
 
 .1 
 
 4. 
 
 'lOOOO 
 
 i 
 
 4. 
 
 10000 
 
 4. 
 
 10000 
 
 5. 
 
 100000 
 
 a 
 
 5. 
 
 100000 
 
 1 
 
 5. 
 
 100000 
 
 4> 
 
 6. 
 
 1000000 J ^ 
 
 6. 
 
 1000000 J 
 
 s 
 
 6. 
 
 1000000. 
 
 s 
 
 19S4. 
 
 Make the number 
 
 1985. 
 
 Make the number 
 
 1986. 
 
 Make the number 
 
 
 . 48946.04 
 
 
 3.65 
 
 
 137.006 
 
 1. 
 
 10-) 
 
 1. 
 
 10-^ 
 
 
 1. 
 
 lO-v 
 100 8 
 
 2. 
 
 100 s 
 
 2. 
 
 100 
 
 
 2. 
 
 3. 
 
 1000 ! - 
 
 3. 
 
 1000 
 
 — 
 
 3. 
 
 1000 •* 
 
 4. 
 
 ' 10000 '" 1 
 
 4. 
 
 10000 
 
 ■• CO 
 
 4. 
 
 10000 1 1 
 
 5;. 
 
 V 100000 ,jp 
 
 6. 
 
 100000 
 
 
 6. 
 
 100000 H 
 
 6; - 
 
 ' 1000000 ■> 
 
 ' '■ 1 
 
 6. 
 
 1000000.. 
 
 
 6. 
 
 1000000. 
 
 
DECIMAL FRACTIONS. 
 
 INI 
 
 01 
 
 )■ s. 
 
 s 
 
 a 
 
 1987. 
 1988. 
 1989. 
 1990. 
 1991. 
 1992. 
 1993. 
 
 114.35. 
 
 Make the following uumbers each 10 timu greater : 
 1 — 47; 2.— $2.60; 3.-6.2; 4.-5.30 5.- 
 Make the following numbers each 100 times greater 
 1.- 3.18 ; 2.— 632 ; 3.— J5.39 ; 4.- 8.3 ; 6.- 0.02!5. 
 Make the following number* each 1000 times greater : 
 1. - 97 ; 2.— $24.60 ; 3.- 0.019 ; 4.- 28 ; 5— |1.05. 
 Make the following numbers 10 times smaller : 
 1.— 82; 2.-6; 3.- $518 ; 4.-0.07; 6.- f 3.00. 
 Make the following numbers 100 times smaller : 
 1.- 604 ; 2.- J5.15 ; 3.- 7.4 ; 4.- $202 ; 8.- $5.40. 
 Make the following numbers 1000 times smaller : 
 1.-1344; 2. -$33.09; 3.-14.5; 4.- 65 ; 5.- 0.0165. 
 Alake the number 15.04 : 1.— 10 times greater ; 2.— 1000 
 times smaller ; 3.— 100 times greater ; 4.— 10 times smaller ; 
 5 — 100000 times greater ; 6.— 100 times smaller. 
 
 Oral Exercisca. 
 
 1994. How many tenths in a unit 1 hundredths f 
 
 1995. How many tenths would be required to make a unit t 
 
 1996. How many hundred-thousandths would be required to make one 
 teu'thousandth ? 
 
 1997. How many thousandths in a hundredth? How many ten- 
 thousandths ? 
 
 .1998 What number of ten-thousandths will be required to make • 
 unit ? 
 
 1999. In one tenth how many thousandths ! 
 
 2000. How many thousandths in a unit I 
 
 2001. In one thousandth, how many millionthst 
 
 2002. How many ten-thousandths in one tenth t 
 
 2003. To what are one hundred tenths equal? one hundred hundredths ! 
 
 2004. How many thousandths in one thousand ? 
 
 2006. To write a thousandth, how many figures wil. be required ? 
 
 2006, How many to write a millionth ? 
 
 2007. How many figures in ten-milliouths ? in hundred-thousandths J 
 
 8 
 
•* RRDUCXrOX OF PECIMAIR. 
 
 REDUCTION OF DKCIMAIii. 
 
 126. The Reduction of Decimals is tho process of 
 changing thoir form without changing thoir value. 
 There are two cases : 
 
 1. To reduce decimals to common fractions, 
 
 2. To reduce common fractions to decimals. 
 
 126. Case I. To reduce a decimal to a common fraction. 
 Example. Reduce .75 to a common fraction. 
 Solution. .75 expressed as a common fraction, is j'j*,, which 
 
 reduced to its lowest terms equals j. Hence 
 
 127. "Ryile.— Write the denominator under the decimal 
 omitting the decimal point, and reduce the fraction to ite 
 lowest terms. 
 
 ■e«lnee the following a«eim«la to common ^^aetlonst 
 
 2008. .46 2013. 9.48 
 
 2009. .60 2014. 18.726 
 
 2010. .48 2016. .076 
 
 2011. .180 2016. .0826 
 
 . 2012. .0176 2017. .01026 
 
 128. Case II. To reduce a common fraction to a decimal 
 Example. Keduce ^ to a decimal. 
 
 Soliitiou. 8 = 4 of 8. 8 equals 80 tenths, and i of 30 tenths is 8 
 tenths and 6 tenths remaining. 6 tenths equal 60 hundredths^ and | of 
 60 hundredths is 7 liundredths and 4 hundredths remaining. 4 
 hundredths equal 40 thousandths, i of 40 thousandths is 6 thousandths • 
 therefore i=.675. Hence the 
 
 129. Rule.— 1. Annex ciphers to the numerator and divide 
 by the denominator ; 
 
 2. Point off as many places in the quotient as there are 
 ciphers annexed. 
 
 Rmlnee the followlns eommon A«etloiu «• declnuUs i 
 2018. i 2023. ^ 
 
 S - 3024. ^^ 
 
 ; 2025. II 
 
 * 2020. 11 
 
 2019. 
 2020. 
 2021. 
 2022. 
 
 2027. 
 
ADDITION OP DECIMAIJS. 
 
 96 
 
 Example. Required the sum of 23.04. 675 63" and 
 7509.857. 
 
 Opkuation. 
 Solution. Write the numbers so that the figures of •>.•} 04 
 the sauie onler stand iu the same column, and proceed as «r5 «.r» 
 in the a.idition of whole numbers. 75(i9.857 
 
 8208.529 
 
 130. Rule.— 1. Write the nmib^ra so that the units of tfie 
 tame order shall atand in the mine column ; 
 
 2. Add, as in whole numbers, placi„si the decimal point at 
 Its proper place in the num. 
 
 KxprriHeN. 
 
 2028. 
 
 0.8 
 0.2 
 0.4 
 0.01 
 
 Aus. 
 
 2029. 
 
 0.715 
 1.20 
 3.5 
 1.07 
 
 2030. 
 
 Ads. 
 
 4 21 
 0.352 
 2.2 
 0.4012 
 
 A US. 
 
 2031. 
 
 0.12015 
 3.022 
 15.0254 
 0.3503 
 
 Ans. 
 
 2032. 
 
 32 
 0.40 
 0.102 
 0.226 
 
 2033. 
 
 Ans. 
 
 0.700 
 
 0.210 
 
 0.342 
 
 12.025 
 
 Ans. 
 
 2034. 
 
 0.923 I 2035. 0.003 
 
 5.007 
 
 0.05 
 
 !.:003 
 
 An.s. 
 
 0.06009 
 213.4 
 0.1215 
 
 Ans. 
 
 2036. 0.4964-0.03+0.1816+0.074 0.18. 
 
 2037. 0.02+0.108+0.316+0.24+0.007. 
 
 2038. 0.2801+0.0034+0.0025+0.7. 
 
 2039. 0.05072+0.5072+0.072+0.65. 
 
 2040. 0.2302+0.91402+0.702+0.08. 
 
 2041. 0.1023+0.83+0.00442+0.7+0.954. 
 
 2042. 0.90086+0.121+0 21+0.12115+0.82. 
 
 2043. O.24O.2I+O.2I6+O.2OI5-O.OOO453I0.04. 
 
 2044. 0.0024+0.64121^0.0032+0.203-0.76^0.03. 
 
 2045. 12.025+4.25+4.003+218.4^57.10032^3 09 
 8046. 247.07+76.295+7849.089+84676.007. 
 
96 
 
 AnniTION OF DK< IMALS. 
 
 2047. 3.0025 f 32.4053 i 313.006 tl7S. 17 f 11213.7. 
 
 204S. 23.45RO(i7f0.4()"8ft f ir.2204 ; 27,1 j-0.003. 
 
 204D. 4754 807 t 29.006 f 671*387.07 + 84690.695 + 757878.454 -f 
 
 68U374.2 
 
 7.0. 
 
 2050. 40.87 J f{75.755 -f 74781.38!) f- 897576.5 + 49854.354 + 
 
 07ti4Sl> «75. 
 
 2051. 4877tJ.37 f- 84.35 + 7409.879 + 489374.207 + 684978.054 + 
 
 97.95. 
 
 2052. 687.85 ; 078798.475 f 705875.809 + 74297.75 + 397689.876 + 
 
 79787.705. 
 
 2053. 8.45 -f 7509,875 -\ 870474.709 + 97895.395 4- 789784.7 + 
 
 895887.870. 
 
 2064. Add together 25 and 4 tenths, 1205 and 6 tenths, 9 and 52 
 thousandths, fifty and 19 hun.lr.Hlths. 104 and 2 hundred-thouHandths. 
 
 2055. Add 3 and 25 thousandths, 1075 and 45 hundredths. 90 and 
 482 thousindths. 
 
 2050. Find the sum ofl2025 and 8 tenths, 5702 and 44 thousandths. 
 77and HOthousundths. 
 
 2057. What 38 the total of 17 hundred-thousandths, 600 ten-thou- 
 saudthM 2303 thousandfh.s. 15 ten-thousandths, 37 hundredths, nineand 
 45 nuiidred-thousaiidths, 1 and 91008 .en-thousandths ? 
 
 2058. Find the total of 1023 ten-thousandths, 21 hundred-thousandths. 
 96 thousandths, 9 thousandths, and 1032 hundred-thousandths 
 
 , JJ^^'.^f*"'* " *^' '""" °^ *^ ""^ ^ hundredths, 104 and 8 tenths. 
 1003 and 25 thousandths, 7 and 1038 ten-thousandths ? 
 
 2000. Add 814 and 27 hundredths, 12 and 704 thousandths, 1003 and 
 4 tenths, and 57 and 1004 ten-thousandths. 
 
 2001. Find the sum of 113 and 25 hundredths, 12915 and 423 ten- 
 thousandths, and 45 and 2131 hundred-thousandths. 
 
 2002. WJiat is the sum of 507 ten-thousandths, 12 and 2131 ten- 
 thousivndths, 452 and 233 hundred-thousandths, 5 and 36 hundre<lths ? 
 
 50fi?r •f;-^\f"^'^'',o" """^ ^ t<-'"th8.305 and 4 ten-thousandths, 
 66678 milhontiis, and 12780 and 125 thoasaudths 
 
 2004. What is the total of 1130 and 42 tenths, ioo hundredth.. 10503 
 teu-thoHsandths. and 78 and 710003 millionths ? 
 
 2005. Find the sum of 1203 thousandths. 1003 and 70 tenths. 78I0and 
 845 ten-millionths. and 37 and 302 hundredths. 
 
757878.454 I- 
 154.354 f 
 584078.064-I. 
 »97«89.876 + 
 
 89784.7 -f 
 
 ths, 9 nnd 52 
 aiiHaiKlths. 
 idths, 96 and 
 
 thousandths, 
 
 '00 tcii-thou- 
 ths, nine and 
 
 thousandths, 
 
 ths. 
 
 tnd 8 tenths, 
 
 >s, 1003 nnd 
 
 ind 423 ten- 
 
 1 2131 ten- 
 
 indredths ? 
 housandths, 
 
 dihs. 10563 
 
 IS, 7810 an (\ 
 
 SUBTIIACTION OF DECIMALS. 97 
 
 SUBTRACTION OP DECIMALS. 
 
 Example. Subtract 73.435 from 156.78. 
 
 Sohitiou. Place tlietenuyns for the subtraction of whole 156.78 
 
 nHiiiburs so that the units of the sunic order be in the 3nme 78.43" 
 
 coiuiiin. rinco tlie decimal point 3 figures from tlie right, 
 
 nnd the dilference is 83345 thousandths or 83.346. 83.345 
 
 131. Rule.— 1. Write Me numbers so that thejignrea of the 
 same order stand in the same column ; 
 
 2, Sidifract as in whole numbers and place the decimal 
 l>oiut in its proper place in the difference. 
 
 l-'xrr<*lii<^. 
 
 2006. 
 
 764907.05 
 
 - 87929.795 
 
 2067. 
 
 240.572 
 
 — 26,372 
 
 2063. 
 
 346176.007 
 
 - 78487.878 
 
 2069. 
 
 741 7236 
 
 — 330 6126 
 
 2070." 
 
 656450. 0.';4 
 
 - 78677.09 
 
 2071. 
 
 702.432 
 
 — 601.53 
 
 2072. 
 
 376570.005 
 
 - 87745.15 
 
 2073. 
 
 9S7.5293 
 
 — 983.4193 
 
 2074. 
 
 7r.2475.754 
 
 — 89287.95 
 
 2075. 
 
 5.86196 
 
 — 5.7C006 
 
 2076. 
 
 897450.07 
 
 — 98776.C95 
 
 2077. 
 
 87.5009 
 
 — 13.916 
 
 2078. 
 
 423750.5 
 
 — 66879.75 
 
 2079. 
 
 27.72369 
 
 — 7.72138 
 
 2080. 
 
 350842.25 
 
 — 47974.745 
 
 2081. 
 
 246.72361 
 
 — 127.9506 
 
 2082. 
 
 75J754.7 
 
 - 37679.25 
 
 2083. 
 
 5.80106 
 
 — 2.59 
 
 2084. 
 
 267475.75 
 
 — 79757.975 
 
 2085. 
 
 37.52 
 
 — 18.642 
 
 2086. 
 
 764704.23 
 
 — 87957.747 
 
 2087. 
 
 27 .132086 
 
 — 19.8421 
 
 2U88. 
 
 465742.5 
 
 — 98298.25 
 
 2089. 
 
 1.3 
 
 — 1.2456 
 
 2090. 
 
 576^27.0 
 
 — 89550.957 
 
 2091. 
 
 47.006 
 
 — 46.29864 
 
 2092. 
 
 654652.5 
 
 — 73475.76 
 
«8 
 
 sunrnACTioN of dec imals. 
 
 2098. 
 
 51.019 
 
 17.02984 
 
 2094. 
 
 • 843276.75 
 
 - 77787.985 
 
 2095. 
 
 387. 
 
 — 300.6721 
 
 2096.- 
 
 357402.5 
 
 — 69776.756 
 
 2097. 
 
 4.16019(5 
 
 4.06309 
 
 2098. 
 
 654565.5 
 
 - 78749.895 
 
 2099. 
 
 0.00831 
 
 0.0077 
 
 2100. 
 
 467517.5 
 
 - 89349.756 
 
 2101. 
 
 23.501006 
 
 9.4619 
 
 2102. 
 
 489476.376 
 
 — 4787.45 
 
 2103. 
 
 6.1 
 
 — 0.011196 
 
 2104. 
 
 467465.75 
 
 — 8234.975 
 
 2105. 
 
 0.7002 
 
 0.56203 
 
 2106. 
 
 748760.4 
 
 — 27'>429.75 
 
 2107. 
 
 112.023 
 
 — 91.90909 
 
 2108. 
 
 476435.5 
 
 — 285489.875 
 
 2109. 
 
 0.5 
 
 0.0006 
 
 2110. 
 
 378989,01 
 
 - 189471.875 
 
 2111. 
 
 37. 
 
 — 0.02345 
 
 2112. 
 
 641764.05 
 
 - 576376.476 
 
 2113. 
 
 0.00235 
 
 — 0.000139 
 
 2114. 
 
 8/0079.04 
 
 — 19878f 958 
 
 2115. 
 
 0.1 
 
 — 0.019 
 
 2116. 
 
 678576.5 
 
 — 289709.769 
 
 2117. 
 
 0.023 
 
 — 0.007412 
 
 2118. 
 
 487854.5 
 
 — 198965.428 
 
 2119. 
 
 45.00035 
 
 39.000419 
 
 2120. 
 
 745600.05 
 
 - 87740.276 
 
 2121. 
 
 477456.72 
 
 - 98748.809 
 
 2122. 
 
 789576.5 
 
 — 99767.357 
 
 2123. 
 
 742576.853 
 
 — 179407.07 
 
 2124. 
 
 754252.5 
 
 — 272189.756 
 
 2126. What must be added to eighty-three units and four thousand 
 cue hundred and ninety-three hundred-thousandths, to have nine 
 hundred and eighty-seven and fifty-two thousand nine hundred and 
 twenty hundred-thousandths ? 
 
 2126. Diminish three hundred units and twenty-three ten-thousandths 
 by twenty-seven and nine hundredths. 
 
 2127. Subtract fifty-seven and fifty-three thousandths from ouo 
 fine hundred and two hundred and nineteen hundred-thousandths. 
 
 2131. 
 
 2132. 
 
 2133. 
 
 2134. 
 
 2135. 
 
 2136. 
 
 2137. 
 
 2138. 
 
 2139. 
 
 2140. 
 
 2141. 
 
 2142. 
 
 2143. 
 
 2144. 
 
 2146. 
 
Mt'LTIl'LirATION' OF DECIMALS. 
 
 M 
 
 2128. How much do three huudrod and forty-five and seventy-two 
 thousand three hundred and sixty-one hundred-thousandths, exceed three 
 hundred and forty-four and eight- thoasand two hundred and three ten- 
 tliousandths ? 
 
 2129. What remains when seven ty-six tenths are diminished by seventy- 
 six thousandths ? " 
 
 2130. How much greater are two hundred and thirty-seven and seven 
 hundred and two hundred-thousandths than one hundred and thirty-six 
 and twenty-five millionths ? 
 
 MULTIPLICATION OP DEC ^ALS. 
 
 Example. Find the product of 48.5 by 6.23. 
 
 Solution. We multiply as in whole numbers, and if the 
 multiplicand alone were tenths the answer would be 30215.5, 
 but since the multiplier is also hundredths, the product is one' 
 hundredth of 30215.5, which by moving the decimal point two 
 places to the left becomes 302.155. Hence the 
 
 48.5 
 8.23 
 
 1455 
 970 
 2910 
 
 302.155 
 
 I' thousand 
 
 have nine 
 
 indred and 
 
 hons^ndths 
 
 from one 
 Ithfl. 
 
 132. Rule.— Multij)Iy as in whole numhers andpoinloffas 
 many decimal places in the product as there are decimals in 
 both multiplicand and multiplier, prefixing ciphers if necessary. 
 
 2131. 
 
 787254 
 
 2132. 
 
 765679 
 
 2133. 
 
 794377 
 
 2134. 
 
 487789. 
 
 2135. 
 
 883749. 
 
 2136. 
 
 3548S5. 
 
 2137. 
 
 79.5678. 
 
 2138. 
 
 287407. 
 
 2139. 
 
 198793. 
 
 2140. 
 
 25490. 
 
 2141. 
 
 647y72. 
 
 2142. 
 
 47907. 
 
 2143. 
 
 774357. 
 
 2144. 
 
 567800. 
 
 2146. 
 
 980017. 
 
 .25 X 
 '.854 X 
 225 X 
 095 X 
 .005 X 
 .27 X 
 ,745 X 
 ,617 X 
 ,001 X 
 005 X 
 829 X 
 853 X 
 907 X 
 004 X 
 004 X 
 
 Exercises. 
 
 74 
 
 2146. 
 
 78 
 
 2147. 
 
 69 
 
 2148. 
 
 57 
 
 2149. 
 
 89 
 
 2150. 
 
 459 
 
 2151. 
 
 766 
 
 2152. 
 
 897 
 
 2153. 
 
 974 
 
 2154. 
 
 678 
 
 2155. 
 
 984 
 
 2156. 
 
 685 
 
 2157. 
 
 668 
 
 2158 
 
 786 
 
 2159. 
 
 678 
 
 2160. 
 
 764527 
 
 176986 
 
 149653 
 
 239576 
 
 690523 
 
 470075 
 
 450845, 
 
 705496, 
 
 970075. 
 
 845974 
 
 943766. 
 
 345678. 
 
 745643. 
 
 645676 
 
 937004 
 
 .907 X 
 i.4C5 X 
 ,805 X 
 003 X 
 414 X 
 237 X 
 74 X 
 855 X 
 
 08£ 
 
 075 
 
 45 
 
 075 
 
 25 
 
 X 
 
 V 
 X 
 X 
 X 
 X 
 X 
 
 679 
 
 8479 
 
 4987 
 
 7968 
 
 47907 
 
 89423 
 
 47496 
 
 9496 
 
 79826 
 
 20327 
 
 87048 
 
 44695 
 
 84796 
 
 29.125 
 
 9.876 
 
100 
 
 MULTIPLICATION OF PECIMALS. 
 
 2161. 
 
 674347 
 
 X 154.7 
 
 2193. 
 
 0.79646 
 
 2162. 
 
 471089 
 
 X 9-765 
 
 2194. 
 
 0.45654 
 
 2163. 
 
 345807 
 
 X 29.026 
 
 2195. 
 
 0.3747 
 
 2164. 
 
 674257 
 
 X 49.054 
 
 2196. 
 
 7.4748 
 
 2165. 
 
 647835 
 
 X 42.05 
 
 2197. 
 
 0.9876 
 
 2166. 
 
 980075 
 
 X 547.076 
 
 2198. 
 
 8.07594 
 
 2167. 
 
 975687 
 
 X 906.078 
 
 2199. 
 
 0.6632 
 
 2168. 
 
 547374 
 
 X 700.09 
 
 2200. 
 
 0.0797 
 
 2169. 
 
 856374 
 
 X 696.007 
 
 2201. 
 
 0.4356 
 
 2170. 
 
 937095 
 
 X 670^07 
 
 2202. 
 
 8.907 
 
 2171. 
 
 534624 
 
 X 53.076 
 
 2203. 
 
 5.045 
 
 2172. 
 
 950357 
 
 X 149.078 
 
 2204. 
 
 9.565 
 
 2173. 
 
 453089 
 
 X 7808 
 
 2205. 
 
 6.426 
 
 2174. 
 
 789376 
 
 X 764.576 
 
 2206. 
 
 2.6789 
 
 2175. 
 
 687009 
 
 X 87.870 
 
 2207. 
 
 4.8066 
 
 2176. 
 
 746589 
 
 X 698.765 
 
 2208. 
 
 7.6675 
 
 2177. 
 
 859407 
 
 X 524.689 
 
 2209. 
 
 4.205 
 
 2178. 
 
 975009 
 
 X 47.007 
 
 2210. 
 
 6.4765 
 
 2179. 
 
 607456 
 
 X 874.95 
 
 2211. 
 
 808954.306 
 
 2180. 
 
 670407 
 
 X 854 354 
 
 2212. 
 
 804950.075 
 
 2181. 
 
 651476 
 
 X »7.005 
 
 2213. 
 
 764205.456 
 
 2182. 
 
 542805 
 
 X 37,450 
 
 2214. 
 
 689424.760 
 
 2183. 
 
 807904 
 
 X 752.459 
 
 2215. 
 
 547485.927 
 
 2184. 
 
 0.76425 
 
 X 0.054 
 
 2216. 
 
 589770.054 
 
 2185. 
 
 0.87665 
 
 X 0.746 
 
 2217. 
 
 579745.089 
 
 2186. 
 
 0.4896 
 
 X 0.37 
 
 2218. 
 
 879476.875 
 
 2187. 
 
 0.6646 
 
 X 0.05 
 
 2219. 
 
 474606.086 
 
 2188. 
 
 0.706 
 
 X 0.89 
 
 2220. 
 
 685467.057 
 
 2189. 
 
 0.4586 
 
 X 0.07 
 
 2221. 
 
 764562.080 
 
 2190. 
 
 0.6458 
 
 X 0.03 
 
 2222. 
 
 679406.907 
 
 2191. 
 
 0.03767 
 
 X 0.024 
 
 2223. 
 
 974354.02 
 
 2192. 
 
 0.0747 
 
 X 0.145 
 
 2224. 
 
 676489.007 
 
 X 
 
 X 
 X 
 
 X 
 X 
 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 
 X 407. 
 X 874. 
 X 307. 
 
 X ». 
 
 X 6. 
 X 4. 
 X 87. 
 X 47. 
 X 47. 
 X 78 
 X 876 
 X 676 
 X 976. 
 X 847. 
 
 76 
 495 
 1.405 
 009 
 004 
 479 
 40(P4 
 .7409 
 405 
 217 
 007 
 907 
 (107 
 975 
 764 
 7475 
 805 
 005 
 09 
 54 
 06 
 07 
 225 
 009 
 96 
 05 
 09 
 04 
 47 
 007 
 25 
 
 2225. What is the proauct of twenty-three by twenty-two and thirty- 
 five ht'udi-edtiis? 
 
 2226. Multiply twenty-five and forty-three thousandths by nine and 
 two h\uidred and sixty-four thousandths. 
 
 2227. What is the product of twenty-seven and five hundred and five 
 thousandths by seventy- two hundredths ? 
 
 2228. How much are one hundred and sixteen and one hundred and 
 twenty-four ten-thousandths multiplied by thirty-four thousandths? 
 
 2229. If you multiply fifty-seven thousandths by thirteen and one 
 hundred and sixty-seven thousandths, what will be the product ? 
 
 2230. What is the result of sixty-three teu-thousuudtha multiplied by 
 seventy-two hundred thousandths ? 
 
 2231. What number do you obtain by multiplying thirty-fire 
 Inintlredths by thirty-seven millionths ? 
 
 2232. 
 2233. 
 2234. 
 2235. 
 2236. 
 2237. 
 2238. 
 2239. 
 2240. 
 2241. 
 2242. 
 2243. 
 2244. 
 2246. 
 2246. 
 
DIVISION OF DECIMALS. 
 
 101 
 
 0.85 
 
 9.75 
 
 4.495 
 
 0.405 
 
 7.009 
 
 0.004 
 
 0.479 
 
 9.4004 
 
 0.7409 
 
 9.405 
 
 3 217 
 
 3.007 
 
 7.907 
 
 3.007 
 
 4.975 
 
 3 764 
 
 9.7475 
 
 9.805 
 
 407.005 
 
 874.09 
 
 307.54 
 
 9.05 
 
 6.07 
 
 4.225 
 
 87.009 
 
 47.95 
 
 47.05 
 
 78.09 
 
 876.04 
 
 576.47 
 
 976.007 
 
 847.0 25 
 
 DIVISION OF DECIMALS. 
 
 ind thirty- 
 
 r nine and 
 
 :ed and fire 
 
 ndred and 
 idths f 
 1 and one 
 ct? 
 iltiplied by 
 
 thirty-fiye 
 
 Operation. 
 7.90(518 (3.14 
 
 628 
 1570 
 
 "mi 
 
 942 
 
 2198 
 
 2198 
 
 2.537 
 
 Example. Divide 7.96618 by 3.U. 
 
 Solution. Divide as in whole numbers and 
 the quotient is 2537 ; now since the dividend is 
 the product of the quotient and the divisor, 
 the number of decimal places in the dividend 
 must equal the number in the divisor and in the 
 quotient ; hence the number of decimals in the 
 quotient equals the number of places in the 
 dividend dimishcd by those of the divisor ; 
 there are then 5 less 2 = 3 decimal places in 
 the quotient ; the answer then is 2.537. 
 Hence the 
 
 133. Rule. Divide as in whole numbers^ and point off as 
 many decimal places in the quotient as the number of decimals 
 in the dividend exceeds the number in the divisor. 
 
 Note. — 1. When there are not so many decimals in the dividend as in 
 the divisor, annex ciphers to make the number of places equal. 
 
 2. When the number of figures in the quotient is less than the excess 
 of decimal places in the dividend OTer those in the divisor, prefix ciphers 
 to the quotient. 
 
 3. When a division has a remainder, decimals may be had in the 
 quotient by adding ciphers to the dividend and continuing the division. 
 
 Exercises. 
 
 2232. 
 
 76.04 
 
 -*- 
 
 8 
 
 2233. 
 
 89.026 
 
 .. 
 
 _ 
 
 14 
 
 2234. 
 
 74.205 
 
 _ 
 
 _ 
 
 25 
 
 2235. 
 
 45.255 
 
 - 
 
 - 
 
 15 
 
 2236, 
 
 84.015 
 
 - 
 
 - 
 
 30 
 
 2237. 
 
 195.3 
 
 _ 
 
 _ 
 
 45 
 
 2238. 
 
 87.017 
 
 - 
 
 _ 
 
 50 
 
 2239. 
 
 307.50 
 
 - 
 
 _ 
 
 12 
 
 2240. 
 
 550.85 
 
 - 
 
 - 
 
 40 
 
 2241. 
 
 635.85 
 
 - 
 
 _ 
 
 75 
 
 2242. 
 
 673.46 
 
 _ 
 
 _ 
 
 72 
 
 2243. 
 
 647.96 
 
 - 
 
 - 
 
 32 
 
 2244. 
 
 716.451 
 
 -J 
 
 _ 
 
 434 
 
 2245. 
 
 607.88 
 
 -J 
 
 - 
 
 550 
 
 2246. 
 
 745.801 
 
 . 
 
 !- 
 
 764 
 
 2247. 
 
 415.02 
 
 -»- 
 
 719 
 
 2248. 
 
 905.025 
 
 
 — 
 
 795 
 
 2249. 
 
 874.05 
 
 
 _ 
 
 978 
 
 2250. 
 
 967.85 
 
 
 _ 
 
 796 
 
 2251. 
 
 807.025 
 
 - 
 
 _ 
 
 986 
 
 2252. 
 
 60. 
 
 
 _ 
 
 0.08 
 
 2253. 
 
 144. 
 
 
 _ 
 
 0.36 
 
 2254. 
 
 216. 
 
 
 _ 
 
 0,03 
 
 2255. 
 
 525. 
 
 
 _ 
 
 0.015 
 
 2256. 
 
 672. 
 
 
 _ 
 
 0.0012 
 
 2257. 
 
 1280. 
 
 
 _ 
 
 0.32 
 
 2258. 
 
 1010. 
 
 
 _ 
 
 0.025 
 
 2259. 
 
 123. 
 
 _ 
 
 _ 
 
 1.20 
 
 22C0. 
 
 542. 
 
 
 _ 
 
 2.5 
 
 2261. 
 
 464. 
 
 -J 
 
 h 
 
 6.40 
 
102 
 
 DIVISION OF DECIMALS. 
 
 2262. 
 
 643. 
 
 22(J3. 
 
 747. 
 
 2264. 
 
 795. 
 
 2265. 
 
 875. 
 
 2266. 
 
 8945. 
 
 2267. 
 
 9764. 
 
 2268. 
 
 29754. 
 
 2269. 
 
 379745. 
 
 2270. 
 
 924807. 
 
 2271. 
 
 895476. 
 
 2272. 
 
 4205684. 
 
 2273. 
 
 7466854. 
 
 2274. 
 
 0.175 
 
 2275. 
 
 0.14 
 
 2276. 
 
 0.16 
 
 2277. 
 
 0.125 
 
 2278. 
 
 0.54 
 
 2279. 
 
 0.5406 
 
 2280. 
 
 0.3954 
 
 2281. 
 
 0.7155 
 
 2282. 
 
 0.795 
 
 2283. 
 
 0.3754 
 
 2284. 
 
 0.3217 
 
 2285. 
 
 0.5742 
 
 2286. 
 
 0..?251 
 
 2287. 
 
 0.4 
 
 2288. 
 
 0.9 
 
 2289. 
 
 0.0075 
 
 2290. 
 
 0.0025 
 
 1.60 
 
 2291. 
 
 5 2474-{- 0.72 
 
 4.5 
 
 2292. 
 
 4.7054 - 
 
 ~ 0.80.. 
 
 9.60 
 
 2293. 
 
 7524 - 
 
 4.0072 
 
 2.5 
 
 2294. 
 
 70 2J7 - 
 
 7.9 
 
 76.805 
 
 2295. 
 
 ;Vt74 - 
 
 2.819 
 
 32.005 
 
 2296. 
 
 47 1154 - 
 
 9.007 
 
 395.125 
 
 2297. 
 
 16.017 ^ 
 
 8.05 
 
 395 14 
 
 2298. 
 
 17.042 -i 
 
 9.05 
 
 79.305 
 
 2299. 
 
 54.5 -; 
 
 7.95 
 
 547.085 
 
 2300. 
 
 84.375 ^ 
 
 16..^ 
 
 !»87.675 
 
 2301. 
 
 97.6 -H 23.51 
 
 4761.25 
 
 2302. 
 
 157 050 -t 
 
 9.1 
 
 0.5 
 
 2303. 
 
 457.075 -J. 
 
 - 12.079 
 
 0.56 
 
 2304. 
 
 845.08 •+ 
 
 47.805 
 
 0.4 
 
 2305. 
 
 509.74 -+ 
 
 - 27.56 
 
 0.25 
 
 2306. 
 
 405.7 -f 
 
 79.27 
 
 0.75 
 
 2307. 
 
 817.405 -r 
 
 99.99 
 
 0.30 
 
 2308. 
 
 352.1 -^ 
 
 12.812 
 
 0.25 
 
 2309. 
 
 379.035 -{- 
 
 9.009 
 
 ,0.5 
 
 2310. 
 
 807.4 -f. 
 
 29.05 
 
 0.26 
 
 2311. 
 
 957.025 H- 
 
 17.005 
 
 0.032 
 
 2312. 
 
 6428.5 -L. 
 
 340.5 
 
 0.740 
 
 2313. 
 
 7467.08 -=- 
 
 154.4 
 
 0,7526 
 
 2314. 
 
 8421.51 H- 
 
 111.11 
 
 0.437 
 
 2315. 
 
 6703.01 -5- 
 
 201.1 
 
 0.2107 
 
 2316. 
 
 7507.4 -i- 
 
 107.6 
 
 0.105 
 
 2317. 
 
 8421.55 -:- 
 
 235.07 
 
 0.12 
 
 2318. 
 
 9205.04 ■+. 
 
 717.004 
 
 0.14 1 
 
 2319. 
 
 5412.02 -H 
 
 641.07 
 
 fivftf' "T^f^^'^y *™" "e 7 aud fifty.five hundredths contained in 
 tive thousand three hundred and fifty-five ? 
 
 2321. The product of two numbers is one hundred and eightyfive and 
 Z ? , 1^ ""? '^''''^•"'^ thousandths ; one number is one and four 
 
 lo*^^ ''^^*y"^'''*''°"^^''"'^'*»«^ what is the other number » 
 .J!;' A "":°yj'"^" '"'' y°» -«k- two and six hundredths from 
 lorty.two and eight hundred and sixty-four thou.sandths ? 
 
 2323 Divide forty-two and five tenths by fifteen and three hundred 
 and eighty-five thousandths ? "unarea 
 
 2324. The product of a multiplication is nine thousand nine hundred 
 and Beventy.four ten-thousandths and the multiplier is oneTindred a^d 
 hve thousandths. What is the multiplicand ? ""area and 
 
 2325. By what number will you divide fifty.six thousandths to have 
 one thousand four hundi-ed thousandths as quotient ? 
 
 2326 The dividend is two hundred thousandtlis and the quotieut two 
 hundredths ; wliat is the divisor ? 4"o"eui two 
 
BILLS. 
 
 103 
 
 4 
 
 ■4- 0.72 
 
 4 
 
 -J- 0.80.. 
 
 4 - 
 
 ^ 4.007-2 
 
 
 ^ 7.9 
 
 4 - 
 
 ^ 2.819 
 
 4 - 
 
 ^ 9.007 
 
 
 i- 8.05 
 
 
 i- 9.05 
 
 
 i- 7.95 
 
 
 f- 16.5 
 
 H 
 
 1- 23.51 
 
 -J 
 
 9.1 
 
 -J 
 
 <- 12.079 
 
 ~ 
 
 - 47.805 
 
 . 
 
 - 27.56 
 
 -5 
 
 - 79.27 
 
 _: 
 
 - 99.99 
 
 -i 
 
 - 12.812 
 
 _^ 
 
 9.009 
 
 — fi 
 
 - 29.05 
 
 -r 
 
 • 17.005 
 
 -1. 
 
 - 340.5 
 
 -j- 
 
 154.4 
 
 -i. 
 
 111.11 
 
 -5- 
 
 201.1 
 
 -7- 
 
 107.6 
 
 
 235.07 
 
 -»- 
 
 717.004 
 
 -1- 
 
 641.07 
 
 i C 
 
 ontained in 
 
 gh 
 
 ty-five and 
 
 01 
 
 le and four 
 
 lUI 
 
 nber » 
 
 dr 
 
 edths from 
 
 hn 
 
 36 hundred 
 
 in 
 
 s hundred 
 
 hi] 
 
 ndred and 
 
 m 
 
 s to ha>e 
 
 1« 
 
 Dtieut two 
 
 2327. By what number will yoii divide two hundredths to have a 
 quotient of two hundred-thousandths ? 
 
 2328. What is the quotient of 564 and 48 hundredths by 36 f 
 
 2329. The product of two fractions is 9, one of the factors is 1 and 8 
 tenths ; find the other. 
 
 niLi^. 
 
 134. A Bill is a memorandum of articles sold to a person 
 with their prices. 
 
 Models or Bills. 
 
 Mr. Paul R. Dillon, 
 
 Quebec, January 6, 1893. 
 Bouffht of S. P. Lf-.amy. 
 
 5 lbs. Coffee k | .86 
 
 12 «• Lard 14 
 
 4 •« Ham 12 
 
 8 " Salt Beef .10 
 
 12 " Butter 22 
 
 6 •• Cheese .16 
 
 15 " Maple Sugar .08 
 
 Seed Payt, 
 
 S. P. Leahy. 
 
 II 
 
 80 
 
 $9 56 
 
104 
 
 BILM. 
 
 Messrs. Collins tc Co., 
 
 Levis, March 6, 1893. 
 
 Bought of Stki'hrn Buos. 
 
 6 prs Men's shoes, buff. -i $1.80 
 
 6 " Lady's «• 1.2o 
 
 * " Boy's " 80 
 
 8 " Children's Laced shoos 90 
 
 6 •• Men's shoes, calf 3,50 
 
 3 '• Lady's " , buff 1.50 
 
 £ecd Fayt, 
 
 Stephen Bros. 
 
 per J. Healy, 
 
 Mr. L. T. Moors, 
 
 Montreal, January 4, 1893. 
 Bought of J. C. Hart, 
 
 7yds. Ribbon t j gl 
 
 10 " English Tweed 2.26 
 
 10 *• Merino << j yg 
 
 8 " Ked Flannel 
 
 6 " Flanders Linen 
 
 4 " Grey Cotton . 
 
 Total 
 
 .30 
 .45 
 .08 
 
 12 bush. 
 
 16 
 
 
 8 
 
 
 20 
 
 
 86 
 
 
 45 
 
 
 24 
 
 
bILLB. 
 
 lot 
 
 Mr. F. rERUY, 
 
 . Halifax, July 7, 1893. 
 EoMght o? Kdwaiid Fbaseii, 
 
 _ 6 doz. Hhubarb at $ .30 
 
 3 buucheB Radish " .40 
 
 8 •• Asparagus " .20 
 
 2 bushels Spinage " .75 
 
 4 pints Strawberries " .25 
 
 6 Cucumbers •• .05 
 
 2 bunches Carrots •« .12 
 
 2 " Turnips «« .10 
 
 Tola: 
 
 Mr. A. Pattoit, 
 
 Quebec, October 2, 1893. 
 Bougrht of Joseph McDonald, 
 
 12 bush. Oats at | .45 
 
 16 
 8 
 20 
 35 
 45 
 24 
 
 Barky No. 1 " .68 
 
 " No. 2 " .65 
 
 Peas.... " .85 
 
 Potatoes " .48 
 
 Spring Wheat " 1.09 
 
 Autumn « " 1.07 
 
 Eecd Fayt, 
 
 Joseph McDokald. 
 
 Per D. Kbabnst. 
 
100. 
 
 BILLS. 
 
 Mr. h. C. MoiMiiMsoN, 
 
 Montreal, Mny lo, 1803. 
 
 To D. R. Barrow, 
 
 Oi:. 
 
 Aj.iil 
 
 Miiy 
 
 For M. KiU, Ijf yds. Broadcloth.. . . /© 94.60 
 
 1| yds. Lining /© .35 
 
 Cut and furnisliing 
 
 6|yd8. Vei-vins, Mantle Cloth fQ) 5.10 
 
 2iyd8. Blk. Velvet, for furnishing 
 
 and collar ® 5.20 
 
 Buttons and cut 
 
 CO 
 
 40 
 
 Mr. J. A. Drayton, 
 
 Three Rivers, Sept<'uib»'r 6, 1893. 
 
 To Arthur Kelly. 
 
 Dk 
 
 Mnivli 
 
 .\|>ii) 
 
 iM;iv 
 
 20|21b8. Ginger atf .15 
 
 60 « Whiting •• .09 
 
 3bbl8. Salt •• 1.18 
 
 4J do2. Eggs «« .20 
 
 5 lbs. Butter «• .13 
 
 3 bottles Blue Ink •« ,36 
 
 4 gal. Kerosene oil •< 1.12^ 
 
 12 lbs. Soap «• .08i 
 
 5 " Valentia Graps «• .09 
 
 25 lbs Prunes •« .11 
 
 64" Cheese «« ,18 
 
 ... 
 
BILLS AND AfCOrNTS. 
 
 107 
 
 Jlr. 0. SwEBT, 
 
 Quebec. December 5, 1898. 
 To T. 0. MonRisoN, Dn. 
 
 IH6» 
 Jan. 
 
 F.b. 
 
 Jan. 
 March 
 
 To 45 lbs. Coffee at $ 40 
 
 " 18 yds. Broadcloth •• 3.50 
 
 " 30 " Meiino «« .75 
 
 Cb. 
 
 20 By 20 bush Oats at $ .45 
 
 c 
 T 
 
 Reed Payt. 
 
 T. G. MoRuisKON. 
 
 I 
 I BILLS AND ACCOUNTS. 
 
 2380. Montreal. Feb., 2nd, 1893, Mr. John Hogan bought of Mr 
 Jos. Levin, viz : 7 lbs. Chocolate at 25 cts. ; 15 lbs. Caudles at 22 cts • 
 12 lbs. White Sugiir at 15 cts.; 18 lbs. Flour at 24 cts. What is the 
 amonut of the bill ?A 
 
 "^5^1. My. John Kearney of Quebec sold to H. Perrault, Feb 6th • 
 18 yds. Lace at $2.45 ; 5 pairs Kid Gloves at 45 cts. ; 12 Ladies Fans at 
 70 cts.; 2 Lace Curtoins at 55 eta.; 4 doi. Lamb Skins at 25 cts i«r 
 pair ; 12 Needle Cases at 24 cts. What> the amount of his i.urchase (^ 
 
 2382. Feb. 24th, A. Orsali bought oi^. Kearney ; 2 doz. Colored 
 Shirts at 17.80 ; 3 doz. Handkerchiefs at |4.40 ; IJ doz. Neok-tiesat 
 •3.40 ; i doz. Shirt buttons at 12* cts. apiece ; 12 yds. Uose ribbon at 
 16 cts.; lOJ yds. Cotton at 18 cts. Find the amount of tUe bill, 
 
108 
 
 8ILL8 AND ACCOUNTS. 
 
 I 
 
 It' 
 
 2333. J. Sweeney of Chicago sold J. McGee, Jan. 6th, 1893, vii : 37 
 yds. Sheeting at 26 cts;; 43 yds. Merino nt 82 ot;.; Feb. 6th: 75 yds. 
 Holland Linen at 45 cts.; 209 yds. Calico at 14 cts.; 330 yds. Wrapping 
 Linen at 16 cts. What is the footing of the bill ? 
 
 2334. Miiy 15th, 1893, C. Hart sold to E. Cadieux : 8 " Lessons in 
 English", Elementary Course, Pupil's E.lition at 25 cts.; 2 "Lessons in 
 English," Elementary Course, Teacher's Edition at 75 cts.; 6 •• Lessons in 
 English," Intermediate Course, Pupil's Edition at 40 cts.; 2 "Lessons 
 in English," Intermediate Course, Teacher's Edition at fl.OO ; 4 
 "Ijcssons in English," Sup«'rior Course, Pupil's E'lition at 60 cts.; 1 
 "Lessons in English, "Suprior Course, Teacher's Edition at $1.76. Find 
 the amount of the purchase ? 
 
 2335. March 18th, 1893, Mr. F. Irwin bought of T. Love : 4 yds. 
 Silk at f3.60 ; 4i yds. Kibbon at 56 cts.; 6f yds. Serge at 72 cts ; l.\ 
 yds. Cassimere at $2.20 ; IJ yds. Blue Cloth ut §3.40 ; 8 pair Slippers 
 at 36 cts.; 2i yds. Linen at 68 cts.; If doz. Shirt Collars at 92 cts. 
 What is the amount due ? 
 
 2336. March 20th 1893, Mr. T. Doran bought of Brown Bros : 52 
 lbs. Muple Sugar at 7i cts.; 4 bbls. Flour (extra) at $7.80 ; 9i lbs 
 Cheese at 16 cts.; 15 lbs Currants at 8 cts.; 7 lbs. Black Pepper nt 
 42 cts.; 20 lbs Butter at 24 cts.; IJ bush. Peas at 70 cts.; 3 bush. 
 Beans at $1.10 ; 14i lbs Ham at 16 ; What is the amount of the bill ? 
 
 2337. Mrs. Jas. Shea bought of Messrs Duggitn Bros, on May 21 : 1 paii 
 Black Socks at $1.07. July 2ud, 2 pair Hunting Shoes at $2.90. Sept. 
 10th, 2 pair Gaiters at $1.80 ; 1 pair English Laced Slioes at $1.30. 
 What is the amount of the bill ? 
 
 2338. Mr. T. O'Connor sold M. Fanning as follows ; March 9th, 
 1893, 15 pair Hunting Shoes at $3.75 ; 8 pair Woolen Socks at 86 cts. 
 April 17th, 12 pair Gaiters at $2 72. March 26th, M. Fanning gave in 
 payment: 12 bbls. Apples at $3.15; April 25th, $10.50 cash. How 
 much does he still owe ? 
 
 2339. C. Hart sold W. O'Brien as follows : May 3rd 1893, 15 lbs. 
 White Sugar at 14 cts.; 7 lbs. of Butter at 18 cts.; 4 gals. Petroleum 
 oil at 45 cts.; 7i lbs. Coffee at 32 cts.; 12 lbs. Rice at 7i cts.; 9 lbs. 
 Tea at 48 cts.; 6 bbls. Apples at $1.80 ; 20 gals. Syrup at 72 cts.; 1 bag 
 Salt at 37 cts. ; 15 lbs. Prunes at 8 cts. What is the amount of this 
 transaction ? 
 
 2340. J. C. Kearney of Pt St. Charles soM W. C. Rogera, June 4th 
 1893 : 20 lbs. Coflfte at 24 cts.; 50 lbs. Brown Sugar at 7 cts.; 75 lbs. 
 Starch at 13 cts.; 12 gals. Syrup at 65 ots.; 90 lbs. Butter cakes at 9 
 cts.; 54 lbs. Sweet Biscuits at 11 cts. What is the footing of ihe bill ? 
 
fttLI.8 AND ACCOUNTS. 
 
 109 
 
 1893, viz : 37 
 
 6th: 75y,U. 
 
 fila. Wrapping 
 
 1 " Lessons in 
 
 2 " Lessons in 
 6 " Lessons in 
 
 2 •• Lessons 
 at $1.00 ; 4 
 I at 60 cts.; 1 
 it 81.76. Finil 
 
 Love : 4 yds. 
 
 at 72 cts ; ].\ 
 
 > pair Slippers 
 
 lars at 92 cts. 
 
 wn Bros : 52 
 
 .80 ; 9i lbs 
 ack Pepper nt 
 cts.; 3 bush, 
 of the bill ? 
 [ay 21 : 1 paii 
 $2.90. Sept. 
 loes at f 1.30. 
 
 March 9tli, 
 ks at 86 cts. 
 iniug gave in 
 I cash. How 
 
 1893. 15 lbs. 
 3. Petroleum 
 'i cts. ; 9 lbs. 
 '2 cts.; 1 bag 
 sunt of this 
 
 frs, June 4th 
 
 cts.; 75 lbs. 
 
 er cakes at 9 
 
 5 of rlie bill ? 
 
 2341. S. Carslcy sold F. Irwin, July lUh, 1893: 5 yds, of Black 
 Cloth at 13.50 ; 1 Satin Waistcoat at |5.50 ; 3 yds. Gray Linen at 19 
 cts.; 10 yds. Gray Fringe at 68 cts.; 3 pes. Ribbon at 31 cts. ; 3 yds. 
 nik. CnHsimore at $2.25 ; 7i yds. Alpaca at 55 cts.; 16 yds. Lining at 
 lojcts.; 4 skcius Silk at 54 cts. ; 4 yds. Wadding at 6 fts.; 9 yds. 
 White Flannel at 90 cts.; 2 Cravats at f 1.1 2i ; 4^ yds. Green Fasten- 
 ing at 58 cts.; 6 Collar Shirts at 15^ eta. What is the amount of the 
 fn voice t 
 
 2342. March 10th, 1893, A. Howard sold C. Cunningham : 18 lbs. 
 Tobacco at 32 cts. ; 25 lbs. Powdered Tobacco at 40 cts. ; 72 lbs. Tobaci-o 
 in leaves at 18 cts.; 54 lbs. White Sugar at 12 cts.; 20 lbs. Soup at 
 14 cts.; 45 gals. Molasses at 37 cts. April 8th, ho received in payment 
 $3.00. What amount remains due I 
 
 2343. June 5th, P. McKenna bought of Hart k Tuckwell of Mont- 
 real : 32 bis. Apples at $'.^.95; 56 cases Oranges at |2.25 ; 16 cases 
 I.rf>mons at $1.80 ; 40 boxes Raisins at $2.75 ; 20 boxes Figs at $1.04). 
 What is the amonnt of the bill ? 
 
 2344. May, 20th, 1893, W. Rogers of Ottawa sold J. J. McGee : 40 
 lbs. of Sugar at 7 cts.; 15 lbs. Coffee at 36 cts.; 76 bush. Potatoes at 45 
 cts.; 12^ gals. Syrup at 40 cts.; 95 lbs. Sugar Biscuits at 8 cts. What 
 was the amount of the sale ? 
 
 2345. On Feb. 4th, 1893. Mr. G. Harris bought of A. L. Fortier : 
 17 yds. Broadcloth at $5.25 ; Feb. 15th, 29 yds Cassimere at $1 . 62 ; 
 March 18th, 60 yds. Linen at 17 cts.; March 14th, 49 yds. Canvas at 
 27 cts.; the 15th, 18 yds. Blue Cloth at $3.19 ; July 17th, 27 yds. 
 Grey Cloth at $2.75 ; Sept. 3rd, 75 yds. Red Flannel at 61 cts. Mr. 
 Hnnis gave on account : Feb. 28th, 1893, Cash $83 ; July 25th. 14 bis. 
 of Flour at $7.20. Having settled on Sept. 4th, what was the balance 
 due ? 
 
 2346. January 10th 1894, A. Richards sold to S. V. Poston : 174^ lbs. 
 Quinquina at 60 cts.; 321^ Gum lacque at $1.45 ; 607^ lbs. Rhubarb at 
 $2 90 ; 720 lbs. Gum Arabic at 25 cts.; 509^ lbs. Sassafras at 15jt cts. 
 What is the amount Oi the sale t 
 
 2347. April 15th, 1893, Mr. H. Farrel bought of Oi-sali O'Hara : 8 
 spools White Thread at 7 cts.; 6i yds. Merino at $1.08 ; 7^ yds. 
 Prints at 15 cts.; Cloth and Lining for coat $7.60 ; IJ yds. Cassimere 
 for pants at $3.12 ; Lining for imnts 37 cts.; 18^ yds. Irish Linen at 
 52 eta.; 3 yds. Green Ribbon at 35 gts.; what was the ainoant of tha 
 purchase ? 
 
 2348. Sold by D. Raymond to M. A. Scott. August 28th, 1893 ; 12 
 Jbs. Brazilian Colfeu at 37i cts.; 9 lbs. Oreeu Tea at 66 cts.; 2 boxes 
 
llO 
 
 BItL« AND ACOOUlfTI. 
 
 rii'volate 70 Ibi. at 22 cU.; 2 W'*"* Grapeg at |3.26 ; 26J Ibf . Porto 
 Utan fwnonadti at 7 ctt.; 34J lbs. i Herat 19 ct».; Onioua 82 ot«.; 4 
 yda. BUflk Cloth at $2.76. ; 9i yds. Belgium Linen at 27 ct».; 6 pair Kid 
 Olcves at 87 eta.; 1} doi. White Handkerchiefs at $2.16 ; what amount 
 does A. Scott owe ! 
 
 2349. On May 17th 1893, J. Hardy k Co sold to Mr. P. X. Burns, 
 the following : 2} doz. Common Glasses at 40 cts. ; 1^ doz. Blue Plates at 
 76cts.; 3 gals. Honey at 90 cts.; i gal. Molasses at 46 cts.; 3i gnls. 
 Linseed Oil at fl .26 ; 16 lbs. Cheese at 18 cts. ; 4 lbs. Salmon at 12 cts. ; 
 i doz. Bottles Olive oil at 66 cts. each ; 2 lbs. Pepper at 45 cts ; 12 lbs. 
 Fresh Butter at 26 cts.; 74 lbs Pork Chops at 10 cts.; find the amount 
 of this sale ? 
 
 2360. bold by L. Gingras to Madam H. Smith, Juue 20th 1893 : 
 6 lb». Coffee at 32 cU.; 7 lbs. Sugar at 8 cts.; Pepi>er 16 cU.; 12J 
 lbs. Maple Sugar at 10 cts.; i lb. Tea at 64cto.; IJ gals Syrup at 
 70 cU.; 4 bush. Dry Apple* at f2.12 ; 1^ doz. Small Plates at 48 cts.; 
 H lbs. Bice at 6 cts. ; 6 lbs. Black Tea at 56 cts. ; 8 Tablets Perfumed 
 Soap at 8 cts. ; 20 lbs. Mackerel at 9} cts. ; 6 lbs. Candy at 22^ cts. ; 
 find the amount of the sale ? 
 
 2351. May 9th 1893, T. Lynch k Co. sold to J. Conlon : 14 yds. 
 Heavy Cloth at $3.60; 18 yds. Satin at fl.l2i ; 24 yds. Merino at 
 f 1.90 ; 48 yds. Cassimere ot $1.87i ; «* yds. Colored Flannel at 76 cts. 
 Find the amount of the bill ? 
 
 2352. June 10th 1893, J. 0. Kearney bought of J. Sweeney the 
 following articles : 7 J lbs. Green Tea at 85 cts. ; 14^ lbs. Black Tea at 
 46 cts.; lOf lbs. Pepper at 64 cts.; 21 lbs. Common Tea at |1. 07 ; 19 
 lbs. Superior Tea at f 1.60 ; ]8i lbs. Soo-Choo Tea at 96 cts. What is 
 fbeamonnt of the bill ? 
 
 2353. W. O'Brien owes M. R. Sullivan for merchandise : July 16th 
 1893, 8 gross Shirt Buttons at 86 cts.; July 17th 1893, 16 d'^/ Woolen 
 Stockings at |3.l8i ; July 17 1893, 3 doz. Shirt Front* Ht 6r.i5 , 
 August 2nd, 1893, 12J yds. Ribbon at 27 cts.; 30 pair Glove »t O'-.aln , 
 4 doz. Napkins at $2.85 ; 22J yds. Ticking at 46 cts. Find the 
 amount I 
 
 2364. R. O'Neil sold to J. Sweeney, July 11th 1893 : 478 gals. 
 Alt«'aat92ct8.; 308i gals. Old Rum at |1.85 ; 610| gaU. Holland 
 Oint ti 12; August 6th, 207j gals. Rum at |1.80 ; 119i gals. 
 Coji'-w. -.i-i; .•*-,». 22nd= 401 gals. SootohQin at f 1.05. Received 
 inpay»e:,, (V*. ^th, 30 bbls. Salmon atf8.75 ; Nov. 6th, Checque 
 onM-^n: Vi- 3«,Ak for|70 ; 'f^^. gist, C^hf600, Whst amount remaini 
 4a« \o Jl, Q'is M I 
 
BILU AND ACCOrSTI. 
 
 Ill 
 
 5| Ibi. Porto 
 us 82 ct«. ; 4 
 
 I.; 6 pair Kid 
 ihtkt amount 
 
 f. X. Burns, 
 lue Plates at 
 8.; Signls. 
 m at 12ct8.; 
 Ota ; 12 lbs. 
 the amount 
 
 20th 1893 : 
 15cts.: 12i 
 kls Syrup at 
 s at 48 cts. ; 
 a Perfumed 
 at 22^ cts.; 
 
 >a : 14 yds. 
 . Merino at 
 3l at 75 cts. 
 
 2355. June 18th 1803, C. WiUon bought of P. Dowi s : IJ lb. 
 Red Radish at 75 cts.; 14 oz. Pepper at 5 cts.; 5 oz. Cucumbers at 9 
 cts.; 8| oz. Lettuce at 12 cts.; 19 oz. Onions at 10 cts,; 6 oz. Asparagus 
 at fl cts. ; 8 oi. Carrots at 6J. What is the amount of the bill I 
 
 2356. Roes k Co.. of Montreal sold to E. McMillan, Quebec : 
 March Jii'l, 1893, n)pr. Men s Calf Boots at $3.75 ; 28 pr. Boots, 
 Chihlrtu's at 8fl cts.; March 15tli, 40 pr. Slippers at 85 cts,; April 3rd 
 M(u'sSiipp«i • at fl.16 ; April 3rd, 120 pr. Ladies Laced Bouts ot ?1. 25. 
 H<' ,:oeivcd in payment : Nov. 27th, Cash f280 ; April 15th, 110 cases 
 L> uiuns at $3.20. What amount remains due to Hoss & Co. 
 
 2357. July 4th, 1893, R. Powei of Quebec sold to C. Jones : 23 yds. 
 Silk at 95 cts.; 15 yds. Ribbon ot 45 cts.; 12 yds. Muslin at 18 cts.; 
 July 10th, 4 yds. Blue Cloth at |3.60 ; 3 yds. Bik. Cloth at f4.50 ; 9 
 yds. Satin at 11.25 : 1 Cravat |1. 30 ; Aug. 15th, 5 pair Calf Boots at 
 18.50; 3 doz. Sleeves at $2.40; 1 doz. Buttons 50 cts. On this, 
 imymeut was made as follows : July 20th, 8 bbls. Apples at $3.20 ; 15 
 bush. Potatoes at 22 cts.; Aug. 20tb, Cash $7.80. When the account 
 was settled, what balance was due t 
 
 2358. L. O'E/me of Pt. St Charles sold toO. Taylor : 50 lbs. Maple 
 Sugar at 7 cts. ; 75 lbs. White Sugar at 13 tts. ; 20 lbs. Coffee at 24 cts. ; 
 IS gals. Syrup at 66 cts. ; «0 lbs. Sweet Biscuits at 9 cts. ; 64 lbs. 
 Bttttai Biwjults at 11 ots. What is the amount of 0. Taylor's bill I 
 
 weeney the 
 lack Tea at 
 t$1.07 ; 19 
 I. What is 
 
 : July 16th 
 lo/ Woolen 
 
 a ttb .r»f. ''5 , 
 
 it ^i.al A. 
 
 Find the 
 
 : 473 gals. 
 B. Holland 
 119i gals. 
 Received 
 1, Cheoqua 
 int renuini 
 
112 
 
 MI8CKLLANE0US PBOOLEUa. 
 
 MISCELLANEOUS PROBLEMS. 
 
 2359. A fruit merchant sold 4000 apples during a week ; at the rate 
 of 10 appk-s for 5 cts ; find the amount of the receipts ? 
 
 23C0. Henry gave § of 33 oranges to his sister ; how many had he 
 roniniiiing ? 
 
 2301. A merchant sold 4910 yds of cotton, what did he gain, al the 
 late of $2.06 on every 100 yds. 
 
 2302. We received cases of merchandise each weighing 852 lbs 
 inchuling the boxes ; what is the net weight of the 6 cases of merchan- 
 di.se knowing that each box weighs 70 lbs ? 
 
 2303. Reduce 10| units to an improper fraction. 
 
 2304. When 740 eggs cost $7.40, how many dozen can be purchased 
 with S2.28 ? 
 
 2305. If to pay 3 loaves weighing 4 lbs each, at the rate of 3 cts. a 
 l>ound, you ^ve a baker a 25 cent-piece and an other of 60 cts. ; how 
 much change will you receive ? 
 
 2366. A wire 18 yards long is to be employed to make points, each 
 point is 9 lines long ; how many dozen points can be made ? 
 
 2307. A man having 50 sheep, sells J of them and then buys 32 
 otliers ; hoAv many has he now ? 
 
 2368. 1 bought 10 dozen hats at $2.76 each. 1 gave in payment 40 
 yards of cloth at $2.50 a yard. How much do I still owe ? 
 
 2369. A crockery dealer buys 3600 plates for $140, transportation costs, 
 $3.00 and commission $1.20 ; what will be his profit if he seUa them at 
 the rate of 100 for $5.10? 
 
 2370. How many units are contained in the fraction ijf* I 
 
 2371. Thirteen barrels of wine cost $636, $190 were paid for duty and 
 §54 for transportation. How much should I sell it a pint to gain $146 on 
 llie whole, knowing that a barrel contains 30 gallons? 
 
 2372. A person bought 16 dozen pencils at 9 cts. a dozen ; what is 
 his gain if he sells them at one cent apiece ? 
 
 2373. I bought certain goods for $152. If I had sold them $8.00 more 
 I would have gained $12. How much did I sell them for ? 
 
 2374. Reduce to the same denominator J, ^and ^. 
 
 237.'». Seven heii-s are to share in a donation of $8689 ; two of them 
 give iheif part to 24 oi-phans. How much will each orphan receive ? 
 
 2376. A Father was 48 years old when his son was bom, and 62 years 
 old at the birth of his daughter ; what will be the age of the father and 
 daughter when the sou is 16 years old ? 
 
MIROELLAKROrS PnOBLKMS. 
 
 118 
 
 ; at the rate 
 
 aauy had he 
 
 gain, at the 
 
 ling 852 lbs 
 ) of merchau- 
 
 be purchased 
 
 ate of 3 cts. a 
 ) cts. ; how 
 
 points, each 
 ? 
 lieu buys 32 
 
 payment 40 
 
 rtation costs, 
 sells them at 
 
 I 
 
 for duty and 
 i^in$146ou 
 
 m ; what is 
 
 18.00 more 
 
 vo of them 
 ceive ? 
 nd 62 years 
 > father and 
 
 8377. A woikmau gained $30.25 in 75 days. How much would he 
 have received, had he worked 15 days less ? 
 
 2378. James gave $70 for a watch, and ^ of this sum for a chain ; and 
 he sold the two for $90. How much did he lose ? 
 
 2379. When 10 shirts are bought for $3.50; how much should each 
 shirt be sold to gain 90 cts. on the whole ? 
 
 2380. The sum of two numbers is 1439 and their difference 318. What 
 are the two numbers t 
 
 2381. Two men working together during 30 days gained $72 ; one of 
 them gains, $1.25 a day ; how much does the other gain ? 
 
 2382. Nellie had $360 ; she spends ^ for a pouey, J for a watch and 
 i for a sleigh. How much has she left ? 
 
 2383. If I buy 3 oranges for 5 cts. ; how many could I purchase for 
 $1.90? 
 
 2384. A gentleman boards in a hotel for 80 cts. a day ; how many 
 weeks did he remain knowing that he paid $44.80 ? 
 
 2385. 1 bought 3546 oranges at 2 cts. apiece ; how much will I gain 
 if 1 sell them at 30 cents a dozen ? 
 
 2386. A retail dealer bought 8 dozen of hats at $1.90 ; and givts in 
 payment 46 yards of velvet at $2.15. How much more does he owe ? 
 
 2387. Two pieces of linen cost $71.28. I sell 15 yards for $21.00 and 
 by so.doiug gain 32 cents per yard. How many yards are there in the 
 two pieces ? 
 
 2388. What is the simplest expression of }| ? 
 
 2389. The apartments of a family are composed of 4 like pieces ; one of 
 which is divided into two cabinets for the children ; the rent is $160, 
 a year what should be paid for 3 mouths ? 
 
 2390. What is the price of an orange knowing that 486 dozen cost 
 $147.80 1 
 
 2891. A workman puts 18 cents aside each day; what shall be his 
 savings at the end of 12 years, 3 of which contain 366 days and the 
 others 365 ? 
 
 2392. A bag of wheat weighing 200 lbs costs $4.50. How much should 
 I f cU it a lb. to gain 6 cts. on a pound ? 
 
 2393. Reduce to the same denominator f ^ and }f ? 
 
 2394. A man spends 10 minutes in smoking a pipe ; find how many 
 hours will he spend in a year, knowing that he smokes 3 times a day 7 
 
 2395. In a family, they eat 2 loaves of bread of 4 lbs each at 6 cts for 
 two lbs, what is the expense for bread at the end of a week of 7 days I 
 
 2396. A farmer while bringing eggs to the markets breaks 35, gives 3 
 
114 
 
 UlNOELtAKEOUB FBOBLEUS. 
 
 11^ 
 
 to the poop, and sells 7 dozen on the way and arrives with 476 ; how 
 many had he when he started ? 
 
 2397. A farmer starts out with 480 eggs ; he breaks 27 and sells 6 
 dozen on the way ; how many had he when he arrived at the market ? 
 
 2398. Two persons start (he same day ; one from Quebec and the otliii 
 from Three Rivers ; one travels 6 miles and the other 9 miles a day. 
 The distance between these two cities is 90 miles. In how many days 
 will they meet and how many miles will each have traveled ? 
 
 2399. A fruit dealer sets out with 600 oranges, he throws 42 bad ones 
 away and when he arrived at market he had 456. How many did he sell 
 on the way ? . 
 
 2400. A little boy picked | of a bushel of strawberries and sells half ol 
 them ; how many gallons has he left ? 
 
 2401. A clerk who gains $45 p«r month, was paid $315 ; how many 
 mouths remain to finish the year ? 
 
 2402. What is the salary of a clerk per year knowing that he received 
 $450 for 9 mouths ? 
 
 2403. Coude died 108 years before Florian ; Fenelon 29 years aftti 
 Conde, Bossuet 11 years before Fenelon and Florian died in 1:94. Find 
 the year of the death of each of these men. 
 
 2404. A baker wants $115 more to buy 70 bbls flour at $6.30 ; how 
 much money has he T 
 
 2406. A hatter bought 16 hats which be sells for $42 and gains 40 
 cents on each hat ; how much did a hat cost him ? 
 
 2406. A person bought a house for $10367.20, repairs amounted to 
 $637.96. For how much did he sell it knowing that he gained $392.10. 
 
 2407. From a sum of $1746, 14 sergeants took $52 each. What 
 portion of the remainder shall each soldier receive knowing that there 
 are 450 soldiers ? 
 
 2408. I wish to divide $544 between 15 persons ; if the first 7 receive 
 $24 each ; how much shall each of the remaining 8 receive ? 
 
 2409. What shall be the price of 10 dozen of penknives when 6 cost 
 $4.50? 
 
 2410. What will be the cost of 7 barrels of apples, if 2i barrels cost $9 ? 
 
 2411. How much money had John, knowing that after his parents had 
 given him ^10, he gave to 12 beggars 25 cts. each and had $21.50 
 remaiiiiug? 
 
 2412. Charles bought a piece of cloth at $2.40 a yard. In selling it 
 for $3, h I mnkes a gain of $30. What was the length of the piece ? 
 
 2413. Au individual has an annual revenue of $2630. lu 12 years 
 
MISCeLlANEOVA FRODLEMS. 
 
 115 
 
 ith 476; how 
 
 i 27 and sells Ci 
 t the market ? 
 c and the othii 
 9 miles a day. 
 •w many days 
 id ? 
 
 ft's 42 bad ones 
 lany did he sell 
 
 ud sells half ol 
 
 5 ; how many 
 
 liat he received 
 
 29 years after 
 Q 1794. Find 
 
 S6.30 ; ho^v 
 
 and gains 40 
 
 amounted to 
 ined 9392. IG. 
 
 each. What 
 ig that there 
 
 first 7 receive 
 ? 
 when 6 cost 
 
 )arrel8 cost $9 ? 
 lis parents had 
 1 had $21. 5U 
 
 In selling it 
 he piece ? 
 lu 12 years 
 
 he puts aside $8460. What were his daily expenses allowing 365 
 days for a year ? 
 
 2414. What is the cost of some goods knowing that they were sold for 
 $1600, and that if they had been sold for $175 more, the gain would 
 have bei!n $575 ? 
 
 2415. I bought 45 pieces of cloth of equal length, at $2 a yard. In 
 reselling them at $2.40 I gain $900. What is the length of each piece ? 
 
 2416. WImt sum docs Louis possess knowing that if I gave him 
 $14.50 he could pay a debt of $75.50 and would have $12.75 remaining] 
 
 2417. H. Harrington says that if his salary were augmented by $28.80, 
 lie could siKJiid $1.30 each day. Wliat is his revenue '< 
 
 2418. A furniture dealer receives 60 cases and pays $1846 for the lot. 
 .^' cost $34 each ; 20 cost $18 each. What is the price paid for the 
 rciuainder ? 
 
 2419. 50 dozen of pencils cost $6 ; how many will $5 buy ? 
 
 2420. A person bought 4 baskets of pears each of 75 dozen at 9 cents 
 a dozen ; if they are sold 14 cents a dozen, how much will be gained ? 
 
 2421 . A hundied bricks cost $5 ; what must be paid for 3 carts which 
 which contain 1380 each ? 
 
 2422. NVhat will a drummer get for selling 6 casks of wine of 85 gals, 
 each, at the rate of 80 cents for every 10 gallons sold ? 
 
 2423. If 100 needles cost 30 cents ; how many can be had for $2.40 I 
 
 2424. A fruit dealer bought 5400 lemons on condition that he would 
 receive 112 for every hundred. How many should he receive ? 
 
 2425. A traveller walks during 12 days at the rate of 16 miles a day, 
 if he wishes to retui'u iu 8 days, how mauy miles will he have to 
 travel per day ? 
 
 2426. A man travels during 32 days at the rate of 20 miles per day, 
 he wishes to recommence his voyage and take 8 days longer. At what 
 rate will he have to travel per day ? 
 
 2427. A cask was made up of 52 gals, of wine at $1.20 and 8 gals, of 
 water. What is the price of a gallon of the mixture ' 
 
 2428. What is the price of a butt of wine containing 55 gallons, 
 knowing that it is a mixture of 37i gals, at 75 cents and 17i gals, at 
 60 ceuts ? 
 
 2429. What is the price of a butt of wine of 60 gallons, knowing 
 that it contains 37i gals, of wine at $0.50 and 22i gals, at $1.10 ? 
 
 2430. A merchant bought 654J yds. of cloth lor $915.99 ; 957 yds. 
 of Linen for $190.51 ; 456i yds. of Calico for $9.00 and 145Jyd8. of 
 Kibbou for $116.36. How many yards did he buy and how much did h« 
 pay? 
 
116 
 
 MISCELLANEOUS PROBLEMS. 
 
 w 
 
 2431. In a church four collections were made ; the first netted |37.00- 
 the second $9.00 more than the first ; the tliird $52 and the fourth as much 
 as the first and second together. How much money was gathered in the 
 4 collections ? 
 
 2432. A merchant bought 16 plates at 6i cts.; 24 dishes at 11 cts • 
 64 glasses at 4i cts. ; 36 decanters at 1 7 cts. ; he sells the plates at 7i cts ■ 
 the dishes at 12i cts.; the glasses at 7i cts., and the decanters at 25 cts.' 
 what will he gain on each article ? ' 
 
 2433. In a family the father receive $1.25 per day, the mother 65 
 cents ; if the expenses are $1.40 per day ; how much will be saved in a 
 month of 30 days of which 26 are working days ? 
 
 2434. What is the amount of the following bill : 17 yds. Fine Serge at 
 75 cts. ; 18 yds. of Drugget at 15 cts. ; 15 yds. Scarlet Stuff at $4.50 ; 16i 
 Menno at $4.72 ; 25| yds. Print at 36 cts ; 17 yds. Gray Stuffat$3.70 ? 
 
 2435. A work comprises 12 sheets: it each sheet cost $35 for com- 
 position and $2i for press-work ; what will 8000 copies cost ? 
 
 2436. Four persons divide $16999.50 between them, what will each 
 receive if the first gets $1157 more than the second ; and the second 
 $1249 more than the third, and the fourth $325 more than the third ? 
 
 2437. A shoemaker finishes 16 pair of shoes for $42 ; he sold half of 
 them at $2.80 a pair. How should he sell the balance to gain $5.20 
 on all ? 
 
 2438. A merchant buys nuts at 16 cts. a hundred and retails them at 
 10 for 2 cts. What will he gain daily, if he sells $14 worth ? 
 
 2439. A detachment of 15 soldiers received $14.50 for 2 days pay. 
 Another detachment received $20.80 for 13 days. How many men in the 
 last company ? 
 
 2440. A man set out on a journey and traveled at the rate of 20 miies 
 for 9 day.s, he returned at the rate of 12 miles a day. How long did he 
 take to return ? 
 
 2441. I owe $556.75 : I gave in payment 123 yds. Merino at $1 66 • 
 111 yds. Calico at 42 cts.; $184.15 Cash and the remainder in Linen at 
 • cts. a yard. How many yards of linen did I give ? 
 
 2442. May 12th, 1893, I bought of J. Kearny : 18 Ploughs at $11 ; 
 23 Saws at $3.50 ; 90 Spades at 86 cts. ; May 30th 1893, 86 Shovels at 
 50 cts.; 46 cwt. Iron at $12 ; June 7th 1898, 17 Hammers at 62 cts • 
 12^ Mill Saws at $12.12. June 7th, I paid on account $140 ; July 2nd 
 $775. What balance do I still owe ? 
 
 2443. A bookseller buys 20 reams of paper at $1.70 ; 3 dozen books 
 
 at 16 cts. each; 60 gross pens at 17 cts. ; 6 registers at 47 
 
 cts. 
 
netted $37.00; 
 burth as much 
 ithercd in the 
 
 lies at 1 1 cts. ; 
 ites at 7i cts. ; 
 ers at 25 cts. ; 
 
 ;he mother 65 
 >e saved in a 
 
 Fine Serge at 
 «$4.50; 16} 
 tuff at $3. 70? 
 ?35 for com- 
 t 
 
 liat will each 
 id the second 
 he third ? 
 e sold half of 
 ) gain $5.20 
 
 tails them at 
 
 I 
 
 2 days pay. 
 r men iu the 
 
 3 of 20 miles 
 long did he 
 
 >o at $1.66 ; 
 in Linen at 
 
 ghsat$ll ; 
 
 3 Shovels at 
 
 8 at 62 cts. ; 
 
 J July 2nd 
 
 ozcu books 
 47 cts. : 5 
 
 MISCELLANEOUS PROBLEMS. 
 
 117 
 
 dozen pencils at 1 J cts., and 28 dozen penknives at $3.20 a dozen. 
 What change should he receive on $200 ? 
 
 2444. 137 joists were sold, 43 were paid $731 ; each of the others 
 were sold for $5.50 euch less than the first lot. What was the price of one 
 of the second lot ? 
 
 2445. In a shop there are 40 workmen, 15 are paid $1.30 per day, 18 
 $1.05 and the otherj $1.60 ; what gain will the contractor make if he 
 receives $17660 and pays $468 for rent, the workmen being employed 
 
 for 297 days ? 
 
 2446. James bought 987 yards linen at 63 cts.; 15 pieces each of 
 93§ yards at 45 cts. ; 7 pieces each of 101 yards at 39 cts. ; he gave on 
 account 17 pieces of cloth each 24J yards at $1.95 ; 15 pieces calico 94| 
 yirdseach at 17 cts. ; the balance was paid cash, what amount was given T 
 
 2447. A contractor purchased 20 loads each of 3400 bricks at $5.10 a 
 thousand, he paid 30 cts. a thousand for transportation and 10 cts. for 
 loading. What did he spend ? 
 
 2448. A horse dealer sold horses for $44834.40 ; he lost $4.74 on each 
 horse sold, his total loss was $1478.88. How much did each horse cost t 
 
 2449. June 30, 1893, C. M. Hart, sold W. Rogers, 473 gals Alcohol at 
 95 cts. ; 308 gals Old Rhum at $1.90 ; 610 gals Holland Gin at $1.05 ; 
 Aug. 5, 207 gals Rum at $1.75 ; 119 gals Cognac at $2.10 ; Sept. 22, 
 401 gals Scotch Whisky at $1.15. Mr. Rogers has paid as follows ; Oct. 
 4, 30 brls Salmon at $8.75 ; Nov. 6, Cash $520 ; Nov. 22, a drait on 
 London at 30 days for balance. What was the amount of the draft. 
 
 2450. I had at my disposal $1139 to do a certain piece of work ; every 
 day the receipts were $79.60 and the expenses $33. How many days did 
 the money last t 
 
 2451. A speculation that was commenced with $8000 capital lasted 
 478 hours, the receipts amounted to $380 every day. What were the 
 daily expenses ? 
 
 2452. From a sum of $76366.75, $813.25 were given to the poor, each 
 of 43 persons received $247.25 ; the remainder was divided among a 
 certain number of persons each receiving $168.55. How many persons 
 
 were there 1 
 
 2453. Reduce to the same denominator the following fractious f, }, 
 
 f. rr- 
 
 2454. I owe $4867 to Thomas : I pay him at one time $3475, afterwards 
 
 I give him $950, and I sell him 10 cords of wood for $44 ; if he deducts 
 $1795 ; how much do I still owe him ? 
 2466. I mix 647 dozen of oraugcs at 15 cents with 355 dozen at 23 
 
lis 
 
 MlSCEI.LANEOl S l"nOllI,F.M8, 
 
 cents ; at what price per dozen should I sell them so as to gain S-*! 70 
 on the whole ? ■ e. v- . 
 
 2456. The daily receipts of a factorj' are $522, the expenses during 
 174 days were $7308 ; find the daily gain ? 
 
 c^lt^L ^" ?"'"^ ^* '"'''' °^ ''*"' '""'^ containing 57f gallons, 1 lost 
 51 02. 50 on the cost price of $1881. 20. At what price per gallon did 1 
 
 2458 John sold 217 riding-coats for $1844.50 ; on each coat he spent 
 §4 J7 for cloth ; 95 cents for lining and $2.08 for cutting and make up. 
 " liut did he gain on each coat ? 
 
 2450. In a family the father earns $1.50 a day, Alex earns 90 cts , 
 Henry 50 cts. and Peter 25 cts. How much do the four earn in 17 
 months, working 25 days each month ? 
 
 2460. A clerk's income amounts to $2041.75, his daily expenses are 
 «4.25; how much will he have saved if he works 3 years, of 365 d.vs 
 each ? ./ . J 
 
 2461 If a clerk received $2041.75 as salaiy for 7 months; what 
 sliouhl lie receive for a year ? 
 
 2462. A mechanic receives $45 a month as salary, suppose he dmws 
 *40o ; now much remains due on his salary for one year. 
 
 2463. If 96 eggs cost 90 cts. to a merchant who retails them at 8 for 
 10 cts. ; what would he gain on 2 bis each containing 480 ? 
 
 2464. Peter bought one dozen penknives for $5.40, if he sells them at 
 00 cts. apiece, what gain will he make on 8 penknives ? 
 
 2465. What is the amount of a bill for 27 yards Silk at $3. 75. 75 yards 
 Cloth at $2. 45 and 29 yards Velvet at $1.75? 
 
 2466. What will be the cost of 58 lbs. of Beef, if 2 lbs. cost 32 cts. ? 
 
 2467. A hoj-sedealer bought 18 horses for which he paid $50 each 28 
 at $68, 15 at §40. and 22 at $35 ; he sells 24 at $68, 21 at $70, 18 at 
 $41.20 and the remainder at $39. What is his gain ? 
 
 2468. A boy wears yearly, 3 pair of pants at $1.11, 2 coats at $3.30. 2 
 vests at 50 cents, 2 pair of shoes at $1.20, 1 hat at $1.42 and 3 pair 
 stockings at 25 ; if his father earns $1.60 per day and his mother $1 50 • 
 
 IT'V""^? '"" ''"^ ''""' *° ''°'^ '" ^'^y '^' '^^P^"^^^ of their son ? 
 ^40J. ihe Uiflerence between two numbers is 504, the smaller is 9207 
 what^would remain if from the greater you subtract 748 ? ' 
 
 2470. I sold 180 barrels of oil at $43.60 a barrel and made $1782 net 
 S:nn ; what was the price per barrel ? 
 
 «iL^"<;.'^'r '"'r o''' '"^'"'''' ^^^^- ^^' '^^' ^''' g*^"" «t °°e time 
 $1346,35 then $2346.75 ; what remains to be i>aidknowing that the 
 Ufbtof the second is $5464.80 ? e " 
 
MISCELLAKEOrs mODLKMa. 
 
 119 
 
 I gain 821.70 
 
 lenses during 
 
 gallons, 1 lost 
 gallon did I 
 
 coat he spent 
 nd make up. 
 
 irns 90 cts., 
 r earn in 17 
 
 Expenses are 
 of 365 d;iys 
 
 >nths ; what 
 
 le he draws 
 
 lemat 8 for 
 
 sells them at 
 
 75, 75 yards 
 
 it 32 cts.? 
 each, 28 
 870, 18 at 
 
 at $3.30, 2 
 Jnd 3 pair 
 ;her $1.50; 
 r their son ? 
 ler is 9207, 
 
 $1782 net 
 
 t one time 
 g that the 
 
 2472. A father of a family takes 7 hours for rest, 10 hour* for work 
 and 2 hours for his meals ; what time does he employ for each of these 
 occupations during a week of 6 days ? 
 
 2473. A man-of-war having made a seizure, the captain received 
 $18740.25 ; 11 officers each $9643.75 ; 15 sub-officers each $5649.05 and 
 240 men each $943.75 ; what was the amount of the seizure ? 
 
 2474. A clerk whose yearly salary is $840, received $700 ; how many 
 month's salary did he lose ? 
 
 2475. 1 bought 340 volumes for $204, I paid $150 on account ; how 
 many volun»es remain to be paid ? 
 
 2476. A wheel turn? 24 times a minute, and each turn the carriage 
 advances 5| yds.; what space would it cover in 2 hours 25 minutes ? 
 
 2477. HI had sold goods for $2537.60, 1 would have gained $840 ; 
 for how much did I sell them knowing that I gained $715 ? 
 
 2478. I gained $543.25 on goods which 1 sold ; if 1 had gained 
 $631.40 I would have sold them $4927-35; for how much were the 
 goods sold T 
 
 2479. If I had $924 more, I could pay $12432 and I would have $643 
 left ; how much have 1 ? 
 
 2480. Owen having a certain sum of money borrows $590 ; he pays a 
 debt of $847.75 and receives $545.85 which were due to him ; he finds 
 on his return home that he has $946.86, after spending $12.45. What 
 sum had he at first ? 
 
 2481. What is the cost of a house, knowing that it it had been boughtfor 
 $1875 less, by selling it for $87977 the buyer would have gained $6476 1 
 
 2482. A farmer mixed 120 bushels of wheat at $1.25 with 83 bushels 
 at $1.18 and 74 bushels at $1.05. He sold the wheat at $1.21 a bushel ; 
 how much did he gain ? 
 
 2483. A bookseller buys 756 volumes at 43 cts. a volume ; as he 
 received 13 books for 12, he gets 819 which he sells at 47 cts. a volume ; 
 what is his gain ? 
 
 2484. One of my friends borrows $450.75 from me, another$879.25 ; I 
 paid $14825 and I have $248 loft. How much had I before lending any? 
 
 2485. Wolfred lends $875.25 ; and he lacks $346.75 to pay two debts 
 one of $1425.85 and one of $978.75. How much had he before lending 
 any ? 
 
 2486. A lot of goods were bought for $8460 ; how much most it be 
 sold so a<3 to gain i of the cost price plus $174.45 ? 
 
 2487. A lot of goods were bought for $760.40 ; if they had been sold 
 for $46.70 more I would have gained half the cost price. How much 
 were the goods sold for ? 
 
120 
 
 MISCKLtANKOUS PROBLEMS. 
 
 2488. If a merchant in selling goods for $1240 gains i of the cost price 
 plus f 40.80, how much did he pay for them ? 
 
 2489. The 1st of four persons has $1607 ; the 2nd $181 less th^ui tlie 
 first ; the third has $76 more than the second ; the fourth $206.70 less 
 than the first. What is each one's share ? 
 
 2490. Three partners share in a certain sum ; the 1st takes $450.60, 
 the 2nd takes the double of the first minus $46.70, the 3rd takes k of the 
 first and ^ of the second plus $64.75 ; what is the sum tiivided ? 
 
 2491. Two men are to share $945.75 so that the part of the second be 
 double that of the first ; what are the two parts ? 
 
 2492. A wood-dealer buys 546 cords of wood, half at $2.75 a cord and 
 the rest at $3.03. How much did he disburse if he paid 12i cts. per 
 cord for cutting it T 
 
 2493. On adding $194.40 to a certain sum it becomes three times it- 
 self. What is the sum ? 
 
 2494. On adding $146.80 to a certain sum, it wants $24.20 to be 
 trii>led. What is the sum ? 
 
 2195. A lot of goods were bought for $1240.80 ; how much must I sell 
 them to gain ^ of the cost price ? 
 
 2496. After taking $496.45 from a certain sum ; $845.75 more should 
 be taken in order to have one-third of the sum ; what is this sum ? 
 
 2497. I have $345.75 ; how much should I borrow to pay two debts, 
 one of $879.85 and the other $1245.95, and buy 12 yards of cloth at 
 ^4.871 a yard ? 
 
 2498. I bought goods for $946.20 and by selling them for $43 moro 
 than I did I would have gained | of the cost price. How much did 1 
 sell them for f 
 
 2499. Three persons spent a certain sum : the first spent $784.30, the 
 second $241.00 more than the first, and the third $301.70 more than the 
 second. What were the amounts spent by the last two T 
 
 2500. A wine merchant bought 12 casks at $87 each. He sells 4 for 
 $380, how much must he receive for the others so as to realize a profit of 
 $156 on the whole ? 
 
 2501. A merchant pays $3 for every 100 plates he buys, he bought 
 1640 ; now how much must he sell each plate to gain $9.20 on the whole, 
 knowing that 40 were broken during the trip and that other expenses 
 amounted to $2.40 ? 
 
 2502. What will 1 pay for 34 barrels of wine of 55 gallons each, which 
 cost $78 a barrel, knowing that the duty on wine per pint is 6 cts. and 
 transportation, 76 cts. per b&rr«l ? 
 
MHCRLLANEOtrS rKOBLSlM. 
 
 121 
 
 r the cost price 
 
 less th:ui the 
 $206.70 less 
 
 akes $450.60, 
 takes i of the 
 ideH ? 
 
 he second be 
 
 75 a cord and 
 [ 12^ cts. per 
 
 tree times it- 
 
 124.20 to be 
 
 sh must I sell 
 
 more should 
 B sum ? 
 
 two debts, 
 is of cloth at 
 
 for $43 more 
 much did I 
 
 $784.30, the 
 ore than the 
 
 ) sells 4 for 
 :e a profit ot 
 
 s, he bought 
 •n the whole, 
 her expenses 
 
 each, which 
 is 5 cts. and 
 
 2508. A tap which gives 14 pints in 1 minute, fills a basin in 2 hours. 
 How many gallons can the basin hold ? 
 
 2504. A basin can hold 2980 gallons ; how long will it take to fill it, 
 the tap running 12 pints a minute ? . 
 
 2505. Two taps which run 12 and 16 pints respectively can fill a 
 basin in 3 hours 15m.; how many gallons can the basin hold ? 
 
 2506. A basin can hold 5688 g^illons and can be tilled in 3 hours 57 
 minutes, by two taps one of which gives Id gallons a minute ; how 
 many gallons must the other give ? 
 
 2507. A bookseller pays $3.50 for a certain book ; how much will he 
 sell a dozen so as to gain 70 cts. on each book ; knowing that he gives 13 
 books for 12 H 
 
 2508. A bookseller pays $14.50 a dozen for 852 books ; but he reci'ives 
 13 for 12. What is his gain, if he sells each volume $1.65 i 
 
 2509. A merchant bought 50 doz. of locks at 91 cts. each, and got 13 
 for every 12 ; in aiTanging them he lost 2. What will he gain if he 
 sells the others at $1.10 each I 
 
 2510. A merchant received a box contairing 50 turkeys which should 
 be sold at 90 cts. each. He gave five to his friends. What should he sell 
 the others so as to lose nothing ? 
 
 2511. A man bought 48 dozen of glasses at 14 cts. apioce and he 
 received 13 for a dozen. He sold them at 20 cts. apiece. What was hid 
 gain? 
 
 2512. A man bought 12 volumes at $200. He received 13 for 12. What 
 did each volume cost him T 
 
 2513. A milkman brought to the city 18 gals, of milk which he 
 desired to sell at 20 cts. a gallon. But an accident caused the loss of 3 
 gals., what should he sell the remainder for so as to lose nothing ? 
 
 2514. What is the length of a piece of cloth that cost $175.50, 
 knowing that I sold 25 yards for $87.50 and gained 50 cents a yard ? 
 
 2515. 1 bought 60 pieces of cloth of equal length at $2.60 a yard and 
 sold them at $3. 10 with a gain of $2100. What is the length of each piece ? 
 
 2516. A merchant bought 80 yards of cloth for $240 : what is his gain 
 on 50 yards which he sells at $3.10 a yard ? 
 
 2517. I bought 16 apples for 14 cts. and sold them for 20 cts. : 
 what will be my gain on 400 apples T 
 
 2518. A man buys 16 apples for 14 cts. and sells them for 20 cts. : 
 what will be his gain on a sale of $18 ? 
 
 2519. A watch gained 20 hours during 60 days : how many minutes 
 did it gaip. hourly ? 
 
122 
 
 MTBCELLANEOC* BROBLZMS. 
 
 2620, During the last 86 hours, a watch gained 2 minutes erery 8 
 hours ; what o'clock is it when the hands point to 26 minutes to 6 ? 
 
 2621. From 4 o'clock in the morniug, a watch gains 2 minutes every 3 
 hours, what i.s the time when the hands mark 7 p. m. ! 
 
 2522. A watch gains 3 minutes every 4 hours, what will it have gained 
 tt the end of a week ? 
 
 2523. A watch lost during the last 33 hours at the rate of 2 minutes 
 every 3 hours, what hour will the clock mark when it is 8 minutes past 
 3 o'clock. 
 
 2524. A clock was started at 6 p. m. and lost 3 minutes every 2 hours, 
 what hour will it mark at 10 a.m. next day ? 
 
 2525. A person promises to give 90 cents to the poor every time he 
 gains $12.25 ; what should he give when he gains |47 ? 
 
 2526. A merchant gives fl.75 in alms for every $17.75 he gains ; what 
 sum did he gain when he gave $38.50 in alms ? 
 
 2527. Every time a man gains $13.75, he gives a certain sum to the 
 poor ; find this sum knowing that when he gave $7 to the poor he had 
 1185.60 remaining? 
 
 2628. Each time a boys saves $6.75 his father gives hiit> «1.25 ; if the 
 boy saves $81, what will he have after his father adds his um ( 
 
 2529. For every $75 a boy gains, his father pays him $1.50; what 
 sum did the boy gain when, after his father's gift, he had $99 ? 
 
 2530. Each time a young man earns $6.25, his father gives him rt 
 certain sum, what was this sum, if when the young man earns $93. 76 his 
 father gives him $1.26 ? 
 
 2531. § of a sum of money is $96, what is the sum. 
 
 2532. A man spends § of his money, then i and after 4, what has he 
 remaining on $600 ? 
 
 2533. John has half as much as Joseph, who has j of $96, What was 
 John's money ? 
 
 2534. A ship cost $7500. Peter's share is i, John's is | of Peter and 
 Joseph's the balance ; what does each own. 
 
 2535. J of 56 is the § of *rhat number ? 
 
 2536. f of $900 is the J of J of John's fortune, what has he ? 
 
 2537. One fraction is | and the product if, what isthe other fraction ? 
 2638. Tobias spends i of the day in study, | in recreation, | in sleep 
 
 and the rest in business ; how long does he give to business J 
 
 'Ne|5?rD 
 
ites erery 8 
 :eH to 5 ? 
 nutes every 3 
 
 t have gained 
 
 of 2 minutes 
 ninutes past 
 
 very 2 hours, 
 
 ury time he 
 
 gains ; what 
 
 i sum to the 
 poor he had 
 
 1.25 ; if the 
 
 m? 
 
 M.50 ; what 
 
 9 ? 
 
 gives him a 
 
 18 $93. 75 his 
 
 rhat has he 
 , yifh&t was 
 if Peter and 
 
 e? 
 
 ler fraction ? 
 
 I i in sleep 
 
 CONTENTS. 
 
 Addition 6 
 
 Addition of Fraction^ 70 
 
 Addition of Decimals '.I5 
 
 Apothecaries' Weight ^4 
 
 Avoirdupoids Weight Si 
 
 Bills and Accounts ... I J7 
 
 Circular Measure i^8 
 
 Common Fractions 04 
 
 Cubic Measure ^^ 
 
 Currency S2 
 
 Decimal Fractions 88 
 
 Denominate numbers 82 
 
 Division 36 
 
 Diviacn of Fractious 74 
 
 Division of Decimals 101 
 
 Dry Measure S7 
 
 English Money S3 
 
 Exercises in Numeratiuu 4 
 
 Fractions C4 
 
 Liquid Measure 86 
 
 Measure of Length S5 
 
 Measure of Time 87 
 
 Mental Arithmetic 52 
 
 Mental Exercises in Fractious. . 75 
 
 Miscellaneous Problems Ill 
 
 Models of Bills 103 
 
 Multiplication 25 
 
 Multiplication of Fractions... 73 
 
 Multiplication of Decimals. . . 9i> 
 
 Notation 9 
 
 Notation of Decimals 91 
 
 Numeration 1 
 
 Numeration of Decimals 89 
 
 Oral Exercises in Numeration. 6 
 
 Oral Exercises in Decimals. . . 93 
 
 Practical Problems in Addition. 18 
 
 Practical *' Subtraction... 21 
 
 Practical " Multiplication. 81 
 
 Practical " Division 47i 
 
 Practical " Fractions TJ 
 
 Preliminary Definitions 1 
 
 Problems in Mental Aritbmetio. 65 
 
 Reduction of Fractions 67 
 
 Reduction of Decimals 94 
 
 Review Problems 32 
 
 Review of 4 Simple Rulcii ... . 47 
 
 Roman Figures 4 
 
 Solid Measure 86 
 
 Subtraction 17 
 
 Subtraction of Fractious 71 
 
 Subtraction of Decimals 97 
 
 Square measure , « » . ■ 85 
 
 Troy weight 83 
 
A 
 
 . Ll 
 
 t^ 
 
 /- 
 
 ;, 
 
 I 
 
 up 
 
 'V 
 
 H.^- 
 
 R5 
 
 1 
 
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 (i:^ 
 
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 1A^ 
 
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 At r« a 
 

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