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MACVICAR, LL.D., Principal Prebbytf.rian CoLLKaE, Montreal. * ^•^ » TORONTO : CANADA PUBLISHING COMPANY, MONTREAL :— DAWSON BROTHERS. 1880. 'm cy Entered according to Act of Parliament of Canada, in the Vear 1879, by Dawson Brothers, in the Office of tha Minister of Agriculture. uiRAirr I I-AVA^-^ PREFACE. THE objects specially uiined at in this work are to train th« pu})il to accuracy and rapidity in the operations of the four elementary rules of Arithmetic, to accustom him to habits of careful ob!:^ervation on the methods of solving practical problems, and to render him so familiar with fundamental principles and processes as to r^ ike advanced work natural and easy. The lollowiiujf points indicate tlie plan of the book: 1. In every subject the lirst steps are presented objectively, followed by sutlicient slate and written exercises to define and fix lirmly in the mind of the pui)il the truths illustrated. 2. The work from the beginning is so arranged that each step forms a natural and complete preparation for the step fol- lowing. Hence tlio pupil is led to understand clearly the prin- ciples on which each operation depends before he is re 5 8 ii PRE FA CE. 5. The nature of fractions is presented objectively, and the pupil taught clearly how to represent various fractional units, how to change a fraction from one fractional unit to another, how to change wholes into any given fractional units, and given fractional units into wholes. After this, exercises are given requiring, iu the simplest form, the use of addition, subtrac- tion, multiplication and division of fractions. These pages, while purely elementary, are so complete as ta give the child such a knowledge of fractions as will fit him to perform the operations ordinarily occurring in prujtical life. 6. The book closes with denominate numbers, giving all ti tables the pupil requires to know, with carefully graded exer- cises illustrating each table. Hints and directions to teachers are not introduced through- out the work, because they would prove injurious to the pupil, for whom it is exclusively intended. Full instructions and a complete method of presentation will be found in the Teach- er's Edition of the Elementary and Complete Auith- METios, by M. Mac Vicar, Ph.D., LL.D., Principal of th:^ State Normal School, Potsdam, N. Y., published by Taintor Brothers, Merrill & Co., New York. The present work is specially adapted for use in Canadian Schools, while based upon the Elementary Arithmetic j- .st named, which was prepared by Dr. M. Mac Vicar and the undersigned. D. H. Mac Vicar. Montreal, January, 1879. CONTENTS. Page Notation and Numeration — Numbers from 1 to 10 5 Exercise in use of Signs » 10 Numbers from 10 to 100 U Numbers from 100 to 1,000 17 Numbers above 1,000 ....tr 19 Definitions, Bules , , 24 Boman Notation 25 Addition 27 . Addition Tables 31 Definitions, Rule 46 Subtraction 47 Definitions, Bule 64 Multiplication 65 Definitions, Rules 77 Applications, Canadian Money « 79 Measures of Weight -. 81 Divisioii ,... 83 DefinitioUii, Rule 102 Applications, Dry Measure 103 Liquid Measure 104 Exercises on Exact Division, greatest common divisor. . . 105 Exercise on Multiples 106 Fractions, Oral Exercises 107 Reduction , 112 Addition 117 Subtraction c > 118 m It CONTHNTij. Multiplication 119 Division ,. 123 Definitions 126 Denominate Numbers, Canadian and United States Money. 127 English and other Money 129 Exercises in Units ofWeight 131 Units of Length 133 Exercises in Units of Surface 135 Exercises in Units of Volume 137 Units of Capacity 1 39 Units which vary in Size 143 Units of Time I44 Answers >,,,,, , . , , 145, u :: % 119 . 123 . 126 . 127 129 131 133 135 137 139 143 144 145» ARITHMETIC NUMBERS FROM 1 TO 10. ONE. 1 . The following illustrates the method of presenting num- bers from one to ten, Tlie teacher should vary the illustra- tions by the use of diflferent objects and of the Numeral Frame and blackboard. 1. Show me one book. One boy. One pencil. One desk. One window. One slate. 3. Show me one hand. One door. One finger. One knife. One head. One ear. One eye. 3. What is a single thing called ? Name a single thing. 4. One means a single thing. The figure 1 stands for one. T VV^O. 2. 1. Show me two fingers. Two thumbs. Two girls. Two boys. Two ink bottles. Two slates. Two books. 2. How many eyes have you ? How many ears ? How many hands ? How many feet ? 3. One dog and one dog are how many ? One and one are how many ? Two dogs less one dog are how many ? 4. Two desks less one desk are how many ? Two slates less one slate ? Two less one are how many? 5. Two means one and one. The figure 2 stands for two. 6 NOTATION AND yVMERATIf)N. THREE. 3, 1. Show me three boys. Three windows. Three fiujrers. 2. Three dogs less one dog are how many ? Three books less one book ? Three less one are how many ? 3. How many are two and one? How many ones in twoV In three ? How many twos iu three, and what left? 4. Count three. Name three boys. Three girls. 2 and 1 are how many ? 1 and 1 and 1 are how many ? 5. Two and one make three. The figure 3 stunds for three. FOUR. 4t 1. Show me four balls on the Numeral Frame. Three balls. Two balls and two balls. 2. Two hats and one hat are how many ? Three hats and one hat ? Two hats and two hats ? 3. How many hats taken from four will leave one? Will leave two*? Will leave three ? Will leave four ? 4. How many two boys in four boys? How many three boys, and how many left ? 5. Three and one make four. The figure 4 stands for four, FIVE. 6. 1. Show me five balls on the Numeral Frame. Four balls. Three balls and two balls. 2. How many are two desks and one desk ? Two desks and two desks ? Four desks and one desk ? 3. Five fishes less one fish are how many ? Less two fishes ? Less three fishes ? Less four fishes ? 4. How many are 2 and 1 ? 2 and 2 ? 4 and 1 ? 3 and 2? 3 and 1 ? 2 and 2 and 1 ? 6. Four and one make five* The figure 5 stands for five. .1 NOTATION AND NUMERATION. SIX. 6. 1. Sliow me six balls on the Numeral Frame. Three balls and two balls. Five balls and one ball. 3. Six trees less one tree are how many ? Six trees less two trees ? Six trees less three trees ? 3. Two books and one book are how many? Two books and three books ? Two books and four books ? 4. 3 and 1 are how many ? 3 and 2? 3 and 3 ? 6 less 1 arc how many ? 6 less 3 ? 6 less 3 ? 6 less 4 ? 6 less 5 ? . 5. Five and one make six. The figure stands for 8/a?« SEVEN. 7. 1. Show me seven balls on the Numeral Frame. Five balls and two balls ? Six balls and one ball ? 2. Six plums less one plum are how many ? Less two plums ? Less three plums ? Less five plums ? 3. How many 3 plums in 7 plums, and how many left ? How many two plums, and how many left ? 4. 3 and 1 are how many ? 4 and 2 ? 4 and 3 ? 5 and 1 ? 5 and 2? 3 and 3? 5. Six and one make seven. The figure 7 stands for seven. I EIGHT. 8. 1. Show me eight balls on the Numeral Frame. Four balls and three balls. Two balls and six balls. 3. Eight peaches less one peach are how many ? Less two ? Less three ? Less ^our ? Less five ? Less six ? 3. How many fours in eight ? How many twos ? How many threes, and how many left ? How many ones? 4. 6 and 1 are how many? 3 and 2? 3 and 3? 7and 1? 6 and 2? 5 and 3? 4 and 4? 5. Seven and one make eight. The figure 8 stands for eight. 8 NOTATION AND NUMERATION, NINE. • O. 1. Show me nine balls on the Numeral Frame. Six balls and three balls. Four balls and three balls. 2. Five leaves and one leaf are how many? Five leaves and \ hree leaves ? Eight leaves and one leaf ? i). 6 and 1 are how many ? 4 and 2 ? 4 and 3 ? 4 and 4 ? 4 and 5? 3 and 6? 2 and 7? • 4 How many are 5 less than 9 ? 3 less than 9 ? 5. How many 3's in 0? How many in 9? How many in 8, and what left? How many 2's in 4 ? How many in 8 ? 6. 3 and 2 and 2 are how many? 4 and 1 and 3? 2 and 3 nnd 4 ? 4 and 2 and 2 ? 5 and 1 and 2 ? 7. Eight and one make nine. The figure 9 stands for nine* TEN. 10. 1- Show me ten balls on the Numeral Frame. Six halls and four balls. Three balls nnd five balls. 3. How i.iany are 9 cherries and 1 cherry V 8 cherries and 3 cherries? 7 cherries and 3 cherries ? G cherries and 4 cher- ries ? 5 cher.'ies and 5 cherries ? 3. How many 5 cherries in 10 cherries? How many 3 cher- vieH? How many 4 cherries, and how many left? 4. In how many ways can you make 10 cherries into two i!:roups of cherries ? 5. 10 cherries less 3 cherries are liow many ? Less 1 ? Lnss4? Less 2? Less 9? Less 5? 6. 7 and 2 are how many ? 7 and 3 ? 7 and 1 ? 5 and 2 ? 5 au'l 4 ? 5 and 3 ? 5 and 5 ? 8 and 1 ? 8 and 2 ? 4 and 2 ? 7. Nine and one make ten. The figures 10 stand for ten. The figure O, which is oa,lleJ clplun' or zero^ has »»o value m itself. U. in the c \ Co ydi NOT AT 10 N' AND i\ UJI E RATION. le. Six ves and and 4 ? ny in 8, 2 and 8 mds for ne. Six lies and i 4 cher- jT 3 cher into two Loss 1 V 5 and 2 ? and 2 V 'or ten . »o valiif I EXERCISE IN MAKING FIGURES. I Jl . C^opy neatly from this picture of a slate all the figures in the order in which they are given. /?Y' 'j-- / ■J :J .;' 4 7 / '' ■':J ■> ■y -J o J -T J cV U -/- '^ /> ^ / /'S S-6 ^/ ^ ^ o 6 are Fifteen. 1 ten and (i are Sixteen, 1 ten and 7 are Seventeen, 1 ten and H are Fiijhteen, 1 ten and f> are Nineteen. 8. Ten and one are how many V Twelve and one ? Fourteen and one ? Seventeen and one ? 9. Seventeen less one are how many? Tliirteen less one? Nineteen less one ? Fifteen less one ? 10. 11 + 1 are how many V 17 + 1? 15 + 1? 13 + 1? 18 + 1? 13 + 1? 14 + 1? 10 + 1? 19 + 1? 11. Write the figures that stand for eleven. For twelve. For seventeen. For thirteen. For nineteen. NOTATION AND NUMERATION. 13 EXERCISES IN GBOUFING. 15. 1. Make on your slate 3 groups of ten marks, and 3 groups of ten marks, thus : % t«HS» 3 tens. ' = Twenty. S -[ = Thirty. 2. Wiiat does Twenty meaal Thirty? Forty? 3. Make iu the same manner 4 groups of ten marks • 8 groups of ten marks ; 6 groups of ten marks. 4. What does Fifty mean ? Sixty ? Seventy ? Eighty ? Ninety ? 6. How many is sixty more than fifty ? Fifty than forty ? C. Four tens are how many? Seven tens? Five tens? Tlireetens? Nine tens? 7. Make on your slate 10 groups of ten marks each. Ten yroups of ten marks aach, 1 Hundred marks. 8. What is meant hy 1 hundred marks? 1 hundred hooks? 1 hundred boys? 1 hundred men? 9. How many does 9 groups of ten marks lack of being 1 hundred marks? groups of fen marks? 10. A group of 8 boys, one of 9 boys, and one of 3 boys, will together make how many groups of ten boys ? 11. 8 apples, 3 apples, 5 apples, and 9 apples, will make how many groups of ten apples 14 NOTATION AND NUMERATION, WRITING AND READING TENS. 16. 1. Write the figures that stand for ten. 9 and 1 are ten. Written 10, 2. What two figures stand for ten ? How are they wfttten ? Which is on the left hand ? Which is on the right hand ? 'd. Make ten marks on your slate two times : Thus, llilllllll IIIIIIIHI 4. Write the figures that stand for two tens, 2 t^ns are twenty. Written 20, 5. Make ten marks on your filate 3 times ; •! times ; 5 times ; 6 times ; 7 times ; 8 times ; 9 times ; 10 times. 6. How would you write the figures that stand for three tens, four tens, five tens, six tens, seven tens, eight tens, nine tens ? 7. Repeat this tabl^ : 2 tens are twenty* 6 tens are sixty, 3 tens are thirty, 7 tens are seventy, 4: tens are forty, 8 tens are eighty ^ 5 tens are fifty, tens are ninety, 10 tens are 1 hundred. o. What two figures together stand for eig7it tens ? Which is on the left hand ? Which is on the right hand ? 9. How many are 3 tens ? 6 tens ? 9 tens ? 4 tens ? 17. Express in figures : 10. Two tens. 13. Three tens. 11. Four tens. 14. Five tens. 12. Six tens. 15. Nine tens. 19. Read the following : 60. 30. 70. 30. 50. 16. Eight tens. 17. Four tens. 18. Seven tens. 90. 60. 40. 70. 90. ^'. NOTATIOX AND N IT ME RATIO N. 15 s. wfttten ? md? 5 times ; ree tens, 6 tens? y* Which bens. 3ns. tens. 00. NUMBEBS FROM 20 TO 100. 17. 1- Write the figures that stand for two tens andon^. 2 tens and 1 are Awenty^ouf, Written 21, 3. Write the figures that stand for three tens and one, 3 tens and 1 are Thirty -one* Written SI, 3. Write the figures that stand for four tens and one. For six tens and one. For nine tens and otw, 4. How many are 2 tens and 1 ? 3 tens and 1 ? 7 tens and 1 ? 5 tens and 1 ? 8 tens and 1 ? 9 tens and 1 ? 5. Write the figures that stand for two tens and two, 2 tens and 2 ar, Twenty-^wo, Written 22, G. Write the figures that stand for 4 tens and 2. For 6 tens and 2. For 8 tens and 2. For 9 tens and 2. 7. How many tens in Twenty "two, and how many over? In Thirty-two ? In Seventy-two ? 8. How many are 2 tens and 6 ? 3 tens and 87 6 tens and 5 ? 8 tens and 4? 9. How many are 30+7? 40 + 9? 80+5? 70 + 6? 60 + 3? 90+2? 10. How many are 20+1? 25 + 1? 27+1? 32 + 1? 36 + 1? 56 + 1? 89 + 1? 11. How many are 37 less 1 ? 56 less 1 ? 74 less 1 ? 80 less 1? 931688 1? 12. Name the numbers in orde . from one to on>e hundred ; thus, one, two, three, etc. 13. Bead the following numbers : 20 15 17 70 11 33 56 18 29 80 57 79 68 94 57 86 79 99 41 45 IG A > TA T I .V .1 yn y umera ti o x. Ill ARITHMETICAL TABLE No. 1. 18. 1. Copy on your slate columns A and B of this table. Read each number on your slate. 1. A. B. c. B. E, F. C^. H. ■ (9' ■J. / 7-^ / 4 / / V 'V / 1 9. 8. 4. • ^ , / ^ ■■/ 6. V. / ■ -V ' / •1, "- / ^ / ;• \ \ ■; / ^^ 8. 9. 10. 0. ■ / r — ■■ _v //■ * 2. Coi)y on another part of your slate columns B and C, the» C and D, and so on, Head the numbers as before. N 2. are 3. dred " 4. >«i I ! NO TA TION A ND N UME K A TION. 17 NUMBERS FROM 100 TO 1000. *;« lO. 1. Write the figures that express ten tens* 10 tens are one hundfcd. Written 100» 2. How many ciphers used to exvess one hundred? Where are they written V Where is the 1 written ? 3. Express by figures two hundred ; four hundred; six hun- dred ; seven hundred ; five hundred ; nine hundred 4. Express by figures eleven tens, 11 tens are one hundred and ten* Written 110. 5. IIow many ciphers used to express one hundred ten ? 6. Write by figures 13 tens; 15 tens; 17 tens; 19 tens; 21 tens ; 20 teno ; 25 tens ; 59 tens. 7. ITow many ciplicrs used* to express 30 tens? 50 tens? 60 tens? 40 tens? 90 tens? 8. Write by figures one hundred foi-ty ; five hundred eighty ; eight hundred seventy ; four hui.v«red twenty. 9. Express by figures ten tens and one, 10 tens Bind 1 are one hundred and one. Written 101. 10. How many ciphers used to express one hundred onef Where wrii,ten? Express by figures the following numbers : 11. Three hundred one; five hundred one; nine hundred one ; seven hundred one. 12. Three hundred four ; six hundred two ; eight hundred five ; two liundred nine ; nine hundred nine. 13. Two hundred sixty-one ; five hundrod seventy-nine. 14. Nine hundred nine ; nine hundred ninety-nine. 18 NOTATION AND N UM E li A Tl N, SLATE EXER'^" >. 20. Copy on your slate and read the following : (1-) (3.) (3.) (4.) (8.) 309 406 506 905 906. 107 SOS 805 902 805 402 405 608 607 909 301 402 302 806 606 205 209 6O4 8O4 907 (6.) (7.) (8.) (9.) (10.) 120 140 131 289 454 S60 670 523 973 '897 fy20 380 474 884 898 560 760 882 579 555 820 680 796 845 999 Express in figures the following : 11. Two hundred five. 20. Eight hundred fifteen. 12. Five hundred seven. 21. Nine hundred nine. 13. Seven hundred two. 22. Two hundred \ sixty. 14. Eight hundred twenty 23, Six hundred e ighty-ono. 15. Six hundred ninety. ■ 24. Five hundred thirty-five. 16. Four hundred sixty. 2.1 Eight hixndred fifteen. 17. Three hundred seven. 26. Two hundred seventy-four. 18. Two hundred eighty. 97. Six hundred s xty-!\ine. 19. One hundred twenty-one. 28. Two hundred e;gli1y-on(?. NOT A T i O A A.\B N UME RATIO N, 19 (6.) 906 805 909 606 907 NUMBERS ABOVE 1000. SLATE EXERCISES. 21. 1. Expreas in figures ten hundreH, 10 hundred are one tJiousand, Written 1,000* 2. How many ciphers used to espress one thousand ? Where ere they written ? What place from the right of the number does the 1 occupy ? 3. Write in figures three thousand ; five thousand ; eight thousand ; nine thousand ; 4 thousand ; 6 thousand. 4. Express in figures ten thousand, 10 thousand are written 10,000, 5. How many ciphers used to express ten thousand? What place from the right does the 1 occupy ? What separates the 10 from the three ciphers ? G. Write in figures fifty thousand ; seventy thousand ; lorty thousand ; 50 thousand ; 80 thousand. 7. TTow many ciphers must be placed to the right of 13 to make ii denote 13 thousand ? Espress in figures the following numbers : 8. Fifteen thousand. 13. Twcnty-four thousand. 0. Tliiity-five tliousand. 14. Eigliiv-six thousand. 10. Nine thousand two. 15. Five thousand nine. 11. Seven thousand fifty-five. 10. (5ne thousand eighty-one. 12. Forty-six thousand one 17. Seventy-two thousand five. 18. Twonty-ono thousand seven hundred ninety-nine. 19. Forty-four tliouf«^ place from the right represents units of the first order, the 4 in the second place units of the second order, the 9 in the third place units of the third order. 3. The orders of units in a number are formed into groups of three. Each group is called a Period, 4. The figures in the first period on the right represent unltSf in the second period thoiisandSf in the tliird period millions, as shown in the following 4' 9 TABLE. r i> l! Periods. 3d 2d. 1st. >- Millioi * IS. Th ousands. ^ Units. Names r — > ^ «H CM «M >H O o ti o o S-, o o Units. en m 73 —4 CO 01 T3 !/3 ai a rcss in Roman Notation the following : 1. Three. 2. Seven. 3. Four. 4. Nine. T). Twelve. 0. Seventeen. 7. Nineteen. 8. Fift(>on. 9. Twenty. 10. Fourteen. II. Thirty-three. 13. Forty. 1.'?. Forty-four. 14. Sixty. 15. Fifty-nine. 26 ROMAN NOTATION. EXERCISES IN ROMAN NOTATION- 87. Read each of the following numbers : 1. X. 8. L. ir>. CII. 32. DC. ^. XI. 9. VL. 10. ex. 23. CD. o O. IV. 10. XL. 17. XC. 34. Die. 4. XIX. 11. LX. 18. CXX. 25. DCV. 5. XIV. 13. LIX. 19. CL. 26. DC(^XV 0. IX. 13. LVIII. 20. CIL. 37. M. 7. XXIV. 14. LXXXIV. 31. CIC. 28. CM. A\ 'rite in Ronuiu Notation the following numbers : 1. Twentv-four. 7. One hundred nine. 13. 10001 2. Seventy-nine. 8. Five hundred four. 14. 3005. 3. Eighty-three. 9. Three hundred seventy 15. 5009. 4. Ninety-four. 10. Seven hundred six. 10. 2084, 5. Fifty-seven. 11. Two hundred eighty. 17. 1877. 6. Thirty-nine. 13. Four hundred two. 18. 1854. Read each of the following numbers 1. X. 6. L. 11. MDCCCLXXVII. 16. D. 2. V. 7. XX. 12. MMDCLXIX. 17. XV. 3. XI. 8. LX. 13. MCCLIX. 18. TS.X 4. vi. 9. C. 14. MMMDLVIII. It). XXV 5. IV. 10. OX. 15. MCDXVII. 20. XD. Express in Roman Notation tlie following : 1. Ten thousand. 2. Four thousand. 3. Six thousand. 4. Two thousand. 5. Nine thousand. 6. Eight thousand five hundiod. 7. Five tliousand two hundred. 8. Three thousand six hundred. 9. Ten thousand one hundred. 10. One thousand fiftv-rine. DN. DC. CD. Die. DCV. DCCXV M. CM. 3. 10001. 14. 3005. 5. 5009. [G. 2084, .7. 1877. 8. 1854. I. D. \ XV. I. XXX. '. XXV. ». XD. mdred. 1(1 rod. lulrod. lied. ADDITION. OEAL AND SLATE EXERCISES. 38. 1. Add 3 pears aud 5 pears. Three pears and five pears are added thus : Tilings are added by putting them together. 2. Three pears and five pears are how many ? 3 and 5 are how many ? , 3. Add 7 blocks and 3 blocks, thus : 7 btocka + 3 blocks = lO blocks* 4. Seven blocks and 3 blocks are how many ? 7 and 3 are how many ? 5. Finding how many two or more groups of objects will make when put together is called Addition f and the number found is called the SifiH. Find tlio sum : 6. Of 4 caps and 3 caps. 7. Of 3 pencils and 3 pencils. 8. Of 2 desks and 4 desks, 9. Of 5 ])ens and 2 ])ens. 10. Of 4 chairs aud 5 chairs. 11, Of 3 tables and G tables, 12, Of 5 books and 4 books, 13, Of 2 boys aud boys, 14, Of girls and 4 girls. 15, Of 7 blocks and 3 blocks. i^ \ 1 28 AD D IT 10 X, SLATE EXERCISES. 30. 1. Find, by making- marks ou your slate, the sum of 7 marks and 6 marks ; thus, 7 marlk's tnarks 10 tnarlis nud 3 marks. 1 tell and 3 = Find in this wav tlie pum : 2. Of markf and 5 marks, 8. Of 8 marks and 9 marks. 4. Of 7 marks and 4 marks. Thirteen, 5. Of 9 marks and 3 marks. C. Of 4 marks and 9 marks. 7. Of 9 marks and 9 marks. Copy on your slate and find, by using objects, the sum for each example in the following exercises : ^ + .? = ? 8+l = 'i 5+l='i 7-ri=? 0+1 = ^ G+l-^'r 6+3 = ? 2+3 = ? 2+3 = ? J + c? = ? 2+J^ = ? 3+4 = ? 8+2 3+2 9 9 r)+2 9+2 /T ■:•> 9 + 3 9 9 /v 7+3 i+3 r> 3+.^ = 6+4 = 9 9 7+4 9+4 9 9 t 9 « 9 9 9 9+1 = ? 4+1=? 7+2 = ? 6+2 = ? 6+3 = 8+3 = 5+4 4+4 9 9 9 40. how mar SOLUTK which is 8 1. A 1 cows has 3. In i many tr( 4. 'l b( much di 5. In J pupils ai 0. At ADDITIOX, 29 lie sum of d 3 marks. ?ll. id 3 marks, id 9 marks, id 9 marks. le sum for 9 9 + .? = ? 3 '+.? = ? ORAL EXERCISES. 40. 1. Mary had 5 apples and lier brother gave her 3 more ; how many apples had she then ? SoLUTiox.— She had as many apples as the sum of 5 apples aucl 3 apples, which is 8 apples. 2. A man has G white cows and 3 black ones ; how many cows has he in all ? 3. In a o-arden there are 7 peach trees and 3 apple trees ; how^ many trce3 are there of both kinds ? 4. I bought a coat for 8 dollars and a hat for 5 dollars ; how much did I give for both ? 5. In a certain class there are 4 hoys and 5 girls ; how many pupils are there in the class ? G. A boy rode 6 miles in the cars and 3 miles in a carriage ; how many miles did he travel? 7. There were 7 mugs upon a shelf and Ada placed three more there ; how many mugs were then on the shelf? 8. Six birds wore l^pon a tree, and four more alighted ; how many birds on the tree ? 0. Edward caught four trout in one brook, two in another, and three in anotlier ; how many trout had ho in all ? 10. A turkey weighed G pounds, but afterwards gained two pounds ; what did tlu) turkey then weigh ? 11. If a house has 7 windows on one side, and four on anot)ier, how many windows has it in all ? 13. Five caps are hanging in a row, and soon four more are hung up ; how many caps in all ? 115. A poor man earned five dollars by sawing wood, one dol- lar by carrying coal, and four dollars by planting a garden ; how many dollars did he earn in all ? 14. A flag has 4 red stripes and 5 white stripes ; how many stripes has it in all? 15. Frank had 9 cents and his sister Jessie gave him 3 more ; how many did he then have ? 80 ADDITION. SLATE EXERCISES. 41. Copy on your slate and find, by using objects, the sum for each example in the following exercises : 5+6 ? 2+4 ? 2+5-- 7+4 = = 9 • -9 « 6+8-? 4+5 = ? 5+5 ? 8+4-? 8+3-'i 6+3-1 6+2 = 6+7 = = 9 • = 9 • 3 9+5 = ? 4+6 = ? 5+6 ? 7+6 = ? 7+3 = '> 5+6 = 1 5+7 = 8+7 = • = 9 • 3 7+7-^? 7+2 = ? 9+7 ? 6+7 = ? 3+8-? 6+8-1 5+8 = 4+8 = = 9 • = 9 • 4 9+7-? 9+S-? 4+8-? 8+8-? 4+9 ? 7+9-? 3+0 = 4+9 = = 9 = 9 • 5 6+9"? 8+9 ? 5+9 ? 0+9 ? 6 7+7 = ? c9+£^ = ? 6N-^-? 5+5 = ? 9+5 = '} 5+G = ? 9+7 = ? S+7 = ? 5 3 9 2 6 3 1 8 8 4 7 4 6 5 5 ADDITION, 31 }; the Slim + 5-- +^- +6 + 6 + 7 + 7 9 9 9 ADDITION TABLES. 42. Practice on each of the following tables separately. Thus, jpy the numbers on your slate in the order given, find the .sums and write tlieni under the numbers, then erase them and write them again and again from memory. Tahte "/ Twos. 5 o O 4 8 1 3 2 3 2 2 9 G 2 7 9 2 2 8 2 2 Taftfe of Threes, 5 6 2 3 4 3 3 3 3 3 1 7 G 8 9 3 3 3 3 Ta6/e of I'ours, 3 8 3 6 2 4 4 4 4 4 7 9 3 9 1 4 4 4 4 4 Table «/ rives. G 3 1 8 5 5 5 5 5 5 7 4 3 8 9 5 5 5 5 5 Table o/^ i'tjces. 5 1 8 3 6 6 6 6 6 6 3 4 8 9 4 6 6 6 6 G Table of Sevens. 3 4 7 9 1 7 7 7 7 7 5 9 8 2 6 7 7 7 7 Table of Eights. 7 8 5 3 4 7 8 8 8 8 8 9 8 3 1 8 8 6 8 Table of Xiuos. 9 8 4 6 5 8 3 9 9 9 9 9 1 7 6 5 9 9 9 9 9 9 f 33 ADDITJOX, OBAL EXEBCISES. 43. 1. John had one cluster of four grapes, another of seven, and another of three ; how many grapes had he ? Solution.— lie had as mauy grapes as the sum of 4 grapes, 7 grapes, aud 3 grapes, which is 14 grapes. 2. Norman had four red tops, two blue tops, and five white tops ; how mauy tops had he ? 3. My house contains 2 parlors, 1 sitting room, 1 dining room, 1 kitchen, 4 chambers, 5 bedrooms, and an attic ; how many rooms iu all does it contain ? 4. A man takes two daily papers, four weekly papers, and three monthly papers ; how many papers does he take in all ? 5. My garden has six rows of beans, four rows of peas, and three rows of turnips ; bow many rows does it contain? 6. A farmer has a spade worth three dollars, a mallet worth one dollar, a hatchet worth one dollar, and a gun worth five dollais; how many dollars are they all worth? 7. 1 have four gold rings, eight brass rings, and two silver rings ; how many rings have I ? 8. Oliver has 4 slate pencils, and Kate has G lead pencils and 5 slate pencils ; how many pencils have both ? 0. A farmer has 9 cows and 8 oxen ; how many cattle has he mallV 10. Harvey paid 10 cents for a slate, 2 cents for a pencil, and 6 cents for a sponge ; how much did they all cost ? 11. A man bought a saddle for dollars, a bridle for 3 dol- lars, and a whip for 1 dollar ; how much did they all cost ? 13. What is the sum of 5 + 8 + 4 + 3? 13. There are 3 pears on one i)]ate, 5 on another, and 9 on another ; how many pears on the three plates ? 14. Warren's mother gave him 15 cents, he earned 9 cents, and found 7 cents ; how many cents did he then have ? 15. A lady has 7 Iron spoons and 3 more silver spoons than iron ones ; how many spoons has she in all ? 5. :f 17. 18. •f2ai 19. additic 20. 800+: 21. 70+4( i ADDITION, i33 notlier of grapes, and five white 1 dining tittic ; liow )apers, and ko iu all ? f peas, and tin '.' allet worth worth five I two silver pencils and lattle has he a pencil, and lie for 8 dol- all cost ? ler, and 9 on rued 9 cents, lave ? f spoons than OBAI. EXEBCISBS. 44. 1. How many ones are there in 11 and 4 ? in 7 and 8 ? 10 and 5? in 13 and 7? • 3. How many ones are there in 27 and 6? in 36 and 6 ? in 55 d 7? in 66 and 7? in 93 and 8? 8. How many are 3 and 1 ? 11 and 3? 34 and 6 ? 33 and 3? and 3? 81 and 5? 4. How many are 3 and 7? 13 and 5? 33 and 6? 74and3? 106 and 4? 643 and 4? 553 and 4? 5. How many are 8 and 7 ? 16and7? 35and7? 75and7? 465 and 7? 18 and 8? 36 and 8? 346 and 8? 6. How many are 9 and 3? 49 and 3? 59 and 3? 9and6t 70 and 6? 339 and 6? 469 and 6? 7. How many are 8 and 7? 38 and 7? 36 and 7? 9 and 8? e»and8? 859 and 8? 8. Add by 3's from 1 to 33 ; thus, 1, 3, 5, 7, 9, 11. Add 0. By 3's from 3 to 50. 10. By 3's from 4 to 74. 11. By 3'8 from 3 to 78. 13. By 5's from 3 to 84. 13. By 5'8 &om 6 to 96. 14. By 7's from 3 to 87. 15. By 6's from 5 to OS. 16. By 7'8 from 4 to 89. 17. Add by O's from 3 to 105 ; from 5 to 87 ; from 7 to 119. 18. Add from 1 to 76 by repeating the successive additions •f 3 and 3 ; thus, 1, 3, 6, 8, 11, 13, etc. 19. Begin with 4 and add to 105 by repeating the successive additions of 3, 8. and 4. 20. How many are 30 + 5? 60-f7? 300+40+6? 700 + 90+3? 800+30+4? 600+50+7? 31. How many are 30 + 40? 50 + 60? 70 + 40+6? 80+30? 70+40? 90+80? 80+60+8? I 34 ADDITION. SLATE EXERCISES. 45. Copy on your slate and find the sum for each example ID the folluwiui? exercises : 1 f % ■ AM ' ii i 1^1 Ifl i 300+50+G •? 700- ^60+4 ? 600+40+9-? 900- ^50+6 = ? 500+80+1 ? 900- ^70+5-? 2 503+50 '? 308+50 ? 504+ 60-? 66+iOO ? 88+600 ? 13+800-? 80+ 504=? 80+509-? 80+209=? 3 33+5 ? 47+8-? 55+9=? 63+5-? 57+8-? 75+9 = ? 83+5 ? 67+8-? 85+9 ? 73+5 ? 77+8-? 65+9=? 4 37+6+6+6=9 . 42+ ■5+5+5 ? 59+4+4+4-? 26+8+8+8=? 25+9+9+9 = ? 34+ .f+Y+7 = 9 57+5+5+5 ? 65+3+3+3=? i % shown table, copy a ADDITION. ARITHMETICAL TABLE No. 2. ch example ■800=-^ +9 = 1 + 9 = ? +5> = ? +5 '+7 1+3 * = 9 = 9 1. A. B. c. D. E. F, G. H.| i\/ / ,-1 _ ^ , /' 1 1 > > / ' 'y 7 4^ ! J2^. 3. 2 .i^ .// U. 6 7' 4. 1 1 ) iV 9 / ') J S' 6 5, 6 -- — ' / / - A/ ■> / 1. ) 9 y _2 «• •z. 7 } :') / / y 9 / / 1 a 9. 10* 9 / s- 6 J 9 CJ^ 4 1 46. Copy neatly on your slate examples from this table, aa shown on next page. Make the figures as they are in the table. Find the sum of each example, then erase them, and copy and find the sum again and again. '1?§- 36 ADDITION. SLATE EXEBCISE TABLE NO. 2. Columns of Three Figures, 4r7. 1. Commence with column A, opposite J, and copy three figures for the first example ; then opposite "4^ and copy three more for the second example ; then opposite 5, and copy tliree more for the third example. Continue in this way to the bottom of the column and you will have on your slate : 1 "' i I I (1) (2) (3) (4) (5) (0) (7) (8) o 5 2 4 6 8 4- 5 6 2 4- 6 3 4 5 8 2 I 6 3 A 5 8 9 2. Copy examples from each of the other columns in the same manner and find the sum for each example. Columns of Four or Moi'e Fiyures, 48. 1. Commence with column .1, opposite i, and copy the required number of figures for the first example. Copy the second, third, etc., examples in the same manner as those with three figures. 2. Copy in this way from each column in the table, examples with four figures in a column ; then five figures ; six figures ; seven figures ; eight figures. Note.— The teacher should illaptratc on the blackboard, tojonngpapilt, the method of copying examples from this and following tables. The ])upU Bhonid bo required to practice on examples with three and four numbcff; until he can give the sums almost at sight of the flgurei ; longer columnB can then be given. Definite work from thie* and 9nbfteqnent tables should be asHigned to the popil to prepare, on hie slate or on paper, at his seat and at home. ADDITION, 87 \ 2. If and copy 2f and copy 3f and copy is way to the ilate : 5 8 (8) 5 8 9 B in the same SLATE AND BOABD EXERCISES. 49. Find the sum of Explanation.-I. The sum of 7, 9, and 8 ie found by forming groups of ten. Thua, the 7 and make 1 ten uud 6, and thiB 6 and 8 make 1 ten and 4. Hence, 7, 9, and 8 make 2 tens and 4. 2. The Bum of 7, 9, and 8 is the same whether these figures represent unita^ tens, or hundreds, etc. Hence, when their sum ie found, if they repreeein, units, as in the first example, the sum is units ; if tliey represent tens, as in the second ex- ample, the sum is tens ; it hundreds, hundreds, etc. 50. Analyze on your slate each of the following sets of numbers, thus : (1) (3) (3) 8 80 800 9 90 900 7 70 700 24 240 2400 8SS9 =-8000+500+30+9. 3080 = 3000+ 80. 7402 = 7000+4.00+ 2. res. i, and copy Copy the 18 those with (1) 6740 8042 4305 (2) 5578 6909 7025 (3) 3063 6704 5380 (4) 68953 70507 38005 (5) 70406 40069 80340 (6) 37506 93540 60320 6 1 . Find the sum in each of the following examples : )le, examples six figures ; o young puplli, lies. ith three and of the figure! ; assigned to the lome. 1. TO + 5. 4. 7200 + 80 + 4. 7. 90 + 60. 2. 800 + 60 + 3. 5. 6003 + 400. a 700 + 600. 3. 600 + 80 + 9. 6. 70 + 50. 9. 5000 + 9000. (10) (11) (12) (18) (14) (15) 80 400 9000 40000 9000 4005 60 700 5000 80000 6000 7008 20 800 7000 30000 8000 2006 50 600 8000 90000 6000 8009 38 ADDITION-, I \ SLATE AND BOARD EXERCISES. 52. 1. Find the sum of 245, 508, ;05, and 25i). Explanation.— 1. Wo write the numbers so that figures reprcs-eutiug the tauiu ortlcr of units stuud iu the t-ame column. 2. We add the units' column, as in (4:9), naming only the successive sums, thus, (», 14, ri, 2r. We write the 7 unitx under the units' column. 3. We add the 2 teiL-^oi the uuits' column to the tens' column, adding the tens' column by narainp, a- before the successive sums; thus, 2, 7, 10, 22. 2G tens, or 2 hundred and 6 tens. We write the 6 (ens under the tens' column. 4, We add the 2 hundred to the hundred's column, and proceed as with the units and tens. We write the 18 hundred under the hundred'sjfolumu. 245 508 795 259 1807 r **J5. Copy on vour slate and add and explain, as above, each of the following examples : (3) (3) (4) i'^) (6) (7) . 50:} 00 370 2075 48060 52708 00 660 8080 59083 3501 970 759 63 0708 702 983 5839 93 605 635 7538 70839 90780 58 457 78 3789 5909 038 543 43d 6497 25394 30348 45570 (8) (9) (10) (11) (13) (13) ?M 209 8437 5674 805 8500O 8970 9500 589 8009 93 3905 8008 8877 03 730(50 7158 40038 57 634 437 7950 8390(5 9(5077 0:53 3735 6895 30509 506 4940 59V)8 476 703 4877 2398 82596 755 65 4325 7 -37 7433 8579 979 420 512 44553 740 31164 vM: ADD IT [0 lY. 39 ES. here so that liis stand iu 1:9), naming t. \Vc write 1 to the teas' L'yt*ive sums ; 3 6 (ens under ceed as with ed'sjfolumu. ibovc, each (7) . 52708 5830 96780 038 45570 (13) 85000 3905 40038 90077 4940 82590 8579 31104 ARITHMETICAL TABLE No. 3. ''ft 1. ^ JB» €?• s^« £;• r. ^ A / • / 'J J / ■J cV ■ / 7 6 7 \ 1 1 7\ 6 \ S / ^ 8. 4. ;«• 6. 1 /. ^■^^ d~' O / K. ^ ' 1 /'/ / .f . ) r / 8. o •J / 9 rO 9. ■ / /■ /^' 9 /I./ / A' // 10. 1 /y .■/ d' (• 9 s 54. Copy examples as shown on next page from this table and from Table No. 2, on page 35. Continue this practice until you can add rapidly and accurately. Answers to examples from the Tables are t,Mvon at the end of the book. r- 40 ADDITION. 1 EXAMPLES FROM TABLES NO. 2 AND 3. 1 Exercises tvith Ntunbers of Two Figures. 1 5 ■l J (8) (9) 30 54 54 26 65. 1. CJopy examples with two numbers from Table No. % page -35, then from Table No. 3, page 39. Use columns A and B. Commence opposite 1, and take two numbers for the first example, then opposite 2, and take two more numbers for another example, and so on to the bottom of the table. The examples taken in this way from columns A and B, Table No. 8, are as follows : (1) (2) (3) (4) (5) (6) (7) 65 53 20 67 42 36 65 63206742366530__ 2. Copy in this manner examples from columns b and c ; c and D ; d and E ; £ and f ; f and o ; a and n. 3. Copy in the same way examples of three numbers ; four numbers ; five numbers, etc. Find the sum for each example. Exercises with Ntunbers of Three or More Figures, 66. 1. For lumbers of three figures use any three columns that follow each other, as abc, def. 2. For numbers of four places use any four columns that fol- low each other, as BCDE, BFOH. 3. Commence with examples of three numbers, then take four, five, aud so on up to eight numbers. 4. Copy the numbers from the table in the same manner as those of two figures. Thus, the examples with three numbers from columns abc, Table No. 3, are as follows : (1) (3) (3) (4) (5) (6) (7) (8) 658 537 205 673 428 360 657 304 537 205 673 428 360 657 304 540 205 673 428 360 657 304* 540 265 ADDITION, 41 AND 3. \ires, able No. 2, , and take f and take on to the way from (0) 64 26 B and c ; bere; four L example. Figures, e columns s that fol- then take manner as 3 numbers m WBITTEN EXERCISES. 57. 1. Howmanypoundsinthreeloadsof hay, each weigh- ing 2325 pounds? In five loads, each weighing 1983 pounds ? 2. How many acres in four farms, each containing 198 acres? 3. A fanner sold 293 bushels of wheat to one man, 185 to another, and 86 to another. How many bushels did he sell? 4. Henry Scott sold a span of horses for $275, a carriage for $395, and harness for $65. How much did he receive ? 5. A farmer has 95 sheep in one field, 187 in another, and 264 in another. How many sheep has he in all 1 6. A merchant sold 175 yards of cotton on Monday, 386 yards on Tuesday, 139 yards on Wednesday, 98 yards on Thursday, 216 on Friday, and 397 on Saturday. How many yards did he selliuall? 7. A man sold a house for $8894, a horse and carriage for $586, and seven tons of hay for $95. How much did he receive for the whole? 8. Peter Eaton paid for a tub of butter $24, for eight cords of wood $49, and four barrels of flour $36. How much did he pay in all ? 9. How many pounds of butter in five tubs, each weighing 85 pounds ? In three tubs, each weighing 78 pounds ? 10. Wliat is the sum of $472, $843, $366, and $95? Of $307, )^283, $94, $569, and $85 ? Of $836, $1372, $995, and $48? 11. How many bushels in three loads of wheat, each contain- ing 83 bushels ? In seven loads, each containing 69 bushels ? 12. A grocer bought three cheeses, each weighing 54 pounds, and four, each weighing 69 pounds. How many pounds did he buy in ail ? 13. Find the sum of $356, $257, $423, and $87. Of $936, $504, $240, $50, and $203. Of $504, $641, $237, $2140, and $731. i I 42 ADDITlOy 1 ; CiLNADIAN MONEY. 58. 1. The Sign | stands for the word dollars. Thus, |9 is read nine dollars. 2. The letters c^ stand for cents* Thus, 24 ct. ia read twenty-four cefUs. 3. ^^^^en dollars and cents are both given, the cents are expressed by writing them after the dollars with a period between them. Thus, $5 and 37 ct. are written $5.37. 4. When the number of centa is lesB than 10, a cipher must occupy the first place at the right of the period. Thus, $15 and 9 ct. are written |15.09. 5. In arranging numbers for addition, dollars must be placed under dollars and cents under cents, in such order that the periods in the numbers stand in the aame column ; thus, (1) (2) ^3) 142.69 $840.36 $9v,..D5 8.25 93.08 60.32 346.54 307 03 300.04 Add as If there were do periode in the numbere, and in the sum place a period between the second and third fi^Tire from the right. The figures •n the left of the period express dollars, those on the right cents. 59. Read, arrange and add the following : 1. $6.36 ^ $99.43 + $507 + $70.50. 2. $364.03 + $30.52 + $709 80. 3. $3.00 _ $805.30 4- $34.09 + $600.04. 4 $490.08 + $5.25 + $46 -f $208.07. Express the following in figures and with the proper signs. 6. Thirteen dollars and forty-eight cents. 6. Two himdred three dollars and seventy cents. i. Four dollars and seven cents. 8. Eight hundred dollars and forty cents. m ADDITION. 43 SLATE EXERCISES. 00. Copy and find the sum of each of the following : (1) (2) , (3) (4) {^) $30T.0-2 $S00.G0 $583. $37.06 $573. 84.09 905.07 609.00 802.40 65.32 500.00 32.06 28 75. 802.05 400.75 708.39 436.90 90.03 850.73 239.08 400.05 800.07 342.79 90.50 (6) (<) (B) (9) (10) $900.05 $26.80 1854.05 1389. $101.01 57. 13.14 60.2:^. 57.65 79. 406.13 590. 100.10 105.10 255.39 73.00 268.39 530.05 780.23 893. 5.59 85. 8.5.70 96.0*5 500. 260. 703.04 705.04 40S. 46.90 Read, arrange on your slate in columns, and find the sum : 11. Of !i;8.25, $27.48. $13.06, ;^407.39, and $80.05. 12. Of $273.06. $75, $306.02, $.500, and SS30.73. 13. Of .t.506. $39, $G<>2.15, $290.87, and $730.42. Express the following in figures and with the proper sigps : 14. Seven dollars and nine cents. Eighty-four dollars and six cent??. 15. Two hundrt'd ten dollars ar ' three cents. 16. One dollar and nine cents. Five dollars and ninety cents. 17. Sir hundred thirty dollars and eight cents. 18. Use the sign $ and express Al' cents ; 79 cents ; 95 cents ; 8 cents ; 4 cents ; 1 cent. 19. 79 cents ; 50 cents ; 7 cents ; 6 cents ; 10 cents ; 9 cents.. 20. One hundred one dollars and one cent. 21. One thousand one dollars and one cent. \ u ADDITION. WBITTEN EXERCISES. <$1. 1. Bought twelve pounds of sugar for $1.68, two pounds of tea for $1.90, and eight pounds of butter for $2.40. "What did the whole cost ? -> 2. Paid $1.15 for cheese, $4.93 for coflee, $3.85 for flour, and $7.09 for potatoes. How much did I pay in all ? 3. Sold three barrels of apples for $12.75, fifteen bushels turnips for $3.75, and four cabbages for 60 cents. How much -did I get for the whole ? 4. Paid one man $38.02, another $307.45. How much did I pay in all ? 5. Henry bought a gun for $17.70, a pair of skates for $3.45, and a hunter's knife for $2.45. How much did the whole cost ? 6. Bought a coat for $22.85, and a hat for $5.54. How much did I pay for both ? 7. A lady paid for goods in one store $14.86, in another ■$37.79, and in another $6.05. How much did she pay in all? 8. A grocer sold to one man $84.63 of groceries, to another $16.20, and to another $9.07. How much did he sell in all ? 9. Bought three books for $5.73, six quires of paper for 90 cents and a gold pen for $6.85. How much did they all cost? 10. Ada paid for a dress $23.34, a hat $5.87, a shawl $17.64, and ll pair of gloves $1.95. How much did she pay in all ? 11. James sold 2 barrels of apples for $6.95, a bushel of pears for $3.45, and 4 baskets of peaches for $4.25. How much did lie get for the whole ? 12. George bought 10 cords of wood for $43.50, a tub of butter for $20.75, and 17 bushels of potatoes for $8.50. What was the cost of the whole ? 13. A farmer received in one year $806.95 for wheat, $256.38 for corn, and $95.86 for oats. How much did he receive in all 1 14. Paid for wheat $736.25, for oats $121.10. How much did I pay f o" all ? i,^ ADDITION. 45 $1.68, two 3r for $2.40. )r flour, and •en bushels How much much did I es for $3.45, whole cost ? How much in another pay in all ? B, to another lellinall? )f paper for did they all lla^vl $17.64, ly in all ? a bushel of How much ,50, a tub of 18.50. What 'heat, $256.38 eceive in all ? [ow much did WHI'x'TEN EXERCISES. Gli. 1. Thomas Austin bought 3 horses for $527, cows for $181, and 12 sheep for $63.85 ; what did he pay for all? 2. A man gave to his wife $1145, to his daughter Jano $205.60, to his daughter Agnes the same amount, and to liis son $305.58 ; how much money did he give to all ? 3. lu a certain city there are 5 schools ; in the nrst are 789 pupils, in the second and third, each 935, in the 2o;'rth 1100, and in the fifth 886 ; how many pupils in the five schools? 4. Elmer earned $80.29, his father gave him $47.13, then he earned $62.08 more ; how much money had he ? 5. If I deposit $207.18 in a bank on Monday, $466.97 on Tuesday, $136.08 on Wednesday, $37.20 on Thursday, $200.28 on Friday, and $1060 on Saturday, how many dollars do I deposit in the six days ? 6. A man buys a village lot for $2652, upon which he builds a house which cost him $1907.75, he pays $20.32 for fencing, $49.09 for having his lot graded, and $35.48 for laying a side* walk ; how much money will pay for all ? 7. James Thompson owed one man 26 dollars and 4 cents, he owe^ another man 475 dollars and 90 cents, another $1406 and 8 cents ; what is the amount of his indebtedness ? 8. John Bedford went to the grocery and bought the follow- ing items : 2 barrels of fldur for $13.75, 13 pounds of butter for 3 dollars and 8 cents, 4 g^lons of syrup for $4.60, 25 pounds of meal for $3 and 7 cents, and 13 gallons of vinegar for 6 dollars and 30 cents ; what did he pay for all ? 9. A nurseryman sold 185 peach trees, 3146 apple trees, 230 plum trees, 2024 cherry trees, 876 pear trees, 256 quince trees, and has still remaining 4892 trees ; how many trees did he have before he sold any ? 10. William Henderson paid for groceries for the week $7.89, for meat $2.37, for other articles $2.05, and for a suit of clothes $28.75 ; how much did he pay in all ? * i i I i It 46 ADDITION. \ \ DEFINITIONS. 63. Addition is the process of uniting two or more num- bers into one number. 64. Addends are the numbers added. 65. The Sum or A^nount is the number found by addi- tion. 66. The Process of Addition, when the sum is greater than ten, consists in forming units of the same order into groups of ten, so as to express their amount in terms of a higher order. 67. The Sign of Addition is + , and is read plus. When placed between numbers, thus, 8 + 3 + 6 + 2 + 9, it means that tliey are to be added. 68. The Sign of Equality is =, and is read equal; thus, 9 + 4 = 13 is read nine plus four equal thirteen. RULE. 69. /. Write the numbers to he added in such a manner thM figures representing the same oi'der of units stand in the same column. II. Add each column separately, commencing with the units. Ill When the sum, of any column is expressed by two or more figures, place the right-hand figure binder the column, and add the number expressed by the remaining figures to the next column. IV. Write under the last column its entire sum. Proof. — Add the numbers by commencing at the top of the columns. If the results agree, the work is probably correct. m lore num- SUBTRACTION OBAL EXEBCISES. 70. 1. If 3 pears be taken from 8 pears, how many will t-e left? 3 pears taken from 8 pears leaves 3. Things are Subtracted by taking them away. 3. 9 books less 5 books are how many ? Less 2 books ? 4. Henry has 8 pears and James has 5 ; how many more pears has Henry than James 1 8 pears 5 pears compared toith 3 pears shows that Henry has more than James. 5. How many are 8 pears greater than 5 pears ? 6. Comparing two numbers, to find how many the one num- ber is greater than the other, is called Subtraction* The greater of the two numbers compared is called the Miimendf the lesser the Subtrahend, 11. The number which indicates how many the minuend is greater than the subtrahend is called the Difference, 8. The Sign (— ) stands for the word less; thus, 7—3 = 4 is read, seven less three equal four. I I) < I ill 'f I 48 SUBTRACTION. SLATE EXEBCISES. 71* Copy the following exercises and practice on each sepa* rately. Thus, find the differences and write them under the numbers, then erase them and vrrite them again and again from memory. S9S68479 11111111 4. A •8 wards 3 5 6 7 9 10 4 8 5. R i. I i I ■3 2 i. i ence ii G. ilOW 111 7. h 5 4 7 9 10 8 11 6 1 more r I §. I i. 3 3 s i 8. L more t 5 7 9 11 •4 10 6 8 IS 9. A manv : 10. I I I 4 4 ■5 d 4 4 more ^ 11. ' how 11] 6 9 11 8 13 10 7 14 ' 13. and th 6 5 5 5 5 •6 6 5 5 13. 1 pike, { 14. 12 10 8 13 15 11 14 7 orange 1 (^ 6 6 6 6 6 6 6 6 10, dollan S r li Tli Ar TION, 49 ORAL EXERCISES. 72. 1. James had six cIovCkS and sold two of them to George ; how many doves had he then left ? Solution.— He had aa mauy doves as the dilTei-ence between 6 doves and a dovt'fl, which is 4 doves. 2. Jolin had a knife with four blades, but he broke three of tiieiii ; how many blades did the knife then have? 3. Nine girls werci. playing together, but five of them were called home by their mothers ; how many remained? 4. A wheel had twelve spokes, but three of them were after- wards broken out ; how many spokes were left ? 5. Robert is 11 years old and Mary is 7 ; what is the differ- ence in their ages? C. One cat caught eleven mice and ar )ther caught three ; how many more mice did one catch than the other ? 7. Ivan has eight rabbits and Hubert has five ; how many mon^ nibbits has Ivan than Hubert? 8. Laura has 6 dolls and Mabel has only two ; how many more dolls has Laura than Mabel ? 9. A long ladder has 17 steps and a short one has 8 ; how many more steps has the long ladder than the short one? 10. A jeweler has 19 gold rings and 5 silver ones ; how many more gold rings has he than silver ones ? 11. There were 18 apples on a tree, but the wind blew off W; how many apples were then left ? 13. A farmer set thirteen fence-posts ; six of them were oak and the' rest cedar ; how many were cedar? 13. Samuel caught seventeen fish ; three were perch, three pike, and the rest trout ; how many trout did he catch ? 14. A boy had nine cents and gave five of them for an orange ; how many cents had he left ? 15. William had 15 dollars and gave away 6; how many dollars has he left ? . ' ii W 1 I .? . 1 if F n M I ? 50 SUB TEA OTIO N, SLATE EXEHCISES. 73. Copy the following exeriises and practice on each sep- arately, as directed in (71). Continue the practice until you can give the differences at sight of the numoers. 12 9 8 11 10 IS u 16 7 7 7 7 7 7 7 7 13 IS 11 9 8 10 16 u 17 8 8 8 8 8 8 8 8 10 13 11 -<- <..■' 3 17 14 16 12 9 9 9 9 S 9 9 9 8 12 3 4 6 6 17 8 4 13 2 12 8 18 3 11 9 • 9 16 7 6 7 5 12 8 s 18 7 IS 9 18. 9 12 4 18 19 9 3 27 4 35 2 — 4!) 5 28 3 2S 2 S9 6 SUBTRACTION, 51 OBAL EXEBCISES. 74. 1. How many are 8 less 6 ? 11 less 6 ? 14 less 6 ? 2. How many are 16 less 7 ? 13 less 7 ? 9 less 7 ? 15 less 7 ? lCless7? 14 less 7? 39 less 7? 3. How many will remain if 8 be taken from 8 ? From 10 ? From 14 ? From 17 ? From 12 ? From 16 ? From 29 ? 4. How many are 11 less 9 ? 17 less 9 ? 13 less 9 ? 19 less 9 ? 12 less 9 ? 18 less 9 ? 5. How many are 13-8? 17-9? 26-5? 13-5? 15-7? 24-3? ^9-4? 86-3? 99-9? 6. If 7 tens be taken from 9 tens, how many tens will remain? 8 tens less 3 tens are how many ? 80 — 20 = how many ? 7. Express in figures 5 ter^; 8 tens; 6 tens; 12 tern; 15 tens ; 9 tens ; 18 tens ; 26 tens; 57 tens ; 16 tens. 8. Express 9 tens and 5 tens each in figures. 9 tens less 5 tens are how many ? 90 less 60 are how many ? 9. Eighty trees less 50 trees are how many trees? 10. Express in figures 7 hundred ; 4 Tiundred ; 12 hundrei,; \% hundred; \% hundred ; 2^ hundred; 1 A hundred; \^ hun- dred. 11. Express 9 hundred and 3 hundred each in figures. 8 hundred less 3 hundred are how many ? 12. Nine hundred less one hundred are how many ? 13. Thirteen tens less seven tens are how many? 130 less 80 are how many? 120 lees 90 are how many ? 14. Fifteen hundred less eight hundred are how many? 1500 less 800 are how many ? 1400 - 600 = how many ? 15. A farmer had 9 hundred bushels of wheat and sold hundred ; how many bushels had he left V 900 — 000 = how many ? 1(5. Express in figures thousand ; 8 thousand ; 19 thousand. 17. Seven thousand less five thousand are how many ? 7000 less 5000 are how many ? 6000 — 2000 = how many ? = 1 i! 52 S UBTRA CTION, SLATE EXERCISES. 75. Copy on your slate and perform tlie sut>tTactio& Id eacli of the following exercises, thus : 7 70 700 7000 500 5000 4 40 400 4000 300 3000 8 30 300 3000 200 2000 Observe, that when 4 is takon frow 7, the reniainder Is 3 ; hence 4 nnits taken from 7 units the remairaor must be 3 units, 4 tens or 40 taken from 7 tens or 70 the remainder must be 3 tens or 30, and so on with hundred, thousands, and so forth. 60 800 8000 - » ' 60 600 6000 80 300 3000 - 3 . 20 200 2000 900 9000 120 110 180 150 500 5000 60 70 50 80 7000 5000 9000 - 4 - 1400 1200 1600 4000 3000 7000 800 300 900 70 9 79 - 5 ■ 000 80 7 687 80 4 84 400 50 2 453 6 907 502 7008 2004 5804 2301 8976 8242 6598 2178 9786 2514 SUB TE A CTION. 53 SLATE EXERCISES. 76. Separate each of the fallowing numbers into two parts, so that one part will consist of 1 ten, or of 1 ten and the units of the number, thus : ^iO ^ 20 + 10. 78 = 60-*-18. 359 = 340 + 19. Continue to separate in this manner, on your slate, the foDowing num- bers, until you can ^ve the parts at sight of each number. 20 60 31 1 71 62 33 73 24 40 30 61 32 92 63 28 64 70 90 91 52 72 93 54 94 50 21 41 82 22 43 74 44 80 51 81 49 2 53 88 34 84 36 65 26 56 77 43 98 29 85 25 96 97 67 78 28 69 45 55 36 37 27 38 39 99 75 76 66 87 67 68 59 49 95 46 86 47 i^ 58 89 79 77. Write on your slate in irregular order the tens from 10 to 90 and subtract 2 from each, thus : I ■ I il t 40 20 60 JO 70 50 80 10 90 2 2 2 2 2 2 2 2 2 88 18 58 28 68 48 78 8 88 Observe^ that in each example we simply subtract 2 from 10; thus, in taking 2 from 40 the 40 la regarded as 30+ 10, and the 2 taken from the 10, leaving 8, this 8 added to the 30 gives the remainder 38. Subtract in this manner successively 1, 2, 3, 4, and so on up to 9. When the remainders are found, erase them and write them again and again from memory, until you can write them at sight of the two numbers. 1 1 W ! M 64 SUBTRACTION. SLATE EXERCISES. 78. Write on your slate in irregular order the tens and 1 unit from 21 to 91 inclu3ive, and subtract 3 from each num- ber, tlius : 31 _2 19 Observe, that in each example the number A:om which the 2 is snbtracted is separated into two parts, as in (76). Thus, in subtracting 3 ft-om 31, the 31 is regarded as 30+11, and the 3 is taken from 11, leaving 9 ; adding this 9 to the 30 giva the remainder 39. Subtract in this manner successively 3, 4, 5, 6, 7, 8, and 9 from each of these numbers. In each case, when the subtrac- tion is performed, erase the remainders and write them again and again from memory. Practice in this way upon each of the following exercises : 31 51 81 2 2 2 d9 49 79 91 61 41 71 2 2 2 2 89 59 39 69 42 72 32 52 82 22 62 92 J J _3 3 J 8 J J Practice as directed, upon subtractings 3, then erase it and practice in the same manner upon 4, then 5, then 6, 7, 8, and 9, 58 4 83 4 33 4 63 4 93 4 43 4 23 4 73 4 Practice upon 4 as directed, then 5, then 6, 7, 8, and 9. 84 34 64 24 74 44 94 54 6 5 5 5 5 5 5 5 Practice upon 5 as before, then upon 6, 7, 8, and 9. SUBTRACTION, 55 SLATE 'HIXEHCISES. 79. Practice as directed in 1(78) ou the following exercises : 1 76 46 86 86 6G £6 56 96 7 7 7 7 7 7 7 7 After practicing upon 7, erase it and use 8, then 9. 2 47 67 57 97 37 87 27 77 8 8 8 8 8 8 8 8 Subtract 9 from each number iu the same manner. 3 38 58 98 48 78 28 68 88 9 ^ _9 J 9 _9 9 9 80. Analyze the numbers and perform the subtraction iu each of the following examples, thus : Find the difference between 85 and 47. Observe, that the 7 units in the BQbtnthend cannot be taken from the 6 units in the minuend. Hence we separate the minuend into 70+ 15 and take the 7 units from the 15 units, and the 4 tens, or 40, from the 7 tens, or 70, leaving 38, the difference between 85 and 47. Minuend, Subtrahend, Difference, 85 = 70+15 47 = 40 + _7 88 = 30+ 8 Perform in this way the following subtractions : 1. 53 - 26. 6. 85 - 37. 11. 361 - 34. 2. 82 - 55. 7. 63 - 44. 12. 284 - 58. 8. 61 - 27. 8. 52 - 25. 13. 757 - 29. 4. 95 - 79. 9. 31 - 13. 14. 368 - 35. 5. 64 - 35. 10. 82 - 46. 15. 471 - 43. W \\ I !' I. ' 1^ 56 S UB TR A C Tl X. OKAL EXERCISES. 81. 1. How many will remain if 6 be taken from 11? 6 from 21 ? « from 41 ? G from 91 ? from 141 ? 2. How many will remain if 5 bo taken from 13 ? 5 from 23 ? 5 f ]oni 53 ■? 5 from To ? 5 from 253 '? 3. What number must be added to 7 to make 14? To make 34 ? To make 44 ? To make 84 ? To make 134 ? 4. There are 24 hours in a day ; if you sleep 7 hours, how many liours are you awake ? 5. I sold a cow for 38 dollars, which was 9 dollars more than it cost ; how many dollars did it cost? 6. A man paid 49 dollars for some hay and 7 dollars for some straw ; how much did the hay cost more than the straw? 7. A tree had 73 apples on it, but the wind blew ofT 8'of them ; how many remained on the tree? 8. There were 82 houses in a certain town, but 6 of them were destroyed by fire ; how many houses remained? 9. There were 55 persons on a train of cars, and at a certain Station 5 got olf and 13 got on ; how many were then ou the train ? 10. Amy has 27 lines to read in her primer and she has read C ; how nnuiy more lines has she to read? 11. Judson caught 39 trout, but the 7 largest fell back into the Walter ; how many did he have to cany home? 12. Farmer Esty had 132 sheep ; five of them were black and the rest white ; how many were white? 13. A school contains more boys than girls, and there are 8vT boys ; how many girls are there? 14. There wero 230 houses in a village, but a fire burned 8 of them ; how many remained? 15. 283 minus 5 are how many? 357 minus 9? 574 minus 8? 613-7? 115-9? 845 -G? 88-9? 97G - 7 ? 89-3? 37-8? 317-4? 10. An orchard has 7 more apple trees than cherry trees, and there are 73 apple trees ; how many cherry trees are there ? »r->t:i -ittiiitiimmtami ...v SUBTRACTION, 57 SLATE AND BOABD EXERCISES. 82. Find the difference between 437 and 179. Minuend, Subtrahend, Difference, 437 m 258 Explanation. — 1, We write the lesser number under the greater, eo that units of the same order are in the same column. 2. Since 9 units cannot be taken from 7 units, we regard the minuend 437 as 420+ 17, and take the 9 wiits from 17 units, leaving 8 units. 3. Since 7 tens cannot be taken from the 2 tens that are left in the minu- end, we regard the 490 of the minuend as 800+120, and take 7^cn*or70 from the 12 tens or 120, leaving 5 tent or 60. 4. We take the 1 hundred from the 3 hundred left in the minuend, leav- ing 200 ; hence the difference between 437 and 179 is 258. Proop, 179 + 258-437. 83. Perform the subtraction in each of the following exam- ples, anc' sxplain and prove as above. 1. Take 248 from 524. 18. 3759- 1985. 2. Take 385 from 732. 19. 8362- 4766. 3. Take 59G from 963. 20. 6425- 3847. 4. Take 478 from 654. 21. 4231 - ■ 1777. 5. Take 289 from 467. 22. 9443- 6888. 6. Take 653 from 821. 23. 7333- 3556. 7. Take 361 from 533. 24. 5555 - 3666. 8. Take 487 from 762. 25. 8232 - ■ 6444. 9. Take 555 from 743. 26. 6524- 2879. 10. Take 296 from 854. 27. 9365- A987. 11. Take 359 from 532. 28. 3694 - 2867. 13. Take 89 from 2311. 29. 6325 - 4838. 13. Take 425 from 613. 30. 4363- 1795. 14. Take 96 from 3624. 31. 9564- 8298. 15. Take 587 from 936. 82. 5346- 3769. IG. Take 293 from 462. 83. 2436- 857. 17. Take 69 from 4326. 34. 8363- 976. '•^ I) •! :%i ^1 '■ f I 58 SUB Tit A CTION. SLATE EXERCISES. 84. Find the difference between oOO and 7. 500 __7 493 Explanation.— There are no units from which to take the 7 ttnits, hence we regard the 500 as 400 + 90 + 10, and take the 7 units from the 10 units, leaving 3 units. Ilence we have remaining 400+90+3 = 493, the diflference between 500 and 7. PROOf, 493+7 = 500. 85. Perform the subtraction in each of the following exam- ples, and explain and prove as above. (1) 30 (3) 800 (3) 500 (4) 600 (5) 900 (6) 400 4 2 5 6 3 7 (7) 7000 (8) 9000 (9) 3000 (10) 8000 (11) 6000 (13) 4000 8 4 5 3 6 9 (13) 4000 (14) 6000 (15) 8000 (16) 3000 • (17) 9000 (18) 5000 37 25 63 57 74 46 (19) 150 (30) 1200 (21) 1800 (32) 210 (23) 510 (34) 710 4 7 5 3 2 8 (35) 1900 (36) 8100 (27) 8000 (88) 5100 (29) 3100 (30) 61000 53 69 37 02 74 41 (31) 7004 (32) 13000 (33) 4000 (34) 61000 (;]5) 11000 (3G) 10000 807 0008 502 7004 8006 3003 r I 1. 2. 3. 5. 9. 10. ^1 : !•' SUB TRA CTIOX. 5i ARITHMETICAL TABLE No. 4. 1. A. B. C. D. £«» F. a. in i d I 1 ■> ! ! ^ i 1 'J / ^' / n V / '■1 / V / /■ / / •y / / /' / / / } S' y/ s / r / \ J J / /I/ ■ /, /' 5 ,/ { :y 1 y ■ 1 A, ^ / 1 / ■ ; / — i / 2. 3. 4. 5. 0. t. & 9. 10. ; ) nr ! i •"H I 8(>. Copy examples as shown on next page from tliia table ftnd from Table No. 2, on page 35. Continue this practice until you can find accurately, almost at sight of the figures, the dif' ference between any two numbers. 60 SUB TEA CTIOX. EXAMPLES FBOM TABLE NO. 3. lHjcet'cises with Numbers of Two i'iguresm 87. 1. Use columns A and 13, Take for the first exam- ple the figures opposite 1 and 2, for the second example the figures opposite 2 and 5, etc. Write the lesser number under the greater. The examples from columns A. and S are the following : (1) (2) (3) (4) (5) (6) l7) (8) (0) 65 53 67 67 42 65 65 54 54 63 20 20 42 36 36 30 30 26 2. Copy examples in the same manner from B and c ; c and D ; D and e ; E and F ; F and 6 ; 6 and h. 3. Copy new examples, taking one number from columns A and B and the other from oolomnB B and C, thna: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) 65 53 20 73 42 60 65 30 59 65 5837_567283657j4026 4 Copy examples in iiis way, taking the numbers from columns b and c, and c and d ; c and d, and D and E ; D and E, and E and f ; e and f, and f and o ; f and 6, and G and h. Eocercises with Numbers of Three or more Figures, 88. 1. Copy examples with numbers of three figures from columns ABC in the same manner as the first set with tAvo figures, then from columns BCD, CDE, def, efg, fgh. Examples with numbers of four or more figures may be copied in the same way by using the required number of columns. 2. Use for one number columns ABC and for the other num- ber columns bcd ; then BCD and cde ; and so on. SUBTR A CTION. 61 WRITTEN EXERCISES. St>. 1. Henry has $74 and James has $29. How many dollars lias Henry more than James? 2. What is the difference between $436 and $279 ? Between 11824 and $968 ? Between $1035 and $632 ? 3. A man had $935 in the bank, and took out $369. How many dollars had he then left in the bank ? 4. A grocer bought 482 pounds of maple sugar, and sold 295 pounds of it. How much has he still left ? 5. I had $145 in my pocket-book and paid out of it to one man $49, to another $48. How much had I then left ? G. A man owning 934 acres of land, sold to one man 283 acres, to another 215. How many acres has he still left ? 7. A boy had 41 marbles and bought 62 more ; he then lost 49 of them. How many had he left ? 8. A grocer bought two tubs of butter, the first containing 63 pounds, the second 85 pounds ; he sold out of the first 29 pounds, out of the second 48 pounds. How many pounds has he left in all? 9. A grain merchant bought three lots of wheat as follows : 584 bushels, 239 bushels, and 463 bushels ; he then sold out of what he bought 1098 bushels. How many bushels has he left ? 10. A farmer has in one stack of hay 28 tons, in another 53 tons, and in another 47 tons ; he has sold in all out of the three stacks 99 tons. How many tons has he left ? 11. A merchant had a piece of cloth containing 469 yards ; he sold to one man 132 yards, to another 184 yards, and to another 62 yards. , How many yards of the piece had he then left ? 12. A man deposited in the bank at one time $238, at another $ 172, and at another $684 ; he drew out in all $1097. How much has ho still left in the bank ? 13. A farmer had 143 tons of hay and sold 19 tons ; how many tons has he left ? li Hi •4 ij ., 62 SUBTRA CTION. CANADIAN MONEY. 90. 1. Take $18.67 from $43.35. $43.25 _18^ $24.58 Explanation.— 1. Write the leeeer number nnder the ^eater, so that the periods are in the same column. When there are no centg, place two ciphers on the right of the period. 2. Subtract as if there were no periods, the 1867 from the 4S25, and place in the remainder a period between the second and third figure from the righ^ 3. I'Tie figures to the right of the period express the number of cents, and those to the left the number of dollars ; hence the remainder is read, twenty- four dollars and fifty-eight cents. Perform the subtraction in the following : (2) $49.76 23.51 (7) $835.21 586.59 (3) $97.35 43.14 (8) $362.04 128.17 (4) $83.52 81.27 (5) $58.93 29.65 (9) (10) $730.42 $2034.07 583.90 1293.69 (6) $387.26 159.84 (11) $430^V05 2083.97 ii^l 12. I was to pay a man $3.19 and gave him a 5 dollar bill. How much change did I receive ? 13. Sold a load of wheat for $87.52 and received in pay only $43.95. How much am I yet to receive ? 14. Bought a book for $2.35 and gave the bookseller $10. How much change did he return V 15. A man owed me $37.43 ; he has paid $12.97. How much is still due me ? 16. A boy went into a grocery with $12, and paid for sugar $2.13, for tea $1.85, for butter $3.47, and for flour $4. How much of the $12 had he left ? 17. A man earns $18 a week and his family expenses are $13.42. How much docs he save each week? SUBTRA CTJ Ou\. 63 WBITTEN EXERCISES. 01« 1. A man had in his purse $413.52, and paid a debt of ^85.68. How much had he left in his purse? 2. Bought a coat for $29.75, a vest for $4.83, and paid on both $23.27. How much is yet to be paid ? ;j. William Robertson lent his neighbor $405.45, on which be has received $239.87. How much has he yet to receive? 4. A farmer sold a firkin of butter for $52.35, a cheese for $19.07, and a load of wheat for $83.25. He paid out of the money received $67.93. How much had he then left ? 5. Henry Mills bought a horse for $253, a harness for $37.45 and a buggy for $207. He paid on the whole $283.87. How much is yet to be paid ? 6. Out of $792.32 I paid a debt of $409.72. How much have I left ? 7. Sold a horse for $247, and took in exchange a yoke of oxen at $97 and a lot of sheep at $68.75. How much is still •lie me? S. Alexander Smith deposited in the bank $630.48, and after- wards drew out $375.87. How much has he in the bank ? 9. A merchant sold a lady 12 yards of cloth for $17.39, 7 yards of ribbon for $2.95, a shawl lor $29.17, and gloves for !jtl.35. She paid on the whole bill $36.83. How much did she leave unpaid ? 10. A farmer bought rf'cow for $87, a lot of sheep for $203.85, and a span of horses for $264. He paid on the whole $352.97. How much has he yet to pay ? 11. Out of a 60 dollar bill I paid $2.35, $7.84, $23.27 and $8.05. How much of the bill have I left ? 12. A lady had $99.50 \ len she went into a grocery. She paid $7 for sugar, $20.39 ior butter, $2.13 for spices, $9 for flour and $39.67 on an old account. How much of her money had she left? 'Si II 1 • - H •4 4 •^i' ( r 11 64 SUBTRACTION. DEFINITIONS. 1)2. Subtraction is the process of finding the diflference between two numbers. 93. The Minuend is the greater of two numbers whose difference is to be found. 94. The Subtrahend is the lesser of two numbers whose difference is to be found. 95. The Difference or Remainder is the result ob- tained by subtraction. The Process of Subtraction consists in comparing two numbers and resolving the greater into two parts, one of which is equal to the difference of the two numbers. 90. The Sign of Subtraction is — , and is reRd minus. It indicates that the number written after it is to be taken from the number written before it ; thus, 12 — 5 = 7. BULE. 97. / Write the subtrahend under the minuend, placiuff units of the same order in the same column. II. Begin at the rights and find the difference between the units of each order of the subtrahend and the coi'responding order of the minuend, and write the restdt beneath. III. If the numhrr of units of any brder of the subtrahend is greater than the number of units of the corresponding order of the .rdnucnd, increase the latter by 10 and subtract ; ttien dimin- ish by 1 the units of the next higher order of the minuend, and proceed as before. VTXOOY.—Add the remainder to the srthtrafiend ; if tJie sum is eqiial to the minuend, the work if probably correct. 2. 2 tir 3. 6 til 4. The read 3 tin 5. Exp and the s 3ti 4ti^ 6. FinI 7. WlJ adding ll said to /I 8. TaJ times an piicatm 9. Till cand, 1 10. tI is to bo 1 11. M ProdiM MULTIPLICATION. ORAL EXERCISES. 98. 1. 3 lines + 3 lines + 3 lines are how many lines? — 4- ■" 4- ^ are 9 lines. Three times 3 lines arc 9 lines. 3. 2 times 3 lines are how many? 5 times 3 lines? 3. 6 tim«s 3 pears are how many pears V 7 times 3 pears ? 4. The SiffU x stands for the word tunes. Thus. 5x3 is read 3 times 5, and means 5 4-5 + 5. 5. P]xpres3 each of the following by using both the sign x and the sign 4- . Thus, 3 times 4 = 4x3 = 44-44-4, 3 times 4. 4 times 0. 2 times 8. 5 times 4. 4 times 7. C times 5. 6. Find by adding how many 2 times 6 are ; 4 times 7. 7. When we memorize these results and can tell without adding how many 2 times 6, 4 times 7, and so on &t3, we are said to nniltiplij. 8. Taking one number, by using memorized ronults, as many times as there are ones or units in another, is called I\Ialti~ plication. 9. Tlie nuinber taken or multiplied is called the Multipli- cand, Thus, in 5 times 9, the 9 is the multiplicand. 10. The number that shows how many times the multiplicand is to be taken is calliul the Multiplier. 11. The result obtained by multiplying is * called the I^roduct, - Ni » \ i . tf I I h 66 '■} MULTIPLICATION. ORAL EXEBCISES. 99. 1. Five boys went fishing ; each caught two fishes, which they put in the same basket ; how many fishes were in the basket ? 2 + 2 + 3 + 3 + 3 = ? How many are five 3's ? 2. A man planted two rows of trees in his garden ; if there were three trees in eacli row, how many were there in all ? 3 + 3 = ? How many are two 3's ? 3. Simon picked two clusters of grapes, each cluster contain- ing 4 grapes ; how many grapeg did he pick? 4 + 4=:? How many are two 4's ? 4. Edith's mother gave her 4 books, and each book had three pictures; how many pictures in all? 3 + 3 + 3 + 3 = ? How many are four 3's ? 5. There are three clover-leaves on a stem ; how many leaves shall I have if I pick five stems? 3 + 3 + 3 + 3 + 3=? How many are five 3's ? 6. Ralph's father gave him six dollars a mouth for three months; how many dollars did he get in all? 6 + 6 + 6 = ? How many are three 6's ? 7. If a class learn four pages at one lesson, how many pages will they learn at four lessons? 4 + 4+4+4 = ? How many are four 4's ? 8. A man sold five hats, getting four dollars for each hat ; how many doll ars did he get in all ? 4 + 4 + 4 + 4 + 4 = ? How many are five 4's ? 9. If five leaves are on one twig, how many leaves will be on six such twigs? 5 + 5 + 5 + 5 + 5 + 5 = ? Hoav many are 8ix5'8? 10. If one chest liPs five drawers, how many drawers will four chests have ? 5 + 5 + 5 + 5 = ? How many are four 5's ? 11. ir there are four eggs in each nest, how many eggs will there bo i a sflfvcn nests ? 4 + 4 + 4 + 4 + 4 + 4 + 4 = ? How many are seven 4'8 ? 31 UL TIP Lie A TION. 67 fishes, were in if there in all? contain- ? How lad three ? Ho\T luy leaves ? How for three f6 + 6 = ? finy pages low many each hat; = ? How s will be Qany are ivers will »ur 5's ? pggs will ow many SLATE EXEBCISES. 100. Copy separately each of the following tables : Find the product for each example by addition and write it on your slate thus : 5y 2 2 5 2 8 2 ■ 2 8 6 Jf- 'r 2 9 Find the product of each pair of numbers as before t\nd write it under the numbers. Then eruse all thc^^ic i>roduc;f:-i and con- tinue to rewrite them from memory, until you can wiile them at sight of the numbers. iW. •tt 68 MULTIPLICATIO X SLATE EXEBCISES. 102. Find the product for the following examples and ex- plaii> each example thus : (1) 4x3. Four multiplied by 3 are 13. (3) 40 X 3. Four teiu multiplied by 3 arc 13 tens , or 120. Table o (3) 400 X 3. 3r 1300. Four hundred mu Itiplied by 3 are 13 hundred, 0x3 6x4 6x8 Table of Twos applied. 6x5 3x3 30x5 300x3 3000 X 6 3x8 30x3 300 X 6 2000 X 2 Table oj 3x4 30x7 300x9 3yoo X 8 0x3 3x6 30x4 200 X 5 3000 X 5 9x0 2x9 20x8 200x7 2000 X 7 9x4 9x8 Table of Tlireea applied. 30x4 300x8 3000 X 6 30000 X 9 30x7 300x3 3000 X 8 30000 X 7 13x3 30x5 300x9 3000 X 5 30000 X 5 13x5 30x9 300 X 7 3000 X 30000 X 8 30x6 300x3 3000 X 4 30000 X 6 104 out the , Table of JTour .V applied. 6 o 40x2 400x7 4000 X 5 40000 X 9 40x5 400x4 4000 X 9 40000 X 5 hj 40x8 400 X 8 4000 X 6 40000 X 8 Find under them 1 40x6 400x3 4000 X 8 40000 X 3 40x9 400 X 9 4000 X 4 40000 X 7 Table of Fives applied. 50x7 500 X 6 nOGO X 4 50000 X 8 m-A 50x9 500x8 5000 X 9 50000 X 3 60 X J 50 X 5 500 X 4 nooo X 5 50000 X 6 60 X 50x8 500x0 5000 X 7 50000 X 2 60 X M UL TIP LICATIO N, 69 J 'K SLATE EXEECISES. 10.*5. Copy Beparately each of tlie following tables and find the product for each example by addition. Thus, Ox 4 - + G + 6 + G = 24. I' 'I Tahlr ot Sixes, Table of Sevens. Table of Eights. Ox 2 OxG 7x3 7x8 8x4 8x7 Gx4 0x8 7x5 7x2 8x3 8x3 0x8 Cx7 7x7 7x6 8x0 8x5 Cx5 Gx9 7x4 7x9 8x8 8x9 Tahlv of Xlnes, J'able of Tens. Table of Elevens. 9x8 9x7 10x5 10 xG 11x3 11x6 9x0 9x3 10x7 10x3 11x5 11x4 9x4 9x9 10x4 10x9 11x3 11x9 9x8 9x5 ^ 10x8 Table of 10x3 Twelves. 11x8 11x7 12x2 12x4 12 X 3 13 x6 13x10 12x5 12x7 12 X 8 13 x9 13x11 1 04. Write each of the foregoing tables on your slate with- out the sign x thus : 6 G C 6 6 G 6 6 3 4 8 5 6 3 7 9 Find as before the product of each example and write it under the numlxTS. Then erase all these products and rewrite them from memory as in (101). ♦ Tftblc of Sixes applied. 60^3 60x5 60x7 60x4 GOO X 3 600x8 GOO X G 600x9 GOOO X 5 6000 X 8 6000 X 6 GOOO X 9 60000 X 7 60000 X 9 60000 X 4 60000 X 8 I i i.:ll ■ i tiki M 70 MULTIPLICA TION, SLATE EXERCISES. 105. Copy each of the following examples and find the products. Thus, 4007 X C = 24043. Observe, when you multiply the 7 units by 6, you have 4 tens and 2 iinits^ which you write in the tens and units place ; when you multiply the 4 thousands hy 0, you have 24 thousands. 707x3 707x5 707x3 808x3 808x7 808x4 9009x5 9009 X 8 9009 X 3 Table of Sevens applied. 7007 X 6 70707 x 7 7007 X 9 70707 x 5 7007x4 70707x8 Table of Eights ajyplied. 8008 X 6 80808 x 2 8008 x 5 80808 x 8 8008 X 9 80808 x 4 Table of Nines applied. 90909 X 2 90909 x 9 90909 x 6 90909 x 5 90909 X 4 90909 x 8 700707 X 8 700T07 X 6 700707 X 9 80808 X 6 80808x9 80808 X 7 90909 X 6 90909 X 9 90909 X 7 106. Find the product for each of the following examples and name the tables you apply in each case. Thus, 90705 x 8 = 372115. In multiplying the 5 units by the 8 the table of Jives is applied, in multiplying the 7 hundreds by the 3 the table of sevens is applied, in multiplying the 9 ten- thousands by the 3 the table of nines is applied. 1. 30906x7. 2. 80405x3. 3. 20003x8. 4. 20705x8. 5. 50908x4. C. 80306x7. 7. 90305x7. 8. 30806x9. 9. 70409x5. Multiply and explain the following : 10. 10x4. 11. 100x7. 13. 1000x8. 13. 4x10. 3. 4. 5. 0. 17. 18. 19. 30. MULTIPLICA TION. SLATE EXERCISES. 71 107. 1. Multiply 483 by 6. 483 6 2898 Explanation.—!. The number to be multiplied contains 4 hundred 8 tens and 3 units^ and each of these parts are to be taken 6 time,':*. 2. Six times 3 units malte 18 unity, or 1 ten and 8 units. We write the8 units in the units' place and reserve the 1 ten to add to the tens. 3. Six times 8 tens vasikc 48 tens, whicli, with the 1 ten reserved, make 49 tens or 4 hundred and 9 tens. We write the 9 tens in the tent?' place, and reserve the 4 hundred to add to the hundreds. 4. Six times 4 hundred make 24 hundred, which, with the 4 hundred re- served, make 28 hundred or 2 thousand 8 hxindred. Multiply and explain in this manner each of the following examples : 2. 385 by 3. 7. 5934x8. 12. 80360 X 3 3. 092 by 7. 8. 230G X 4. 13. 59007 X 6 4. 864 by 6. 9. 8509 X 5. 14. 30835 X 4 5. 497 by 4. 10. 6083 X 7. 15. 79068 X 5 G. 853 by 9. 11. 3095 X 9. 10. 99999 X 7 17. Multiply 83604 by 7 ; by 9 ; by 3 ; by 8 ; by 5. 18. Multiply 509307 by 3 ; by 5 ; by 7 ; by 8 ; by 2 ; by 9. 19. Multiply 83 hundred by 10 ; by 6 ; by 9., 20. Multiply 903 thousand by 7 ; by 5 ; by 3 ; by 8. (! )l 1% n 21. 70707 X 5. 30. 3333;) X 7. 39. 80808 X 9. 22. 30303 X 8. 31. 88888 X 9. 40. 79065 X 7. 33. 90909 X 6. 32. 55555 X 3. 41. 38 409 X 5. 24. 50508 X 9. 33. 44444 X 8. 42. 02537 X 3. 25. 90009 X 7. 34. 77777x4. 43. 90900 X 0. 36. 99999 X 4. 85. 23222 X 5. 44. 43925 X 8. 27. 66666x5. 86. 80907 X 6. 45. 89374 X 9. 28. 50505 X 6. 37. 39564 X 9. 46. 59648 X 5. 39. 83092 X 8, 38. 80709 X 2. 47. 83095 X 7. in. 73 J/ U L Tl Phi C A TI X. 1' I OBAL AND WBITTEN EXERCISES. 108. 1. A mason earned 13 dollars a week and spciit 4 dollars ; how mucli did lie save in G weeks ? Solution.— He saved G times the difference between $12 and $4, which is $48. 2. flow man}' are 2 times 7, ])lus r> ""i times 8, plus 7? 6 times 8, plus 3 ? 7 times 13, plus 9 ? 3. How many are 5 times 6, minus 4? 4 timet; '■'<, iiinus 6? 4 times 11, minus 9 ? 8 times 7, minus 8 ? 4. At 40 rents a yard, wliat would 7 yards of cambric cost ? 1?. yards? 13 yards? 8 yards? 10 yards? 5. How many cents will 13 doves cost, at 9 cents apiece ? At 11 cents apiece ? At 13 cents apiece ? 6. Bought 15 barrels of apples, at $3 a barrel, and a barrel of crackers for $5 ; how much did the whole cost ? 7. A merchant sold 7 coats at !f5l3 apiece, 8 vests at i?4 each, and 10 yards of broadcloth at $7 a yard ; how much did he re- ceive for the whole ? 8. Bought 13(5 chairs at $3 each, 8 sofas at $25 each, and 9 tables at $9 each ; how much did the whole cost ? 9. Gave $39 each to 6 men, paid for 39 yards of cloth at $4 a yard, and for a coat |30 ; how much money have I spent? 10. At 5 dollars a cord, what will 39 cords of wood cost? 87 cords? 384 cords? 79 cords? 11. In a week there are 7 days ; how many days in 4 v^ecks? In 8 weeks ? In 6 weeks ? In 33 weeks ? 13. Bought 13 boxes of soap, each containing 39 bars ; how many bars in all ? 13. What is the cost of 13 acres of land at |30 an acre? At $59 ? At $84 ? At $1 85 ? At $507 ? At $953 ? 14. Jacob Mclntyre can earn 100 dollars a month, and it costs him 63 dollars a month to upport his family ; how much can he save in one year ? 109. 257 10 2570 3. Placii In the ber by 1( Multip 1. Mul 2. Mul 3. Mui 4. Mu 110. (1)] EXPLA inp;acii)li in the iSec 2. In (: muUiplio( in tlic un cipher. Obser plicaud Knits ai manner MULTIPLICA TION, 73 \i SLATE EXERCISES. 109. Multiply 357 by 10. Explanation.— 1. In 267 the figure 7 expresses 7 ^initSy the figure 5 expresses 5 tens^ and the figure 2 expresses 2 hundred. 2. Each of these figures will express 10 limes what they now do if moved one place farther to the left. 3. Placing a cipher at the right of 257 moves each figure one place farther io the left ; hence multiplies each order in 257 by 10. 257 10 2570 In the samo manner annexing two ciphers multiplies a num- ber by 100 ; three ciphers by 1000, and so on. Multiply and explain in this manner each of the following: 1. Multiply 93 by 10 ; by 100 ; by 1000 ; by 10000. 2. Multiply 709 by 100 ; by 10000. 3. Multiply 490 by 10; by 100 ; by 1000; by 10000. 4. Multiply 9730 by 1000 ; by 10000. 110. Multiply 59 by 30. (1) {First step, 59x10= 590. [Secmdstep, 590 x 3=1770. ,n\ j Both steps in { one operation, 59 30 1770 Explanation.— 1. In the First Step in (1) 59 is taken 10 times by annex- ing a cipher ; hence 590 is 10 times 59. Now, by faking 590 three times, as in the Second Step, we have 30 times 59 ; Jicncc HiO is 30 times 59. 2. In (2) we unite the two stej)s in one oponition by regarding the W} as mullipiied by 10, or as 59 tens, and multiplying by 3 ; hence we write a cipher in the units place in the product, and write 3 times the 59 to the left of tho cipher. Obseroe, that to multiply by hundreds we regard the multi- plicand as expressing hundreds, and hence write ciphers in the nnits and tens place in the prodtict. We proceed in the same manner in multij)lying by thousands, and so on. 4 i t K % uH 1% i ■ m ft h 74 MULTIP Lie A TI N. SLATE EXERCISES. 111. Multiply and explain cacli of the following examples r 1. 85x50 37 X 4000 5007 X 60000 2. 73x80 95 X 7000 8045 X 30000 o 92 X GO 4G3 X 9000 3906 X 70000 4. 54 X 90 627 X 5000 4509 X 50000 5. 367 X 30 890 X 3000 7000 X 90000 6. 509 X 70 70x40 8009 X 40000 7. 76 X 200 90x60 9300 X 20000 8. 39 X 400 800 X 700 5090 X 80000 112. Multiply 783 by 45. (1) 783 Multiplicand. 45 Multiplier. 783 X 5 783x40 3915 1st partial product. 31320 2d partial product, 35235 Whole product. (3) 783 45 3915 3132 35235 Explanation.— The multiplier 45 = 40 + 5; hence we multiply the 783 first by 5, then by 40, and add theee two products as shown in (1), giving 85335, which is 40 + 5 or 45 times T83. Observe, tliat when multiplying by the 40 the cipher at the right of the product need not be written, as shown in (2). The position of each figure in 3132 under 3915 indicates what order it represents. Thus, the 2 is placed under the tens in 3915; hence we know that it expresses 2 tens. Multiply and explain each of the following : 1. 476 X 53. «. 839 X 78. fj. 587 X 95. 4. 396x37. 5. 6. 7. 8. 705 X 69. 389 X 84. 936 X 78. 598x42. 9. 837 X 635. 10. 954 X 827. 11. 386 X 349. 13. 749 X 594. 1. 5. tT 8. ~^ lO. 717 12. i 1 113. Mi 1. Coi in addit EPG, PG For e diately M Take! BCDEP, Takel the rigl ^ULTI PLICA TION, 75' ARITHMETICAL TABLE No. 8. tnples : 00 )00 )00 [)00 ooo 000 000 1000 !5 ply the 783 I (1), giving ler at the (2). The fhat order > in 3915; < 635. <827. <349. <594. A. B. c. i>. li. F. G. H. 1. J. 1. 1 6' 9 2 5 8 4 6 3 9 a. 4 5 3 7 9 6 5 3 8 9 7 3 6 4 6 3 8 9 2 5 2 5 9 8 5 4 8 7 2 3. 4. 5. 8 3 4 1 6 9 3 5 9 7 2 9 7 3 3 8 5 9 2 6 «. 7. 6 5 7 9 2 4 8 4 9 3 8. 9 5 2 1 4 8 6 4 8 G 5 7 9 5 7 9 6 8 3 7 o. 10. 7 4 4 8 2 9 7 5 9 4 4 8 8 6 5 8 9 4 5 9 11. 12. 9 7 5 8 7 (7t o 9 4 8 6 113, Copy examples from this table as follows : Multiplicand three figures ; Miiltiplier one, 1. Commence opposite 1 and take multiplicands in order, aa in addition (^1\ from columns ABC, then from bcd, cde, dep, EFG, FGir, GHI, and hij. For each example take as the multiplier the figure imme- diately under the right-hand figure of the multiplicand. Multiplicand five figures ; MnltipUer one. Take multiplicands in order from columns abode, then from BCDEP, CDEPG, DEFGII, EFGHI, FGHIJ. Take for multipliers, as before, the figure immediately under the right-hand figure of the multiplicand. * II % X% '4, 76 31 UL TIP Lie A TION.. ; I li SLATE EXERCISES. Multiplicand four fi (J lives ; Multiplier two* 114. 1. Take the multiplicands from Table No. 5, as be- fore directed. Use first columns abcd, then bcde, cuef, defg, EFGii, FGiii, and onij. Take as multipliers the two figures immediately under the two right-hand orders of the multiplicand:^. The first live examples taken in this way from columns abcd aro : 1692 68 4368 59 2759 37 5937 63 8463 95 I ; LI • 3Iulti2*lic(fnd six figures ; 3Iultipliei' four, 2. Take the multiplicands first from columns abcdep, then BCDEFG, CDEFGII, DEFGHI, and EFGIIIJ. Use as multipliers the f. The Multiplicand is the number taken, or multi- plied. 117. The Multiplier IB the number which, denotes how many times the multiplicand is taken. 118. The Vroduct lathe result obtained by multiplica- tion. BULES. 1 19. I. Wiiu tJie multiplier under the multiplicand, so tJiat units of the same order stand in the same column. To multiply by numbers less than 10. II. Begin at the right hand, and multiply each order of the multiplicand by the multiplier. Write in the product, in each case, the units of the result, and add the tens to the next higher result. To multiply by 10, 100, 1000, etc. HI. Annex as many ciphers to the multiplicand a^ there are ciphers in the multiplier. To multiply by numbers greater than 10. IV. Multiply the multiplicand by each significant figure in the multiplier successively, beginning at the right, and place the right-hand figure of each partial proi net under the order of the multiplier used. Add the partial products, which icill give the product required. Proof. — 1. Repeat the work. 2. Use the multiplicand as multiplier ; if the results are the same, the xoork is probably cor- rect. li if s » 1 * i ' li 'i ' 'n n I ill ■ i ;i \\ I I 78 MULTIPLICATION, WRITTEN EXERCISES. 130. 1. A drover bought 56 cows at 38 dollars eacli, and 49 oxen at $59 each ; what did he pay for all ? 2. There are 80400 seconds in one day ; how many seconds are tliere in 397 days ? Ans. 25G60800. 3. A grocer has 48 boxes of r dsins, each box containing 36 pounds ; how many pounds in all the boxes ? 4. A flour merchant sold 286 barrels of flour, each barrel con- taining 196 pounds ; Low many pounds did he sell ? 5. lu a certain orchard are 15 rows of apple trees ; there are 12 trees in a row and 4500 apples on each tree ; how many apples on all the trees ? Ans. 810000 apples. G. One man owes another $118. He gives in part payment 6 sheep at $4 per h?ad, and 3 cows at |27 apiece ; how much does he still owe him ? Am. $13. 7. A farmer bought 7 cows at $35 each, a span of horses for $225, 4 calves at $5 each, and a colt for $45 ; what did he pay for all? Ans. $535. 8. How many lemons in 350 boxes, if each box contains 274 kmons? u4?^s. 95900 lemons. 9. How much would a man earn in 19 years, if he received a salary of 975 dollars a year ? Ans. $18525. 10. A man bought at one time 14 tons of hay at 16 dollars a ton, at another time 24 tons at 18 dollars a ton ; what did he pay for all ? Am. $656. 11. How much more must be given for 96 head of cattle at 47 dollars per head, than for 28 liorses at 155 dollars each ? 12. If 05 ])ushc]s 0^' oats can bo raised on one acre of ground, how many bushels ran be raised on 96 acres? 13. If a cotton mill manufactures 789 yards of cloth in one day, how many yards can it make in 805 days? 14. The piufits of a bank amount to $8500 per month ; how much will they amount to in 15 months ? 3. APPLICATIONS. CANADIAN MONEY. 121. Canadian Money is tlic legal currency of the Domiuioii of Canada. It is composed of dollars, cents, and mills. The doU !l * t I II », if ••4 t M 80 MV L TIP Lie ATI O iV. \ ': WEITTEN EXEECISES. 122. 1. Find the cost of 8 yards of cloth at $2.45 for each yard. '^ Explanation.— 1. Since 1 yard cost $2.45, 8 yards must cost 8 times $2.45, whicli are $19.60. 2. We find 8 times $2.45 by multiplying as if there were no period between the 2 and 45. 3. We put a period in the product two places from the rig/U, and prefix the sign ($) to the whole. }?2.45 8 nd.GO «? Multiply and explain in this manner the following : (2) (3) (4) (5) (6) $4.87 $9.37 $32.82 $25.49 $8.57 5 9 14 37 28 7. Sold a horse for $195.80, and 45 bushels of wheat at $1.39 a bushel ; how much did I receive for both ? 8. Bought 59 sheep at $3.27 each ; how much did I pay for the whole ? 9. Find the cost of 45 yards of cloth at $2.85 a yard. 10. At $.435 a pound, what are 73 pounds of coffee worth? 11. A farmer sold 753 bushels of wheat at $1.83 a bushel, and paid out of what he received $893.57. How much had he left? 12. A lady bought 7 yards of ribbon at $.45 a yard, 18 yards of silk at $2.25 a yard, 2 pairs of gloves at $1.50 each, and G4 yards of cotton at $.14 a yard. How much did she pay for the whole ? 13. A merchant sold in one day 532 yards of cotton at 15 ct. a yard, 89 yards black clotli at $2.45 a yard, 150 yards of ribbon at 25 ct. a yard, 3 shawls at $10.75 each, and 47 yards of silk at $1.85 a yard. What was the amount of all that ho sold during the day ? 14. What is the cost of 15 cords ef wood at $5.50 a cord? MULTIPLICATION. 81 MEASUEES OP WEIGHT. 123. Ti*oy Weight is used in weighing gold, silver, and precious stones, and in philosopliical experiments. Table of Units. 24 grains (gr.) make 1 pennyweight . pwt. 20 pennyweights " 1 ounce . . . . oz. 13 ounces " 1 pound .... lb. I I 124. Avoirdupois Weight is used in weighing gro- ceries and all heavy and coarse articles. lb. cwt. T. Table of Units. 10 ounces (oz.) make 1 pound . . . 100 pounds " 1 himdredweight 20 cwt. or 2000 lbs. " 1 ton ... . 1 pound contains 7000 grains Troy. Observe, the old ton of 2240 lb. is still in use. The following denominations are also used : 100 pounds of grain or flour make 1 cental. 100 pounds of dry fish ** 1 quintal. 100 pounds of nails " 1 cask or keg. 196 pounds of flour •* 1 barreJ. 200 pounds of pork ** . barrel. I tl HI 125, 1. How many ounces in 4 lb. 9 oz. Troy? Solution.— Sine*! In 1 lb. Troy there are 12 oz., in 4 lb. there must be 4 times 12 oz., which is 48 oz. ; 48 oz. plus 9 oz. equal 57 oz. 2. How many ounces in 7 lb. Troy ? In 8 lb. ? In 12 lb. ? 3. How many pennyweights in 3 oz. ? In oz. ? In 10 oz.? Iu7oz.? In 3 oz. 5 pwt.? 4. In 4 lb. 3 oz. Avoirdupois, how many ounces? 5. How many pounds in 3 T. 170 lb.? In 5 ^J\ 84 lb. ? In 14 T. 230 lb. ? 6 82 .Y ULTiPLICjiTlO X, m \\ WRITTEN EXERCISES. 126. 1 How many pennyweights in 8 lb. 5 oz. 7 pwt.? 8 lb. 5 oz. 7 pwt. 12 101 oz. 20 Solution.— 1. Since 12 oz. make 1 lb., in any number of pounds there are 12 times as many ounces as there are pounds. Hence we multiply the 8 lb. by 12, giving 96 oz., to which we add the 5 oz., giving 101 oz. 2. Again, since 20 pwt. make 1 oz., in any number of ounces there are 20 times as many pennyweights as there are ounces. 2027 ])%n. Henc^ we multiply the 101 oz. by 20 and add in the 7 pwt., giving 2027 pwt. 2. How many grains in 11 oz. 6 pwt. 18 gr. ? 3. What will be the cost of 6 lb. 15 pwt. of goid-dust at $1 a pennyweight ? 4. In 5 cwt. 14 lb. 8 oz., how many ounces? 5. How many pounds in 8 T. 12 cwt. ? 6. What will 2 lb, 5 oz. of candy cost at 2 cents an ounce ? 7. What will be the cost of 1 T. 3 cwt. 75 lb. of Lay at one cent a pound ? 8. How many pounds in barrels of fiour? 9. Express 8 lb. 8 oz. 17 pwt. in grains. 10. What will be the cost of 5 kegs and 1 1 lb. of naiiH at 4 cents a pound ? 11. Express 8 cw . 29 lb. 14 oz. in oiuaces. 13. In T. 15 oz., how many ounces? 13. What mnst I pay for 28 bar^'els of pork at 12 cents a pound ? 14. Find the cost of 4 cwt. 56 lb. of sugar at 1 1 cont.s a pound, and 2 quintals of fish at 7 cents a pound. 15. If it tak-- i i H K CI t I •I 86 DIVISION, - ; OBAL AND SLATE EXERCISES. / 130. Find how many 2's in GO, or divide 60 by 3. Explanation.—!, We know, as fliown in the First step, that in ()0 there are 10 dxcs. We know aloo, as phown in the Sec- ond step, that there are 3 twos in 6 ; consequently in 60 there are 10 times 3 twos or 30 tivos. Hence GO-i-2-30. First step, 60 = 10 sixes. ^Second step, 6-f-2 = o. Hence 60-^3 - 10 times 3, or 30. Divide and explain in this way each of the following exam- ples : » I. How many 2's in 14? In 40? In 400? In 4000? In 40000 ? 3. How many 3's m 13? In 130? In 170? In 1400? In 16000'^ In 18000? 3. Divide 800 by 3 ; 9000 by 3 ; 36 by 4- ; 24000 by 4. 4. How many 5's in 35? In 1500? In 10? In 1000? In 250? In 4500? In 35000? 5. How many 3's in 18? In 180? In 18000? In 3100? 6. Divide 340 by 3 ; 8000 by 4 ; 16000 by 3 ; 28000 by 4. 7. Divide 450 by 5 ; 35000 ^y 5 ; 30000 by 4 ; 25000 by 5. 8. How many 3's in 969 ? Observe, that 969 = 900 + GO + 9, and that you can find at once the number of S't" in cjach of these part:?, and then add the resuUs, which will give the 8'6 in 909 thus : ( 900 -^ 3 = 300 ) 969 -r- 3 = ] 60 -f- 3 = 20 >• = 333. ( 9 -^- 3 = 9 ) 9. How many 2's in 286 ? In 644 ? In 868 ? In 686 ? 10. Divide 888 by 4 ; 699 by 3 ; 484 by 4 ; 24864 by 3. I I . How many 3's in 969 ? In 639 ? In 396936 ? In 93600 ? In 3G00OO ? In 693000 ? 13. How many 5'« in 035 ? In 985 ? In 775 ? In 8495 ? lu C3;35 ? In U5 '^ t DIVISION, 87 know, \ep, that \s. We the Sec- \iwos iti ■2^30. SLATE EXERCISES. 131. Copy each of the following exercises on your slate, and practice in writing- the quotients at sight of the divisor and dividend, as directed in (liiO). 1 G)_18 6)24 7)^8 7)70 8)^3 8)16 6 HO 6 )60 7)35 7)21 8^ 8)64 6)J:3 6 )54 7)_56 7)_63 8)40 8)96 6)^ 6)73 3 7)14 7 )43 8)_56 8)48 6 )36 6)48 7 )77 7)84 8)_73 8)34 6)^3 6)^6 7)_7 7 HO 8)_88 8)80 9)J17 9)18 9)J.5 9)63 9)9 9)90 9)36 0)99 9)81 9)^54 9) 108 132. Divide and explain each of the following examples as directed in (130). 1 . How many 6's in 30 ? In 346 ? In 3400 ? In 24000 ? 2. How many 8'9 in 50? In5G00? In 3300 ? In 72000? 3. Divide 45 by 9 ; 4500 by 9 ; JJ5 by 7 ; 35000 by 7 : 0400 by 8. 4. Divide 490 by 7 ; 40 by 8 ; 4000 by 8 ; 0300 by 9. 5. How mnny 9's in 450? In 7300? In 54000? In 81000? 6. How many 7's in 380 ? In 4300 ? In 0300 ? In 35000 ? • n «> *% It* ! I « I II •' •' ft 88 DIVISION. WEITTEN EXERCISES. 133. 1. At 4 dollars per barrel, how many barrels of flour can be bought for §3600 ? 3. How many barrels of apples at $3 per barrel can be bought for!ft690? For $936? 3. If a ton of coal cost $T, how many tons can be bought for $147? For!ft3507? For $6300? 4. If a man can earn two dollars a day, how many days will it take him to earn ,$862 ? 5. At !^5 a cord, how many cords of wood can be bought for $3500" For $1550? For $4500? 6. If a steamboat run 9 miles an hour, how long will it take her to go 7200 miles ? 7. If 6 yards of cloth make a suit of clothes, how many suits cin be made from 3600 yards ? From 4800 yd. ? 8. How many sheep at $4 apiece can be bought for $160 ? For $280 ? For $3608 ? For $240.8 1 9. If Charles can earn $8 in one week, in how many weeks can he earn $240 ? $480? 10. At $5 a week, how many weeks' board can be had for $100 ? For $150 ? Foi; $350 ? ' 11. If a stage-coach travel 7 miles an hour, how many hours will it take her to travel 4200 miles ? 12. A farmer put two bushels of grain in a bag ; how many bags will it take to h old 4682 bushels ? 13. How many times 3 is 9630! Is 3690? Is 9369? 14. How many calves at $4 apiece can be bought for $2184 ? For $2800? For $3608? 15. How many times 6 cents are 5460 cents? 1260 cents? 4806 cents ? 3606 cents ? 16. At 4 dollars a barrel, how many barrels "f n]iples can be bought for 2 180 dollars f For $2840 ? For $3080 ? 17. Divide 284840 by 4 ; by 2. I Et DIVISION. 89 OBAL AND SLATE EXEBCISES. 134. 1. How many 4*8 in 14 and how many remaining? Observe, tht . -^-ou know from the multiplication table that Z fours are 12, and hcDce you c,.. iell at ouce that 14 contains 3 fours and 2 remaining. Find in this manner orally the quotient and remainder for each of the following examples. Then practice upon your slate in writing the quotients and remainders under each exam- ple, separating them by a dash, thus : 3)7 5)28 4)36 8)39 3)17 8-1 5—3 6—3 4-7 5—3 ^L? ^Ii5 ^11? ^\3 ^)i? ^\3 ^L?? ^11? 4)J1 4)^ 4)33 4)_29 4)J0 4)_13 4)^ 4)J4 5)19 5)34 5)33 5)43 5)29 5)43 5)33 5)33 6)^ Q)m 6)^ 6)^ %)JA 6)_59 6)_33 6)_51 6)58 6)5^ 6)38 6)^ 6 HO' 6^ 6)^ 6)58 7^ 7)^32 7H5 7)_37 7)_35 7)_01 7)^ 7)_60 7)36 7)38 7)53 7)09 7)41 7)53 7)66 7)40 8)19 8)_3G 8)_39 8 )_33 8 )_33 8 )_47 8 1^30 8 )J6 8)38 8)44 8)31 8)33 8)49 8)51 8)38 8)53 9)_24 9)^43 ^)m 9)^79 9)J)0 9)^9 9)^ 9)80 9)30 9)53 9)39 9)87 9)60 9)40 9)39 9)70 7% I IMAGE EVALUATION TEST TARGET (MT-S) 1.0 I.I ;f i^ iiiiiM •^ 1^ 1112.2 1^ 1.8 1.25 1.4 1.6 ^- ^n ► m ^ /a /, •i «, first, that the form in (1) is the same as tliat on which practice was given in the last exercise. Observe, second, that in the form in (2) the worls: is shortened thus : 1. The multiplication of the divisor 7 by each of the partial quotients is not written, as in (1). 2. The ciphers are omitted from the products 2100 and 5»j0, the significant figures 21 and 56 being in each case placed so that the order of the dividend they are under indicates the order they represent. 3. Only one figure of the dividend is taken down at a time, this being all that is necessary to give another quotient figure. Perform the division in each of the following examples, and ■write the work on your slate, as shown in (2). 1. 874-f-2. 12. 2915-5-5. 23. 4865-5-7. 2. 1678-5-2. 13. 4434-5-6. 24. 6642-^9. 3. 1578-^2. 14. 5022-5-6. 25. 5373-4-9. 4. 1035-5-3. 15. 2910-5-6. 26. 7524^9. 5. 2214^3. 16. 3759-5-7. 27. 5688^6. C. 1752^-3. 17. 0041 -^ 7. 28. 1S954-5. 7. 2572-5-4. 18. 5243-^7. 29. 8613-5-9. 8. 3350 -t-4. 19. 6096^8. 30. 1971-5-3. 0. 1556-f-4. 20. 4632^8. 81. 4784-5-8. 10. 3090-^5. 21. 0064-5-8. 32. 5751-5-9. 11. i„3:]5-5-5. 22. 3908-4-8. 83. 8613-5-9. 1 1 DIVISION. 93 DBM. as that on that in the uotients is significant le dividend is being all pies, and !h-9. !-;-9. -^5. -f-9. -1-3. -h8. -f-9. -^9. ■ SLATE AND WBITTEN EXEBCISES. Short Division, 138. 1. Find how many 7's there are in 2695, thus : 7 ) 2095 Explanation.— The work is shortened still more by I writing only the quotient figures, and holding all the niim- 385 bers in the memory while performing the required oper- ations, thus: 1. We observe, as in the former plan of working, that 7 is contained 3 hundred times in 26 hundred. Writing the 3 under the hundueds of the dividend to show that it represents hundreds, we subtract mentally 3 hiiri' dred times T, or 21 hundred, from the 26 hundred, leaving 5 hundred, or 50 tens, to which we add the 9 (ens of the dividend, making 59 tens. We proceed in the same manner with the tens and units. Division by numbers not greater than 13 should always be performed in this manner. Nothing should ever be written but the quotient. This form of division is called Short Division. Divide and explain in this manner the following : 2. 4018-' 7. 3. 1985-f-5. • 4. 5912^8. 5. 3924-^9. 6. 29432-J-4. 7. 34188-5-6. 8. i4511-^3. 9. 12820-4-5. 10. 68901^7. 11. 38742-i-6. 12. 30976-5-8. 13. 32661 -^9. 14. If a boy earn l"^ in one week, how many weeks will it take him to earn $2569 ? 16. If a canal-boat travel at the rate of 8 miles per hour, how long will it take her to travel 4344 miles ? 5376 miles ? 3784 miles ? 16. How many times can 9 bushels of wheat be taken from 7881 bushels ? From 2457 bushels ? 17. How many pieces, each 7 inches long, can be cut from a roll of paper 3045 inches long ? 18. How many times are $9 contained in $8040 ? In $8415 ? 'i '.4 i'i 94 DIVISION. ARITHMETICAL TABLE No. B. ij^ A. B. c. i>. K. F. «. H. 1. J. 1. 4 1 3 9 8 4 7 2 8 7 3 9 5 6 G 8 9 2 2. ;{. 5 2 7 3 8 4 6 3 8 9 6 2 5 7 8 4 7 7 D 4 a S 7 5 8 8 J 4. r». «. 3 7 5 8 3 '2 G 4 9 7 7. 5 S 2 5 9 7 4 3 7 9 3 G 8 4 6 9 o 9 6 8 8. O. it o 9 6 8 O 9 2 5 4 lO. 6 o 4 7 8 8 4 9 5 6 4 9 3 7 7 8 3 6 9 8 8 7 5 4 9 5 8 11. Iti. 9 7 189. Copy examples from this table as follows : Dividend three fifjures ; Divisor ofu\ 1. Comn^ence opposite 2, and take the numbers for dividends from Aiic, tlien from BCD, then cde, def, efg, ran, ghi, iiij. 3. For oav?h t^xample, take as the divisor the figure imme- diately above the right-hand figure of the dividend. The first six examples from columns abc are : 8)194 4)530 6)383 3)748 8)375 5)539 Dividend five fiffures ; Divisor one. 1. Commence opposite 2, and take the dividend from columns AncDR, then from bcdep, then cdefo, defgii, efottt, foittj. 3. Take as the divisor, in each example, the figure imme- diately above the right-hand figure of the dividend. DIVISION, 95 8. - — 1. J. 8 EXEHCISES ON EQUAL FABTS. 140. 1. Make 13 into two equal paris. 12-^-2 = 6 Hence 12 = 2 sixes. 'ExvLANATion.— Observe, that in 12+2=6 the divisor denotes how many times the quotient 6 can be taken out of 12. Conse- quently the quotient 6 is one of the two equal parts of 12, and hence 12 = (j + G. 2. Find one of the two equal parts of 12 ; of 16 ; of 18 ; of 20 ; of 10; of 16 ; of 14 ; of 24 ; of 22 ; of 56 ; of 08. 3. One of the two equal parts of a number is called one- hdl/'f and is written 1 over 2, thus J. J of 12 is 12-f-2 = 6. 4. Find one of the . ree equal parts of 12 ; of 18 ; of 27 ; of 15 ; of 33 ; of 24 ; of 36 ; of 99 ; of 48 ; of 87. 5. One of the tJiree equal parts of a number is called one- thirdf and is written 1 over 3, thus J. J of 15 is 15-^3 = 5. 6. One of the four equal parts of a number is called o^ie' fourth ; one of the fim equal parts one-fifth, and so on. 7. One of any number of equal parts of a number is written by placing one over the number that denotes the number of equal parts into which the given number is made, thus : One -fourth is written \. One-Jifth is written l. One-sixth is written J. One-tenth is written -j^^ One-twelfth is written ^-^ 5. — ( . \ of 20 is 20-T- 4 \ of 35 is 35-^ 5 J of 24 is 24-^ G :^^ 4. -iVof 80is>i0^10 -iV of 84 is 84-r-12 --. *M :i •4 t t 'J And so on Avith any number of equal parts. 8. Find onc-eightJi of 8 ; of 24 ; of 48 ; of 50 ; of 73 ; of 40 ; of 96 ; of 500 ; of 480. 9, If a house and lot is worth $5050, what is one-fourth of it worth? One-half of it? 96 DIVISION. WRITTEN EXERCISES. 141, 1. If 60 cents be equally divided among 3 beys, how many cents will each have ? 3. If 9 oxen cost 480 dollars, what is the price of one ox ? 3. If 8 yards of tweed cost 792 cents, what does one yard cost? 4. Sold 7 tons of hay for .$119 ; how much did T receive for one ton V 5. A company of 8 persons own equal shares in a store worth $25672 ; what is each man worth ? 6. If $5484 be divided into 3 equal parts, what is the value of each part ? 7. There are 7 farms of equal size that contain in all 2415 acres ; how many acres in each farm ? 8. A farmer has 3864 bushels of wheat, which fill 8 bins of equal size ; how many bushels in each bin? 9. A father left an estate of $37805 to be divided equally among his five sons ; how much would each receive ? 10. A grocer bought 7 chests of tea of equal size ; there were 1757 pounds in all ; how many pounds in each chest ? 11. If a railroad train moves 250 miles in 8 hours, how many miles does it move per hour ? 12. Sold 9 acres of land for $882 ; how much did I receive for one acre ? 13. Divide $9324 equally among 6 men. 14. A railroad, owned by 9 men who paid equul sums fo» building it, cost !?258876 ; what did it cost each man ? 15. A grist mill is worth |38052 ; what is one-fourth of it worth? One-sixth? One-twelfth? 16. Bought 5 houses for $40325 ; how much did I pay for ^ach house ? 17. Sold 4 horses for $580 ; how much did I receive for each lio vse ? lcft^ DIVISION. 97 3 bcytf, how- one ox ? >es one yard receive for store Avorth s the value in all 3415 • 8 bins of ed equaJly ? tliere were ? Uow many I receive sums fot rth of it ■ pay for for each 11 SLATE AND BOARD EXEBCISES. 142 Divide 14800 by 37. 87 ) 14800 ( 400 Explanation.— When the divisor contains 1 AACiCi ^^^ ^^ more figures, we can find the quotient i'toUU figures by finding how many times the left-hand ^T-'^ ,f the divisor is contained in the fewest left-hand figures of the dividend that will contain it. Thus ;], the left-hand figure of the divisor, is contained 4 times in 14, the two left-hand figures of the dividend ; hence we conclude that 37 is con- tained In 148 hundvA 4 hundred time •, Multiplying 37 by 4(X/, we find that .37 X 40() = 14800. Hence 400 is the correct quotient. Divide in this way the following : 1. 2220-1-74. 7. 60500^65. 3. 7470-J-83. 3. 4340^62. 4. 2100-f-o4. 5. 7C50-i-85. 6. 7360-5-92. 8. 12600^42. 9. 43500-5-87. 10. 28800-5-32. 11. 26500^53. 12. 63600-5-67. 13. 525000-5-75. 14. 252000-5-84. 15. 558000-5-93. 16. 087000-5-43. 17. 768000^96. 18. 623000-5-89. 19. Divide 27300 by 39. 3y ' 27300 ( 700 Observe^ that by pursuing the same course as ' oiyoAA before, we find in this example that 3, the left- "^^ ^ hand figure of the divisor, is contained 9 times in 27, the two left-hand figures of the dividend ; but when we mult'ply 89 by 900 we have 85100, a number greater than the divi- dend, and hence 90' is not the correct quotient. Trying 800 in the same manner, we find it is too large a quotient ; hence we take 700, which we find to bo the correct quotient. The correct quotient figure in examples of this kind can be found only by trial. Perform the division in the following: 1. 1350-5-27. 2. 2340-5-39. 8. ll200-^2S. 4. d3600-5-43. 5. 342000-5-38. 6. 20800C-^26. 7. 358000-^25. 8. 273000-5-35. 9. 415000-*-45. ;3 k :i t '5 08 Dl VIISION. 1 SLATE AND BOABD EXEKCISES. Long Division, 143. 1. Divide 9282 by 26. 26 ) 9282 ( 357 78_ 148 130 182 182 Explanation.— 1. When the divisor consists of two or more figures, the reoults caunot be held in the memory while we perform the operations ; hence we proceed thus : 2. We find by trial that 26 is contained in 92 hundred 3 hundred times. Multiplying' the divisor 26 by 3 hundred^ we have 78 hundred, which we subtract from the 92 hundred, leaving 14 hundred, or 140 fens, to which we add the 8 tens of the divi- dend, giving 148 tens. 3. We now find by tried that 26 is contained in 148 tens ^ (ens times. Multiplying the divisor 26 by 5 tens, we have 130 tens, which we subtract from the 148 tens, leaving 18 tens, or 180 units, to which we add the 2 units of the dividend, giving 182 units. 4. We find again by trial that 26 is contained in 182 units 7 units times. Multiplying the divisor 26 by 7 we have 182, which takon from 1R2 leaves nothing ; hence the division is complete, and 357 is the quotient of 9282 divided by 26. P( jrfonn and explain the division in the follow] ing: 1. 1125-5-45. 13. 649-5-36. 25. 59653-5-187. 2. 5976-^-83. 14. 120597-J-328. 26. 140378-5-276. 3. 2623-1-43. 15. 46648-^136. 27. 250489-5-382. 4. 16002-^63. 16. 63455^259. 28. 480159^699. 5. 28952-5-56. 17. 92115-4-345. 29. 630121-5-798. 6. 57810-^-94. 18. 91093-5-239. 30. 132525-4-285. 7. 18430-4-81. 19. 103326-5-568. 31. 684187^168. 8. 29822^31. 20. 80307-^439. 32. 89458-4-137. 9. 43890-^93. 21. 100192^351. 33. 361246-4-476. 10. 127098-^614. 22. 120058-5-228. 34. 80084-5-292. 11. 228984-^203. 23. 22796-4-48. OK 292082-4-387. 12. 48204^-309. 24. 120223-4-64. 36. 77728-4-145. No un GH ab ui al b fc DIVISION, 99 :S£S. isor consists of inot be held in ie operations ; ontainecl in 92 i»^- the divisor 'ed, vvliieh we ig 14 hundred, ms of the divi- w ^ (eiis times, ch we subtract dd the 2 units f 7 units times, om 182 leaves aotient of 9288 59653 i0378 50489 10159 10121- 2525- 4187- D458- 1246- 3084- JC82H f728-f- i-187. -5-276. ■f-382. ^699. -798. f-285. -168. -137. -476. -292. -387. 145. SLATE ANB OHAL EXERCISES. 144. Take examples lor practice from Arithmetical Table No. 5, p. 94, as follows : Dividend four figures ; Divisor two, 1. Commence opposite 2, and take the dividends from col- umns ABCD, then from bcde, then cdef, defo, efgh, fghi, GHIJ. 2. For each example take as divisor the figures immediately above the two right-hand figures of the dividend. The first five examples from Cv iumns abcd are : 85)_1947 47)_5369 69)^836 36)^8^ 82 ) C7^8 Dividend six figures / Divisor three, 1. Commence opposite 2, and take the dividends from col- umns ABCDEF, then BCDEFG, CDEFGH, DEFGHI, EFGHIJ. 2. For each example take as divisor the figures immediately above the three right-hand figures in the dividend. 1. At 12 cents a pound, how many pounds of sugar can be bought for 36 cents ? For 60 ct. ? For 96 ct. ? For 120 ct. ? Solution.— Since 1 pound cost 12 cents, as many pounds can be bought for 30 cents as 12 cents are contained times in 36 cents, which are 3. 3. At $3 a yard, how many yards of cloth can be bought for $6? Forij^lS? For|75? For $861 ? 3. How many melons at 9 cents each can be bought for i'7 cents ? For 81 cents ? For 815 cents ? For 657 cents ? 4. Tf a man earns $5 a day, in how many days can he earn $15? $25? $40? $50? $500? $450? 5. At, $4 n head how many sheep cnn be bought for $24? For$SG? For $48? For $80? For $280? II' Ny I t I'l 100 DIVISION. OBAL AND WRITTEN EXERCISES. , . i 14o. 1. If 24 cents are divided equally among G boys, how many cents will each boy receive ? Solution.— To give each boy 1 cent requires 6 centti. Hence each boy will receive as many cents as 6 cents are contained times in 24 cents, which are 4. 2. What is the price of 1 yard of ribbon, when 5 yards cost 25 ct. ? 35 ct. ? 45 ct. ? 80 ct. ? 100 ct. ? 400 ct. ? 8. How m^lch does a man earn each month, if he receives for 6 months work |56? $60? $150? $360? 4. What is the price of one acre of land, when 7 acres cost $21? $35? $42? $56? $63? $140? $280? 5. If 3 yards of silk cost $9, what will be the cost of 8 yards ? Of 12 yards ? Of 15 yards ? Of 45 yards ? Solution.— Since at $9 for 3 yards the price of 1 yard is $3, the cost of 8 yards is 8 times $3 or $24. 6. If 5 peaches cost 15 cents, what will be the cost of 3 peaches ? Of 7 peaches ? Of 12 peaches ? Of 25 peaches ? 7. If 9 oranges cost 36 cents, what will be the cost of 4 oranges ? Of 16 oranges ? Of 32 oranges ? Of ??7 oranges ? 8. If 25 yards of cloth cost $75, what is the cost of one yard ? Of 5 yards ? Of 9 yards ? • 9. I paid $270 for 15 tons of hay ; what did I pay for one ton? For 4 tons ?, For 7 tons ? 10. If James can hoe 336 rows in 21 days, how many rows can he hoe in 5 days ? In 16 days ? 11. A drover bought cows at $42 per head, and paid for all $13440; how many did he buy? 12. A grocer bought 283 barrels of molasses, for which he paid $7358 ; what was the price of one barrel? Of 35 barrels? Of 160 barrels ? 13. How many pounds of butter at 24 cents per pound will pay for 16 yards of calico at 12 cents a yard? el 3 'K. !ISES. ; boys, how lence each boy 84 cents, which 5 yards cost ? ! receives for 7 acres cost of 8 yards? |3, the cost of 3 cost of S eaches ? » cost of 4 ranges ? one yard ? 3r one ton ? nany rows aid for all which he ) barrels ? )und will DIVISION. 101 WBITTEN EXERCISES. 146. 1. If a man earn $325 a year, how long will it take him to earn $2925 ? $4225 ? 2. A drover paid $8375 for 67 horses ; what did he pay for each ? What did he pay for 16 horses ? 3. I have a farm worth $8460 ; what is one-half of its value ? Oue-third V One-f ou rth ? One-fifth ? 4. How many barrels of apples at $4 per barrel will pay for 2 barrels of sugar at $14 a barrel, and 4 pounds of tea at one dollar a pound ? • 5. If 345 bushels of wheat weigh 11040 pounds, what is the weight of one bushel? Of 28? Of 96? Of 150? 6. Divide 165164 into 314 equal parts. 7. A farmer raised 2470 bushels of oats on 65 acres of land ; how much did he raise on 9 acres ? On 20 acres ? On 28 acres ? On 46 acres ? 8. How many barrels of potatoes at $2 a barrel must be given for 7 barrels of flour at $8 a barrel ? 9. A person sells 5 cows at $25 each, 8 horses at $75 each, and agrees to take his pay in sheep at $5 a head ; how many sheep does he get ? 10. A father dying left an estate of $48064 to be equally divided among his wife, four sons, and three daughters ; how much does each receive ? 11. How many dozen of eggs at 12 cents per dozen must be given for 4 boxes of raisins, each containing 15 pounds, at 15 cents per pound ? 12. In one pound there are 16 ounces ; how many pounds in 15808 ounces ? 13. Divide $97128 into 213 equal parts. 14. I have $60250, with which I buy land at $125 an acre; how many acres can I buy ? 15. Divide 38950 into 25 equal parts. K ( ! 'I I w 4 t 11 103 D [VISION, ! , ^ DEFINITIONS. 147. Division is the process of finding how many times one number is contained in another. 148. The Dividend is the number divided. 141), The Divisor IB the number by which the dividend is divided, 150. The Quotient is the result obtained by division. 151. The RetnainderiB the part of the dividend left after the division is performed. 152. Short Division is that form of division in which no step of the process is written. 1 5?-$. Long Division is that form of division in which the 8iMractio?i necessary in the process is written. I 1 I It BULE. 154. /. Find hoto many times the dimsol' is contained in the feioeat figures at the left of the dividend that will contain it, and lorite the resvltfor the first figure of the quotient. II. Multiply the dioisor by this quotient figure, and subtract the remit from th" part of the dividend that was used; to the remainder annex the next lower order of the dividend for a new partial dividend and divide as before. Proceed in this manner mth f>ii:h order of the dividend. III. If there he at last a remainder, place it after the quotient, with the divisor underneath. Proof. — Multiply the divisor hy the quotient and add the re- mainder, ifttny, to the product. This result will he equal to the dividend, whtu uie dioldon has been performed correctly. ow many times APPLICATIONS. the dividend y division, dividend left ision in wliicli sion in which stained in the mtam it, and and siibtract rtst'd; to the 'id for a new this maimer the quotient. add the re- equal to the ttly. OBAIi AND SLATE EXERCISES. 155. Dv\f Measure is used in measuring grain, fruits, etc. Table of Units. 2 pints (pt.) make 1 quart . . . qt. 8 quarts " 1 peck . . . pk. 4 pecks " 1 bushel . . bu. 1. In 1 peck how many pints ? In 2 pecks? In 8 pecks? In 24 quarts ? In 3 bushels ? In 10 bushels ? 2. In 448 pints how many pecks ? Solution.— Since 2 pints make 1 quart, 448 pints must make as many quints at» 2 quarts are contained times in 448 quarts, which are 224. Ai^ain, s^iince 8 quarts make 1 peck, 224 quarts must make as many pecks as 8 quarts are contained times in 224 quarts, which ai'e 28. Hence in 448 pints there are 28 pecks. 8. How many bushels in 540 pk. ? In 2080 qt. ? In 1088 pt. ? In 23272 pt. ? In 15104 qt. ? 4. At 8 cents a quart, how many bushels of peaches can be bought for $15.36? For $20.48? For $23.04? Solution.— Since $15.36 are equal 1536 cents, as many quarts of peaches cuu be bought I'ur $16.36 as 8 cents are contained times in 1536 cents, which arc li*2, and 192 quarts make 6 bushels. Observe^ tlie dividend is changed to cents to be of the same name as the divisor. 5. At 12 cents a peck, how m»^856? It I 4 w 1 -I . .. (1 ! 1 ; 1 : » , f > i 1! W\ 104 DIVISION, ORAL AND SLATE EXERCISES. 156. Liquid Pleasure is used to measure all kinds of liquids. Table of Units. 4 gills (gi.) make 1 pint . , . pt. 3 pints " 1 quart . . . qt. 4 quarts " 1 gallon . . gal. 31 J gallons " 1 barrel . . bbl. 63 gallons " 1 hogshead . hhd. 1. How many pints in 12 qt. ? In 25 qt. ? In 10 gal. ? In 30 gal. ? 2. How many gallons in 16 qt. ? In 28 qt. ? In 64 pt. ? In 96 pt.? InieOpt? 3. Express 48 pints in gallons ; 72 gills in quarts. 4. In a cistern there are 2835 gal. of water ; how many hogs-' heads does it contain ? 5. If one quart of molasses cost $.23, what will be the cost of 4 gal.? 7 gal.? 18 gal. ? 2hhd.V 6. In 5 lihd. how many qt. ? How many gills? 7. At 4 cents a pint, how many gallons of milk can be bought for $4. 48? For $8.64? For $9.60? Solution.— 1. Since 1 gallon makes 8 pints, at 4 cents a pint 1 gallon can be bought for .32 cents. 8. Since 1 gallon can be bought for 32 cents, as many gallons can be bought for $4.48, or 448 cents, as 32 cents are contained times in 448 cents, which are 14. 8. At 5 cents a pint for vinegar, how many gallons can be bought for $4.40? For $5.60? For $7,60? 9. When maple syrup costs 16 cents a quart, how many gal- lons can be bought f or $1 . 28 ? For $7. 68 ? For $47. 30 ? 10. At cents a quart, how many gallons of kerosene can be bought for $1.44? For $2.52? For $3.24? For $26.64? Ex> 3. 3. 4. DIVISION. 105 Ib'S. U kinds of )gal. ? In 14 pt? In aany hogs-' e the cost be bought i gallon can Dns can be I 448 cents, s can be lany gal- e can be 4? EXERCISES ON EXACT DIVISORS. 1 *>7, 1. What numbers will divide 13 without a remainder ? A nnmber that \*Ill divide another without a remainder is called an Exact Divisor. t Fiud all the exact divisors of each of the following numbers : 2. 15. 5. 20. 8. 42. 11. 40. 14. 48. 3. 21. 6. 27. 9. 36. 12. 56. 15. 33. 4. 35. 7. 30. 10. 28. 13. 63. 16. 64. 17. Wliat number is an exact divisor of each of the numbers 4, 0, and 10 ? Of each of the numbers 9, 15, and 27 ? • A number which is ai) exact divisor of each of two or more numbers is called a Common Divisor. 18. Find the common divisors of each of the following sets of numbers : 13 and 16. 15 and 25. 18 and 30. 42 and 28. 36 and 63. 60 and 84. 55 and 45. 40 and 64. 48, 28, and 32. 15, 45, and 36. 54, 18, and 48. 28, 42, and 63. 19. What is the Greatest Common Divisor of 8 and 12 ? Of 18 and 30 ? The greatest number that is an exact divisor of each of two or more num- bers is called the Oretttrst Common Divisor, 20. Find the greatest common divisor of each of the follow- ing sets : 15 and 20. 80 and 31. 18 and 27. 82 and 72. 45 and 54. 42 and 35. 23, 55, and 99. 80, 60. and 84. 54, 63, and 72. 21. Wliat is the greatest common divisor of $10 and $15 ? Of |20 and $50 V Of -f 3o and $84 V 01 ij)^:5 and $63 ? m '^ t 4 I I. 1 ll >t> 106 DIVISION. EXERCISES ON MULTIPLES. 158. 1. Twenty-four is how many times eight f How mauy times six? How many times ticeUe f How many times twenty-four? A number which is one or more times another number is called a Mul- tiple of that number. 2. What is a multiple of 3? Of 6? Of 4? Of 8? Of 10? Of 7? Of 11? Of 9? Of 12? 3. Name three multiples of 9 ; of 5 ; of 8 ; of 12. 4. Find the first three multiples of 17 ; of 23 ; of 29. Thus, Ist multiple is 1 ; , 2d multiple 17 x 2 = 34, 3d multiple 17 x 3 = 51. 5. Find the first 4 multiples of 25 ; of 37; of 63; of 95; of 84 ; of 235 ; of 347 ; of 836 ; of 793 ; of 965. 6. How many multiples can you find for 19? For 35? For 69 ? For any given number ? 7. Find a number which is a multiple of 4 and of 6. Thus, 4 X 6 = 24, hence 24 is a multiple of both 4 and 6. 8. Find a number which is a multiple of 7 and of 9 ; of 5 and of 8 ; of 6 and of 11 ; of 3 and of 9 ; of 9 and of 12. A number which is a multiple of two or more numbers is called a Com- mon M%iltlplH of these numbers. 9. Of what numbers is 12 a common multiple f Is 21 ? Is 45 ? Is 63? Is 48? Is 72? Is 64? Is 88? Is 108? Find a common multiple : 10. Of 5 and 8. 13. Of 7 and 19. 11. Of 9 and 6. 14. Of 4 and 2*. 12. Of 12 and 7. 15. Of 5 and 37. 16. Of 13 and 29. 17. Of 32 and 28. 18. Of 43 and 15. I'J. Of how many cents is 20 cents a- multiple? 30 cents? 25 cents ? 56 cents ? 72 cents ? I ■i IS. nrjUf How many timegs called a Mul- >f8? Of 10? f29. le 17x3 = 51. J3; of 95; of ror35? For >f 6. • 9 ; of 5 and called a Com- i21? Is 45? f 13 and 29. e 32 and 28. ' 43 and 15. 30 cents? J FRACTIONS. ORAL EXERCISES. 150. 1. One of the two equal parts of a whole thing is called i>i\e~h 1 "R^mfl aBi4r. 7 1810 11 8 ±o^« 1. iteaa ;,, v, .i, o» i?» i(f»T5> itf» iio> it- 2. What is the numerator of g ? The denominator? What does the numerator show "l The denominator ? 3. Express by figures nine-tenths. Five-thirteenths. Twenty- thirty-fifths. 4. How many numbers must be used to express sewn- fiftccnthH by figures ? What does each number show ? 5. What is meant by ? of an apple ? | of a garden ? ^ of a farm? 6. tlow can you find the fifth of a sheet of paper? The three. ifths? The one-ninth ? The five-ninths? 7. How much of an apple is three-thirds of it? Five-fifths of it? 8. What docs \ of a garden mean ? g of a bushel yt corn ? 9. In order tliat Henry may give ^ of an orange to James, what must he do with tLe orange, and why ? 10. One-fiftli of GO is how many ? Of 35 ? Of 80 ? Solution. J of GO = 60-i-5 = 12. 11. Find \ of 27 ; i of 40 ; ^ of 63 ; ^V of 96; ^V of 144. 12. Find g of 35 ; f of 24 ; f of 42. Solution. J of 35 is 7. Hence J of 35 must be 3 times 7, or 21. 13. Find the | of 15 ; the ^\ of 24 ; the f of 35 ; the f of 45 ; the » of 80 ; the f of 63 ; the -jV of 72. 14. What is f of $28 ? f of $36 ? j of ,"-63? Solution. ^ of $28 is $4. Ileuco f of $28 must be 3 times |,4, or $12. 15. What is 4 of 35 pounds of starch ? Of 45 lb. ? 16. A farmer had 84 cords of wood and sold ? of it at $4 a cord. How murh HiH he receive for what he sold ? 17. Koliert had $03 and gave 5 of it to his brother Henry. How many dollars has he loft ? irden? ? of a FRA CTIO NS. OBAL EXEBCISES. Ill lOJJ. In this cxerciHo study carefully the illustrations given, 1. A fraction may he represented by equal lines, thus : 2 8 l*art taken. Whole. Observe, that in |, the denominator 3 represents the w/iole, or 8 tJdrds, and the numerator 2 represents 2 thirds, or tino parts of the same size as those represented by the denominator. Hence, 3 equal lines for the denominator, and 2 ecjual lines of the same length for the numerator represent correctly tho number of parts that form the whole or unit, the number of parts taken, and the relation of the parts to each other as rep. resented by the fraction |. 2. Represent by lines I, ^, |, }, f, ^', f, j%. 3. If you make r/iie-halfot a line into two equal parts, what kind of parts will you thrn have, and why ? 1 2 2 4 J'nrt taken, Whole, Kxnniine this illuBtration carefully, observing what han hcen done to chanyc the J to J, then answer the question. 4. If onehnlf\B made into three equal 2^arts, what will be the name of the parts ? If into four equal parts ? 5. In I how many fourths f IIow many sixtJis ? How many cighthn ? IIow many tenths f How many twelfths, and why Y G. IIow many sixths can you make of one-half of an apple ? flow many fourteenths, and why? 7. One-half of a bushel is equal to how many sixths of a bushel ? Tenths of a bushel, and why ? i Bl w Ik % 112 REDUCTION OF FRACTIONS. lil t * i ' » i 164. 1. How many sixtlia in one-third of a line, and why? 1 8 ^■a 2 6 Study careftiUy this illustration, then answer the question. 2. In ^ how many ninths, and why ? How many fifteenths ? 3. To make thirds of a sheet of paper into eighteenths, what must be done with them, and why ? 4. In f, how many twelfths? How many twenty-fourths, and why? 2x4 2x5 ? Illustrate by lines. 3x4 3x5 6. When both the numerator and denominator of a fraction are multiplied by the same number, what change is made in the fraction, and why ? 7. When one-fourth of a line is made into three equal pa/rt9,, what will each of these parts be called, and why ? 1 4 ■ ■■ 8 12 wmm ^^ ^^ wmmt HHB m Study carefully the illustration, then answer the question. 8. Why is \ of an apple equal to f of it ? 9. In ^ of a pound of raisins, how many twentieths of a pound ? 10. Why is 7 = -. — ?r = •. — X = 1 — 7 ? Illustrate by lines. 4 4x2 4x3 4x4 11. Principle. — Multiplying both numerator and denomina- tor of a fraction by the same number does not change the value of the fraction. H I REDUCTION OF FRACTIONS, 113 ne, and why ? y-fourths, and /entieths of a ORAL AND WRITTEN EXERCISES. 165. 1. How many thirds of a line in two-sixths of it ? 3^3 6-i-3 1 8 Observe, that when evei-y two of the sixths tire put into one, as shown in the ilUistration, the whole Hue in made into three equal parts, and one part taken. Heuce, two-sixths of a line make one-third of it. 3. How many thirds in ^ of one apple ? In f ? In x\ ? 3. Change /^ to fourths ; || to fifths ; ^'^ to halves. 4. Principle. — Dividing both the numerator and denomina- tor' of a f7'actio7i by the same number does not change the value of the fraction. 5. UovfmBXij thirds m*^1 Inf? In |§? In^'. 6. Change | and -^^ each to fourths, and explain. 7. Express yV» A* ^^^ ly» ®^ch as sixths. When two or more fractions have the same denominator, they are eaid to have a Comnion JDenominator. 8. Change ^ and ^ each to the common denominator 6. 9. Change ^, ^, and ^, each to twelfths; to thirty-sixths. 10. Change ^q, ^^, and J-f , each to fifths, and explain. 11. Express f , f, and /^, each as twenty-fourths. 13. Change | and f to a common denominator. Observe, § and } can each be changed to ffteenths (1 64—11) 3_3x5_10 4_4x3_13 8 ~ 3 X 5 " 15 ' 5 ~ 5 X 3 ~ 15 Thus, 13. Change to a common denominator § and f ; ^ and f ; I and f ; f and f ; f and § ; ^ and ^^V- g i ^ IN \^ lf ^i 11! M 114 REDVCTTON OF FRACTIONS, WRITTEN EXERCISES. 166. 1. "\^'hat is the length of J of a rope that is 168 feet' long ? Of I of it ? Of ] of it V Of /^ of it ? Of {\ of it ? 2. A loud of hay weighs 3'268 pounds. What is the weight j of I of it ? Of ;; of it ? Of 1 1 of it •> 3. A man hud $3143 in the bank, and took out | of it. How much money had lie still in the bank ? 4. A merchant having a piece of cloth containing 184 yards,] sold I of it. How much of the piece was still left? 5. What part of a sheet of paper is \ of \ of it? | of ^ of it?' i of tV of it ? \ of i'^ of it V 1 of ^., of it ? / C. Bought a pound of candy and made it into 6 equal parts, ' and gave • of one part to George. What part of the pound hbii George received ? 7. How many dollars are ^ of ^ of $84 ? ^ of | of $90 ? 8. $13 are | of how many dollars? Solution.— Siucc $12 arc § of the required number of doUart?, tlie \ of $12, or $6, must be ii. Agaiu, biuce $6 are I of the whole, \ mu»t be 3 times $6^ or $18. ^&. $9 are J of how many dollars '[f 10. $34 are 4 of James' money. How much money has he? 11. J- of a farm contains 161 »cres ; how many acres in the farm ? 12. 36 is f'^^ of what number? 18 is ? of what number? 13. A grocer sold 184 pounds of butter, which is ^ of what he has still loft. How much butter remains in the store? 14. Change § to tenths; f to fortieths ; ? to eighty-fourths. 15. If I own I of a garden, how many tioenty -fourths of it do I own? How many ninety-sixthif 16. Change to a common denominator | and | ; y'^ and f ; f and -J ; ,\ and § ; ? and ^ . 17. Find iV of 480 ; -U^ of 09400 ; f of 301 ; f of 423. A CTTONS, CISES. !1CJ them RED rrrrox of fr actions. ORAL AND WRITTEN EXERCISES. 115 f a rope that is 168 feet I 1C>7. 1. In three eqr tl lines how many fourths of one of )fit? Of-j'Vofit? 1 them? What is the weight IS 1 took out I of it. How >th containing 184 yards, ras still left ? i of i of it? i of ^ of it? f it ? de it into C equal parts, What part of the pound! 84? ^ off of $90? !cl number of doUare, tlie J of }e 3 times $6^ or $18. w much money has he ? ; how many acres in the f of what number ? itter, which is f of what mains in the store ? is; f to eighty-fourths. ly twenty -fourths of it do tor f and | ; ^V and f ; of 301 ; I of 423. WHOLE LINES. POURTHB. 12 fourths. Solution.- In 1 lin« '-''ire are 4 fourths. Hence in 3 lines there must be 3 times 4 fourth!', which ».re 12 fourths, as shown in the illustration. 2. In 7 i)Ounds of coffee, how many thirds of a pound ? 3. Ilowmany fourths of 1 bushel in 5 bushels? In 9bushels? In 12 bushels ? In IG bu. ? In 29 bu. ? In 100 bu. ? 4. Express 6 gallons as halves of a gallon; as thirds; as ninthH ; as fifths ; as tenths ; as twelfths. 5. In 5^ feet, how many thirds of a foot? SoLt'TiON.— In 1 foot there are 3 thirds, and in 5 feet there must be 6 times 15 thirds, which arc 13 thirds. 15 thirds plus 2 thirds are 17 thirds ; heuc(! in 5? foot there arc V of a foot. Obfcrre, 1st. A wliolo number and a fraction written together, as 5S, is called a Mixiul JS'utnher, 2(1. A fraction whore the numerator is equal to or g^rea^er than the de- nominaUn", as {, J, is called au Improper I'mctton, 6. How many fourtJis of a yard in 6 J yards ? In 9| yards ? 7. Change to cigJiths 8i| feet ; 5^ pounds ; 9| gallons. 8. Express in twelfths ^:{^ dollars ; Z^» bushels ; 8}^ tons. 9. How many tenths of one bushel in 40-/^ bushels of wheat? In98i'obn.? In337i«ybu.? In639/'nbu.? 10. How many sixteenths of one pound in l^-^r pounds of sugar? In9i'\lb. ? In 35^^^,.; lb. ? Inl38Hlh.? In 375^^1. lb.? 11. How many ffteei'ths of one yard in 3f*- yd. ? 12. Express in thirteenths \Z{.^ dollars; 9^^ yards; 37^^^ lb. ; [39/^ tons; 82 ^'V. gallons. I I . 'I • I >f :l i ■ lib FRACTIONS. ORAL AND WRITTEN EXERCISES. 168. 1. What part of one bushel is one peck ? IWv pecks ? Three pecks ? ^<9i," of a pound ? 0. How many dollars in $!| ? In $V ? In $V • f" $V ? In IV? In|«'^5? Inl^p-?' Change each of the following fractions to a whole or mixed number : 7. 8. 9. 10. 8 m 4 . 18 11. V- 12. "9" 13. V 14. V 1 R 12 8 16. -V. 17. ^\ 18. -^K 19. 20. 21. 22. ia8i> il • 1 73 5 an • 1(18 5 7F • 7430 15 B • 23. One pint is what part of a quart? Of a gallon? 24. One quart is what part of a gallon ? 15 (quarts are how many fourths of a gallon ? 25. How many gallons and fourths of a gallon in ^^ gal. ? In *^"- gal. ? In J :j^- gal. ? In ^:^"- gal. ? 26. How many quarts in "'i" of a galloii ? In -'j' gal. ? 27. What part of a pound Avoirdupois Is I ounce, and why? Is 3 oz. ? Is 5 oz. ? la 9 oz. ? Is 13 oz. ? 28. Express ^v, of a pound Avoirdiii)ols as ounces, and explain why the change can bo mndo. 29. How many pounds and oz. in '^ of a pound, and why? Tico pecks ? Is how many in 9 pecks? one bushel, in < are contained I pound V In r"*? Tn $V? olo or mixed in i2Mi» n? rts are how ^^'gal.? Ill al. ? , and why ? [vnd explain Lud why? ADDlTIOy OF FRACTIONS. 117 ORAL AND WRITTEN EXERCISES. lot). 1. Find the sum of 4. fifths, 2 fifths, and 3//«/iS. Solution.— The sum of 4 fifths + 2 fifths + 3 fifths is 9 fifths, which is equal to .?, or 1^ 2. How many are 7 eighths + 5 eighths? 6 sevenths ■{• 5 secciiths? 3. lIowmanyareHf + v? i + HV A + A + A? Read and find tlie sum of each of the following examples: 4. ? + ?+!• 7. 4 1 (! _L 6 IT + IT + IT- 10. 7 1 i 1 3 5. Kl + lJ. 8. S + "ff + ¥• 11. Y+7 + ;• G. i^+T^ + T^. 9. 4 1 B 1 7 a + TT + ¥• 12. 1 1 1 7 1 « -8-+8 + S- 13. If you want to express the sum of 5 chairs and 3 tables, how would you write the number, and why ? 14. To add 2 thirds and 5 sixths, what must be done, and why ? Fractions that have different denominators must be changed to others having the panic denominator before they can be added. lo. Fhid the sum of k and 'j ; of § and § ; of f and | ; of f and ^. 10. Find the sum of i + H i J of f + f + ^^ ; of f + -^^ + ^f^. 17. Find the sum of 1+^; of -|+ J ; of ;| + f.. Obsen)e, thirds and fouiiiis can eacli be made into twelfths ; fifths and third:* into fifteenths ; fourths and (d 1 i I H I i ll 118 SUBTRACTION^ OP FRACTIONS. 1 i '11' MM •VI ORAL AND WRITTEN EXERCISES. 1 70. 1. What is the difference betweeu I and f V Solution. 7 ninths minus 5 ninths are 2 ninths, which are |. 2. What is the difference between i and % ? f and f ? -^ and Y^? Viandrlr? H a^fl r: ? 3. How many are f ^ less than {'q ? {\ less than ^\ ? f| less than %\ ? I ;] less than f f ? ^¥5 less than f^| ? 4. Find the difference between ^ and ^ ; | and f ; g and f . Observe, J can be changed io fourths, I to eiuhths, I lo ninths. Perform the subtraction in the following : 5. A-i 13. 1-f 21. 8_3 39. 4f-i. 6. j\-h 14. 1-i 22. 4 3 4' 30. 21-i. 7. 14 a IS 3' 15. 2-^. S3. 5_1 tf a- 31. 6i— i 8. 1 7__5 19 «• 16. 5-i 24. ?-|. 32. 3|-|. 9. 19 3 ^4' tf 17. 1-f. 25. ^-|. 33. 9H-I 10. H-1^- 18. 8-f. 26. I-tV 34. 5,«,-f 11. 4 5 19. 1-?. 27. l.-J^ s 16 iw 35. 2!1~3. 12. a7~lS^* 20. 9-i 28. A-i. 36. 4«-^ 37. James had $3 and gave | of a dollar to William. How much money has he left ? 38. Mary owes a store bill of ^ of a dollar. If she hands the clerk '\ of a dollar, how much change should she rebeive V 39. Find the difference between ^l and %l ; $|| and $f;. 40. Henry had $4 and gave $| to James. How much had he left V Find the difference between : 41. $3;1 and f ». 44. %^ and $42. 42. 5^8 and %l 45. $5f and %\\. 43. .$0| and %%\. 46. $8^ and $3^^. 47. I oz. and | oa. 48. § lb. and \ lb. 49. g gal. and f gal. JYS. MULTIPLICATION OF FRACTIONS. 119 'ill <''>l SES. andf? ^ [\? ffless "• ' and |. hs. '*. 2'V 1 4«_r> iam. How hands the eive ? Id $,■•. ich had he and I oa. md I lb. and J gal. ORAL EXERCISES. 171. 1. Find I of ^ of a given line. Obs!:rve, I of a line is equal | of the same line, thus : I'art taJceu, wmmmr mmtarj, Having made the given tMrd into two equal parts, we have I, and can i\ow take the half of it, thus : 1 of 2 From these two illustrations we have the following Solution. \ is equal to J, and J of 'i is J ; Lriice, i of J is J. Solve and explain in this way each of the following : 2. What is i of l ? J of i ? iofi? iofi? 3. What is J of-[? iofi? iofr^ iof|? 4. What is 1 of i ? koik'i iofi? iofj? 5. Wiiat is ! of ; ? iofj? iof ■? iofl? 0. What is I of J? i of ] ? iof^? iof^? 7. CJcorge had | of a dollar and gave J of what he had to Ada. What i)art of a dollar did Ada receive? 8. What part of a peach is }, of h of itV i of I of it? 9. Henry owned i of a boat and sold I of it to James. What part of th(^ boat did James own V 10. What part of a garden is i of .[ of it? 1 of | of it ? 11. Kohert borrowed ;", of Henry's money, and gave I of it to Maggie. What part of Henry's money did Maggie get? 12. Mary bought I of u cuke and gave } of it to Susie. What part of the cake did Susie receive ? 18. What part of my money is ] of J of it ? j of >f it ? w r Ill if: 120 3IUL TIP LIGATION OF FRACTIONS. ORAL EXERCISES. 172. 1. What part oi' au orange is J of % of it? Solution.— Since i ol' i of au omuge is -,'5 of it, J of | of it must be 2 times r'j, whicli are ,-4. 3. What part of an apple is \ of } of it? { of 5 of it? ] of gofit? 1 off of it? ^ off of it? ^ of ^ of it? Find the required part in the following : 3. h of f 9. ioff. 15. I of |. 21. I of U- 4. iof ■. 10. -1 of tV- 10. i of |. 23. hoiil 5. ^ of /v. 11. ^ nf s T 01 ij. 17. iof^. 23. 1 nf ~» U 0^ 1 5* 6. ^of^ 13. 1 Of |. 18. iof iV 24. 1 of " 10 "^ 1 ()• 7. ^of^ 13. ^ Of t'^. 19. 4 of A. 25. iVof t6o 8. i of ,V 14. i of t\. 20. ^ of ,v. 26. iV of /,f. 27. What part of a peach is | of J of it ? SoLXTTioN.— Since J of J of a peach is fV of it, g of ^ of it must be 2 times x\, wiiichare ,";. 28. What part of a cake is 5 of 4 of it ? -J of ^ of it ? 29. A boy bought ] of a pound of candy and gave I of it to Lis sister. What part of the pound did his sister receive ? 30. What part of a gallon is * of ■; of it ? I of | of it? Find the required part in each of the following : 31. ^ of l 34. ^ of I. 37. I of ^\. 40. -^, of -,\^. 33. li of ?. 35. -iVof •] 38. fl of I. 33. ;| of 5. 36. 3!^ of {\. 39. fV of i ftl. ^jj 01 yi-ijj. ^'*' Iff 01 (o?T" 43. SuHio had a pear, and gave \ of J of it to Mary. \Miat part ol' the pear had she then left? 44. A boy had I of a dollar and gave away 2 of it. What part of a dollar had he ilieu 1 "ft ? 45. Williiini liad ,! of a melon and gave jj of it to Robert. Wl)at i)art of the whole melon had he then left? be *V bu> iiii mi po foi^s. t? of it miist be 8 of it? I of TOO' riT ol' list be 2 times 'it? e r^ of it to 'ceive ? )fit? A of Air. A of •' '1 i-y- ^^'llat it. What :o Robert. }[ULTIPLICATION OF FRACTIONS. 121 ORAL AND WRITTEN EXERCISES. 1 7o. 1. At J of a dollar lor one yard of cloth, what will be the cost of 8 yards ? Solution.— Since 1 yard cost $J, 8 yards must cost 8 times $J, which are $V, eq"'i' $^- 2. Fhid the cost of 7 bushels of apples at ^ of a dollar for one bushi'l. At I of a dolfar. At -| of a dollar. 3. How much will pounds of tea cost at $f per pound ? At %l per pound? At %l per pound ? At $f per pound? 4. A father gave to each of 3 children ^ <>f a dollar. How much money did he give away in all ? 5. A man gave to each of 7 beggars i of a dollar. How much did he give away in all ? ('. \Vliat is the cost of f of a pound of sugar, at 15 cents a pound ? Solution.— Suice 1 pound co«t 15 cents, I of a pound must cost I of 15 cents, which are 3 cents, and 5 of a pound must cost 3 times 3 cents, which are i) cents. 7. What is the cost of \ of a pound of candiea, at 86 cents a pouu.l ? At 24 cents a pound ? At 48 cents a pound ? 8. Wliat is the cost of !; of au acre of land, at $32 an acre? At $48 an acre ? At $72 an acre? At $90 an acre ? 9. What is the value of y\ of a garden, worth $48? Worth $84? Worth $108? Worth $144? Worth $2400? 10. If a load of hay cost $12, what is the value of \ of it? Of -; of it ? Of ■{ of it ? Of I? of it ? 11. If a farm is worth $0240, what is I of it worth ? f of it? ,\ofit? II of it? (Vofit? If.ofit? Observe, J of $9240 = $!)240-f-5 == |1818; hence, I of $9"-M0 = $1818x8 = 12. What is the cost of 48 bushels of corn, at !^ of a dollar per bushel ? At -j'.v of a dollar ? At -j",,- of a dollar ? 13. What is tlto cost of 30 jounds of tea at f of a dollar per pound? At ;, of a dolliir? , G ^ i V i .>• -.22 3IULTIPLICATI0N OF FRACTIONS, \ \ %\ '■• ■ ill ' iiU ; i !• ORAL AND WRITTEN EXERCISES. 1 74. 1. If 1 biishel of corn cost ^|;, what will be the cost of 4J bushels V Solution.— 1. 4^ bushels are equal to V of a bueheL 2. Since ^l is* the cost of 1 bu., i of $3, or $-,\, is tlie cost of \ of a bn. ;]. Since I,'-, in, the cost of \ of a bushel, 19 times f j'^- or $y;;, equal |3t\, is the cost of V\ or 4^ bushels'. 3. If 1 yard of cloth cost $-', what will he the cost of 3| yards ? Of 5] yards ? Of 2 ? yards ? Of 4f yards ? 3. If 1 bushel of apples cost $|, what will be the cost of 41 bu. ? Of ^ bu. ? Of 52 bu. ? Of 7^ bu. ? Of 10^ bu. ? 4. Multiply ;i by §; f by | ; f by | ; g by t\ ; -« by «. Observe^ I multiplietl by s, or ^ x 3, means the same as $ of §, or i of J ; hence the solution is the same as given (1 72—37). Perform the work and explain each of the following : 8. IT X#. 6. 7. yj X ^, lU. -fg- X Y» 11, 12. 13. A4 TffTT' 80 ' 14. 8.1 V, 15. f^x|. 17. If 1 pint of milk cost 4| cents, v/liat will be the cost of 3? pints ? Solution.— 1. 3J pints are equal to V- pints, and 4J ccnt« are equal to f cents. a. Since I cl. are the cost of 1 pint, J of f ct., or ^^, ct., must be the cost of J of a pint. .3. Since 1°, ct. are the cost of J of a pint, 17 times ^^ ct., or '/J- ct., equal \^^r, cents, must be the cost of Yi or 3? pints. 18. If 1 bushel of pears cost )«;2f , what will be the coat of 4| bushels ? Of 3i bu. ? Of 71 bu. ? Of 6| bu. ? Of 9| bu. ? 19. What is the cost of 4J! yards of olnth, at $1^ per yard? At $3i per yard ? At $2^ per yard ? At $4| per yard ? 20. What is the cost of I of a yaixl of cloth at iSG a yard? 21. I of $75 is 2 times what a coat cost ; what was the price of the coat ? 'lOJYS, DIVISION OF FE ACTIONS, 123 I be the cost of iofabu. ■ $r", equal |3i\, le cost of 3| i? e the cost of 10^ bu. ? of 3, or I of I ; e tlie cost of aro equal to f t be the cost of ' 'ir ct,, fqnal » coat of 4* )i^bu.? i per yard? rd? a yard ? s the price ORAL AND WRITTEN EXERCISES. 1 7«>. 1. How many times can ^ pound of tea bo taken from 2 pounds ? From 3 pounds ? From 5 pounds ? From 8 pounds ? Solution.— In 2 pounds there are 4 halves, hence 1 half can be taken 4 times from 2 pound's. 3. How many times can i be taken from 1? From 2? From J? o. How many fourths in 2 peaches? In 4 peaches? In 8 peaches ? 4. How many times are %% contained in $3 ? In $4 ? In $8 ? Solution.— $2 aro equal to %% and 5 are contaiued 3 times in %. Observe, the dividend and divisor are made, before dividing, into the same fractional parts. 5. How many times are | of an ounce contained in 3 ounces ? In G ounces ? In 9 ounces ? In 12 ounces V In 2 ounces ? 6. How many times are i of a gallon contained in 8 gal. ? In 12 gal. ? 7. How many apples at -| of a cent each can be bought for 6 cents? Solution.— As many as g of a cent are contained times in 6 cei^ts, which are 9. 8. How many books at |f each can be bought for |6 ? For $9? For|3? For $12? For $30? For$GO? 9. When coffee can be boiight for %{^ a pound, how many pounds can be bought for |10 ? For $30 ? 10. How many pounds of butter at $| a pound can be bought for $3? For $5? For $8? For $4? For $9? For $20? 11. If a bushel of apples costs | of a dollar, how many bushels can be bought for $15 ? 12. If a yard of cloth costs $^ , how many yards can be bought for $20? 13. If a quire of paper costs % of a dollar, how many quires can I get for $18? ^ 1 1 J r 1/ II 124 DIVISION OF Fit ACTIONS, ; V i' •/' 'rtj if ii 'f \ " J ,!■' OBAL AND WRITTEN EXERCISES. 17(>. 1. How many times can g be taken tVom I 'I Solution.— As many tiiues as 2, the nnmerator of tlio divisor, is con- tained limes in 6, the numerator of the dividend, which are 3. 2. How many times can JV ^^ taken from {\'i From V\'l From^"^-? Fromi^? Fromjl? From ^5 ? 8. {-, are contained liow many times in ^.^ 'I In j*. V In \l ''• In^tf Iiil*? Ini?? Inin In^^? Perform and explain the division in the following : fi 48 i_ B Q 40_j_ 7 "• So • 5 0- ^' T(i~Tff' 4 7 8 6_j }• O 14_. TST -TIT' *• 7T~Tf «'• Tlf~T]I' 4 15-i- a K 12-!- 10. How many times is ^ of a quart contained in ^ qt. ? Ob,wrve, the divisor and dividend muet both express the same kind of equal parts, hence the following: Solution.— 5 of a quart is equal to 3 of a quart, and 2 of a quart arc con- tained 2 times in | of a quart. 11, How many times are 5 contained in -{^ ? In |^ ? Perform and explain the following : 19, 1 2 _i_ 1 13 1 f' -!- 1 14. 15. HO_i_r) 1 -i _. 4 1fi ion.i.5 . . .. 17 me. ,^3 18. A boy spent || cents in bu;.-ing- pears at | of a cent each. How many pears did he buy ? Solution.— lie bouj^ht as mauj' pears as I of a cent are contained times in 11 c 'nts. I of a cent arc equal to ,", of a cent, and 1",^ of a cent are cou- tiiined 1) time < in j'i cents ; hence he l)onjj:ht 9 pears. 19 At .$;j n yiii'd, how many yards of cloth can be bought for $|A? For^'V? For^U-J? For $^2^ 30. At $T a peck, how many ]iecka of ])eac]ies can be bought for jl^ Yi ? For $ ^^ V For ^2 ? For (• 7 ? F( .r $ 1 2 V 'S, C OMr A It I S X O F X U M B E E S . 1;>5 JISES. in S V divisoi", is con- 3. V From J,]? " A V In } '^ V mg 4(»j_ 7 . 4A^ « • T:t • T3" in f qt. ? the eame kind of r a quart are con- )f a cent each. contained times f a cent are coii- be bouglit for 'an be bong-lit V COMPARISON OP NUMBERS. 177. 1. What part of 4 is 3 ? Solution.— Since 1 is i of 4, 3 must be 3 times {, or I of 4. Find the part that 3, 2 is of 7. y. 4 is of 8; 4. a is of }). o. () is of 10. 6. 6 is of 18. 7. 9 is of 54. 8. 5 is of 35. 9. 10 is of 24. 10. 8 is of 56. 11. 10 is of 80. 13. 25 is of 100. 13. 200 is of GOO. 14. 2 pocks are what part of 3 pecks ? Of 4 pk. ? Of 7 pk. ? Of 10 pk. ? 15. 1 peck is what part of a bushel ? Of 2 bu. ? Of 3 bu. ? Observe, the two nnmbere compared mnst express the same unit; hence the fiiven bufhelH are expressed in pecks, and then the comparison is made. 1(1. 5 ounces are what part of 9 ounces? Of 15 oz. V Of 35 oz.? Of40oz.? 17. 1 ounce is what part of a pound Avoirdupois? Of a pound Troy? 18. 1 pint is what part of a quart ? Of 2 qt. ? Of 3 qt. ? 19. 7 pecks are what part of 3 bushels? Of 5 bu. ? Of 9 bu. ? • Of7bn.? 20. 10 ounces are what part of 2 pounds Avoirdupois ? 21. I of a i)0und is what part of § of a pound? Obfierve, tliat before two fractions can be compared they must both exi)rcH>' rqual parts of the same kind ; hence the following : HoniTioN.— J of a pound is equal to f, and 2 eighths of a pound are ^ of 6 eighths of a pound. 22. ;\ is what part of J ? J is what part of ^ ? Of ^ ? 23. I is what part of -fw ? f is what part of -{^ ? 24. f, is what part of {§ ? f is what part of ||? 35, « is what part of ^ ? f is what part of \^1 20. I', is what part of '^ ? Ms what part of |{}? ••» y, i 126 FRA CTIOXS. I . i )«' . DEPHnTIONS. 1 78. A Fractional Unit is one of the equal parts ol anythinpr regarded as a whole. 1 70. A Fraction is one or more of the equal parts of a unit or whole. 1.80. The Numerator is the number above the dividing line in the expression of a fraction, and indicates how many equal jmi'ts are in the fraction. 181. The Denominator is the number below the divid- ing line in the expression of a fraction, and indicates how many equal paints are in the icJiole. 1 81i. The Terms of a fraction are the numerator and de- nominator. 1 8*?. li eduction is the process of changing the terms of a fraction without altering its value. 184-. A fraction is reduced to Higher Terms when its numerator and denominator are expressed by larger numbers. Thus, I = xV 185. A fraction is reduced to LiOtver Terms when its mini orator and denominator are expressed by smaller numbers. Thus, /'^ = 1 1 8(>. A Common Denominator is a denominator that belongs to two or more fractions. 1 87. A Proper Fraction is one whose numerator is less than tlio denominator, as f, ^. 1 88. An Improper Fraction is one whose numerator is f'(iual to or greater than the denominator, as |, -^. 189. A Mixed Nuntber is a number composed of an integer and a fraction, as 5|, 132- In lual parts ot lal parts of a the dividing es how many o\v the divid- indicates how erator and de- ? the terms of "nis when its irger numbers. 'ms when its ailer numbers. lominator that nerator is less 3se numerator 7 a* mposed of an DENOMINATE NUMBERS. CANADIAN AND UNITED STATES MONEY. 190. The following table includes Canadian and U. S. money : Table op Units. 10 mills (m.) make 1 cent . . . ct. 10 cents " 1 dime . . . d. 10 dimes " 1 dollar . . . |. 10 dollars " 1 eagle . . . E. $1 = 10 d. = 100 ct. = 1000 m. 1. How many cents in |2? In $4? In $9? In $25? 2. How many dollars in 100 ct. ? In 300 ct. ? In 500 ct. ? In 1200 ct. ? 3. Change $10 to cents ; $23 ; $^; $95 ; $3:2. 4. In $2 how many mills? In $7? In 53 ct. ? In85ct.? 5. Express 435 cents as dollars and cents. Observe, the 400 cents mnke ^4, hence the 435 cents make f4 and 35 cents, which we write thuB : $4.85 (58—3). 6. In 786 cents, how many dollars and cents '? In 932 ct. ? In 5384 ct.? 7. In 300 eagles how many dollars? How many dimes ? 8. Express 8430 cents in dimes. In dollars. 9. Express in dollars and cents the following 375 ct. 856 ct. 732 ct. 205 ct. 430 ct. 1237 ct. 5786 ct. 8527 ct. 1006 ct. 8020 ct. 605 ct. 807 ct. 426 ct. 503 ct. 130 ct. 5360 ct. 9408 ct. 0210 ct. 3040 ct. 7304 ct. *«1 » I 128 D E X O Ml XA TE X I' M B E R S . WRITTEN EXERCISES. 101. The character (i! is followed by the ])rice of a unit or one article. Thus, 9 yards of cloth @ $'2, means 9 yards of cloth at $2 a yard. Find the cost of the following (see Art. 122) : 1. 5 yards of cloth (V? $.20. 2. 9 yards of cloth @ s.35. 3. 7 bu. of wheat @ $1.25. 4. 12 pk. of peaches {il $.85. 5. 8 gal. of vinegar @ $.37. 6. lb. of tea @ $1.48. 7. 9 yards of muslin @ $.38. 8. 14 pairs of boots @ $7.54. 9. 36 yards of ribbon (?. $1.84. 10. 48 yards of silk @ $2.95. 11. 79 bu. of peaches (d} $2.38. 12. 83 acres of land («) $43.25. 13. 56 tons of coal @ $7.45. 14. 93 cords of wood @ $4.53. 15. 237 acres of land @ $65.75. 16. 89 barrels of apples @ $3.46. 17. A farmer sold 46 sheep @ $3, 7 tons of hay @ $14.50, 184 pounds or butter @ $.43, and 35 barrels of apples @ $3.75. How much did he receive for the whole ? 18. A grocer sold a man 16 lb. tea @ $.85, 96 lb. sugar @ 12 ct., 35 lb. butter @ $.38, and 3 barrels of flour @ $8.50. How much did he receive for the whole ? 19. How much must I pay for the following bill of articles : 89 lb. of coflTee @ $.45. 85 lb. of butter @ $.39. 19 lb. of cheese @ $.18. 89 lb. of flour @ 4 ct. 42 lb. of dry beef (^, 19 ct. 64 lb. of sugar @ 13 ct. 20. A merchant bought 346 yards of cotton @ 9 ct., and 86 yards of silk @ $1.36. How much did he pay for both ? 21. A man bought 385 acres of land @ $49, and 36 head of cattle C<^ $42.50. What did the whole cost ? 22. What is the difference in the cost of 57 yards of silk @ $2JB5, and 532 yards of muslin @ $.37? 23. Which will cost the most and how much, 84 barrels of flour (Jl $7.60, or 136 barrels of apples @ '^^Ml DENGl : T' A. : t. '/ ¥ f/i H E R S . 120 of a unit or b 9 yards of bon (7? $1.84. k @ $2.95. lies (li) $3.38. id @ $43.25. I @ $7.45. wd @ $4.53. md @ $65.75. pples @ $3.46. hay @ $14.50, pples @ $3.75. 96 lb. sugar @ flour @ $8.50. 11 of articles : • @ 4 ct. beef @ 19 ct. ir @ 13 ct. ) 9 ct., and 86 both ? nd 36 head of rds of silk @ 84 barrels of 4- EXERCISES IN ENGLISH AND OTHER MONEY. 102. English or Sterling Money is tho money of Great Britain. The Standard Unit of English money is the Sover- eign or Poiind Ster- tiny. A iSovercign is equal to $4.8661 Canailmn Money. Table op Units. 4 farthings (far.) make 1 penny . . . d. 12 ponce " 1 shilling . . . s. 20 shillings " 1 pound . . . £. 2 shillings " 1 florin . . . fl. 5 shillings " 1 crown ... or. 193. French Money is the money of France. The Standard Unit of French money is the Franc of the Republic. A Franc is equal to $.193 Canadian Money. Table op Units. 10 millimes (m.) make 1 centime . 10 centimes 10 decimes 1 decime 1 franc 9 ct. dc. fr. LI j 130 DE2<0 M 1 ^' ATE A UM BEES. EXERCISES IN ENGLISH AND OTHER MONEY. 194. German Money is the money of the German Empire, The Standard Unit of the Ger- man Empire is the MarTc. The mark is subdivided into 100 Pfennings. The coins referred to m Canada are the Marky equal to 33^*^ cents Canadian Money. mver Thaler, equal to lA^^ ct. " •* Siher Groschen, equa' to 21 ct. " " Pfenning, equal to y^^ of a mark. 1. How many farthings in 1 penny? In 3 pence? In 5 pence? In 9 pence? In 1 shilling? In 20 pence? 2. How many pence in 8 shillings? In 5s. ? In 10s. ? In £1 ? 8. IIow many shillingB in 4 crowns ? In 9 florins? In £G? 4. How many pence in 3s. Od. ? In 5s. 9d, ? In £1 8s. 9d. ? 5. How many decimes in 3 francs? In 7 fr. ? In 12 f r. ? In 40 f r. ? G. Express 5 francs in centimes ; in millimes. 7. What is the value in Canadian Money of 1 franc? Of 3fr.? Of7fr. ? OfOfr.? OflOfr.? Of 100 fr. ? OfSOfr.? Of 400 fr. ? 8. What is the value in Canadian Money of £1? Of £2? Of £5? Of £10? Of £100? Of £20 9. IIow many pfennings in 1 mark ? In 7 marks ? • S s. OTHER the German oney. « 3 pence? In ice? 1 10s.? In£l? ins? In £6? 11 £1 8s. 9d. ? ? In 13 fr.? 1 franc? Of ? OfSOfr.? £1? Of £21 s? £> E X MI NA T E N UM B ERS. 13l EXERCISES IN UNITS OP WEIGHT. 195. 1. Ti'oy JJ'rifjJif is used in weighing- gokl, silver, and precious stones, and in philosophical experiments. Table of Units. V 24 grains (gr.) make 1 pennyweight 20 p<'nnyweights " 1 ounce . . . 12 ounces 1 pound pwt. oz. lb. 2. Aputhcrnrics' Weight is used by physicians and apothecaries in compounding dry medicines. V Table of Units. 20 grains (gr.) make 1 scruple . . sc. or 3 . scruples " 1 dram . . . dr. or 3 . 8 drams " 1 ounce . . . oz. or § . 13 ounces " 1 pound . . . ft. Tlie pound, ounce, and grain are the same in Troy and Apothecaries' weight. 3. How many grains in 2 pwt. ? In 5 pwt. ? In 10 pwt. ? 4. How many scruples in 3 10 ? In 3 15 ? In 3 30 ? 5. Express in grains 5 pwt. ; 10 pwt. 7 gr. ; 8 pwt. 13 gr. 6. Express in ounces 3 lb. 4 oz. ; 5 lb. 9 oz. ; 10 lb. 7 oz. 7. Change to grains 2 lb. oz. ; 5 lb. 10 oz. 8. Express in scruples 3 lb . 4 oz. ; ft) 38 3 5. 9. How many powders weighing each grains can be made from 33? From 3 15? From 3I 32gr.8'? Obfifrve, ench number nuiet bo made into gniiii)* before dividing by the 9 grains. 10. How many tablespoons, each weiglilng 3 oz., can be made from 1 lb. of silver? From 5 lb. ? From 12 lb. 8 oz. ? 11. How many ounc("A in n\ lb. ? Tn 2| lb. ? In 4^ lb. ? 11 f . I ¥l|i 133 DE NO 3IIXA TE N UMB ERS. * :!ir ■lit i 7 n'. V. t EXERCISES IN UNITS OF WEIGHT. 190. Avoirdupois Welr/ht is used in weigliiiig gro- ceries aud all heavy articles and drugs ut wholesale. lb. cwt. T. ih Table of Units. 10 ounces (oz.) make 1 pound . . . 100 pounds " 1 hundrcdweiglit 20 cwt. or 2000 lbs. " 1 ton .... 1 pound contains 7000 grains Troy. The following denominations are also used : -\ 100 pounds of grain or flour make 1 cental. 100 pounds of dry fish " 1 quintal. 19G pounds of flour " 1 barrel. 200 pounds of pork ** 1 barrel. 1. How many ounces in 2 pounds? In 4 lb. V In 10 lb. ? 2. How many are the A of 8 oz. ? i of 10 oz. ? ] of 10 oz. ? 3. How many ounces in % lb. ? In | lb. ? In the J of 2 lb. ? 4. How many pounds in 40 oz. ? In 112 oz. ? In li)2 oz.? 5. In 5 lb. 9 oz., how many ounces ? G. In 4 cwt. 37 lb., how many pounds? In 13 cwt. 84 lb.? 7. What is the cost of 2 lb. 13 oz. of candy, at 3 cents an ounce ? Of 4 lb. 7 oz., at 5 cents an ounce? 8. A coal dealer sold 9 T. 12 cwt., at 25 ct. a hundredweight. How uiuch did he get for the whole ? Ohaerre^ Iho tons must bo chnnROd to iHuulredwoli^htiH. 0. When coal sells at 35 ct. a hundredweight, what is the cost of 5 T. 10 cwt. ? Of 8 T. 13 cwt. ? Of 12 T. 18 cwt. ? 10. WHiat is the cost of 5 barrels of flour at 2 ct. a pound V 11. Wliat is the cost of 8 quintals of fish at 7 ct. a pound? At 9| ct. a pound ? 8 ii [QHT. lifc^liing gro BEN uVIX A TE X U M BEE S, loo lb. CAVt. T. 1. al. 1. 1. n 10 lb. ? ] of 10 oz. ? e I- of 2 lb. ? 11 11)2 oz.? ivt. 84 lb. ? it 3 cents an idrechvciglit. wlint is the ? cwt. ? a pound ? 3t. a pound ? UNITS OP LENGTH. li)7. A yard Is the Stcuulavd Uiiii in linear measure. I. Used Table OF Units. d in measuring lines or ordinary distances • 12 inches (in.) make 1 foot .... ft. n feet 1 yard .... yd. 5J yd. or 10?. ft. " 1 rod .... rd. 40 rods 1 furlong . . . fur 8 furlongs " 1 mile .... mi. J] miles " 1 league . . . 1. II. Used in measuring roads and boundaries of land. Tf'fffj inches make 1 link .... 1. 25 links i( 1 rod . . . . . rd. 4 rods (t 1 chain , . . . ch. 80 chains <( 1 mile . . . . mi. III. Used in iiwasuring doth sold by the yard. 2} inches (2| in.) make 1 sixteenth of a yard, -j^ yd. 2 sixteenths (4.V in.) " 1 eighth of a yard, \ yd. 2 eighths (0 in.) " 1 fourth of a yard, -| yd. 4 quarters " 1 yard. IV. Used to measure the kind of distances named. „^ , . , « ' C degree of Latitude on a Me- 60 geographical or , ^ ) • v * t •* i nl^ 1 a ^ r J. -i ?■ make 1 < ridian, or of Longitude on ""iW Htatute miles \ ^ 860 degrees 1iYd i^tatutjo miles 8 geographical mi. 6 feet inches the Equator. 1 circumference of the earth. 1 gpog. mi. \ Tised to measure 1 league ( distances at sea. ( used to measure ( depths at sea. used to measure the 1 hand •{ height of horses at the shoulder. " 1 fathom HI m ii ' 1" 'III I 'I I 134 DENO MINA T E :< UMB EliS. EXERCISES IN UNITS OP LENGTH. 11)8. 1. How many inches in 2 feet? In 4 ft. ? In 7 ft. ? In 9 ft. ? In 20 ft. ? 2, Express in inches 1 yard ; 3 yards ; 10 yards ; 100 yards, 3. How many inches in 4 yd. 2 ft. 7 in. ? Solution.— 1. Since 3 feet make one yard, in 4 yd. there muet be 3 times 4 or 12 ft., and 12 feet plut> 2 feet are 14 feet. 2. Since 12 inches make 1 foot, in 14 feet there must be 12 times 14, or 168 inches, and 108 in. phis 7 in. are 175 in. Hence, etc. Express in inches each of the following : 4. 2 ft. 8 in. 5. 5 ft. 9 in. 6. 9 ft. U in. 7. 1 yd. 2 ft. 8. 3 yd. 1 ft. 9. 7 yd. 2 ft. 10. 2 yd. 1 ft. 7 m. 11. 3 yd. 2 ft. 9 in. 12. 10 yd. 1 ft. 4 in. 13. How many inches in 1^ yard ? In 3^ yd. ? In 5| yd. ? Obeerve^ J of a yard = 18 inches, and | of a yard = 27 inches. 14. How many inches in 1 rod ? In 2 rods ? In 5 rods ? lu 10 rods ? 15. Express in yards, feet, and inches, 129 inches. Solution.— 1. Since 12 Inches make 1 foot, there are as many feet in 129 inches as 12 inches are contained times in 129 in., which are 10 and i) in. remaining. a. Sirice 3 feet make 1 yard, in 10* feet tliere are 3 yards and 1 foot re- maiuinff. Hence in 129 inches there are 3 yd. 1 ft. 9 in. 16. Express in feet and inches 30 in. ; 50 in. ; 78 in. ; 100 in. ; 130 in. 17. Express in yards and feet 14 ft. ; 20 ft. ; 29 ft. ; 40 ft. ; 62 ft. 18. How many yards, feet, and inches in 68 in. ? In 95 in. ? Id 175 in. ? In 273 in. ? 19. How many inches in 1 sixteenth of a yard ? In 2 six- teenths? In 7 sixteenths ? I In 7 ft. v too yards. let be 3 times J2 times 11, or i. 1 ft. 7 in. 1. 2 ft. 9 in. d. 1 ft. 4 in. n 5| yd. ? s. 5 rods? Ill many feet in t-e 10 and 9 In. and 1 foot re- 1. ; 100 in. ; ft. ; 40 ft. ; In 95 in.? In 2 six- D E N MI iV ^1 TE N UMB ERS. 135 EXERCISES IN UNITS OP SURFACE. IIM). 1. A Surface has two dimensions, length and breadth. 2. A Square is a surface bounded i y block 1 foot tliick contains 4 x 8=32 en. ft., and there are 3 euch t^labs in the Mock. 8. How many cubic feet of earth in a bank that is 5 feet deep, 8 feet wide, and 13 foc^t lon^-, nnd what would be the cost of removing the earth at jj of a cent per cubic foot ? II 1|' \% I 138 D E y MIS A TE 2s UMB Eli S, EXERCISES IN UNITS OF VOLUME. 203. Wood 3l€asitre is used in measuring wood, rough stone, and masonry. 204:. A Cofd is a pile of wood, stone, etc., 8 feet long, 4 feet wide, and 4 feet high. 205. A Cord Foot is 1 foot long, 4 feet wide, and 4 feet high, and contains ^ of a cord. Table of Units. 1 cord 16 cubic feet make 1 cord foot 8 cord feet or 128 cubic feet m cubic feet " 1 \ "^"f "' ''""^ * ( or of masonry. \ " Cd. ft. , Cd. Pch. . 1. How many cord feet in 1 cord? In 2 Cd. ? In 9 Cd. ? 2. How many cubic feet in 1 cord foot ? In 2 Cd. ft. ? In 6 Cd. ft. ? In 8 Cd. ft. ? In 10 Cd. ft. ? 3. How many cords in 8 Cd. ft. ? In 16 Cd. ft. ? In 56 Cd. feet? 4. Express, in Cd. and Cd. ft., 368 cubic feet; 696 cu. ft. 5. What is the cost of 3 cords of wood, at 40 cents for every <;ord foot ? 6. What part of a cord is a cord foot ? 2 Cd. ft. ? 7 Cd. ft. ? 7. A pile of wood is 4 feet wide, 6 feet high, and 16 feet long. How many cubic feet in it ? How many cords ? 12 lUME. i^ood, rough feet long, e, and 4 feet Cd. ft. Cd Pch. n 9 Cd. ? I. ft. ? In 6 ? In56Cd. 6 cu. ft. s for every 7Cd. ft.? 6 feet long. DENOMINATE NUMBERS. 139 UNITS OP CAPACITY. 206. Liquid Measure is used in measuring all kinds of liquids, as oil, milk, water, etc. The measures in use are of various sizes, thus : Table of Units. 4 gills (gi.) make 1 pint . 2 pints " 1 quart . 4 quarts " 1 gallon pt. qt. gal. Note. — A barrel of beer contains 36 gals. A hogshead of beer " 54 gals. A hogshead of wine " 63 gals. . The Imperial or standard gallon contains 277.274 cubic inchea- Units used in measuring liquid medicine : 60 minims (tl|) make 1 fluid drachm . f 3 • 8 fluid drachms " 1 fluid ounce . fj. 16 fluid ounces " 1 pint . . . . O. 8 pints " 1 gallon , . . Cong. 1. How many gills in 2 pints ? In 7 pints ? In 9 pints ? In . 12 pints? 2. In 8 quarts how many pints ? How many gills ? 8. Express in pints 2 gallons ; 7 gallons'; 10 gallons. 4. Express in gallons and quarts 276 gills ; 339 pints. « I 140 DE XO MIX A T E X U .V B E R S. # \*-'K EXERCISES IN LIQUID MEASURE. Ii07. 1. Express in pints 5 gal. 3 qt. 1 pt. ; 12 gal. 3 qt. 1 pt. 2. What is the cost of 4 gal. 3 qt. of milk, at 4 ct. a pint ? 3. IIow many gallons in 93 qt. ? In 03 pints? 4 IIow many mluims in f 3 7 ? In f 3 12 V 5. Express in fluid ounces 2 gal. 7 pints. 6. Express in minims 42 fluid drachms ; 83 fluid drachms. 7. A grocer sold 5 gal. 2 qt. of vinegar, at 4i cents a pint. How much did he receive for the whole? 8. A farmer sold 5 gal. 3 qt. milk, at 3i cents a pint. IIow much did he receive for the whole ? « Find the cost of each of the following quantities of milk : 9. 7 gal. 3 qt. at 8 ct. a qt. 12. 10 gal. 1 qt. at 8 ct. a pt. 10. 10 gal. 2 (it. at 9^ ct. a qt. 13. 8 gal. 2 qt. at 3i ct. a pt. 11. 9 gal. 3 qt. at 7| ct. a qt. 14. 12 gal. 3 qt. at 4i ct. a pt. 15. What is the cost of 8 gal. 3 qt. of syrup at 14 ct. a qt. ? 10. One quart is what part of a gallon ? Of 2 gal. ? 17. Three quarts are what part of a gallon? Of o gal. ? 18. IIow many gallons in 4 barrels ? In 2 bbl. ? In 12 bbl. ? In2lbbl.? In 100 bbl.? 19. What is the cust of 4 hogsheads of molasses at 30 cents a gallon ? Of 7 hhd. at 30 ct. a gal. ? 20. A grocer sold 1 hogshead of syrup at 10 cents a quart. IIow much did he receive ? 21. What is the cost of 5 f 3 14 f 3 0, r.t 5 cents for each fluid drachm? 22. A milk dealer supplies a family with 4 quarts of milk each day for 20 weeks, at 3J- cents a pint. What is the amount of the bill lor the 20 weeks ? 23. How many pints of water will fill a vessel which holds 19 gal. 3 qt. 1 pt. ? URE. tal. 2 (]t. 1 pt. It. a pint ? drachms, cents a pint. I l)int. IIow s of milk : t 8 ct. a pt. 3^, ct. a pt. t 41 ct. a pt. L4 ct. a qt. ? :al. ? f 5 gal. ? • InlSbbl.? at 30 cents a ents a quart. ents for eacli arts of milk 3 the amount which holds DEXO 2£ I X A TIC N UJI JJB li S . 141 UNITS OP CAPACITY. 208. /)/'2/ Pleasure is used in measuring grain, roots, fruits, salt, e+c. The measures in use are of various sizes, thus : Table of Units. 2 p'nts (pt.) make 1 quart . 8 quarts " 1 peck . 4 pecks " 1 bushel qt. pk. bu. The following table shows the weight of a bushel of the article named : Wheat, 60 lb. Clover seed, 60 " Peas, 00 " Beans, 60 " Potatoes, 60 lb. Corn, 56 " Rye, 56 •' Flax seed, 58 " Buckwheat, 48 lb. Barley, 48 " Oats, 34 " Timothy seed, 48 " Note.— By the " Weights and Measures " Act of 1873, the Imperial bushel, containing eight " Imperial gallons " of 277.274 cubic inches in each, is the standard bushel in Canada. The following articles, according to the same Act, are to be esti- mated by the Cental of 100 lbs. ; Barley, beans, charcoal, corn, oats, pease, potatoes, rye, salt, seeds, and wheat. In Great Britain, 8 bushels make 1 quarter. \ 142 DENO MIX A TE N UM B ERS. EXEBCISES IN DRY MEASUBE. 209, 1. Express 5 bu. 3 pk. in quarts ; 3 bu. 2 pk. 5 qt. in pints. 2. How many bushels in 12 pk. ? In 17 pk. ? In 128 qt. ? 3. What is the cost of 7 bu. 3 pk. of peaches, at 50 cents a peck ? At 35 cents ? At 65 cents ? 4. A grocer sold 3 bu. 3 pk. clover seed for 9 cents a quart. How much did he receive for the whole? 5. What is the value of a load of beans weighing 2700 pounds, at |1.85 a bushel? 6. A fanner sold 4,250 pounds of oats at 40 cents a bushel, iiow much did he receive ? 7. A grocer sold 12 barrels of apples, each containing 21^ bu., at 33 cents a peck. How much did he receive for the 12 bbl. ? 8. A wheat merchant bought at $1.15 a bushel, 5 loads of wheat, each weighing 3000 pounds, and 3 loads, each weiglijng 4000. What did he pay for the whole ? 9. What is the cost of 4984 pounds of corn at 5 cents a bushel ? * 10. What is the cost of 1 bu. 3 pk. of berries, at 4^ ct. a pint? 11. How many bushels in 234 pt. ? In 510 pt. ? 12. A man bought 10 car loads of oats, each weighing 4590. pounds. How many bushels did he buy ? 13. How many bushels of timothy seed in 360 pounds ? In 540 1b.? In 800 lb.? In 1000 lb. ? 14. What is the cost of 3700 pounds of com meal, when it can be bought at $1.50 a bushel? 15. A grocer bought 40 bushels of potatoes at 75 cents a bushel, and sold them at 22 cents a peck. How much did he gain on the transaction ? 16. When apples sell at 15 ct. a peck, how much are they a bushel ? 17. How many bushels in 12 pk. ? In 32 qt. ? In 126 qt. ? 12 DENOMINATE NUMBERS. 143 riiE. 2 pk. 5 qt. in n 138 qt. ? at 50 cents a cents a quart. eigliing 3700 ents a bushel. aining 2% bu., r the 13 bbl. ? el, 5 loads of jEch weiglijng L at 5 cents a 4^ ct. a pint ? eighing 4590. ) pounds ? In neal, when it at 75 cents a much did he ch are they a In 136 qt. ? UNITS WHICH VARY IN SIZE. 210. 1. circular measure is the arcs of circles. Table of 60 seconds (") make 1 60 minutes ** 1 80 degrees " 1 12 signs, or 360° " 1 Observe the following names of parts 180 degrees, or A of a Cir., are 90 degrees, or | of a Cir., are 60 degrees, or J of a Cir., are 30 degrees, or -^^ of a Cir., are used in measuring angles or Units. minute degree o sign circumference . Cir. of a circumference : called a Semi-circumference. called a Quadrant. called a Sextant. called a Sign. 2. A certain class of articles are counted in dozens or scores, in buying and selling them. Table of Units. 13 units, or things, make 1 dozen. 13 dozen " 1 gross. 13 gross, or 144 dozen " 1 great gross. 30 things " 1 score. 8. The paper trade use the following : Table of Units. 34 sheets make 1 quire . . qr. 20 quires " 1 ream . . iin. 3 reams " 1 bundle . . bun. 5 bundles " 1 bale . . . B. 1. How many degrees in one quadrant? In 4 quadrants? In 7 ? In 5 sextants ? In G signs ? 2. Express 3 degrees in minutes ; 8 degrees ; 3 signs. 3. How many sextants in 1 circumference ? In 3 Cir. ? In 13 Cir. ? In 300°? In 730'? If i ' 144 D E N M I ]S A T E N U M BE KS, f UNITS OP TIME. Pi '}y\ 't'Jrj'tiui 211. Units of I'ime are used in measuring a portion of duration. Table of Units. 60 seconds (sec.) make 1 minute. GO mmutes 24 hours 7 days 365 days, c • 12 caleudar mo. 366 days 1 hour 1 day . 1 week m. hr. da. wk. \ " 1 common year. yr. 1 leap year . . yr. Divisions of a Year. 525 O Winter Spring. ■ \ 1 January, 2 y^^^/uary, March, 4 April, 5 May, Jan. Feb. Mar. Apr. May June ,[aly Aug. 31 days. 28, in leap year 29 da. 31 days. 30 " 31 " G June, June 30 Summer. ■{ 7 July, ,laly 31 8 August, Aug. 31 9 September, Sept. Autumn. \ 10 October, Oct. 11 November, Nov. Winter. 12 December, Dec. ^_ 12 calendar months = 365 days, or 1 year. NoTT5.— The leap years are those that can be divided by 4 without a remainder. 1. How many seconds in 4 m. V In 2 hr. ? In 5 hr.? 2. How many minutes in 1 da. ? In 3 da. ? In G da. 7 hr. ? 8. Express in liours 2 weeks ; 5 da. 10 hr. ; 3 wk. 4 da. 3 hr. 4. How many days in 24 hr. 1 In 06 hr. ? In 7220 m. ? 30 31 30 31 8. 0. 10. 11. 12. 13. a portion of ANSWERS. m. ir. da. wk. yr. yr. p year 29 da. Y 1 year. iy 4 withont a a da. 7 hr. ? :. 4 da. 3 hr. !30 m. ? The answers to oral exerclBCS and the more simple examples have been omitted. The answers for examples taken from the Arithmetical Tables commenca on page 150. 4. 5. (J. 8. 9. 10. 11. 12. IS. Art. 5». '. 20?3. ■. 229G. 22374. 99241. 171703. 20252^. 21400. 2:J085-- 2'?02O. 181359. 103465. 352^59. Art. 57. 1. 3. 4- n. a. 7. S. iK 10. 11. 12. 13. 6975 lb. 9915 lb. 792 A. 564 bu. $735. 546. 1411 yd. $4575. $109. 425 lb. ; 234 lb. $1776; $1378 ; $3251. 249 bu. ; 483 bu. 438 lb. $1123; $1933; $4263. Art. 58. 1. 1397.48. S. $1140.47. 3. $126a41. Art. 59. 1. $181.36. 2. $1104.37. 3. $1442.49. 4. $749.40. 1. >) A. 5. 6. 7. 8. 9. 10. 11. 12. 13. Art. 60. $1531.54. $-,>846.17. $3457.03. $1347.38. $3381.60. $1701.77. $1686.37. $2335.16, $1836.03. $1875.30. $536.23. $1984.81. $2168.44. Art. 61. 1. .J 3. 4. 5.. G. 7. 8. $5.98. $17.03. $17.10. $345.47. $23.60. $38.39. $58.20. $59.90. 9. $13.48. 10. $48.80. 11. $14.65. 12. $71.75. 13. $1159.19. 1. o o o, 4. Art. 63. $771.85. $1901.78. $4645 pu. $189.60. $2107.71. 6'. $4664.64. 7. $1908.02. 8. $29.80. 9. 11609 tr. 10. $36.06. Art. 83, 1. 276. 2. 347. 3. 367. 4. 176. 5. 178. 6'. 168. 7. 169. cV. 275. 9. 188. 10. 558. //. 173. ./;.'. 2252. ./,;. 188. 14. 3528. ir>. 349. 10. 169. 17. 18. 19. 20. 21. ■'2 23. 24. 25. 20. 27. 28. 29. 30. 31. 32. 33. 34. 4256. 1774. 3587. 2578. 2444. 3555. 3777. 2889. 1788. 3645. 4378. 827. 1487. 2468. 1366. 1579. 1579. 7377. Art. 89, 1. 2. 3. 4. 5. 0. 'V / . 8. 9. 10. 11. 12. IS. $45. $157; $856; $353. $56(J. 187 lb. $48. 436 A. 54. 71 lb. 188 bu. 29 tous. 91 yd. $297. 124 tons. 10 ■I- 1 146 AJVSWJi^JiS. jl! iff IK-;: Alt. 90. !|3(>.25. 154.21. $52.35. .S29.28. $227.42. }ji248.02. $2:38.87. $140.52. $740.88. $2.^25.08. $1.81. $48.57. S7.(I5. $24.46. $.55- $4.58. .9 4- 5. 0. / . cV. 1(K 11. 12. in. u. 15. 10. 17. 1. 8. 4- 5- 6. /• 8. 9. 10. 11. 12. Art. 91. $327.84. $11.81. $105.58. $80.74. $218.58. $382.00. Oft $254.56. $14.03. $801.88. $18.49. $21.31. Art. 107. 2. 1155. 8. 4844. 4. 5184. 6. 1988. ;,, il *.; !1 6. 7. 8. 9. 10. 11. 12. IS. 7077. 47472. 9224. 42545. 42581. 27855. 241 OSO. 354042. 128340. 15. 16. 17. IS. 19. 20. 21. 24. 25. 26. 27. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 4U 42. 4^?. 44. 45. 46. 47. 395340. 099993. 585228. 752480. 250812. 008882. 418020. 1527921. 2540585. 8505149. 4074450. 1018014. 4588763. 83000. 49800. 74700. 0821000. 4515000. 2709000. 7224000. 353585. 242424. • 545454. 454572. 680003. 899990. 888880. 308080. 249270. 288881. 799992. 100005. 855552. 300008. 111110. 485442. 350070. 101418. 727272. 558455. 192045. 187011. 545480. 351400. 804806. 29^240. 581005. Art. 113. 1. 25228; 2. 05442. 3. 55705. 4. 10952. 5. 54855. 6*. 32070. 7. 78008. 8. 25110. 9. 581295. 10. 789958. 11. 134714. 12. 444900. Art. 120. 1. $5019. 2. 25000800'. 3. 1728 1b. 4. 50050 lb. 5. 810000. 6. $13. 7. $535. 8. 95900. 9. $18525. 10. $056. 11. $172. 12. 6240 bu. 13. 287985 yd. Art. 122. 2. $24.85. 3. $84.88. //. $459.48. 5. $948.18. 6. $239.90. 7. $258.35. .S'. $192.98. 9. $128.25. 10. $81,755. 11. $484.42. 12. $55.01. 18. $481.55. Art. 126. 2. 5442 ^r. .;. $1455. //. 8232 oz. 5. 172001b. 6. 74 ct. 7. $28.75. cS". 1704 1b. 9. 21528 gr. 10. $20.56. 11. 18278 oz. 12. 192015 oz. 13. $0?2.00. 14. $04.16. 15. 792 pwt. 16. 1000 1b. 35000 oz. Art. 183. 1. 900 bbl. 230 bbl. 312 bbl. 21 T. 501 T. 900 T. 431 da. 700 cd. 310 cd. 900 cd. 800 hr. 000 suits. 800 suits. 40 Hheep. 70 sheep. 902 Hheep. 002 sheep. 80 wk. 00 wk. 20 wk. 30 wk. 70 wk. 11. 000 hr. 12. 2841 bags. 13. 8210. 1280. 8123. ///, 021 calves. 700 calves. 902 calves. 15. 910; 210; 801 ; 001. 4. 5. 6. 8. 9. 10. 17200 lb. 74 ct. $23.75. 1704 lb. 21528 gr. $20.56. 13278 oz. li)2015 oz. *6?2.00. $04.16. 792 pwt. 1000 lb. 35G00 oz. 900 bbl. 230 bbl. 312 bbl. 21 T. 501 T. 900 T. . 431 da. . 700 cd. 310 cd. 900 cd. . 800 hr. . 600 suits. 800 suits. , 40 slicop. 70 sheep. 902 sheep. 602 sheep. 30 wli. 60 wk. 20 wk. 30 wk. 70 wk. 600 hr. 2341 bags. 3210. 1230. 3123. 621 rnlves. 700 calves. !»02 calves. 010; 210; 801 ; 601. ANSWERS. 147 16. 620 bbl. 76'. 749. 7. 345 acres. 0^ 472. 710 bbl. VJ. 837. ,V. 4h3 bu. m. 9jr. 920 bbl. .--fy. 579. 'J. $75 73. 11. Ii;i8. 17. 71210. ,.^7. 758. /O. 251 lb. 7;.'. 150. 142420. i-A 496. 77. 32 mi. L.. 18-1. . ,?,;. 695. U. $98. 74. 307-221. Art. 130. .?//. 738. IJ. §1554. 15. 343. ,^. 786. ,.^1. 597. /4. f287(i4. 76. 245. S. 347. ,?o-. 836. 15. $9513. 7;. 2G7. 4. 583. 27. 948. $6342. IS. 383-156. .5. 837. ,Av. 379. $3171. I'J. idi-'OiH. a. 485. 2',). 957. W. Ib2-4l9. 7. 387. ,;^>. 657. Art. 143. 21. ^b5-157. S. 354. .?/. 598. /. 30. 22. 520-1^0. 0. 734. SJ. 63!). :.'. 90. 2.1 474-44. 10. 856. JJ. 957. 3. 70. 24. 1878-31. 11. 648. 4. 40. 25. 319. 1:J. 607. Art. 138. 5. 90. 20. 508-170. IJ. 859. .9. 574. G. 80. 27. 65r.-279. U. 87 cd. ,7. 397. 7. 900. .,'8. «)80-045. 15. 59 bbl. //. 739. cV. 300. 29. 789-499. 83 bbl. r>. 436. iK 500. 30. 405. 375 bbl. 6'. 7358. 76*. 900. 31. 4072-91. 10. 39 wk. ;. 5098. 77. 500. 32. O.V2-lv4. 17. 179 acres. ffff- \h M ; 7 (I . 10 87 . II' It • .36 ' 215 Art. 168. 15. 35|, 16. 3??. /7. 58 J. i5'. 48^. 19. 53 it. Ji;. 48/ff. 21 641 ^ Art. 169. 15. 1|; li ; 15. 14 •■8 ' ^S- //J 7 . O t . -f 8 ^O- S » '"] J > -1-4 ^^- J ft iq 7.17.17 Art. 170. 41. %^. 42. 14 1 ? > 15 > 4^6. 47. 48. 4D. $4^. $5». W^i oz. aVgal. Art. 173. 11. 1^ $6600; $6720 ; $3090 ; $4312 ; $4381. $30; 'ir'*8 ; $27. 9022;! 188. I Art. 174, 15. I 16. A- 18. $12 J; 19. $104 ; $20| ; $18 iV; $•36,^,. H . $13i^T $21^^ Art. 175. 8. 8 books ; 12 books ; 4 books ; 16 books ; 40 books ; 80 books. 9. 24 pounds ; 72 pounds. 10. 6 pounds ; 15 pounds 24 pounds 12 pounds 27 pounds 60 pounds. Art. 176. 11. 2 times ; 4 times. 12. 3. 13. 5. 15. 16. 17. 19. 4. 6. 5. 7. 4 yd.; 7 yd.; 5 yd.; 9 yd. 4 pk. ; 5pk. ; 3pk.; lOJ pk. ; 18pk. Art. 177. 20. 26. 27. U ¥ » 18 28. V s » 1 Art. 191, 1. $1.00. o. 4. 5. 6. rv /. S. 9. 10. 11. 12. 13. 14. 15. 10. 17. 18. 19. 20. 21. 22. 23. $3.15. ;t^8.75. $10.30. $8.43. $105.56. $6(1. 24. $141.60. $188.03. $8589.75. $417.30. $431.29. $ir)583.75. $807.94. $449.87. $00.12. !t;73.08. $148.10. $3o;}ii,.. $62.89. $114.80. Art. 194. 7. $.108; $.579 ; $1,851 ; $1,787; $1.93; $19.80; $5.79; $77.30. 8. $4,860^; $9,788; $24.33|; $48.665 ; $480.65 ; $97.33. Art. 195. 7. 14400 gr.; 33000 gr. 8. B900; 3 1985. 9. 20; 100; 13. A lis WEES. 1-n rt. 19J. $1.00. $3. 15. J|^a75. $10.20. 12. r?. $8.'v. $;}.43. $105.56. $141.60. |18«.08. *;}r)8o. 75. $417.20. |42I.2!>. $tn582.75. $<3()7.94. $449.87. $00.12. !^73.03. 1148.10. $3();{;),, $62.89. $114.80. It. 194. $.io;}; $.579 ; $1,351 ; $1.7;]7; $1.93; 1^19.80; S5.79; ^77.20. HM% ; ^9.733; ^21.331; ;48.665 ; i486.65 : 97.33. t. 195. t400 gr ; mo gr. > 960 ; ' 1936. ►;100;13. 6. 8. 10. 6 ; 30 ; 76. 11. 42 oz. ; 27 oz. ; 52 oz. Art. 196. 4. 2i lb. ; 71b. ; 121b. 89 oz. 437 1b.; 1384 lb. $1.35; $3.55. $48. 9. $40.60: $60.55 ; $90.30. 10. $19.60. Art. 198. 0. 276 iu. 10. 91 in. 11. 141 in. 12. 376 iu. 13. 54 in. ; 126 in. ; 198 in. 14. 198 in. ; 306 in. ; 990 in. ; 1980 in. 16. 3 yd. 1 ft. 9 in. 16. 2 It. 6 in. ; 4 ft. 2 in. ; 17. 6 ft. 6 in. ; 8 ft. 4 in. ; 10 ft. 10 in. 4 yd. 6 yd. 9 yd. 3 ft. 3 ft. 2 ft. 18. 1 13 vd. 1 ft. ; 20 yd. 2 ft. 19. yd. 2 ft 8iu. 2 yd. 1 11 in. 4 yd. 2 7 in. 7 yd. 1 9 in. 2} in. ; 4^ in. ; 15f in. ft. ft. ft. Art. 200. S. 241 pq. in. ; 1123 sq. in. 6". 32 P. ; 160 P. 7. 408 P.; 1276'P. o. 1 A. i 4i a.. ; 5 A. 9. 25 A.; 5}H A. Art. 202. 7. 96 cu. ft. 8. 48 cu. ft.; $3.20 Art. 206. 4. 2 Cd. 7 Cd. ft.; 5 Cd. 3 Cd. ft. 8 cu. ft. 5. $9.60, 6. I Cd. ; iCd.; |Cd. 7. 384 cu. ft. ; 3Cd. Art. 207. /. 47 pt. ; 101 pt. 2. $1.52. 5. 23i gal. 7 cl. 7 pt. 4. irv'420; 111720. f 3 368. n[ 2520. Fl 4980. $1.98. $1.61. $3.48. $6.27. $2.99. $6.56. $2.38 $4.42 $4.90. 5. G. 7. .9. 9. 10. 11. 13. 13. u. 15. 16. 17. 18 ^%- lUtr 19. 20. 21. 23. Tl 4 irnl. 3600').7il. $75.60; $158.76. $40.33. $37.90. $39.30. 159 pt. Art. 209. /. 184 qt. ; 234 pt. 2. 3 bu. ; 4i bu. ; 4 bu. 3. $15.50; $10.85 ; $20.15. 4. $10.08. 5. $83.35. 6. $50. 7. $39 60. 8. $546.25. 9. $4.45. 10. $5.01; 11. 3|4 bu. ; 7f A bu. 12. 1350 bu. 13. 7^ l)u. IU bu. l()j Ini, 20s bu. 14. 15. 16. ^99.1 Of. IS5.20. 150 Axs m: ix' s. ANSWERS TO AKITHMETICAL TABLES. ii '■'•'•■* Observe, the answers fo examples taken from the Aritliniotical Tnble*. are in every case arruu2:ecl in the order the pupil ia directed to take i he examples from the Ta!)les. The letters over the sets of answers iudicalc tlie columns of the Table used, and the black figures in the margin the number of the answer. Art. 47. Columns of three fignrea. A. 10 B. 18 c. 12 D 16 E. 10 G. 10 H. 1 21 17 2 11 16 19 19 17 10 15 17 3 12 15 20 15 18 12 16 21 4 13 13 20 20 14 13 20 10 5 13 16 14 19 13 20 17 17 6 12 17 14 16 11 24 20 18 7 17 18 15 17 14 20 18 21 8 22 14 20 17 14 20 21 18 «> 4 Art. 48. Columns offoui 'figures. A. 14 B. c. D. 23 E. F. 21 G. 24 n. 1 23 21 24 23 2 17 18 26 24 23 20 18 25 « 15 21 24 23 23 19 25 23 4 17 21 23 20 10 22 25 23 5 18 19 21 21 17 28 23 26 <; 20 24 19 25 19 27 27 23 7 26 22 23 23 16 29 26 25 Art. 48. Columns of five figures. ] 2 <> 4 n A. B. c. D. E. F. o. 20 25 28 28 3'* 'J5 27 '^0 24 30 3'. 28 27 27 10 29 27 20 25 28 30 22 24 30 28 20 30 31 20 20 2 1 30 25 31 30 29 28 27 31 21 30 35 H. 31 27 30 32 31 27 .1 \ S W ERS. 151 'idles. ■tl to t.'iku till" ^woi'f; iiidicali' Iho luaigia tlit Art. 48, Columns <:f six f.gures. A. 23 «. c. D. E. F. G. 3(5 n. 1 31 32 36 35 32 33 2 24 32 33 38 30 30 32 34 {i 24 32 34 31 29 30 3(5 39 4 30 31 35 37 28 33 38 37 •5 35 30 34 3(5 27 40 38 35 II. 10 17 15 17 10 21 20 U 17 17 20 18 18 21 21 18 Art. 48. Ciili.imns of seven figures. A. B. 39 c. D. 40 E. F. G, 41 II. 1 27 35 37 41 40 2 29 35 40 42 34 44 38 43 :$ 32 39 39 40 37 39 43 44 4 39 35 43 43 30 42 40 41 Art. 48. Columns of eight figures. a. H. 24 23 18 25 25 23 }5 23 J3 26 7 23 6 25 II. 31 27 30 32 31 27 A. n. ('. D. E. F. G. 11. 1 32 42 42 44 1 41 49 47 49 2 37 42 45 49 42 47 45 48 3 41 43 47 46 39 48 51 48 Art. r>5. Exercise loitlt two numbers of two figures. AB. BC. 95 CD. DE. 102 EF. 128 FO. GII. 1 118 159 92 1)57 2 73 42 127 83 139 97 85 :i 87 78 92 134 15(5 169 , 101 4 109 101 121 119 102 137 182 r> 78 88 95 156 73 143 141 : '^1 152 a:^s webs. Art. 55-2. Exercise idth three numbers of two figures. AB. 138 BC. CD. DE. EF. FG. GH. 1 100 216 177 187 182 143 2 140 115 162 142 236 176 183 3 129 100 178 194 161 227 188 4 145 161 130 215 170 222 239 5 143 145 160 204 158 193 150 • 6 141 121 130 219 207 184 161 7 149 101 127 192 236 177 190 8 110 109 111 224 160 220 219 Art. 55-2. Exercise udth four numbers of two figures. AB. 205 BC. CD. DE. 236 EF. FG. Gn. 1 173 251 284 261 241 2 182 143 248 202 241 234 267 3 165 166 187 290 229 312 245 4 210 218 204 263 255 •272 248 5 173 149 216 279 212 242 245 O 185 161 136 288 304 263 247 7 175 166 185 272 245 270 228 Art. 55 ~2. Exercise with five numbers c f two fig ures. AB. BC. CD. DE. EF. FG. GH. 1 247 201 337 296 289 319 325 2 218 203 257 298 309 319 324 3 230 223 261 338 314 362 254 4 240 222 251 336 309 321 343 6 227 189 222 348 309 320 331 6 211 226 194 368 313 365 285 Art. 55-2. Exercise with six nurr^ers of two figures. AB. BC. CD. 346 DE. EF. FG. GII. 1 283 261 392 357 404 882 2 283 260 331 346 394 369 333 3 260 227 308 413 368 411 349 4 294 202 257 407 403 S99 429 5 253 254 280 428 318 413 369 ANS WE lis. 153 figures. GH. 143 183 188 339 150 101 190 ^^9 figures. GH. 3li" 267 245 248 245 247 238 ligures, GII. 325 324 354 343 331 ^85_ gurcs. GII. 882~ 333 349 429 309 Art. 55-2. Exercise mth semn nwrnbers of two figures. AB. 348 BC. 318 CD. 430 DE. EF. FG. 454 GIT. 1 440 442 391 2 313 3<;4 378 421 448 418 428 3 314 3(J7 314 483 465 489 435 4 330 327 315 487 415 493 407 Art. 55-2. Exercise with eight numbers of two figures. 1 2 3 AB. 378 307 340 BC. 333 304 333 CD. 407 384 373 DE. EF. 490 545 374 FG. 515 490 563 503 490 583 GH, 483 514 473 Art. 50-3. Exercise icith three number^ f three figures. ABC. BCD. CDE. DEF. EFG. FGU. 1 1400 1016 3177 1787 1883 1843 2 1415 1103 1643 1436 3376 1783 3 1306 1078 1794 1901 1037 3388 4 1401 1630 1315 3170 1733 2239 5 144-> 1409 1704 3058 1593 1950 O 1331 1830 1319 3307 2084 1861 7 1501 1037 1393 1936 2377 1790 8 1109 1111 1124 3300 1020 2219 Art. 50-3. E.r( rcise icith fmx r n umbers of three figures. ABC. BCD. CDE. DEF, EFe. FGH, 1 2073 1751 3536 2384 2801 2641 2 1843 1448 3503 2041 2434 2307 3 1000 1087 1890 2939 2312 3145 4 2118 2304 3003 2055 2572 2748 5 1749 1516 3179 2812 3143 2445 i\ 1861 1636 1388 20O4 3003 3647 7 17(56 10^5 1S73 2745 3470 3738 15-4 AXS WE Its. it ('*.« 'i/1 Art. 50-3. Exercise with five numbers of three figures. ABC. 3501 BCD. 3037 CDE. DEF. 2989 EFG. Fon. 1 3390 2919 3335 15 3203 3057 3598 30(«0 3119 3334 :s 3333 3301 3038 3414 3i(;3 3054 4 3433 3^51 3538 340'.) 3131 3343 5 3389 1933 2348 3509 3130 3331 (>-3. Exercise with four numbers of four figures. ABCD. 20751 IK'DE. 17530 CDEF. DEFd. 23801 • EFGU. 1 25384 28641 2 18448 14502 25041 20434 24367 3 10;587 10890 18929 29312 23145 4 21204 22003 30055 20572 25748 5 17510 15179 21812 28142 21445 « 18036 16388 13904 29062 30047 7 17085 16872 13>745 27470 24728 Art. 5(>-3. Exercise Kith five numbers of four figures. ABCD, BCDE. 20390 CDEF. 33989 DEFG. 29919 EFGH. 1 25037 29225 ii 22057 20598 20009 30119 31224 ii 23201 22038 20414 34102 31054 4 24251 22538 25409 34121 31243 5 22922 19248 22509 35120 31231 c; 21294 22908 19713 37155 31585 Art. 5(»-3. Exercise irlth six numbers of four figures. ABCD. BCDE. 1 * 28040 20492 2 28031 20340 ii 20;]08 23113 : 4 29057 2f500T 5 25580 25828 CDEF. DEFG. 3901)4 EFGH. 34957 30082 33494 34<,!()9 39733 3ii;;8 41711 37149 2('100 41099 41020 28318 43213 32169 166 ANS WERS, Art. 5G-3. Exercise icith seven numbers of four Jig fires. ABCD. BCDE. CDEP. DEFQ. EFGH. 1 2 3 4 35220 31678 31714 32315 32-^0 26821 27182 33187 42442 38248 31866 31915 41454 42518 48689 49192 44591 45228 46935 41967 An 1 lif Art. ii ►6-3. Exercise with eight numbers of four 'figures. ABCD. BCDE. CDEF. DEFO. BFOH. 1 2 38267 37084 a4372 32715 30890 33762 47196 38945 37674 52003 49496 56782 50086 55014 47873 Art. 87. Examples taken as directed in 1 cmd 2. AB. BC. CD. DB. EF. FQ. GB. 1 12 21 19 86 m 78 21 2 33 32 13 67 21 83 73 3 47 68 22 16 38 11 92 4 25 45 51 1 92 21 14 5 6 32 77 36 63 27 27 6 29 3 65 48 17 85 48 7 35 53 27 27 31 1 86 8 ' 24 36 41 6 43 29 9 28 25 52 11 88 15 48 Art. 87. Examples taken as directed in 3 and 4. AB-BC. BC-CD. CD-DB. DB-BF. BF-FG. FG-GH. 1 7 31 5 46 37 27 2 16 33 62 72 73 72 3 15 52 18 16 31 84 4 6 38 24 88 18 . 19 5 14 58 26 55 63 26 6 24 51 87 28 17 28 7 8 17 26 37 35 41 8 26 43 28 21 5 46 9 14 34 63 28 19 8 10 89 7 22 71 84 65 ? A XSWEJiS, 157 Art* 88. Examples with three numJbera taken as directed in 1. ABC. BCD, CDE. DET. EPO. PGH. 1 121 219 186 868 322 779 2 332 313 i;J3 07'> 217 827 3 4rt8 678 216 162 389 108 4 245 449 501 H 921 214 5 m 32:3 704 308 027 273 6 297 35 652 48;? 165 348 1 35:j 527 273 269 301 14 8 230 359 406 57 429 291 9 275 252 511 112 885 152 Art. 88. Examples with three figures taken as directed in o ABC-BOD. BCD-CDE. CDE-DEP. DEP-BPG. EPO-PGH. 1 69 305 54 463 373 2 lor 338 628 727 728 8 148 518 184 169 316 4 62 376 288 382 181 5 142 674 255 M7 526 6 249 513 872 283 172 •y 83 174 2(53 365 341 8 267 428 279 205 54 9 13t 337 628 281 192 10 393 78 229 716 845 Art. 88. Examples with four figures taken as directed in ABCD. BCDE. CDEP. DEPG. EFGH. - 1219 2188 1868 8078 3221 A 8313 3133 1321 6783 2173 A 4678 6784 2102 1011 3892 % 2449 4499 5008 79 9214 K 677 32;36 7037 3627 6278 n 2965 348 6517 4885 1652 Hp 8527 5273 2731 2699 3014 ^ 2359 8594 4057 571 4291 • 2748 2511 5112 1115 8848 158 ANSWFES. Art. 88. Examples trith four figures taken as diverted in !?. 1'^ ABCD-BCDB. BCDE-CDEF. CDEP-DEFG. DEPO-EFGH. 1 ()95 3054 537- 4627 a l(Mi2 3372 6273 7272 3 1482 51&1 1S;J1 KWl 4 (ii4 37(32 2;JH2 : 5 1426 5745 2517 r>i74 6 W87 5128 8717 2:vJ8 7 826 1737 2635 .•Hi.)!) 8 2572 427!) 2795 2u54 9 1.J37 3371 6281 281)8 10 3U22 771 2284 7155 Art. ll.'». Multiplicand three figures, multiplier one. ABC. BCD. CDE. ^ * DEP. EFG. FGII. GUI. HIJ. 1 lOJl 5536 2775 1548 6256 1696 3704 3195 3 21H0 3312 4()!»8 2608 7;38 3460 3712 22S0 3 825 5;J13 2384 7704 3160 292.'5 1778 10!>6 4 ;i558 2811 33(ki ]4!)6 33!)5 2.577 2985 8748 5 rtii4 2315 4473 3528 2781 2184 1470 21.54 6 2233 1755 i!H4 2316 6;}44 3752 34.38 2-178 7 2«2S :J474 («36 4620 22;32 3388 .'5094 3943 8 1392 !m 2808 4795 4295 5373 2928 .5:376 9 1036 12S8 7()14 1868 5400 37!)5 .5337 3748 10 6678 2i:i5 1116 6352 5688 3880 4295 .5.'{46 11 2415 7160 (}678 1644 4374 3472 W80 5154 Art . 1 i .*5. MultipUeand five figures, mvltijilier one. ABCDB. BCDEP. CDEPO. DBFGH. EPGHI. 467701 PGHI.T. 1 ,50775 4i;)r)48 833256 51692 423195 s 262098 110508 136738 4181(K) 147712 5.5-12S0 3 110384 607701 2!»81«)0 866<»25 442778 6r.i;'.i6 ? 5;S43«)6 lH749t» 262395 22-1677 iM2985 773748 B .592173 417528 191781 3M184 1S.'>17() 164ir)4 9 63! 114 78316 766;)44 231752 714138 28M78 # 526336 289«i20 713232 647388 1190!>4 ;3»T!t44 9 554808 172795 2312ft5 617.373 2.57!t28 418:376 466614 7;i8«>8 677400 2133795 608:537 ;3():5748 10 297116 312:352 167(188 63.5880 471295 4:37:ilfi 11 342678 268644 8.59374 219472 ;389480 521154 ■ 1 2 a 4 ii C 1 c fl. 1( IJ 1 1 AXSWEES. 159 'ted in !?. Art. 114. Multiplicand four figures, multipUeT two. PO-EFGH. 4r,27 -i-i'i-i, 1;W1 5474 .•«),)!> 7155 /• one. ■ HIJ. 3195 aaso 10f>6 » 8748 2154 8-178 3043 5;i7fi 3748 5.'J46 5154 1 ABCD. BCBE. CDEF. DEPG. EP6H. PGHI. OHTJ. 1 115056 574775 a33288 17829<5 537832 236964 394315 2 257712 353508 43(H)08 2()7S08 92300 374112 445680 3 102083 5()2104 2802^1 818720 373175 315'plicand Hix figures, mvUipUcr four. ABCDEF. BCDEFO. CDEPQH. DBFGHI. EFGHIJ. 1 1157047688 57962;55496 341822{W!^2 17!«)fV316()4 542a373115 2 2601853l)(;8 35-181 30-J08 4324351324 5(W5815520 2897543175 8281094()38 3777576656 4 37952.3721(5 aOHl 503595 341tH)67507 2017412795 3576267948 5 8107588'.«)8 2(W75-^9M1 5074549074 3681039770 3548075534 6 25;i2;il3996 1810<«)3<)61 2;3795 17992 2809423:318 6741964218 T 3082;J73O115 6.506406246 11 2875115404 7825652 IW 7(I(J0293992 2166208380 4618344474 07?.^. Art. 1159. .Diridend three figures, divisor one. FGHM. 423195 5.54280 6:.(;08 773748 2HM78 387!)44 418.376 30.3748 43731fJ 521154 2 8 4 5 6 7 8 9 10 11 la ABC. BCD. ! 24-2 189-2 1 134 5^5 47-1 92-8 ! 149-1 80-a 1 46-7 379 ' lo: A 8f}-ft 95-2 143-1 56-4 322-2 108 60-5 84-3 149-1 147-1 149 239 86-7 I 73-2 ' 117-6 ! 116-3 31.5-2 ; 105-4 , 76-8 I 268-1 i 51-4 315-2 111-6 319-1 84-2 M-\ 118-<) 23(5-1 1.32 1.39-5 66-3 91-1 59-1 92-7 117-2 106 289-1 3<>-2 123 120-4 98 488 64-5 82 118-2 14.5-4 107-1 88-^1 44 9(J-2 108-1 103 109-5 112-1 56 94-5 82-5 98-1 19.3-3 81-1 96-1 99-1 4.5-5 1.36-1 243-3 171-4 8(1-4 218-1 13(Hi 85-3 165-2 94-1 107-5 94-2 212-1 84-2 74-6 ■I il 160 AyawEES. Art. 139. Dividend five f'gvres, divisor one. ▲BCDE. BCDfiF. CDEFO. DEFQH. EFGHI. FGUI.T. 2 9739 ia^40-3 5315 26118-2 13928-1 4461-4 3 6711-7 I2;ji9-i 13917-2 15979 6627 43718-1 4 56T3-2 10459-a 6248-6 16857-1 24765 61;ifr-6 5 10«89-2 12064-1 41289-1 2866-2 11693-3 9960-3 6 7516-3 10833-1 6480-6 13877-2 4081-1 8832-1 7 17649 14736-1 15789-4 11846-2 8207-2 5622-5 8 12248-3 19132 9245-4 6608-1 19299-1 7218-6 9 4409-2 16139-5 17098 9325-2 6545-5 lir)94-2 10 21619-2 5;i99-6 42988 8538-2 19536-4 19212-1 11 3051-4 10662-4 7731-3 7987-1 9743-3 !t!)73-l 12 19649 11184-1 10526-4 6769-2 14771-4 4824-5 Art. 144. Dividend four fgures, divisor two. ABCD. BCOB. CDEF. DEFO. BFOH. 89-79 F€IHI. 99-5 Quur. 2 22-77 182-14 177-4 99-14 8;3-48 3 114-11 47-29 83-69 273-32 104-50 126-49 80-77 4 41-7 8a-7 63-SiO 77-4;i 100-29 99-88 79-35 5 207-30 78-1 iii-as 61-17 199-25 83-as 166-65 6 45-68 303-« 102-18 105-31 34 88-65 78-23 T 91-16 35-42 296-1 182-6 115-26 78-43 8»-26 8 91-19 122-5 101-33 104-12 112-17 99-61 84-12 9 54-26 248-11 71-83 131-8 80-7 96-69 40-M to 95-25 58-45 220-17 64-88 361-21 102-34 126-45 11 32-26 126-31 47-79 84-5 57-21 106-71 199-7 12 128-8 142-1 249-11 53-21 76-13 61-34 148-18 Art. 144. Dimdend^ix figures, divisor three. ABCDEF. BCDBFO. COEFGH. DBFGQI. EFQHIjr, 2 369^310 8397-72 603-177 837-137 2270-333 3 «{85-ij03 442-517 1425-267 1954-2;)0 1684-647 848-621 4 296-106 420-849 9()7-3»4 1700-68 5 1110-117 650-279 1924-400 874-138 605-93 6 1462-98 1309-115 732-592 860-169 478-23 7 636-321 904^« &5H8-154 730-95 1486-117 8 1812-320 777-5;38 191f}-73 458-826 14-93 478-23 1486-117 14W-198 405-714 1295-418 459-67 974-306