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Autntnnt Matter, Gtadttotu Ave. School, Toronto PRICE .^' CENTS. THE EDUCATIONAL PUBLISHING Cr TOKOMTO, 1899, Entered accordiiw u, Act of Parliamanr ^ /-._ j • i PREFACE. The complaints tlwit busincbs men are makinj,' of the lark of accuracy and ihorouylmcss in the risini,' j-cncii- tion, would indicate a lack oi' system in prcb. iting ilu; subject of arithmetic, or insufficient drill to llniily -round tiie principics presented. \Vc have perhaps been taking up too many subjects, taking them up at the same time, and in the same lesson, and the result is unsalisfactoiy. We have been taking up subjects that rccjuire faculties which are nr)t developed and do not naturally maliue at an early perioci of the child's life. The old rule, One thing at a time, and that done zoll, is being discarded, and we are of the opinion that this is being done at the sacriuce of '.he true development of the child. In the two little " School Helps " which we now place befv^re the public, we have endeavored to supply a set of questions so graded that, under the supervision of the teacher, the pupil himself will take step after step with little " telling,"— so logical as to be natural-so difficult as to call for effort -so fall as to be thorough. The pupil will thus be led to have a con'^nlence in him- »-lf, and be so thorough that he will not need to siop and think to tell how much 6 times 9 is. The province of the teacher has not been invaded by inserting pages to explain how to aHd or subtract ; but the questions suggest the successive steps in the presenting of the s: )ject, and-the books can be used in the teaching of it In the few pages at our disposal we have included over 20,000 c iestions, covering the whole field of public school arithmetic. To secure this great number of questions we have resorted to an t/pcdient whirh wc believe Ui be oriifinal, and which enables us to include three questions in the spate usually occupied by one, by inscrtinK, in brackets, the numbers for the additional questions. These may, or nuiy not, Ije used at the dis- cretion of the teacher ; but even in these we have endeavored to have the questions progressive. The example : " / />oujr/ii a sheep forS (4, 7) dollars, and sold il to frain 2 (s, 3) dollars. How much did I get for it /'• is really three questions involving the addition of Sand 2, 4 and 5, anil 7 and 3. The work has been divided into two parts. The first includes Numcr.uion and Notation, Adchlion, Subtrac- tion, Multiplication, Division, and Weights and Measures, which includes Reduction and the Compound Rules. The second part includes Measures and Multiples, Vulgar tractions, Decimal Fractions, Percentage, Me- chanical Measurements and Type Questions. Each chapter takes up its work sufficiently thoroughly for our most advanced classes, and concludes with an exercise on theory which, we trust, will lead to the mastering of the whys and wl cfores of the rules of Arithmetic. C. (i. F. Toronto, August ioth, 1899. NUMERATION AND NOTATION. Arithmetic is the scisnce which tieats of iuiriil)crs. A Unit it a single t. Af^. A Number is a unit, or a group of units. Numeration is the art of expressing numheis in wouls — orally, or in wr'>'ng. Notation it uie art of expressing numliers hy syi '- — figures, or lettera. '1 here are iwc systems of nutation —Arabic, and Kon.ua. Arabic Notation. Arabic Notation is a method of expressing numbers by means of ten figures- 1, 2, 3, 4, 5, 6, 7, 8, 9, o. Figurat are symbols used lo represent numbers. The Digits are the figures I, 2. 3, 4, 5, 6. 7, 8, 9. is called zero, cipher or naught. It has no value of its own, but is used to give the proper position and value to the other figures. Arabic Notation is a decimal em— ten of each denom- ination making one of the higher de- tination. The Denomination of each figure is indicated by its position in the number. A Period consists of three figure's, named from the right,^ unita, tens and hundreds, respectively. Beginning at the right, the periods are named units, thousands, millions, billions, trillions, quadrillions, quintillions, sextillions, septillions, octillions, non- illions, decfllions, etc. 1,000,000,000,000.000,000,000,000,000,000. 6 MKNTAL ARITHMETIC. Exercise i. (1) Read the following numbers. (2) Wnte them in words (3) Teacher dictate ; pupils write :_ (a) In figures, (b) i„ ^.-ords. 1. 2. 3. 4. 6. 6. 7. 1. 2. 3 4. 6. a. 7. 1. 2. 3. 4. 6. 6. 7. 5, 4, 6, 9, 3, 8, 7^ ^^ ^ ^o, 2o, 3o, 4o, 8o. 6o, 50, 90, 70. 30 ' ;!' ■^'' '^' ='' '^^' -^3. 33, .1. 30. 37, 34, 39, 42, 45, 43, 46 C2 r-r r 63, 68, 66, 67, 75, 74 1: to' I' «!' o^' 5^- n, ^/; ^^' ^^' 7j, 70, 89, 86, 80, 8C • 93, 96, 94, 99, 83, 76, 69, 44, 88, 98 89 45" 37. 68^ 95, 82, 60, 35, 58, 87, 90, 14, 28, m! B. To Z' T' '"' '°°' ^°°' 9°°' 7-. 400. 08 o?'!!''^"' ^^'350,490, 780, 970. ° ' "'' '^' '°3. 107, 103, ,06, 104, no 8354, 6079, 3760, S'cg, gj(„ „^ ' NUMERATION AND NOTATION. ^ D. 1. 1284, 3563, 8745. 3928, 4793. 7436, 2857, 9688. 2. 9406, 2304, 3207, 5801, 7502, 8609, 4703, 6908. 3. 5082, 7046, 3029, 9083, 2028, 6015, 8047, 4094- 4. 3060, 5040, 8020, 9080, 7090, 6030, 4070, 2050. 5. 8001, 9002, 4008, 6009, 5007, 7005, 2006, 3004. 6. 10460, 52736, 92849. 28467, 17928, 67384. 49297- 7. 15075, 50500, 70005, 18067, 60070, 30200. E. 1. 5ooor, 60009, 70500, 90200, 80100, 106255. ^ 2. 28473, 158469, 296384, 477562, 734856, 926510 3. 209080, 706308, 507204, 703406, 802509, 830720. 4. 640830, 950270, 805060, 920005, 370001, 505707, 600006, 500050, 330303. 5. 2850720, 7093460, 9020408, 19070300, 26002380, 15020475, 84006580, 50050200, 60000500. 6. 72000070, 93002001, 48000201, 9(1000020, 48007000, 50080600. 7. 900004300, 250030502, 702300605, 18052000, 70030- 8700, 805000000, 837026384, 286025001, 1200- 20200, 175062026, 300000030, 127072000. In Arabic notation the value of a figure depends on its position in the number. Show this by giving the value of each of the figures in the following numbers : — 734,568,986. 803,560,089. 990,608,094. 397.875.243- 700,504,007. 503,086,240. Give the value of any two consecutive figures. Give the value of any three consecutive figures. Write each of the numbers in words, paying atten- tion to the spelling, hyphens, commas and periods. MENTAL ARITHMETIC. Roman Notation Roman Notation is a method of expressing numbers by means of seven letters. ' The characters in Roman Notation are :— '"«' Tt!' ^"'"' ^'5°' C = ioo; D=5oo; M = xooo. Small letters are sometimes used instead of capitals. Exercise a. A. ea«.1 « T" '^r'*!"" • cJ»*«cter placed before one of equal or leas value is added to it. (i) Read the following numbers. (2) Write them in words. (3) Express them in Arabic notation. Q * T I ^v V ' b^ "'=''''' ^c'^» ^*vii. ?• vt't ^;r^^^' ^^^- *^"^'' d'^-v. dclx. ?•}; ;^";XV.LX. md, dcx. dxxviii. XVI YVVT ^t^.t"' '""^'""^'■' »"dclxv. mcxxv. XV i YVV 't 7 ' "'''^^^^' ^^''^^"■' '"«''^- CCXXYVT t'vt't ""'^''^''^'"' "^dcxvi, mcxxviii. CC, XXXVI, LXII. mdclxvi, mdclxvi, mdclxvi. Express the following numbers in Roman notation :- 4. 6. a 7. 1- 2, 6, 7, 12. 2- i5» 25, 38, 66. 3- 23, 36, 75, 87. 4- 32, 58, 63, 85. f • I2f5, 250, 355, 375. 6. SSOf 520, 580, 635. 7. 625, 637, 756, 767. 1250, 1375, 2560, 3583. 2325, 2156, 3187, 2632. 2153, 1567, 3231, 1725. 2056, 3506, 2605, 1065. 2378, 3028, 2308, 3802. 2738, 2807, 2007, 2008. 3027, 3087, 3078, 3020. NUMERATION AND NOTATION. c. In Roman Notation a character placed before one of greater value is subtracted from it. Write these numbers in Arabic notation. 1. IV, IX, XIV. cmlx, cdlix, cxix. 2. IX, XXIX, XL. mcdx, mxlix, cxiiv. 3. XXIV, XL, XXIX. mcmxcj mcdxxvii, cmxxix. 4. XLV, XLIV, XLIX. dcxlix, cdxciv, dxcvi. 6. XCV,XLVI,XLVIII. dccxcvi, cmlxix, cxcviii. 6. CD, XCIX, CM. dxlix, cxliv, cxciv. 7. CM, XCVI, XLXI. mcmxlix, cdxxiv, xcvi. D. la Roman Notation a dasb placed over a number increases its value a thousand fold. 1. V, X, XX, IV. vi, xii, xl, xc. 2. XV, XL, LXVI, LX. xv, Ixxv, ccxlv. 3. VII, XXI, XLV, XC. cdlxxxv, cmxix, ccxlv. 4. XVII, XXXIII, XLVI. cxixccxxv, cdxxicmxlvii. 5. DCXV.CDIX, DCXCI. dccxcvdlv, cmlxixdclx 6. XXIX, XLVI, LXXV. cmxlxv, dcxcvii, xxix. 7. XCVCDXLVCMXVI. xlcdlviicmxcix, mm. E. Express the following numbers in Roman notation : 1. 14, 19, 24, 39, 44- 2. 49. 64, 89, 94, 99. 3. 204, 309, 444, 494. 4. 449, 499, 94 h 979 6. 904, 929, 947, 999. 6. 405, 946, 946, 694. 369,472,591 800, 104,610, 253047,059 790,203,875 936,049,408 453,094,949 MENTAL ARITHMETIC. Exercise 3. nou,iS."" '""' Arabic N„,a,i„„ is a decimal system „f m.mbe^"' ""= ""f'-nce „e.„.ee„ a figure and a by .he %„'.:: f3,'':,'-S;>™"»r,„a, can be expressed •10 wr . "-^H^^s^^eti by three fipii yo?cS.:"L,^T.e^'Ut",™^i- t" %-es 9, o and 7. ^ '' ^ '^"^^ 3 ; 6, 5 and 8 ; preiedC.he°fi;"u.l'r;.^,7s""'""^^' "-« ""■ be e^' 15. Where is Roman Notation usually used ? di^o^rcToci;^^ ''' ^-'" «^ ^^^ number four, on the 18 ^^'^' '": ""'^"^ ''' '^'^ ''^^^^ ^^'"e of a figure ? 18. Show the relation of each ficr,,,^ , ^"^"re.? the number 555,555^ ^g^ure to each other in ADDITION. Addition is the process of finding the sum of two or more numbers. The Addends are the numf)ers which are to be added together. They must be of the same kind. The Sum is t!.e number obtained by adding two or more numbers. It is also cal cd the Total, Amount, or Aggregate. + (plus) is the sign of addition, and when placed between two numbers it shows they thu are to be added tog^ ler. = is the sign of equality. 4 + 2 = 6, is read, "four plus two, equals six." Exercise 4. How many are : — 3 hats and i hat ? 1 pin and 3 pins ? 2 hats and 2 hats ? 3 caps and i cap } 3 plums and 2 plums } 2 pears and 3 pears ? 3 cherries and 3 cherries ? Exercise 5. 1. Jane has i (2, 3) apples and Will has i apple. How many apples have the two? 2. Tom had 2 (3, i) plums and his mother gave him 2. How many had he then ? 3. Will found I (2, 3) apples under one tree and 3 apples under another. How many apples did he find > 4. Mary has .• (3, i) cents in one hand and 2(1, 3) cents in the other. How much has she in both hands ? 6. A boy had 3 (2, 3) pens and he buys 3 (3, 2,) pens. How many has he now } 6. Rob had 3 (2, 3 ) dollars and earns 2 (3, 2) dollars. How much money has he now ? 7. A boy had 4 (3, 2) figs and gets i (3, 4) fig. How many has he now .'' 1, 2. 3. 4. 6. 6. 7. I boy and i bo)' } 1 girl and i girl.? 2 men and i man } 2 apples and i apple ? I uencil and 2 jjencils.-' 1 book and 2 books .'' 2 books and 2 books ? 12 iMKNTAL ARITHMKTIC. 1. 2. 3. 4. 5. 3. 7. How many are : — Exercise 6. 1 and I ? 2 and I ? 1 and 2 ? 2 and 2 ? 3 iind r ? 3 'Hid 2 ? 3 and 3 ? 1 and 3 ? 2 and 3 ? 4 and 1 ? 1 and 4 ? 2 and 4 ? 4 and 2 ? 4 and 3 ? 3 and 4 ? 4 and 4 ? 5 and i ? 1 and 5 ? 2 and 5 ? 5 and 2 ? 5 and 3? Exercise 7. 3 and 5 ? 5 and 4 r 4 and 5 ? 5 ■ ul 5 ? 6 and 1 ? 6 and 2 ? 6 and 3 ? 1. Jack has 2 (4, 3) niarbles and Will has 1 (i .\ niarble. How n.any have the two together ' ^ ^^ cents ^"Hnl'*'' \*^5' 5) «"»« and Marv has 2 (, ,) cents How much money have the two t'oged'er ? ^ ' ^^ the otheSl *''h^^ P'"' '" ^"" '^""^ '-^"d 2 (c', 4) ]„ mt ouier nancl. How many pens have I '' coLns"3(t1racrer H^L^^ '''^r,''^"^' -^'^^ "^'^ ««'^ 6 On. 1 . ; '""^'^ ''^"^ '^ '" the two ? rd fiWlnn'"" •'''' ^ ^5, 4) dollars in one pocket ind a (4, 6) dollars n, another. How much n.oney in both ? Exercise 8. How many are : — 1. 3 men and 3 men? 4 cords and 3 cords ? 4 roses and 4 roses ? 5 horses and 4 horses ? 3 pens and 5 pens ? 5 weeks and 6 weeks ? 6 days and 7 days ? 2. 3. 4. 6. 6. 7. 7 slates and 3 slates ? 6 pecks and 7 pecks ? gallons and 7 gallons ? o quarts and 8 quarts ? 6 dogs and 8 dogs ? 7 cats and 9 cats ? 5 yards and 9 yards ? r^'^' ADDITION. ADDITION TABIvF 1. Add at sight, or as the teacher points, 1 ' o 1 8 1 1 4 1 y 1 13 1 7 __ ^"■~ "^ — — — — — — — 2 <) •) o 2 2 2 2 <> y 2 4 G 8 1 5 9 1 3 3 3 3 3 3 3 3 3 3 3 i. •> 4 8 6 7 9 5 4 4 4 4 4 4 4 4 4 4 2 1 5 G 8 7 9 4 5 5 5 5 5 5 5 5 5 5 2 3 4 1 G 8 7 9 6 6 G 6 6 G G 6 G G G ;{ If G 4 8 y 7 1 / 2 t 8 I 9 7 s 4 8 2 8 1 8 8 G 8 7 8 8 8 3 8 9 8 5 9 3 9 4 <> 7 9 9 9 9 5 9 9 6 9 1 ^^ -rftNIAL ARITHMETIC. Exercise 9. 5- 3 + 1= 2 + ;= l^'Jl^r 5 + 5= S4 + IL '•^^^= 4 + 3= 4tllZ Itt |6+J3, Exercf«e 10. 1- Will found G h 7^ #..«« • eggs ,n another. Holy .. an'y ''^s d"i5 h"^' "."^ ^ ^6. 5) 2. Rob had 7(7 z\ ,» il^ ^^ ^ '"' ""d •' •"•'»">' had J,e then ? ^^ "•'"■''''^^ ^"^ ^O" =» (7. 5). How 3. A man had -> (7 r\ How „,any h.;d he then ? ^ ''°'''' ^""^ ^°"ght 6 (4, 6). . 4. A man sold -> f 1 '7\ u W.- How ,„a„,. Votl{t2lf> """ "^^ 7 fr- 5) "or.es "o"n,anJ,t/s^ti\|;r,l»„|"<' '^""^''^ "-3(6, 6). • • rhcre are a ^t >7\ i <^iass. How man'y i'^ fn^ ,l;2>;^,^^^"d 6 (6, 7) ^,^,3 ,-„ ^ Exercise n. ^ Supply ,.ec^.rrect number in each blank. 4. 3and.. =^ f4and....=j6 ^t J 5. 4and...- = ^ f^^"f •••=^6 Jt ^J 6. 2and....=^ |4and....=.$8 f+'-'lJ 7. 4and....=8 ?r''"f " " • =*« 6+ " ' " I * $3 and... =$7 o+....«g J T - . , , ^O '-5 ">-; H pq S o H Q "2 B I .a a o •^ I a J3 g s 3 ADDITION. "^flooooooooooooo "*«flooooooooeoe •^aooooooowoooo "Wooooooaotjoo ■OMlAlQiAiouilA " y> Hi ui tii in ui ui *^ -^ -^ •» •» -^ —^ »5 0» Ok O^ I ©1 Oi X 0> » vC Ov » T » o* n 00 00 ao 00 X >o OO QC ^ 80 00 f1 tN r>. In r^ !> ve i> r> ■'T \0 >0 N© ■o >0 T *n m tft Ui ifi ^ i6 MEwf AL ARITHMETrC. BxercUe la. How many are :— 1. I apple, and 2 apples, and . apple, and 2 apples? 2. 2 apples, and .apple, and 2 afc. and , Tpple? 3. 2 p,ns. and 2 p.ns, anc , pin, an'd Vpins, anclTpins ? ". ^ Fin!., ana 2 pms, anci i pin, and 2 pins and-. ni„c > 6 6 7 Ezerds* How many are : — !• I, and 2, and i, and 2? 2, and I, and 2, and i ? 2, and 2, and i, and 2? I, and I, and 2, and ?? 3, and i, and 3, and i ? 1, and 3, and i, and 3? 2, and 3, and 2, and 3 ? 2 S 4. 6. 6. 7. 13. 4. «ind 2, and i, and 3 ? 3, and 2, and % and 4? 3, and 4, and 3, and 4 ? 5, and 2, and 3, and 4? 5. and 4, and 3, and 2 ? 5. and 3, and 4, and 2 ? Exercise 14. 4, and 3, and 2, and 5 ? Ho^LSmoL^VsVon"; """ '-' " <3. 9) cems. l.ft ■ ' *P"^"' S (6, 9) dollai-s and had 8 CS si ,l„ii left. How much money had I at fim ? ' '^ ADDITION. 17 2 3. 4. 6. 6. 7. ExerclM 15. How many are : — 1. I, and 2, anu i, I 2, and r, and 2, and i, and j ? 2, and I, and 2, and i, and 2, and 1, and 2, and i ? 2, and 2, and i, and 2, and 2, and 1, and 2, and 2 ? 3, and I, and 3, and 1, and 3, and >, and 3, and 1 ? 2, and 3, and 2, and 3, and 2, and 3, and 2, and 3 ? 4, and 3, and 2, and 4, and 3, and 2, and 4, and j ? 5, and 3, and 4, and 5, and 3, and 4, and 5, and 3 ? Exercise 16. 1. John had 7 (5, S) cents, and he earned 5 (4. 6) cents. How much had he thci ? 2. I had $5 ($8, $5), and my brother gave me $5 ($4. $b). How much had I then ? ^ ^ 3. A man gave 6 (9, 5) dollars for a horse and 5 (4, 6) dollars for a cow. Find cost of the two. 4. A class contains 4 (6, 7) girls and 5 (4, 6) boys. How many are there in the class.!" 5. Will found 9 (3, 6) eggs, and Tom found 5 (4, 6). How many tlid the two find ? 6. One bag contains 8 (4, 9) apples, and another 5 (4, 6) apples. How many are in the two bags ? 7. A man travels 3 (7, .1) miles one day, and 5 (4, 6) miles another day. How .ar did he go in two days? Exercise 17. Add vertically— up, or down. Add horizontally— from left, or right. 1. I -|-2+l4-2 + I+2+I = 2. 2+1+2+1 -f-24-I-f2 = 3. 1 + 1+2 + 1 + 1+2+1 = 4. 2+2+1+2+2+1+2= 5. 2 + 2+1 +1+2 + 2+1 = 6. 3 + 2+I+3 + Z + I+3 = 7. 1+2 + 3+1+24-3+1 = 3+3+2+2+3+3+2= 2 + 2 f 3 + 2 + 2 + 3 + 2=* 2+3+2+3+2+3+2= 3+2+3+2+3+2+3= 4+2+3+4+2+3+4= 3+4+2+3+4+2+3= 3+5+4+3+5+4+3= i8 1. 2+1 2. 3 + 2 = 3. 3 + 3 = f 3 + 4 = 5. 4 + 4 = 6. 5 + 3 = 7. 5 + 4 = 1. 6 + 4=. 2. 7 + 3 = 3. 5 + 6 = 4. 8+4 = 6. 9 + 3 = 6. 4 + 7 = 7. 3 + 8 = 1. 9+4= 2. 7 + 5 = 3. 8+6 = 4. 9 + 7 = 6. 7+6 = 6. 6 + 6 = 7. 7 + 8 = 1. 3-\-7 = 2. 7 + 7 = 3. 9+6- 4. 8+8 = 6. 5+9 = 6. 9+8 = 7. 9+9= MENTAL ARITHMETIC. BxtrciM |8. 12+1 = '3 + 2-^ 23 + 3 = ■ ' '-4 = i 4- 25 + 3 = 15+4 = 22+1; 23 + 2' 33 + 3- 43 + 4 = 24 + 4 = '5 + 3 = 25+4- exercise 19. 16+4 = i7 + 3 = 25+6 = 2S + 4 = '9 + 3 = 14 + 7 = 33 + 8 = 26 + 4- 37 + 3 = 35+6 = 38 + 4 = 29 + 3 = 24 + 7 = 23 + 8 = '9 + 4 = 27 + 5 = i8 + 6 = '9 + 7 = 17 + 6 = l6 + 6=r 27 + 8:^ Exercke ao. 29+4 = 17 + 5 = 38+6 = 39 + 7 = 27 + 6 = 26 + 6 = 47 + 8- Exercise '3 + 7 = 17 + 7 = 19 + 6 = 18 + 8 = '5+9 = 19+8 = '9+9= 33 + 7 = 27 + 7 = 29 + 6= 48 + 8 = 95+9 = 49 + 8 = 69+9« 32+ M 43 + 2: 53 + 3 = 73 + 4 = 34 + 4 = 85 + 3' 45+4- 46 + 4= 57 + J» 45^6 = 88 + 4 = 49 + 3 = 64 + 7 = 53 + 8 = 39 + 4 = 37+5 = 58 + 6= 29+7 = 47 + 6 = 36 + 6 = 57 + 8 = 43 + 7 = 87 + 7 = 59 + 6 = 78 + 8 = 65+9 = 59+8 = 79+9=- 52 + 1 63 + 2 = 73 + 3' 53 + 4' 94 + 4 = 45+3" 75+4- 86+4 = 77ti=' 65 + 6= 78 + 4=. "9 + 3- 44 + 7=' SS+S'' 49+4 = 67 + 5 = 78 + 6 = 59+7 = 37 + C^ 86+6 = 77 + 8 = 93 + 7 = 97 + 7 = 99 + 6 = 98 + 8 = 85 + 9 = 99 + 8 = 99+9- ADDITION. »9 BxtrclM aa. Add vertically -up, or down. Add horizontally— from left, or riKht. 1. 1 + I+2+1 + I+2+I + I+2 f l + I+2 + f • I+2+I+2+l+2-fl-t-2fl f2-f-l+2 + ? = 2+2+1+2+2+1+2+2+1+2+2+1+2^ 3+2+1+3+2+1+3+2+1+3+2+1+3= 3+2+3+2+3+2+3+2+3+2+3+2+2= 3+4+2+4+3+4+2+4+3+4+2+4+4= 5+3+4+5+3+4+5+3+4+5+3+4+5= 2. a 4. 6. 6. 7. Exercise aj. 1. What two numbers are equal to 4 ? 5 ? 9? 2. In what ways could a man put 3 (6, 9) pijjfs into two pens? 3. In what ways could Charlie share 7 (8, 10) apples with his little sister? 4. Show all the ways in which 5 (9, (>) apples ccnild he divided between two boys. 6. Two men earned $8 ($ I r, $16). H«.vv much did each man earn ? Give every answer ; ossible. 6. The sum of two numbers is 8 (9, >. What arc they? 7. The master asked James 5 (6, ir) questions. How many did he miss ? How many did he answer? Exercise 24, Read these questions, filling the blanks p 1. $7 + $4- $5+.... =$12. 2. $8 + $3 = 3. $6+$5 = 4. $9+ $2 = 5. $6+$7 = 6. $9+$4= 7. $8 + $5 = $7+. $9+. $2+. $8+. $6+. $4+- .=$12. .=$12. .=$12. .-$12. .-Sr2. .=$12. operly : — + 3-10. + 5=10. + 8=10. + 6=10. + 4= 10. + 7 = 'o. + 9=10. 20 MENTAL ARITHMETIC. Exercise 35. [f 1.* ' IS; How many are :- 1. 3 hens and 4 hens ? 2. 7 pears and 3 pears ? 3. 6 books and 4 books ? 4. 5 cents and 2 cents ? 5. 8 hats and 3 hats ? 6. 4 pens and 5 pens ? 7. 9 cows and 5 cows ? 6 men and 5 men? 9 cats and 3 cats ? 3 dogs and 8 dogs ? 5 pins and 5 pins ? 8 desks and 6 desks ? 7 slates and 4 slates ? 4 mice and 9 mice ? Exercise a6. 1. James had 4 (7, 3) apples, and got 7 (8, 9). How many had he then ? 2. Will had 6 (4, 8) cents, and found 7 (8, 9). How much money had he then ? 3. Rob had $8 ($3, $7), and earns $7 ($8, $9). How much money has he now ? 4. Tom had 5 (8, 9) peaches, and buys 7 (8, 9). How many has he now ? 5. John had 9 (6, 4) marbles and won 7 (8, 9). How many had he tiien ? 6. I spent $7 ($9, $5), and have $7 ($8, $9) left. How much money had I at first.? 7. I answered 3 (5, 6) questions, and missed 7 (8, 9). How many were asked ? 1. 2. 3. 4. 5. 6. Exercise ay. How many are : — 9 pencils and 4 pencils ? 6 knives and 6 knives ? 8 apples and 5 apples ? 5 bands and 7 bands ? 7 pears and 5 pears ? 6 caps and 9 caps ? 3 books and (> books ? 5 pages and 8 pages ? 7 cars and 7 cars .'' 8 rails and 9 rails ? 9 roses and 6 roses ? 4 forks and 7 forks ? - _> I - r>-- - I — o-- • -T / .v^..»- 7. 4 squares and 6 squares ? 8 cups and 4 cups ? a: ADDITION. 21 Exercise 38. Add vertically— up, or down. Add horizontally— from left, or right. 1. 4 + 8 [-3+5 + 9 + 6 + 7 + 2+3 + 9 = 2. 7+3+6+8+2+5+4+9+4+6= 3. 8 + 5 + 7 + 2 + 6-»-3 + 9 + 4 + 8 + 2 = 4. 3+2+9+4+8+7+5+6+5+7= 5. 9 + 4 + 2 + 6f7 + 8 + 3 + 5+6 + 3^ 6. 5+7+8+9+4+2+6+3+7+4= 7. 6+9+4+7+5+9+8+4+9+5= Exercise 29. 1. John has $300 ($400, $600), and Mary has $200 ($500, $300). How much money have the two? 2. I paid $200 ($400, $300) for a lot, and $900 ($700. $800) for a house. Find the cost of both. 3. A man has 3,000 (4,000, 5,000) acres of land, and his son has 2,000 (3,000, 6,000) acres. How much land have the two? 4. Will a'e 3 (4, 5) half-apples, and Charlie ate 5 (6, 7) half-apples. How many did the two eat ? 6. Rob has 5 (7, 9) quarter-dollars, and Sam has 8 (6, 7) quarter-dollars. How much money have the two ? 6. I paid 7 (4, 9) half-dollars for a hat, and 3 (8, 6) half-dollars for a cane. Find the cost of Ijoth. * Exercise 30. 1. Begin at i (2) and add by 2's till you pass 50. 2. Begin at i (2, 3) and add l)y 3's till you pass 60. 3. Begin at i (2, 3)and add by 4's till you pass 80. 4. Begin at i (3, 4) an^l ^^^^ ''>' 5'^ t>" >"" P^^s too. 6 Begin at 1 (2, 5) and add by 6's till you pass 100. e'. Begin at 2 (4, 5) 'i^tl -'^dd by 7's till you pass 100. 7. Begin at 3 (5, 7) and add by 8's till you pass 100. 22 1. 2. 3. 4. 6. 6. 7. 23 + 21 = 24 + 22 = 23 + 33 = 32+35 = 35+33 = 32+37 = 43 + 34 = 1. 2. 3. 4. 5. 6. 7. 35+35 = 25+45 = 65 + 25 = 34 + 36 = 43 + 37 = 36 + 34 = 37 + 53 = 1. 68 + 93 = 2. 75+86 = 96 + 37 = 59 + 74 = 63 + 89 = 76 + 98 = 84 + 99 = 3 4. 6. 6. 7. 1. 2. 3. 4. 6. 6. 7. 247 + 326 : 435+228: 637 + 249 = 526+354 = 365+247 = 459 + 238 = 324+637 = M^M'.AL ARITHMETIC. Exercise 31. 32 + 35 = 50 + 36= 45 + 52 = 43 + 35 = 58 + 40= 26 + 53 = 34 + 62 = 63 + 35 = 24 + 73 = ^3 + 33- 28 + 71 = 34 + 45 = 73 + 24 = 65 + 34 = Exercise 32. 28 + 32 = 63 + 27 = 57 + 33 = 28 + 62 = 39 + 21 = 61 + 29 = 47+43 = 35 + 36 = 28 + 33 = 45 + 37 = 28 + 36 = 35 + 55 = 35+49 = 63 + 28 = Exercise 33. 76 + 39= 58 + 67 = 35 + 86= 67 + 94 = 38 + 87 = 66 + 86=- 78 + 96 = 57 + 37 = 76 + 92 = 67 + 87 = 69 + 38 = 89 + 66- 73 + 88 = 64 + 87 = Exercise 34. 528 + 659= 837 + 645 = 744 + 829 = 656 + 927 = 9^9 + 336 = -t35 + 848 = 846 + 548 = 43 + 52 = 36 + 2 1 = 41+37 = 24 + 34 = 26 + 42 = 37 + 52 = 33 + 46 = 24 + 39 = 36 + 2'' 35+: 45 + 28 = 38+45 = 63 + 29 = 35+39 = 75 + 89 = 48 + 79 = 38 + 95 = 47 + 65 = 87 + 78 = 68 + 88 = 87 + 49 = 857 + 629 = 375 + 842 = 937 + 685 = 738 + 594 = 684 + 486 = 379 + 985 = 594 + 738 = ADDITION. ?3 Exercise 35. 1. I spent 3 (6, 5) five-cent pieces, and 4 (3, 5) five- cent pieces. How nuicli did I spend ? 2. I gave Will 4 (3, 6) ten-cent pieces, and John 5 (6, 5) ten-cent pieces. How much did I give a\\a\ .' 3. I have 5 (3, 7) $2 bills in one hand, and 3 (5, 4) $2 bills in the other. How much money have I ? 4. I gave 4 (6, 8) ten-dollar bills for a cow, and 7 (4, 3) ten-dollar bills for a horse. Find cost of both. 5. A has 7 (8, 9) two-acre fields. B has 3 (4, 5) two- acre fields. How much land have they ? 6. I sold 7 (9. 8) five-acre fields, and have yet 5 (4, 5) five-acre fields. How much land have I ? 7. Will picked 6 (7, 6) 4-quart baskets of cherries and 7 (8, 9) 4-quart baskets of cherries. How much did he pick .'' Exercise 36. 1. John has 3(4, 5) cents. Will has 4 (6, 5) cents more than John. How much has Will ? 2. John has 4 (8, 9) cents. Rob i^ts 5 {4, 6) cents more than John, ^low much have the two.? 3. Tom spent 6 (7, 8) rents for a pen, and 5 (9, 6) cents for a book. P'ind llu; cost of the two. 4. Alice is 7 (8, 4) years old. Charlie is 7 ((>, 9) years older. Find the sum of their ages. 5. One hen has 8 (6, 5) white chicks, and 5 (7, 4) black ones. How many chicks has the hen ? 6. One hen has 9 (6, 7) chicks, and another has 7 (8, 9) more. How many chicks are m the two broods ? 7. One farmer has 9 (8, 6) bags of wheat, and another has 9 (8, 6) more. How many have the two ? 24 MENTAL ARITHMETIC. kJ f "A Exercise 37. 1. 6(17, 24) boys :ind 7(18, 28.) girls = 2. 5(13, 27) roses and 8 (18, 24) pansies = 3. 8(16, 26) cows and 6 (14, 23) sheep = 4 5 (15, 29) grammars and 9(18, r8) readers = 5. 7(17, 34) pears and 5 (19, 27 ( pc aches = 6. 9(12, 35) lilacs and 6 (19, 36)tulips = 7. 6(17, 28) robins and 5 (16, 47) h.rks = Exercise 38. Secure the necessary coins, and cjiint out the change for the following instances : — 1. 75c., 50c., 25c;, 80c., 70c., 60c., 40c., from $1. 2. 30c., 20c., IOC, 15c., 35c., 45c., 55c., from $F. 3. 48c., 43c., 39c., 37c., 67c., 84c., 13c., from $1. 4. 21c., 27c., i6c., 9c., 28c., 32c., 98c., from $2. Write down the words you would say as you count out this change. Write down, in order, the names of the coins you would give out. Exercise 39. 1. How much land in two fields, each 6 (7, 9) acres? 2. How much will three lambs cost, at 4 (5, 8) dollars each ? 3. How much berries a-e put into three cans, if 6 (9, 7) quarts are put into each ? 4. How many pupils are in three classes, if there are 3 (4, 6) boys, and 5 (8, 7) girls, in each class .' 5. How many apples on four plates, if there are 3 (4, 5) red apples, and 4 (6, 5) green apples on each ? 6. How many sheep in 3 fields, if each contains 12 (15, 17) black sheep, and 8(15, 28) white ones.? 7. I have 3 (4, 7) $2 bills in one hand, and 5 (6, 8) $4 bills in the other. How much money is that? ADDITION. Exercise 40. 25 ( 1. John read 10 (18, .3) pa^es and James read 10 12 16) pages. How many did ilie two read .-' 2. A mar. sold 12(17, <«) ^'^'cp on Monday and u (14 15) sheep on Tuesday. How many did he sell ? 3. I boaght 14(16, 17) sheep from one man and 11 (,5, 17) sheep from another. How many did 1 l.ny ? 4. Rob has 16 (19, 14) five-cent pieces. Harry has II (r2, i6)-five-cent pieces. How much money have the two boys? 5 Will has 13(16, 18) ten-cent pieces. Tomnasi- (1 6," .8) ten-cent pieces. How much money have they together ? 0. I have 13 (19, 16) 5-acre fields and you have 14 (14 19) 5-acre fields. How much land have v.c . 7. I have 17 (19, '6) dozen eggs after sellmg 13 (13, 18) dozen eggs. How many eggs had 1 at hrst . Exercise 41. 1 A farmer sold a load of oats for $24 ($43, ^45), an^^ a load of wheat for $33 ($34, $52). How much did he get for the two ? 2 A man had $65 ($28, $24) in the bank, and put m $24 ($7 1 , $34)- How much had he in the bank then t "3 1 am 22 (43, 28) years of age, and my father is 23 (35 33) y^ars older. Find my father's age. 4. One bo k cost 45 (7«, 32) cents, ".ad another cos^ ''4 (''8, 35) cents. Find cost of the two. 5. One load contains 42 (63, 54) bushels and another 35 (33, 25). How many bushels m the two f 6. After selling 27 (58, 39) shce]), I have 62 (40. 6^^ sheep left. How many had I at first ? 7. I sold 46 (32, 59) yards of cloth on Monday and 53 (47, 30) on Tuesday. How many yards did 1 sell . \m 26 MENTAL ARITHMETIC. Exercise 4 a. 1. Alice is 6 (7, 9) years old, and Will is 8 (g. u) V ind the sum of their ayes in 4 years. \yn:J\ sum of Will's age and Mary's, is 9(11,16) years. \V li.it will be the sum of their ages in 5 years ? 3. Will has 3 span of horses, Rob has 2 span, and Sam lias 4 span. How many horses have the three ? 4. Charlie has 2 (3, 4) ten-cent pieces, 3 (4, ^) five- rent pieces, and 2 (3, 4) coppers. How much nioney has 6. Sain lives r (2, 2) mile from school, and Rob r> (2, I ) miles from school. How far must they walk each day ? 6. I paid 9 (7, 6) cents for a slate, 6 (8, 6) cents for a pen, -md as much as both for a book. Find the cost of 7. How long a fence will be needed for a lot 8 (7 a) rods long and 7 (6, 8) rods wide ? ^ Exercise 43. 1. Sam was absent from school 2 days in one week 4 days in another, and i in another. How many days vJas 2 I pay $6 ($9, $8) for a sheep, and $3 ($4, $5) for feed. I ind the selling price to gain $3 ($6, $9) '^ 3. Find the sum of the numbers ending in 3, 4 and <; between 20 and 30 ; 30 and 40 ; 50 and 60 ^ 4. Find the sum of the numbers less than 30 which end in 3 (4, 6). -^ 6 What is the sum of the numbers ending in ; (8 o) between 30 and 50 f 60 and 80 ? 40 .md 70 ? 6. A boy shot an arrow 25 (36, 48) yards up the road. How far must his l^rother go to fetch it for him ? 7. Find the sum of the odd numbers between 20 ind 30. *••" W : S- i SUBTRACTION. Subtraction is the process of finding th. difference between I wo numbers of the same kmd. w . i The Subtrahend is the number which is to Ik; subtracted. The Minuend is the number from which the other number is to lie subtracted. .• u • The Remainder or Difference is the n..mber which is found when one numlier is sul.tracted from another. /Minus) is the sign of subtractio,, and, when paced betw'ein tw^nimU. it means that the second number .s to be taken from the first. ^, 6 - a = 4, is read, " six minus two, equals lour. Exercise 44. 1. Will had 2 (3, 8) apples, and gave Tom i. many had he then ? 2. Rob had 4 (7. 9) "n^s, and spent i. How had he left? 3. John had I (5, 6) sheep, and he sold one. many has he now ? 4. A boy had 3 (5, 7) marbles, and he lost 2. many had he then ? 5. A girl had 4 (6, 9) cents, and she gave me i How much money had she then . 6. From 2 (8, 1 1) cents, I saved 2 cents. How did I spend ? 7. I earned $5 ($9. $6), and spent $3- How How many How How cents, much much did I save ? 1. 2. 3. 4. 5. 6. 7. $5 $8 $4 $6 $3 $7 $2 = -$2 = -$2 = -$2 = -$2 = $9-$2 = 3-3--= 7-3 = 6 = 3 = 5-3^ 4-3 = 9-3 = 8-3 = Exercise 45. $9 -$4 = $4 -$4 = $5 -$4 = $3 -$4 = $7 -$4 = $8- $4 = $6- $4 = 27 8-5 = 6-5 = 4-5 = 7-5 = 3-5 = 5-5 = 9-5 = $7- .$6- $5 = $4- $9 $3- $8' $4 = $5 = .%y ■%■!■■ -$5: ■%-2- -%y 28 .^^ MKNTAL ARITHMETIC. Exjrclse 46. What is the difference Ijctwec. .- - !• 9 and 3? 2 3. 4. 6. 6. 7. 7 and 4 ? 5 ."-nd 8 ? 4 ai)d 9? '^ and 7 ? :? and 5 ? y and 6 ? $S and $4 ? S''^ and $j ? $7 and $9 ? $9 and $1 ? $4 and $3 ? $3 and $6 ? 4>6 and $2 ? 6 and 5 ? 9 and 3 ? 3 'irxl 7 ? 5 an n <^;f ^^'^ 5 (7, 3) marbles. He won j C, ,^ , 'ost 2 (4, 6). How many had he then ? ^ ^^' ^^ ''"'^ .7. A man had $i: (Sn(\ ' "o^v often could he Exercise 48. (3, 5) How How How wZ."'"''' i' 7 greater than 2? 4? .? ,, What iiiiitit iNi^ .,,1,1^. -I . • 4 • 3 ."^ 5 r 9 wi, /■■"'"' '.'' ^ sreaier tnan 2? a? -j ? r ? as H'nu"'' '" u'^' ^'"^^ 9 exceed 5 ? 6- What remains after takintr , . r ^ fi-o.n y/ I, ? ,7p 3?;"^ 4, as often as possible, MUM. y.- I, . ,7? 2 p — " ". 7. Take 6 as often as possible from 13, , 7, .6, /^•-j? 50, 75. SUBTRACTION. SUBTRACTION TABI.R. Subtract at sight, or as the teacher points. 29 It 1 1 1 4 1 1 S 1 1 1 7 1 5 1 10 1 2 •> o 2 2 4 2 7 2 10 2 8 2 5 2 9 2 11 2 • > 5 4 *> G 3 3 S 11 3 7 3 12 3 10 3 '■> *i 8 10 7 (5 9 12 11 13 4 44444444 4 5 8 11 13 9 10 14 7 1? .) o 5 5 5 5 5 5 9 12 15 11 7 10 () 8 13 14 t> (] () (i (> G () G 6 6 7 10 14 9 10 12 15 8 11 13 / 7 7 / i 7 / 7 7 7 S 11 1() 13 10 14 15 17 9 1? had r/eft',""" «^'= « (S. «) 1. 2. 3. 4. Exercise 51. 3 ? 5 ? -" '""s' t>e added to 4 ? 7 ? ^ ? SUBTRACTIOV. Exercise 8j. 3t 1. James earned 5 (8, 7) cents, and spent W6 O rents. How much had he left ? ' J V"' 5> 2. Bob earned 3 (4, 6) cents, and saved 2 (2, ;) cents How much money did he spend? ^ 3. Will spent 8 (7 10) cents, and saved 5 (4, ,) rents How much money did he earn ? K.,f ; )^'''*f'' **''"*=^ 7 (3, 5) cents a -.veek, and spent all but 2 (3, 2) cents. How much diil he spend ? 5. Tom earned 6 (9, 8) cents a day. and saved all but 4 ^3i 7) cents. How much did he spend ? h.u\ ^^J"!'*" ^f "<=d 9 (5, 9) cents a week, and saved all bu( o (4, 7) cents. How much did he save ? 7. Mary had 4 (10, 6) cents, and lost all but 3 (6, i) cents. How much had she left ? j v • J' ExercUe 53. 7 L ^nl'°"^l'* ^ ?-^"/°'' 5 < ■' 4) cents, and sold it for 7 (10, 9) cents, i ind my gain. 2. I paid 10(7, 9) cents for a book, and sold it for o (3. 5) cents. F ind my loss. %-r%\ ^^^["^ ^- ^?^' *."^ ^"'' ■'^ ^''^^P' '-^"^I sold it for i? ^3>i I, *6). I- ind my loss or i^ain. 4. I got $9 ($8, $1 1) for a coat that cost $6 ($1, $[.) I-md my loss or gain. ^ 6. By selling a slate for 9 (ra, 16) cents, I lost 2 (5, 7) cents. Fmd the cost. ^^^ ^o^oo^L?"'"f "* ''^^^7 '°°^'5°' '^^°) «"ts, I gained 40 (90, 60) cents. Fmd the cost. thl; V'''"^'^' ''''° ''x^"*"' ^°''5 (8, >2) cents, and sold :^;snr.-T Affii^aff'.j' :. ' /i>L!t^^'yilO. 1 3» MEi.fAI, ARrTH.NfKTIC. Bxerclie s^. 1. A man owed $600 (SUnn r«^\ Exercise 55. -nJir h'o:.^,^:- «„«£ -;;i,Rob has 6 (, „ -'-s in another. Hovv'n'l^J.to^Trrri „"!'' •-*"' ^ ^•^' 7> ^ 6. John has $700 (S-ru. « ^'''^ **^" ''e'tls? 4/t &,,* 'i' -;:x Se^' Tr„,'r.t -•; SUnTHACTIOiV. Exercde 86. 1. Take I (3, 2) from 4, 14, 24, 34, 44, 64, 84. 2. ake 3 .^ 4) from 5, ,5, ,3, 45, ^5, 75^ ,^. d. Jake 4 (3, 2, 5) from 7, 17, 27, 57 ^j, S'/ifyy. 33 Exercise 57. 1. A man has 4 sons, in .1 family of 7 (9, n) How many dauKhters has he ? 2. How many girls are in a class of 8, if 3 (4, 7) of the class are boys ? 3. How many hoys are in a class of 12, if 5 (8, n) are jfirls? 4. How many girls arc in a class of 18 (25, 31) if 14 are i)oys ? j /» «♦ 6. How many boys are in a class of 29 (35, 40), if 16 are girls ? 6. There are 18 girls in a class of ^i (35, 43). How many boys are in the class ? 7. A man has 4 sons, and each son has 3 sisters How many children has the man ? Exercise 58. Tell a story about : — 1. 3 cents 4- 4 cents. 2. 5 men +-2 men. 3. 8 eggs + 5 eggs. 4. 6 nests 4- 3 nests. 6. 7 boys + 6 boys. 6. 4girls + 7giris. 7. 9sheep + 8s!ieep. 5 cents - 2 cents. 8 lambs -4 lambs. 7 flowers - 5 flowers. 9 colts -3 colts. 6 eggs - 4 eggs. 5 (lays - 3 days. 7 days - 2 ilays. $90 4- $60. $70 - $30. $804 $40. $60- $20, $50 - $40. $404- $50, $80 -$50. 34 MENTAL ARITHMETIC. t if Exercise 59. Write the successive remainders .1. 2, as often as possil^Ie, from 11, ^- 3, as often as possible, from 1 s, o. 4, as otten as possiljie, from -'4 ^- 5, as often as possible, from 30,' O. 6, as often as possible, from 43, • Ontcos.ll*(^J*r- f''"") fr » ^Pan of horses, cost ofcach ■' • *^^ '"°'''' """' 'he other. Find cos%^';i-3n,^*3$n^.^3)™re.ha„__a cow, and both 1. 168-25 2. 283-4,. ?• 275-32. 4. 276-65. !• 387-54. g- 497-32. Exercise 61. $237-1125. S358-$237. |3^V-$253. $584-5322. $296- $145. |375-$372. 7 08A .:' PA^~*372. '• 3S6--4S. $584 -$282, 5469-1214. $783 - 1322. $975 -$435- $628 -$206. $247 -$125. $538 -$306. 483-241. 765-354. 934 - 623. 857-4'5- 696-622. 379-237. 548-420. SUBTRACTION. 35 Exercise 62. Alice is 3 (5, 4) is 5 (6, 4) 1. Will '« k'io. 7) years old, and years yof ; er. }' no .'^ lice's aj^e. 2. H.0I is 7 (9. To) » ;ars old, and Mary years you igf r. Kind ne sum of their aj^es. 3. Char ■•,. is f :M^r r, 14) year okl, and Alice is 6(7, 8) years younger, f md the difference in their aj4es. 4. The sum of the aj^es of two hoys is 15 (r6, i8( years. One i" 6 (9, 8). Find the ajje of the other. 5. The sum of the aj-es of two j^irls is 9 (i i, 15) years. One is 3 years older than the other. Kind age of each. 6. The sum of two numbers is 8 (ro, 17). Their difference is 2 (4, 5). Find the numl>ers. 7. How much is the sum of 6 (8, 15) and 9 (7, 10) greater than thtir difference.'' Exercise 63 1. A man can row 4(5,8) miles an hour, in still water. How far can he row in an hour, down a stream lunning 2 (3, 5) miles an hour? 2. A man can row 8 (9, 12) miles an hour, in still water. How far can he go in an hour, up a stream run- ning at the rate 2 (4, 5) miles an hour ? 3 A man can row 6 (8, 9) miles an hour, in still water, and 8 (12, 12) miles an hour, downstream. How fast is the stream running ? 4. A man can row 9 (10, 12) miles an hour in still wat r, and 8 (7, 10) miles an hour, up stream. Find the rate of the stream. 5. I row up stream at the rate of 5 (7, 8) miles an hour, and 7 (11, 14) miles an hour, down stream. Find the rate of the stream. 6. I row 8 (9, 12) miles aa hour, down stream, and 6 (5, 6) miles an hour, up stream. Find rate in still water. ■ 7. A man rows 12 (16, 20) miles an hour, down stream. and 8(ro, 14) miles an hour, up stream. Find the difference between the rate of the stream, and the rate of the man in still water. Ill ! ■ 36 MENTAL ARITHMETIC. 1. a. 3. 4. 6. 6. 7. 1. 2. iri. , , Exerciae 64. r 111 the blanks properly :_ $9-$5 = $8 -$6 = $6 -$4 = $7- $3^ JS-$3 = $3 -$2 = $4 -$4 = Exercise 65. = $800. = $900. = $700. 3 + ....=4 4+.... =8. 5 + .... =6. 8+.... = 10. 6+..,. =9. 2+.. ..=5. 7 + = 7. 30+. 20+ . 3. 40 - . 4. 80+. 5. 70 - . 6. 90- . 7. 60+. 1. 2. 3. 4. 6. 6. 7. 3+. 3+. 3+. 3+. 3+.. 3+.. 3+.. ..=70. . . = SO. •=30. . =90. .=20. .=40. .=80* = 9. . = 19. . 29. • =49- .=69. .=89. = 59- $500+. $400+ . $300+ . $800-.. $900- . . S700 - . . $800-.. Exercise 66. ..=8. .. = 18. ..=48. .=78. .=68. • =$400. • =$500. • =$600. = $300. 5+. 5 + . 5+.. 5 + .. 5+.. 5 + .. 5 + .. = 38. -98. Exercise 67. Fill the blanks properly .— Minuend. 1- 9(12, 21) 2- 8(r4.38) o. , . , 4 ;;;•■■ 6. 12(20,35')' g- '5 (30, 42) 7- $9 ($15, $28) Subtrahend. S (6, 16) 4(8,25) 9(12, 28) 7(10,36) $7 ($8. $19) 50+ . 50+. 50+. 50+. 50+. 50+. 50+. 7- 27- 47-, 37-. 67-. 89-. 57-. -4=8. -5=6. -8=9. -6=10. ■3=7 ■7=ij. ■9=12. =90. = 190. = 390. = 290. = 590. = 790. = 890. = 4- = 14. = 34. -24, = 34. = 54. = 44. Remainder. ^ (/2, 37). 9 (14, 29). 6 (1.3, 34). .SUBTRACTION. 37 Exercise 68. Read the successive remainders as quickly as possible 1- 54-3-2-4-5-6-7-2-3-4-7-4-2 = Z. 63-2-3-4-2-7-5-4-5-4-5-6-8= 3. 68 -_^ -4-6-5-3 4. 5. 6. 7. -6-4-8-2 -5-9= 3 — 8 = 75-6-8-4-5-9-8-9-6-2-4-3 ^3-4-7-8-6-9-9-4-5-5-6-2 85-9-4-9-6-3-4-5-6-7-2-5-6= 76-5-4-6-9-3-8-8-8-6-6-5-4= Exercise 69. 1. The Slim of three numbers is 9(12, 16). Two of Che r..v.obers are 2 (3, 2) and 3 (4, 5). Find the otlier. 2. 1 hree books cost $10 ($12, $16). One cost $2 ($6, $S)- , Another cost $5 ($4, $4). Find the cost of the third. 3. The sum of the ages of three girls is 14 (16, 19) years. One is 5 (3, 6) ; another is 4 (8, 7). Find aye of the thu-d. 4. A, B and C bought a boat for $20 ($25, $30). A paicl $7 ($9, $8). H paid $8 ($6, $12). What did C pay ? O. S3M' won 12 (15, 18) marbles from .'\, B, and C. He vv , . '■<. 9) from A, and 5 (3, 4) from B. How many from . 6. (i , .li! the ways 7 (9, r i) apples could be divided aniong three boys, A, B and C, each getting somt-. 7. Give all the ways Walter could share 6 (8, 10) peaches with Alice and Willie. Exercise 70. Read the succ ssive answers as quickly as possible. 1. 84-4-3-54-6-3 + 7 + 6-3-4+5-8 + 6-7 = 5 4-6-5-^2-8 + 7 + 8-4-5 + 7-9 + 4-5 + 7=: 3+5-2+3+6-5+8-7-4+9 2-;-6+9= 9 + 3 -6 + 7 -5 -6 + 9-44- s -4 -74-8 + 9- 3 = 6+7-4+9-8-6+7+9-6-6-6+7-5+8= 4 + 9 -7 +6 + 8 -7 -6+ 5 +8- (0-6 + 9-7 + 6 = 7+8-9+8-7+8-4+8-6+8-9-9+8-6= 2. 3. 4. 6. 6. 7. 3S lli r^ ■ 1- 305-68= 2. 207-89= 3. 304-57- 4. 203-64= 5. 504-36:= 6. 602-45 = 7. 507-79= Pxerclse 71. $906 -S247 = f7o3-$3..3^ $805 - $2()J:= $508 $34y^ *4o7 $288 = $^x)5 -$3g6 = Exercise 7a. 304-186=. 409 - 1 64 = 602 - 325 --= 504 - 267 = 607-328=^ 400 " 175 = 500-386 = and'sel]";„ 'for g7$,"'; $'«)'" '""'"« l<"i(-(hs. S 3), ^- 1 here were n f.j i .-.\ i of them u-ere pron oui'*''i^o"^n;" '" ''''^- -^"^^ ^ ('«. ^7) , 5. Mary had 9 (.4 ..^ !^ "''*">' '■^'"•'''""l ? How i^any had she itf"' '''^"'' ^"^' 4 ('7. 18) died. '• I lent a man $9 ($.. a- , .x ^ °" '^ • $-^9). How much ■JsiniX^tnlT^''' ^''''^ ^^« (^'9, Minuend . ^., ^Jubtrahend .'.■.■; 1y. "^'^ .... 325 436 .... ^,, /J-... 28/ 356 1. 196-37 = 2. 245-28 = 3. 254-39^ 4. 265 -3,s. 5. 396-85 = 6. 263-46= 7- ^54-37 = Exercise 73. ^263-584 = $354 -$69 = *275- $96 = $286 -$99 = S364-$75 = S283-$68 = $465-596 = 237-63: 343-85 = 426- q 9. 33f-68 = 3-'5-47 = 234-85 = 237-89 = SUBTRACTION. 39 Exercise 74. How many days arc in : — 1. May? January 2. July? April?' 3. August? June? 4. July and August ? 5. Marcli and April ? 6. Novenil)er and JJec. 7. May and June? Septcmlier ? February ? November' December? October ? March? September and October ? July and December r February and November? May and December? Exercise 75. 1. James had 14 (36, 76) marbles, and gave Rob 5 (9, 24), and Will 3 (8, 26). Hou- many lia, 33)- Another is 7 (39, 23). Find the third. 6. I gave $25 ($45, $83) for three sheep. One cost $8 ($16, $26\ A second cost $9 ($19, $27). Find the cost o the third. 7- I bought a cow for $17 ($53, $85), and paid $9 ($16, $19), and $5 ($17, $26). How much is still due ? Exercise 76. How many days are in : — 1. Feb., March, and April? 2. Aug., Sept., and Oct.? 3. May, June, and July? 4. Nov,, Dec, and Jan.? 5. First 3 months of year? 6. The second quarter? 7. The first h.df of year? May, March, and July ? June, Oct., and April ? Jan., April, and May? Aug., June, and March? The last 3 months? The third quarter? The second half of year ? m 40 MENTAL ARITHMKTIC. Exercise 77. t How many days in the month after :— 1. Novciiil)cr , ^ 7 ? o' I 1 ? lA > ,„ 3 3. Apnl2?6? ,0? ,5? ,7? .0? 27>^^a^ 4. January , ? 8? ,, ? ,6? ,9? 24-/;8V-., . 5. Octobers?;' 14? iS? 2, ? 25 ? =8 p ^^i 7. June 4? 8? 10? !4? 21? 23? 26? 28? Exercise 78. 1- I boutfht a lami) for ty /'«'> C/w i /"fii «r^\ 1 1 .. '^7 iJ-o, -K)), and another fnr «» gain'or^L^"' ^"'^^ ^'^'^"^ for $20 ($25, S.8)/"?i:rtL« ai,?taSV(9"^ri^s 'M'J' "^ ^'rr'""^' ^"^ Alice 3 Wh t , r ; "''^""''^">'^''^'t'"-' two answer? o. Uhat IS left after takiuL^ •? r- y\ .. r possible, from i3(2;r, 50)? ^ ^'' '^^' '^^ "^^<=" as down Sch a Jj;er '"" '^ "^ "'^^" '"^^ ^^^ ^-' -"d write Exercise 79. How many days from : - Aug. 10 to Sep. 27 ? Sept. 14 to Oct. 12? Oct. 16 to Nov. 24.? Nov. 18 to J>ec. 25? Mar. 24 to Apr. 17?* July 18 to Aug. 16? June 17 to July 19? I. Jan. 4 to Feb. 8? J^'eb. 17 to Mar. 25 ? 2 , __ _ 3. Mar. -3 to .Apr. 17? 4. April 5 to May 24.? 5. May 8 to June 30 ? 6. June 9 to Juiv i ? '7- July 3 to Aug'. 19? SUBTRACTION. 41 Exercise 80. How many days from : 1. Jan. I to March 28.? 2. Feb. 4 to April 24? 3. March 9 to May 25 ? 4. Jiiwe 24 to Auk. -3 ? 5. Aug. 17 to Oct. 20? 6. Jan. 18 to March 27? 7. Oct. 1 5 to Dec. 1 1 ? April 15 to June 27 .' May f4 to July i? 45.' 4''>? 5. A person was born in 1824. Find his age in 1830, 1838, 1843, '847, 1852, 1855, 1859, 1S76, 1S64, 1897. 6. Find the year of birth of a person who was 7 (9, 15) years old in 1898, in 1893, in 1886, in 1875, in 1847. 7. Five years ago a person was 4 (8, 12, 16, 23, 27) years of age. How old will he be in 4 (6, 8) years ? Exercise 82. Find the d.-ite which is : — 1. 24 days after Jan. 15. 38 days after Dec. 14. 2. 28 days after Aug. 18. 36 days after Oct. 16. 3. 35 days after May ri. 37 days after April ri. 4. 27 days after July 22. 40 days after June 16. 5. 33 days after March 16. 38 days aftrr Sep. 1 1. 6. 29 days .ifter Nov. 24. 50 days after May 24. 7. 32 days after Feb. 1 2. 46 days after Aug. 27. 1'f I 43 MENTAL ARITHMETIC. Exercise 83. 1. How much change should a person receive 're n a tKWlar bill m paying for goods to tlie value of loc > tor ? Soc? 60c. ? 80c. ? 40c.? 90c. ? 7(x:. ? 20c. ? 25c '■ ^cc'? 65c. ? 45c. ? 75c. ? 630. ? 28c:. ? 42c. ? - - ^- 53c. ? 670. ? receive from a two- 2. Hon much change sliould I .....v. ,r.„n a iwo- doliarb,!! when paymg yy.? 84c.? 6i25, 3)34). How much more has B .? 6 A and B have $,5 ($,od, $300). B has $9 ($30, $50). How much loss has A ? ^,l:^^ luu- 1^ u *'''■'', ^" ^^^"^^ ^-°°)- ^ has $5 ($24, $123). Which has the more, and how much? Exercise 85. How much change should remain from a five-dollar bill after paying : — 1. 25c. and 36c. ? 2. 48c. and 33c. ? 47c. and 28c. ? 64c. an^l 37c. ? 75c. and 83c. ? 84c. and 96c. } 79c- and 88c. ? 3 4. 5. 6. 7. 27C., 36c. 28c., 35c. S4C., 38c. 37^; 4SC. and 32c. ? and 36c. ? and 62c. ? and 06c. ? 49c., 58c., and 95c..? 65c., 87c., and 93c. ? 58c., 36c., and 85c. ? ■ ■~ SUBTRACTION. 43 Exercise 86. 'S? 6^> '84:!? >5f'4? 'y^l '«15 S"^ i86^? '464? 200U? J847? >»°°- , N ,25,? 1400? 1832? 1700? «6o4.'' ' ^ r, 2. How many days in ■^^^^''^''f'y^'^'l^Z,''' 'Miv =4 ? Dominion Day? InclepcnacncL u ^y ■ How many days in a leap yc^ir after :- n? Jan. 28? v-f>U ^a? March 1 3.'' Apiiiyr 3. Jan. Feb. 29? March 15? Exercise 87. • 1 I bought two hor.es at $43 ea^^; ^"^ ^f^ ^^•'^'" '° Jn $M How much did I yet for the .pan ? gain :p-4- . .., «->A ruh low much must 2 1 boufjht two Imrsci. at .t.jb c.icii. 1 get lor them to gain $S cm each ? ^. Will was at scbo^;^- ^ ^^ ;;ow'::^my da s^S absent 3 days, and C.harlie 4 "-ly- 5 Aroomis.6(.8,37)yardslong and. 6,14) >a.ds les^"in width. How far is it around the room ? 6 l^ave a dime to pay for 3 cents' worth of pens and 4 ctts'. orti of paper.' How nuu h change do I get ? Exercise 88. Find the age of a person :-- Bom Jan. 15, 1876, and died Feb. i,, 1880 tinni lulv 17, 1878, and died Aug. 24, 188-. on ilay 24 .836, and died July 28 .846 orn Nov. .7, 1867, ^nd died Jan. 28 .872 Wn Dec 23, 1892, and died teb. 28, 1897. 1. 2. 3. 4. 5. 6. 44 in I Ml 1. 2. 3. 4. 6. 6. 7. Add vertically 3''>-i -15+ S3 i 5:5 + 36+ ;;8 + S^' + 77 + ,Uf 74 f 54 + «Sfj + 37 + 5^' + 97 + -3 + 37 + 57 + MKNT.M. .ARnrr.MKTIC. Exercise 89. and horizont.'iily .— 75+96 + 45 + 7^^ ■;^ + 5J + 35 + 37 = 67 (--M i-,s4 + 2r,= ^'^3 + 7« + -9 + 34- 29 + 31 +5r +59 = : 70 + 69+67 + 61 = . Exercise 90. I. A nian was horn in 1841 ds-f, ,8.-,. aim ''*-' '•« ^5 (3^ 34) years old? ^ ^ ' '^57'. Wlicn will wini,;',;:;t:;;?;^';';s;:\i^j^('«54. .863) uowom 4. ^'ihI the sum of the nuniliPio., r to 50. numljeis ondmy ,n 5 (7, «) j,., l3cUe.n'?^.;;;5r"'^''^"'-'---'-^-4(6,J) beLL^3ot.Uo: "' '" ""'"'^^^^ ^"^''"" '-^ 3, 4, o.- 8 How nuich do I slive in a ycir r "*' ^"' °"'"'' "''"^•«- Exercise 91. Add vertK-ally and hori^ntally •_ 3. j5-67 + $3.4S + $6.344-|. ' ?:J^-^J- ••• 5. $6.25 + $6.75 + $..6,^$6.^5;a^5I••• 0. J^-^5 + $3-45+S3.;4 + $4.c)3 + $-.;6-"" M If! SIT BTR ACTION. 45 Exercise 93. 1. Find the sum of the first five digits. 2. Kim! the ;iin5? 3? 7? 9? 8.' ,? 6? 24? 36.' 45? 25.? 56.? 87.? 63? Q->? 245.^ 356.' 428.;' 562.? 874? 985? 849? 287? o i 7i " .!'''' difference between the lareest number 15. What tivo luimbers equal 75 and differ by 29? MULTIPLICATION. Multiplication is tlu> nuthod ■,( fimlin^ the nnu.niil ..f ,i certain nuinl)fr wJu-n il is rf|Hai..l a t;iv. „ mmitK-r ul innc-s. It is a short mk-iIxkI of roiHiiicd iin. The Multiplicand is tin- imiiilK-r to !»• nuiliipli.'l. .-r repeated. The Multiplier is the miinlK.-r whicli u-Ils li-.w <.lui. ihe inultipHcanrl is to l)e rein-aled. It is always an abslrai-l nuiiiU'r. An Abstract Number is one in whirti tlw kiiili<-r arc «m1!c<1 the factors. The Product is the number ol.lained l>y imilliplyin- one numlxjr hy another. It is always similar to the multip icand. The Square of a number is the pr..etween two numl,ers. shows thai the first is ... be in.iltii)'ie.l by ih^ second. 3 X 2 = 6, is read, " three inulli plied by 1^., e-iuals six " How many 1. I apple? 2. 2 pUims ? 3. 2 cents f 4. 3 hats ? 5. 5 birds ? 6. 4 pens ? 7. 3 eggs? Exercise 94* are two limes : - 3 pencils ? 4 windows ? 7 chickens ? 5 robins ? 6 boxes ? 4 windows ? 3 peaches ? 47 7 cherries ? 8 peaches ? 6 '.abbits? 9 (questions ? 8 pictures .'' 7 minutes ? 9 inches ? S books? 7 lainlis ? 5 ^'CCSC? 6 boys ? 9 -iris? 8 ducks ? 9 hens ? l! 48 1. 1X2 = MENTAL ARITHMETIC Exercise 95. 2. 3. 4. 6. 6. 7. 2X 2 = 3x2 = 4X2 = 2x3 = 2X1 = 4X2 = 2 times $2 — 2 times $j = I time $2 = 3 times $2 = 2 times $4== 4 times $2 = 2 times $5 = 2 times 5 = 2 times 6 - 2 times 7 = 5 times 2— • 4 times 2 — -times 8 = limes 9 = $9x2 = $6x2 = $8x2 = $3x2 = $7x2 = $5x2 = •$4x2 = J . Hxerclse 96. (3, 5) pensT '"^^ ^ ^•^"'^' ^"- "-ch must I pay for . <^o^«^St:;^r?)^^/;?^'4/r^^'>^^-^iowmucu 7^irPT;^rj^^^;i;!--^PairP3pairP3pai.P «^ff^:n>;--nm3.^^^ co^ ? 1 :l;::pp r^^^^f . ^«)- ho. muci. wi„ 2 s^ep wJbiS^^^^;?;^:^^-^-;. Ho.manye,,s ---s?^^«?9t^i;^,^r/^-- Exercise 97. ' ^4x3= 3x4=. 3x6 = 3x5 = 3^7 = 3x9 = 3x8 = 3x3 = 1. $1x3 = 2. $2x3 = 3. $3x2 = 4. $4x3 = 6. $5x3 = 6. $3x4 = 7. $3x5 = $5x3 = $6x3 = %xs = 53x6= $7x3 = $8x3 = $7x3 = $6x3 = $8x3 = %X3 = $9x3 = $4x3 = $8x3 = $3x4 = $3x6 = $3x5^ %X3 = $3 X .' = $3x9 = $3x7 = MULTIPLICATION. 49 Exercise 98. Find the cost of : — 1. 2 pounds rice @ 2 (3, 4) cents a pound. 2. 4 pounds sago @ 3 (2, 4) cents a pound. 3. 3 pounds barley ® 5 (3, 6) cents a pound. 4. 5 pounds sugar @ 2 (3, 4) cents a pound. 6. 2 pounds butter @ 20 (30, 50) cents a pound. 6. 3 pounds cheese @ 30 (20, 40) cents a pound. 7. 2 pounds raisins @ 30 (60, 70) cents a pound. Exercise 99. 1. What will it cost to post 2 letters ? 4 letters ? 7 letters.? 9 letters.'' 5 letters.? 6 letters.? 8 letters.? 2. How many feet have 3 hens ? 5 chickens .? 4 robins .? 8 sparrows? 6 swallows .? 9 ducks .? 7 geese .? 3. How many oxen make i yoke .? 3 yoke .? 2 yoke ? 7 yoke ? 5 yoke .? 9 yoke ? 4 yoke .? 6 yoke .? 8 yoke .? 4. How many legs have 2 cows .? 2 cats .? 2 hens ? 2 flies ? 2 spiders ? 2 bees ? 2 cats and 2 dogs .? 6. How much land is in 2 fields, each 30 acres .? 20 acres ? 50 ac >s .? 80 acres .? 60 acres .? 90 acres ? 40 acres .? 6. How wiany ears have 20 dogs? 30 cats? 70 hens? 40 bears? 50 lambs? 30 boys and 60 girls ? 100 men? 7. How many wings have 200 robins ? 300 larks ? 500 bats ? 400 eagles ? 7000 swallows ? 8000 hens ? 9000 ducks ? Exercise 100. What is the cost of : — 1. 2 lbs. sugar @ 3 cents ? 3 cows @ $50? 2. 4 lbs. rice @ 3 cents ? 4 sheep @ $30 ? 3. 8 lbs. sago @ 2 rents ? 7 Iambs (^ $20 ? 4. 5 lbs. barley @ 2 cents ? 2 horses @ $90? 5. 3 lbs. starch ® 8 cents ? 3 mules @ $60 ? 6. 2 lbs. cheese @ 9 cents ? 8 calves ® $30 ? 7. 6 lbs. flour @ 3 cents ? 9 colts @ $20 ? /^ - -^y '•I Hi / ^'^ MENTAL ARITHMETIC. Exercise loi. F.II the Danks with the proper numbers. V -7 — /* 1. 2 3. 4. 5. 6. 7. X2 = 6. • X 2 = 4. . X2 = 8. • X2=IO. X2:=iS. X2=l6. X 2= 12. : X 4X Sx jX • 7x. 6x. 9X. = 6. • • =12. ..=16. ■ . = 15. .=14. .=18. = 27. •••X3 = Si5. •• X2 = $i6. •• X4 = $i6. • X3=$2r. •• X5=:$20. • . X4 = $24. .. X2 = $|8. Exercise loa. 1. flow much must I u.-iv for o «« 1 -r q M^ ^ ** ^''"^y^ • a school week ? s 4 "Tsr rs!;j) '■',^3*--. -h co„,ai„i„, . 4. A ,„a„ earns $, ^dav H ' '" t"' ' ^''■'^• 7. Sam boutrht ; rri R\ .0 ^ t. mes us mauy the n'ext 7,/'""^^ «»^ day, and three y next. Hou' many plums did he buy? Exercise 103. How many are four times •-- 5. 2 cenuf 3 mice' = ,in ' ,'«' '"^'''■''' ""rds^e birds? 7. 3oo,eee.> .oo.ards.. 5«.i„chcs? 4^^ i,es ? ^^^S ? MULTIPLICATION. MULTIPLICATION TABLE. Multiply at sight, or as the teacher points. Every possible combination is included. $« 1 1 1 1 1 1 1 1 1 7 9 4 8 (5 ") 2 1 2 2 2 2 2 2 •> o 9 7 9 4 8 6 3 5 •> 9 3 3 3 3 3 3 3 8 8 7 9 4 8 6 5 3 8 9 4 4 4 4 4 4 7 / 7 7 9 4 8 (> r> 7 8 9 —• — — — — — — — — 5 5 5 o 5 () (> (i () 7 9 5 8 <) (t 7 8 9 Exercise 104. 1. If a sheep costs $4, how much must be paid for 7 sheep.? 5 sheep.? 9 sheep 'i 400 slieep.? 300 sheep.? 2. What is the cost of 400 sheep (^$7} @ $6.? @ $9? @$8? @$2o.? @$3o.? @$5o.? @$4o? @$4oo? ©$300? 3. A boy lives 2 miles from school. How fur must he walk a day.? 2 days .? 4 days .? a school week.? 2 weeks? 4. What must I pay for 2 span of horses if ea^ h horse cost $50 .? $60.? $80.? $200.? $^00? .$4000 $7000.? 6. How many toes has a hen.? 2 hens.? 5 hens.? 8 hens ? 7 hens .? 4 hens .? 9 hens .? 3 hens .? 6 hens ? 6. A walks 4 miles an hour. How far would he walk in 3 hours ? 6 hours .? 9 hours .? 4 hours .? 2 hours .? 7. A boy lives i mile from school and goes home for his dinner. How far does he walk a d.iy .? a week.? 8 weeks .? 9 weeks .? 6 weeks .? 7 weeks .? rjjj 52 MENTAL ARITHMETIC. f: ^'1 Exercise 105. What quantity is 4 (5, 6) times :— 1. $2? $3? $5? $7? $4? $8? $9? $6? $20? $30? $50? 2. ^3? l(>^ £9? £2? /4? ^8? £s? £7^ £40? ^80? 3. 5c.? 4c. ? Sc. ? 7c. ? 6c. ? 3c. .' 30c. .' 300c. ? 3000c. ? 4. 4 hoys ? 2 girls ? 6 men ? 3 deer ? 9 sheep .' 7 ducks ? 5. 3 months ? 4 years ? 7 days ? 5 hours ? 8 weeks ? 6. 90 pints ? 80 qts. ? 60 {,-^allons ? 70 bushels ? 50 pecks ? 7. 30 feet ? 40 yds ? 70 inches ? 60 miles ? 90 rods ? Exercise 106. 1. At 5 cents each, what is the cost of 2 apples.? 4 apples ? 3 pens ? 7 books ? 8 oianges ? 5 lemons r 2. At 5 cents a day, how much will Rob earn in 2 days ? 3 days .? 6 days ? 4 days ? 7 days ? 5 days? 9 daj s ? 3. Each pupil in the class has 5 books. How many books will 5 boys have ? 7 boys ? 4 girls and 5 boys ? 4. My farm is in 5-acre fields. How much land is in 3 fields ? 5 fields ? 8 fields ? 7 fields ? 9 fields ? 4 fields ? 5. A pound of rice "costs 5 cents. Find the cost of 2 lbs., 4 lbs., 8 lbs., 3 lbs., 6 lbs., 9 lbs., =: lbs., 7 lbs. 6. How much will it cost to register a letter? 2 letters ? 5 letters ? 8 letters? 9 letters? 7 letters ? 7. How many school days in a week ? 2 weeks ? 5 weeks? 4 weeks? 3 weeks? 6 weeks? 8 weeks .* Exercise 107. $7x4= ^2x5= $5x3 = $4x7= .^3x5= $5x4= $6x4= ;^6x5=- $5x8 = $4x6= ^9x5= $5x7= $8x4= ^8x5= $5x9= $4x8- i,7X5- $5x6 = $0x4= ^'4x5= $5x5 = 1. 2x4 = 2. 4x4 = 3. 8x4 = 4. 3x4 = 5. 6x4 = 6. 9x4. 7. 5x4== 5x4= 4x5 = 8x4 = 5 xo = 6x4-= 7x5- 9x4= MULTIPLICATION. Exercise io8. 1. 2x6 + 4 = 2. 3x6+5 = 3. 6x6 + 2-= 4. 4x6 + 3 = 5. 7xfj + 3 = 6. 9x6+5 = 7. 8x6 + 4 = 6x .. 6x.. 6 X . . 6x .. 6x . 6x . 6x . .=24. ,.=48. ,.-36- . , - 30. . . = 54- 53 . . x6 = $i8o. . . . x6--$24o. . . . x6-$36o, . .. x6 = $48o. . . . x6 = $540- .. . x6 = $420. . .. x6 = $3oo- Exercise 109. 1. A man earns $1 a day How nnuh fl^^-'^ in . week ? 2 weeks ? 4 weeks ? 5 week. ? S u eck. . 2 How much is my weekly waps if >ny daily waives be$iV$2?$5?$6? 8? $4? $3? $7? $9? 6 How lonv? would it take one man to do a work wl^ch 6 n en ca". do in 7 days ? 7 days ? 9 days ? 20 da . 7 1 buy tovs at 5 cents each, and sell them at . cents. What 'is my gain on 3 toys? 4 toys? 8 to>s? 7 toys? 5 toys? 6 toys ? Exercise no. Find the cost of :— 1. 3 qts. berries @ 2 (3, 4) c 2. 5 lbs. suyar @ 5 (4, ^0 c 3. 7 qts. milk (^ 3 (4, ^^) c- 4. 9 lbs. rice @ 3 (5' 4) '■■ 5. 8 oz. spice @ 4 (3i 5) '"• 6. 6 doz. eggs ® 8 (6, 9) ^ 7. 4 lbs. sago at 4 (5' ^ ^■ 2 lbs. rice @ 7 (8, 9) c 4 doz. cakes (^ 7 (81 9) =• 8 pr. laces (^ 3 (5' 6) ^^ 3 lbs. figs @ 7 (8. 9) c- 6 yds. wire @ 6 (9, 8) c. 9 pk?. oats @ 3 (4, 5) c. 7 doz. plums @ 4 (5» 6) c- I H J. r^i 54 MKNTAL ARITHMKTic. 1. iX7 = 2. 5x7 = 4x7 = 8x7 = 6x7 = 7x.7 = 3 4. 5. 6. £0x7 = £3x7 = £9x7 = £Sx7^ £4x7^ Exercise m. 7x3^ ?X7 = 28. $4^7^ 7x5= ?X7=.y^. $8^7^ 7x4= ?X7=2I. $6x7 = 7x8= ?X7 = 63. $5x7 = 7x6= ?X7 = 4g. $7x7^ 7x7= ?X7=42. $9x7 = Exercise 113. 1- ^f^ 7 yards of cloili maWp a Inri„'e J )-l. a. used ,„ „,a,. . dt. eir^-^IS ZS^? 5fcpsrLfS.'^---£3wee^. Exercise ii3. ^^ hat ,s 8 times (9 times, 10 times) •_ 1- '? 2? 3? 4? 5? 6? 7? 8? 9? 10? 2- S4? $8? $3? $6? $9? ^5? /7? /.? /«? y , 3. a men ? 4 boys ? 6 giris ? 8 women"^; 1 / ,t° ' , 4. 3 yards. 6 feet? 9 inches? 8 rods' 4 n,^^^^^^^^^ MULTIPLICATION. 55 Exercise if^* 1 Tames learns 8 verses a week. How many will he learn in 2 weeks ? 3 weeks ? 6 weeks .? 4 weeks ? 2 Rob sleeps 8 hours a day. How much will he sleep in 2 days ? 8 days ? 4 days? 9 d'lys ? 7 days ? 3 Will earns $8 a month. What is his wages for 3 months? 2 months ? 5 months ? 8 months? 4 months? 4 I buy lambs at $8 each. How much must I pay for 2 lambs ? 3 lambs ? 5 lambs ? 6 lambs ? 8 lambs ? 5. How many shoes are required for a span of horses ? 3 span ? 5 span ? 8 span ? 4 span ? 9 span ? 6 span ? 6. How many pints in a gallon? 3 gallons ? 4 gal- lons? 5 gallons? 8 gallons? 7 gallons? 9 gallons ? 7. flow many legs has i spider ? 2 spiders ? 4 spiders ? 8 spiders? 6 spiders? 7 spiders? 9 ^P'ders ? 5 spiders? a How many fingers has a boy ? 2 boys ? 3 girls ? 5 girls ? 7 boys ? 5 girls and 4 boys ? 1 1 girls and 9 boys ? Exercise 115. 1 At 9 cents a dozen how much must I pay for 2 dozen plums ? 3 doz. ? 5 doz. ? 4 doz. ? 8 doz. ? 7 doz. ? 2. An orchard has 9 ines in a row. How many trees are in 3 rows ? 2 rows? 5 rows? 6 rows? 7 rows ? 3. A horse goes 9 miles an hour. How far Avill it go in 2 hours? 3 hours? 6 hours? 9 hours? 4 hours ? 4. James gets 9 questions a day. How many ques- tions will he get in 3 days ? 2 days ? 7 days ? 4 days ? 5. A man works 9 hours a day. How many hours will he work in 4 days ? 7 days ? 8 days ? 9 days ? 6. How far will a train go in 9 hours going 20 miles an hour? 30 miles? 60 miles ? 40 miles ? 80 miles ? 50 miles ? 70 miles ? 90 miles ? 7. I earn $50 a month and spend $21. How much do I save in 2 months ? 3 months ? 5 nonths ? 6 months ? 7 months ? 4 months ? 9 months ? i. months ? 56 MKVT.M, AkirHMIcriC, HI M-h; * Exercise ii6. Findthe product of :— 1- 2a'Hl S. 9.1.1(1 2. 8 and 2. ^ ami 4. 2 nnd 7. 7 .1 ,d 6. 4 aiid y. 2. 4 and 6. 3. 5 and 8. 4. 3 and 7. 6- 6 and 9. 8 and 9. 6 and 8. 5 ■i'>d 7. 9 and 5. 3 and 8. 2 and 4. 6 and 2. 3 'tiul 5- 9 and 3. 4 and 7. 7 and 8. 5 ami 6. 4 and 5. 9 and 7. Exerclce 117. "n.l. nearer .i„ theVUt^s^f Z^;; t,^ .'^-^- "-v miles anrot'leTpSvelv^'n;'" ''^^ ^^'-^ ^^^^ ^^ ^ ^-^ 5 Hon- far apart lS^ihi!/i ^ ^'""^ '"^'^^ '" 7 (% i r) hcnrs. o^J^:te!j^^Tjll -"- P'-e, and travel Jn How far apart will tul"^^ Tit S^'Zlr '''''''''''■ r , , Exercise n8. ^I'ld the factors of: — 1. 12 2. ,4, 3. .5. 4. lO. 6. 18. 20. 21. 2 "* 24. 25- 27. 28. 30. 3-^ 33- 35- 36. 40. 42. 44- 45- 4S. 50. 54. 55- 56. 60. 63. 64. 70. 72. 75. 81. 84. 88. 90. 96. 99- ioo» 108. MULTIPLICATION. Hvercise 119. Find the continued product of: — 1. 2, 5 and 8. 2. 5, 6 and 4. 3. 4, 9 and 5. 4. 7, 5 and 6. 6. 4« 8 and 2. 7* 8 and 5. 9, 5 and 6. 8, 7 and 3. 5, 9 and 4. Exercise lao. 32 X 5 x6 = 48 X 3 X 5 = 44x6x5 = 42 x8x5 = 36 X 4 X 5 = Exercise lai. Mul'tipiy, using the factors of the muhiphers : — 3, 5 and 7. 1. 24x3x5 = 2. 16x4x5 = 3. 25x8x3^= 4. 36x3x8 = 6. 27x4x5 = 57 5, 7 and 6. 8, 9 and 4. 9, 7 and 8. 4, 4 and 6. 5, 5 and 8. 25x7x4 = 45x5x6 = 35x7x4 = 55x3x8 = 35x5x6 = 15 X i: 2. 25 X 16. 3. 32x25. 4. 24X 15. 5. 35x24. 28x35. 36 X 1 5. 44x25. 32x45. 48 X 55. 35x32. 45 X 24. 25 X48. 75 X 36. 55x16. 32 X 24. 24 X 36. 28 X32. 32 X 36. 42 X 48. Exercise 132. 1. How many faces has a cube? 3 cubes? 5 cubes? 8 cubes? 9 cubes? 7 cubes? 4 cul)es? 6 cubes? 2. How many sides has a square ? 5 squares ? 9 squares > 7 squares ? 8 squares ? 4 squares ? 6 squares ? 3 squares .' 3. How many marbles in a score? 2 score? 4 score? 8 score? 9 score? 7 score? 3 score ? 6 score ? 5 score.? 4. How many are six tens? 8 tens? 4 tens ? 7 tens ? 9 tens? 5 reus? 12 tens? 15 tens? 20 tens? 25 tens? 5. How many ej,'<,'s are in a dozen ? 2 doz. ? ^ doz ? 5 doz. ? 7 doz. ? 9 doz. ? 8 doz. ? 4 doz. ? 6 doz. ? ' «f ^'j ^Jl'^.^""'?^.? '."^V"'''^^^ ''y '^ (5, 8) will give a quotient 01 7? 8? 6? 4? $5.r ;j9? j,i6? 15 sheep? 24 boys? 5« i MENTAL ARITHMETIC. Exercise 12$, 1. 6 + 7 + 3+5 + 5 + 9 t-' + 8 + 2 f6 + 4+ I +9 + 4 = 2. 5+9+i+s + 5+8 + 2 + 7 + 3 + ^> + 4 + 5 + 5 + ''" 3. 7+6+4+8+2+3+7+5+5+4+8+2+9+'= 4. 8 + 5 + 6 + 4-7-3 + 8 + 2 + 9+'-5-5+<'' + 4 = 5. 3+6+4+2+7+3+4+5+5+7+4+6+8+2- 6. 16+ 13+ 17+ 16+14+ '8+ 12+ 19 + 21 +35 + 25- 7. 19 + 28 ■t-22 + 13 + 27 + 25+ 1 5+ 36 + 34 + 19 + 31 = Exercise I34> 1. Find the cost of 3 s'eep ® $8, 4 calves (a $8, 2 lambs Of' $8, and 3 hogs @ $8. 2. Find the total cost of 8 toys (Fv 9 rents, 7 books @ 9 cents, and 5 pens @ 9 c ents. 3. Find the ag^fregate cost of 9 books rij^ 5 cents, 8 books (»' 9 cents, and 9 books w' 7 i ents. 4. Find the cost of 8 'cows @ $25, 25 sheep @ $9, and 25 lambs @ $3. 5. Find the cost of 26 horses (T" $75» ''^>«1 75 cows @ $24. 0. Find the cost of 34 horses @ $46. i»"d 23 cows ® ^32. 7. Find the sum of 23 times $45, 45 tnnes $28, 32 times $45, and 45 times $17. 8. A gave 75 cows worth $37 each to p' for 47 horses worth $75 each. How much cash must ^ ^ay ? Exercise ia5> 1. Multiply 25 by 32, 44, 36, 26, 34, 5^, 66, 84. 2. Multiply 45 W '6. 24, 32, 36, 44, 5"' ^4, 96. 3. Multiply 36 by 15, 25, 45, 35» 55, 75, '25, ^°S- 4. Multiply 72 by 24, 25, ?8, 36, 60, 48, 78, 68. 5. Multiply 64 by 5, 25, 73. 125, 250, 750, 1250. 6. *'ultiply 125 by 24, 36, 48, 72, 32, 64, 9^, 108. .1 MULTIPLICATION. 59 Exercise ia6. 6=»3 + 3"4 + 2 = 5+i = 44., 4.1=3-1-2+ 1=3+1+3 = 2 + 2 + 2= 1+2 + 3, etc. = 3x2^=2x3 = 2x2 + 2=1x3 + 3=1x4 + 2, etc. Make statements siniilar to these about : — 2. 3.4. 5. 6, 7. 8, 9. "o. •• ""'l '2- 4 men, 8 boys, 9 men, 12 sheep, 15 lanibii. 16 hens. Exercise 127. 1. How much' arc 93's? 5's ? 9's ? 7's ? 4's? 6's? 8's ? 2. How many wheels are on 5 wagons? 7 wagons? 9 wagons? 6 wagons? 11 wagons? 15 wagons? 3. A hen lays an egg a day. How many will she lay in a week ? 3 weeks ? 5 weeks ? 7 weeks ? 6 weeks ? 4. How many sides have 3 triangles ? 5 triangles ? 7 triangles? 9 triangles ? 8 triangles? 6 triangles ? 5. At $8 a month, find my wages for 3 months? 7 months? 9 months? i year? i year and 6 months? 6. B steps two feet. How far will he go in 3 steps? 8 steps ? 9 steps ? 1 1 steps ? 45 steps ? 86 steps? 7. How long will it take one pipe to fill a vat that 5 pipes fill in 4 hours ? 8 hours ? 7 hours ? 9 hours ? 8. How many pipes will fill a vat in one hour if 6 pipes fill it in 5 hours ? 7 hours ? 3 hours ? 8 hours? 9 hours? Exercise ia8. 1. Find the square of 3, 8, 6, 7, 9, 4, 2, I. a. How much is 2= ? 3'- ? 4- ? 5" ? 6= ? 7^ ? 8= ? 9= ? io2 ? 20- ? 40- ? 30- ? 60- ? 80-' ? 70^ ? 502 ? 90= ? II-? 152? 25-? 352? 45*'? 652? 852? 752? 95a? 3. i», 2-%3*, 4^ 5^ 6=\ 7^ 8^ 9^ 2o^ 4. Give the third power of 10 ; the fourth power of 6. 6. Find6^ 5^ 4% 3", 23, 8*, 9*, 7*. 5". 2^ (, MKNTAI, AlilTHMKTIC. I f Exercise lap. 1. Find the continued product of 2, 3, 5, 4 and 7. 2. From tlie product of 25 and 36 take 27 times 25. 3. Wliat is the sum, the difference and the product of 13 and « ? 1 5 and 12 ? 24 and 35 ? 45 and 36 ? 4. Rob is 16 years old and Mary is 12. Find the difference in their ages in 8 years, 12 years, 27 years. 5. Alice has 5 (8, 9) cents more than Mary, and to- gether they have 35 (40, 63) cents. How much has each ? Exerchc 130. 1. What is the 'vnriinder when eight is subtracted as often as possilvo fr->ivi 45 ? 63 ? 75 ? 84 ? 93 ? 88 ? 47 ? 65 ? 2. I owed $8j, and paid $36 ($27, $34) at one time, and $29 ($16, $29) at another. How much do I owe yet ? 3. How much will I have left out of $99 after paying $18 two times? 3 times.? 4 times.'' 5 times? 4. The sum of threCj numbers is 70 (83, too). The first and second are 36 and 29. Find the third. 5. The sum of three numbers is 65 (82, 100). If 38 is the sum of two of them, find the third. 6. Hy how much does the sum of 83 (75, 97) and 96 (54, 82) exceed their difference? 7. I have 23 (28, 35) apples and plums. How many of each have I if there are 3(4, 7) more apples than plums? Exercise 131. Give two answers to these questions : — 1. 7 + 7 + 7 + 7 + 7 + 7 + 7- (3 + ^) + (3 ^-::) + (3 + 2)- 2. 5 + 5 + 5-5-5 + 5+5= (4 + 5) - (4 + 5) + (4 + 5)== 3. 6 + 6 + 64-124-12+12+6= (8-5) + (8-5) + (8 + 5)--- 4. 8 + 16+16 f-8 + 24 + 24 + 8-= (6x7) + (6x7) + (6x7)-f (9-:-3) + (y + 3) + (9 + 3^-= (8 + 4) -(8 + 4) + (8 + 4:- 5. 7+ i4 + -' + i4 + 7 + 28 6. 9+ 18 + 18-27 + 36 17 .= iMUI/ri PLICATION. 6i I. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. 6. 7. 1. 2. 3. 4. 6. 6. 7. 13x17 = 12x18^ 15x15- 14X 16:= II X 19 = 23x27 = Exercise 13a. as X 87 - (3 X 7 + 20 X 3qJ = 621. 53x57- 52x58- 65 X 65 a 74X76-=^ 81 x89-= 95x95 = 25x25 = 28x22 = 26 X 24 -= 35x35== 39x31 = 47x43 = 64 X 66 = 73x-7=» 69 X 6 I rra 71 X79-^ 85X85 = 92 X 98 — Exercise 133. 105x105= 153x157- 296x294= 693x697- 109 X loi = 198 X 193= 291 X 299= 594 X 596 = 106 X 104 = 199 X 191 .-- 393 X 397 -- 701 X 709 - 113x117= 196x1941^ 404x406- {92x898^ 754x756-= 999x991 = 118 X 112 = 297 X 293 = -3-1 57- 124x126= 395x305= 252x258 170x13 = 160X 14 = 250 X 25 = 290 X 2 1 = 2S0X 22 = 370x33 = Exercise 134. 530x570= 650x650= 380x330= 740x760= 9930 X 997 = 9930 X 9';8 - 9950 X 995 =:« 996< X) X 994 == 796f)X794 = 5920x50^ = 4930x497 = 990x910 = 860x840 = 460x44= 520x580 = Exercise 135. Find the cost of 26 (37, 52) cous @ $24 (S^t,^ $^R). Find the cost of 470 (5 10, 660) hor.-s (-o j 43 ($59, $6 0- Find the value of 54 (55) sheep @ $5.60 ($5. 5. ). Find the value of 193 (295) lots (f^ $197 ($29;;. What must I pay for 35 (43) cows at $^5 {$^7, $32)? Find the cost of 570 (640, 970) horses ({f> $6 ; ($;6, $$2). I low many sheep in 82 {67) cars, each 780(930] sheep ? ■W5I h i ii 62 MENTAL ARITHMETIC. i 1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. 6. Exercise 136. I9xar= -J (90-i)j2o + i) }- = {2o« - i^) =400- 1 = 399. 19x21 = 18x22 = 17x23 = i6x 24 = 15x25 = 14x26 = 29x31 = 28x32 = 27x33 = 26x34 = 24x36 = 23x37 = 39x41 = 36x44 = 31x49 = 45x35 = 47x53 = 56x64 = Exercise 137. 1. 2 3, 4. 6. 6. 1, 2. 3. 4. 6. 6. 16x24= 55x65= 48x52 = 25x35= 54x46= 63x57 = 27x33= 73x87= 82x98 = 36x44= 64x76= 39x41= 83x97 = 27x13= 64)^56= Exercise 138. Find the value of : — I i sheep $9. 550 books @ 65c. 75x85 = 34x46 = 47x53 = 790 X 8 1 = 770x83 = 780x82 = 650x75 = 630x77 = 820x98 = 560 X 64 = 470x53 = 850xq5 = 340x46 = 280 X 320= 760x840= 21 cows @ $19. 18 books @ 22c. 31 boxes® 26c. 37 cows @ $43. 76olambs@$8.4o. 530 sheep ©$4.70. 5 30 books® $6. 70. 860 hogs® $9.40. 7?oohats @ $6.80. 7800 coats @ $8. 20. 450 cows @ $45. 730 boxes @ 67c. 890 horses @$9i. 620 hats @ 58c. 54 horses @ $66. 560 lambs @ $64. Exercise 139. What change is received from $5 when paying for : — 27 books @ 23c. ? 22 books @ 18c. ? 29 hats @ 2ic. ? 25 brooms @ 15c. ? 25 caps @ 25c. ? 23 caps @ 17c. ? 28 maps @ 22c. ? 24 pens @ i6c. ? 26 pins @ 24 c. ? 19 papers @ 21c. ? 22 vases @ 28c. ? 33 pails @ 27c. ? MULTIPLICATION. 63 Exercise 140. 1. 4x25= 5x25 = = 6x 25- 7x25 = 2. 8x25 = 9x25 = = lOX 25= II X 25 = 3. 12x25 = 17x25 = = 22 X25 = 19x25 = 4. 16x25 = 21 X25 = = 30 X 25= 27x25 = 5. 24x25 = 37x25= = 34 X 25= 35x25= 6. 36x25 = 45x25= = 42 X 25 = 43x25= 7. 48x25 = 49x25= = 46 X 25= 51x25= Exercise 141. 1. 47x11 = 73x21. 87 X3I. 85x41. 37x601. 2. 65 X 11 = 65 X2I. 65 X3I. 64 X 51. 54 X 801. 3. 96 X 1 1 = 48X 21. 43 X31. 93x61. 69 X 501, 4. 75xn = 92 X 2 1 . 92 X3I- 75x71. 48x401. 5. 82X 11 = 57x21. 38 X3I. 48x81. 73x301. 6. 59 X 11 = 64x21. 47 X31. 67 X9I. 95x901. 7. 3^ < " = 86x2(. 96 X31. 36 X 1 2 1 . 86x701. Exercise 14a. 1. 392-8X 25 75X 6- 225 = 28x4- 7x4 = 2. 654- ;x 43 83 X 4- 230- 35X8- 8x21 = 3. 429 -6 X 35 = 69X 3- 107- 47X16- -16x25 = 4. 567-5 X 42 == 36 X 4- 84 = 34X 18- -16x34 = 6. 398-7 X 31 73 X 9- 137 = 27x15 -15x23 = 6. 349-4X 62 = 87>. = 5- 225 = 28x46 -28x21 = 7. 367-3^ 82 95 X 8- 360= 73x68 -53x68 = Exercise i43< 1. 26x24- 22 X28 = 21 X2! ,-20x26- = 2. 27x33- 3< X39 = 54x56-53x57 = 3. 36x44- 35 X45 = 67x73-63x77 = 4. 28x32- 26 X34- 76x74-72x78 = 5. 25 X28- 24 X25 = 83 X 87 - 80 X 90 = e. 36x25- 28 X25 = 56x64-52x68 = 7. 37x25- ■25 X33'' 56x54-25x48 = 64 MENTAL ARITHMKTIC. Exercise 144. 1. I bought 28 (45, 36) cows ( $25 ($40, $31) and sold them @ $36 ($35, $46). Find the to.al loss or gain. 2. I I'ought eggs @ II (15, 16) cents a dozen, and sold tlio;n @ 15 (13, ly) cents a dozen. Find my loss or gain 0:1 1 00 dozen. 3. I bought 72 horses (^ $96, and sold them @ $121 ($80, $112). F'ind the total gain or loss. 4. I bought 56 cows @ $47 ($35, $48), and sold tlirm to gain $23 (J25, $22) on each. What did I get for all ? 5. I sold64cows@$47($63,$55)gaining$i7($i8, $13) on each. How much did they all cost me ? 6. I bought 34 acres @ $55 and 24 acres @ $28. Find gain or loss by selling @ $40 an acre. 7. I bought 45 cows @ $27, and sold 21 of them @ $33 and tlie others @ ^25. Find total gain or loss. Exercise 145. 1. A man can row 5 (7, 9) miles an hour, in still water. How far can he row in 3 (4. 5) hours down a stream run- ning 2 (3, 5) miles an hour ? 2. A man can row 8 (9, 12) miles an hour, in still water. How far can he go in 3 (8, 4) hours up a stream running at the rale of 2 (4, 5) miles an hour ? 3. A man can row 6 (8, 9^ miles an hour, in still water, and 8(12, 12) miles an hour down stream. How far does the stream run in 4 (5, 9) hours ? 4. A man can row 9 (10, 12) miles an hour in still water, and 8 (7, 10) miles an hour, ui> stream. How far will a leaf float down stream in 2 (6, 9) hours ? 5. I row up stream at the rate of 24 (35, 48) miles in 3(5, 8) hours, and 20 (21, 36) miles in 5 (7, 9) hours, downstream. Find the rate of the stream. 6. A man rows 12 {16, 20) miles an hour, down stream, and 8 (10, 14) miles an hour, up stream. How far will the man row in the still water in 6 (45 7) hours ? MULTIPLICATION. 65 Exercise 146. 1. How many plums will I have le t out of 45 after givinfT 6 plums to each of 4 boys ? 6 boys ? 5 boys ? 2. What number taken from 100 leaves 35 ? 46 ? 28 ? 87? 54? 71? 62? 19? 49? 69? 9? 3^-^ 99? 3. Beginning at 10 rows a day and hoeing one row less each succeeding day, I hoed my turnips. How many rows were there ? 4. A train travelling 1 5 (25, 18) yards a se ond, passes a point in 5 (7, 9) seconds. Find the length of the tram. 6. B made 33 bank deposits, each $57, and drew out :i 33 on 1 7 occasions. H ow much had he then in the bank f 6. My salary is $1000 a year. I pay $4 a week for board, $10 a month for my room, and $1 a day for other things. How much do I save in a yeai ? 7. Two trains start together in the same direction at rates of 25 miles and 32 miles an hour respectively. How far apart will they be in 4 (7, 9) hours ? Exercise 147. 1. Find the difference between 64x66 and 63x67. 2. Find the difference between the cost of 34 cosvs @ $36 and 350 lambs @ $3.50. 3. If 45 times 37 = 1665, find 39 times 4;. 4. My salary is J800 a year ; my expenses $8 a week. Find my yearly savings. 5. A gets 16 cents an hour, and B 14 rents. How much will the two earn in 14 hours .? 16 hours ? 28 hours ? 6. Find the difference between the cost of 4 (5, 6) doz. oranges @ 3 for 5 cents, and @ 4 for 5 cents. 7. Two trains travel in the same direction at the rate of 24 and 36 miles an hour respectively. How far apart will they be in 9 hours? 8 hours? 7 hours ? 12 hours? 8. Two trains travel in opposite directions at the rate of 18 and 32 miles an hour respectively. How far apart will they be in 9 hours ? 1 2 hours ? 16 hours ? 25 hours ? 66 MENTAL ARITHMETIC. Exercise 148. 1. How is the product of two numbers obtained ? H. Explain 6x4 = 24. Which is the multiplier ? Name all the parts imd show their relation lo each other. 3. Why must the multiplier always be an abstract number .> 4. Show that 3 times 4=4 times 3. 5. Show that if any two of the three parts of a (|ii«es- tion in multiplication are given the other may be found. 6. What addition questions can be worked by mul- tiplication ? 7. What is the last figure of the product if one of the factors is 5 ? T ? .'' 2 .? 8. What are the partial products in a question in multiplication ? ' 9. To have only two partial products, how would you multiply by 246? 255 ? 364 ? 427? 14,412 ? 10. To have only three partial products, how would you multiply by 36,546? 63,729.? 817,299? 172,814,412.? 11. Show how to prove your answer to a question in multiplication by casting out the 9's. Show the errors to which it is liable. Give two other methods of proving your answer. 12. What is the short method of multiplying by : — 10? 100,? 1000? 25? 250.? 75? 175? 375? 99 ? 999 ? 49 ? 60 ? 98 ? 97 ? 198 ? 290 ? II.? III.? loi ? looi .? 45 .? 63 ? 72 ? 120 ? 360 ? 13. Find two numbers whose product is 6 (15, 21) and whose sum is 7 (8, 10). 14. Fi -id the product of the sum and difference of 24 and 36 ; 23 and 47 ; 64 and 32. 16. How many numbers of two figures can be written with the nine digits.? the ten figures .? 16. What numbers are factors of iS? 24? 36? 48? '.iflf'SL^-^^^ ^^'^spSf'^MSRCS DIVISION. Division is the process of finding how often one number is trlcS '" ''""'"■ ^' '' " '^"^' "^^^^'^'^ "f repeated sub The Dividend is the nunilwr to be divi(Jed. The Divisor is the ni-mljcr by which wc divide. The Quotient is the numl)or which shows how often the divisor IS contained in the dividend. The Remainder is the number which is left after the divisor nas l.een taken as often as possible from the dividend It IS always similar to the dividend. T is the sign of division, and when placed l>etween two Tecondr "' ""^^ '^^ ^"' """'^'"^ " '« ^ divided by the 6-r a = 3, is read, '• six divided by two, equals three." «vo^i ***•*""" C^ "" numl)er is a number which will divide it exactly, i.e., without a remainder. exaSl^"**'**'"°^^ ""'"^'^'' '"* """"''er which will contain it Cancellation is a process of shortening division by remov- ing equal measures or factors from both divisor and dividend. ..l,v3 K* *5",f'* ^n°* "[* 'l»fn'»y '" the number which, multi- phed by Itself, will pro, $33^ $35, ^n^ $5', $55> $53. ^11^ $99, $75, $57- Exercise 151. 1. How often can vou subtract 2 from 2? 4.? 8? 10.? 14? 6? 12? 18? 16? 20? 22? 24? 40? 80? 5.' 9.=" II ? 17? 2. Find tlie cost of one acre, if 2 acres cost $2, $4, $8, $6, $10, $14, $18, $12, $16, $20, $40, $60. 3. How many span are 4 horses ? 6 horses ? 8 horses.? lo horses? i6hors^es? 20 horses .'' 18 horses.? 14 horses? 4. How many twos are in 4 ? 8 ? 6 ? 10? 2 ? 14 ? 18? 16? 12? 20? 22? 24? 40? 60? 80? 42? 62? 84? 5. Will earns 2 cents a day. In how long will he e trn 4 cents ? 8 cents ? 6 cents ? 12 cents ? 1 4 cents ? 18 cents ? 6. Find I of $6. $10, 8 sheep, 12 lambs, 20 cows, 21 mice, 25 trees, 27 logs, 29 pounds, 31 acres, 33 yards. 7. Find I of 6, 8, 12, 16, 18, 20, 24, 30, 36, 40, 48 ; of I, 3, 5, 7', 9, 'I, '3, 17, 21, 27, 41,43, 35, 37, 59- Exercise 152. 1 •-» _i_ 2 =7 2. 4-^2 = 3. 8-r2 = 4. 64-2^ 5. 0-r2 = 6. 10-r2 = 7. 12-^2 = $4-2=: $6^2 = $2-=-2 = i:8-2= ^4-^2 = i:6^2= $8^2= 20 -r 2 = 60-4-2 = 40-f2 = 80 -7-2 = 244-2 = 42-7-2 = 86 -r 2 = 46-4-2 64-4-2 28-4-2 82-4-2 48-4-2 84-4-2 88^3 $10-4-2 $12-: 2 $:4-2 $18-^2 $16-4-2 $20-^2 $22-2 • DIVISION. 69 Exercise 153. 1. I-i-2= ■ $.^2 = 2l-r2 = IO-T-2 = 31^2 = 2. 3-^2 = J5-2 = 23-f2 = 30-^-2- 33^2 = 3. 5-7-2 = $3-2=^ 29-^2 = 50^2 = 35^2 = 4. 7^2 = $7^2 = 27^2 = 70-^2 = 55-1-2^ 6. 9-2 = $9-^2 = 43-^2 = 90 -i- 2 = 77-^2 = 6. II-^2 = $13t-2 = 45-^2 = I IO-r2 = 99-^2 = 7. 13-^2 = $154-2= 67^2 = 113-^2 = 57-^2 = Exercise 154. 1. What number added to itself will make 8 ? 6 ? 12 ? 4? 10? 8 horses? 4 cows ? 6 sheep? 10 lambs? 12 deer. 2. How many will each get, when Will shares 4 anplcs with Alice ? 8 apples ? 12 apples ? 6 apples ? 16 a|)|»les ? 3. How many letters can I jiost for 4 cents? 6 cenis? 8 cents ? 10 cents ? 14 cents ? 1 3 cents ? 9 cents ? 4. How many apples in 4 halves ? 8 hiilves ? 6 halves ? 10 halves ? 14 halves ? 7 halves ? 9 halves ? 5 halves ? 5. How manv 2's in 3 ? 5? 11 ? 9? 15? 13? 21? 27? 29? 41 ? 63? 85'? 31 ? 33? 35? 37? 39? S3? 51 ? 59? 6. How many paiis in 6 shoes? 8 shoes ? 10 shoes? 4 shoes ? 12 shoes ? 20 shoes ? 18 shoes ? 14 shoes ? 7. At 2 pluiTis for a cent, how much must I pay for 4 plums? 8 plums? i6.plums? 14 plums? 12 plums? Exercise 155. What is one-third of: — 1. $3? $6? $9? $.2?$i5?i;i8? ;^24? ^27? £21? 2. 6 sheep? 12 lambs? 15 hens? 18 ducks? 24 bells? 3. 9 stars ? 3 suns ? 6 moons ? 2 1 la^ es ? 33 ponds ? 4. 7 cents? 10 cents? 16 cents? 19 cents? 25 cents? 5. 5 pears ? 8 pears ? 1 1 pears ? 1 7 doz. ? 23 doz. ? 0. ^30? ;^6o? /90? 150c.? 180C. ? $2 10? $2.40? 7. $300? $330? $360? $4.50? $4.80? $6.30? $6.60? MENTA! ARITHMETIC. Exercise 156. 1. 3^3 = 304-3 = 74-3 = 84-3 = 45-^-3 = 2. 6-r3 = 60-7-3 = 104-3- 114-3 = 484-3 = 8. 9-^3 = 904-3 = 16^3 = 144-3 = 424-3 = 4. I2;-3 = 33-^3 = iS^S-^ 23^3 = 75^3 = 5. '5^3 = 3ounds 7. 28 men. 36 feet. 128 rods. j6 tons. DIVISION. 71 1. 124-4: 2. i6~4 3. 24-^4^ 4. 20-r4 = 6. 28-r4 = 6. 36-4 = Exercise 159. 44^4= 64^4= 240-r4 = 68-5-4-^ 360-7-4 = 92-^4- 284-^4 = 72-=-4- 488^4- 76-r4= 5y6-r4 = 96-7-4= 972-^4 = 3-!-^4 = 88 -r4- 84-7-4 = 48^4- 52-r4 = 56-4-= 58-4= ioo-h4= 936^-4 = 664 -^ 4"! 628 -=-4= 736 -r 4 = 752^4= 956 -f 4 = 948^4= 742 ^4 » Exercise 160. 1. IIow many fours are in 8? 12? 20? 16? 32? 28? 40? 44? 48? 36? 24? 400? 800? 200? 100? 2. At 4 for a cent, what will 8 apples cost ? 12 plums ? 20 pears? 16 flowers? 28 pens? 24 cards? i doz. eggs? 3. Find } of $8 ; 12 cents ; 20 cows ; 28 sheep ; 16 acres ; 32 yards ; 40 minutes. 4. How long wrtuld it take 4 men to do a work that one man can do in 12 days? 16 days ? 32 days ? 24 davs? 6. How much have I left after spending } of $8? $12 ? $20? $16? $24? $32? $40? $400? $360? $240? 6. At $1 each, what must I p ly for 4 books? 8 books? 12 hens? 20 hens? 24 ducks ? 16 ducks? 36 knives? 7. What number added to itself 3 times will make $8? $!6? ;^2o? ;^24? 36 sheep? 48 cows? 40 boys ? Exercise 161. 1. 16^2= 15-7-2= 28-^3= I3-^2 = 2. 18-7-3= 16^3- 17^2= 28-^3 = 3. 24-r4-- 21-^4= 21^2= 25-^3 = 4. 15-7-3- 27^4^ 26-7-4= 297-4 = 5. 184-2=^ j,^:-i=: 33-f4= 29^3 = 0. 21 f 3- 207-3= 35^3= i6-r2 = 7. 28-=-4- 30^4= 35-^4- 3^-^-4 = 325^3^ 2I7-r2 = 420-7-4 = 6i8-f3 = 4l2-^2 = 832-^4= 836-^-4= 72 MKNTAI, AUITHMKTIC. Exercise i6a. 1. At $2 each, how many himbs can I buy for $8? Si::? $i6? $2of $25? $27 1 $23 t $47? $05? $89? J35 ? 2. What is the laiK<'J>t number which can be sub- traded 4 times from r6? 20? 28? 32? 24? 36? 48? 40? 3. What number added to itself 2 times will make 6? 9? 15? 24? 12? 18? 27? 36; 39? 48? 60? (;o? 120? 4. How much does eadi get, when Will shares 8 plums with his three brothers? 12 plums ? 20 plums? 5. Will earns 2 cents a day. In how lontf will he earn 4 cents? 8 cents ? 6 cents ? 12 cents ? 14 cents ? 6. How many pears in 3 thirds? 6 thirds? 9 thirds? 15 thirds? 24 thirds? 3otiiirds? 45 thirds? 60 thirds ? 7. What is the cost of 6 apples <^ 12 cents a doz. ? 16 cents? 20 cents? 24 cents? 14 cents? 25 cents? 8. What is 25 cents' worth of sugar at 16 lbs. for $1 ? 20 lbs. ? 24 lbs. ? 12 ll*>s. ? 32 lbs. ? 14 lbs. ? 18 lbs. ? Exercise i63. 1. Divide 5 into 10, 15, 25, 30, $20, $35, $40, $30, 25 sheep, 30 cows, 35 hens, 40 acres, 50 pins. 2. How many 5-acrc fields eq al 10 acres? 20 acres? 15 acres ? 25 acres ' 35 acres ? 45 acres ? 40 acres ? 3. Find the five equal adden 2. How often ran 6 be siil)ira« ted from 12? 18? 30? 36? 24? 48? 42? 6j? 420? 480? 540? 720? 3. How m-Miy times $6 is $1 2 ? $iS ? $xo ? $-»6 ? $24 ? $42? $60? $4S.^ J54? S66? $72? $84? $246? $276? 4. At$i .1 day how many weeks wouUI I bo earninif $18? $24? $36? $48? $30? $:,o? $54? $42? $06? $84? 6. What is the weij-ht of r ham if 6 weigh 24 lbs.? 36 lbs. ? 43 lbs. ? 48 lbs. ? 72 lbs. ? 84 ll)s. ? 96 lljs. ? 6. How many weeks in 12 workinj^ davs ? 18 days? 30 days ? 24 days ? 36 days ? 48 days ? '27 days ? 7. How many hours in 60 niin. ? 120 miii. ? 240 min. ? 360 min. ? 300 min. ? 480 min. ? 600 min. ? 6 )0 min. ? 8. How many feet in 16 halves? 21 thirds? 24 tjuar- ters? 45 fifths? 63 i.-nilis? 72 eighths? 10 quarters f Exercise 165. 1. How much is } of $14? $7? $21 ? 35 ? 42? 63? 49? 28 acres ? 35 quarts ? 56 inches ? 70 yards ? 2. How many times 7 bovs are 14 boys? ?.i bnvs ? 28 boys ? 42 boys ? 56 lioys ? 49 boys ? 35 boys ? 63 boys ? 3. How long would it take 7 men to do a work one man can do in 14 days ? 28 days ? 2 1 days ? 35 days ? 4. What is the size of a flock, if in 7 flocks there are 21 sheep? 35 sheep? 49 sheep ? 56 sheep? 7osIieep? 6. How many weeks in 7 days ' I4davs? 42 davs? 35 days ? 21 days ? 25 days ? so d'a\ s ? 40 days ? 50 days ? 6. A boy earns $16 a month and spends $9. How lonjr would he be saving $28 ? $21 ? $35 ? J49 ? $63 ? 7. At what pri(e will 7 yards of print cost 49c. ? 63c. ? 84c. ? 70c. ? 77c. ? $63? $.56? $.28? $1.40? 8. How many times is 7 contained in 49 ? 63 j,6 ? 70? 42? 45? 50? 60? 65? 75? 80? 85? 90? 100 .> 145? 728? 74 MRVTAL ARITHMKTir. Exercise i66. 1. What is 1 of 8 ? 16? 24? 4o? $32? /40? ^48? 56 Iambs? 04 tows? 80 horse-. ? 72 lambs? 32 boys? 2. How \n:\nv sliL-cp at $8 are worth $16? $21? $48? $3^? J40? $80? i64? $48? S/2? Sj6? 2. At 8 poiiiuls uf sujiar for $1, what is the tost of l6 lbs. ? 3i lbs. ? 24 Ibb. ? 48 lijs. ? 40 lbs. ? 64 lbs. 4. At 8 miles an hour how lonj,' vou'tl a horse take to go 16 mi. ? 32 mi. ? 24 mi. ? 40 mi. ? 64 mi. ? 80 mi. ? 6. What is the sharo of each, when 3 sons and 5 daughters Kct $32c)o c $2400? $4iHK>f $6400? $4800? 6 Whit is the (|iioii(;iit when the divisor is 8 and the dividend is 16? 24? 48? 32 ? 40? 80? 64? 72 ? 96? 7. How many flocks of 8 lamljs tan be made of 24 lambs? 32 lambs? 16 lambs? 25 lambs? 30 lambs? 8. How long wouldit take 16 men to do a work 2 men do in iG days ? 22 days? 24 days ? 8 days ? 72 tlays ? Exercise 167, 1. What number multiplied bv 9 gives 45 ? 36 ? $Si ? $63 ? £72 ? £s4 ? 27 yds. ? 90 ft'. ? 180 miles ? 9r8 qts. ? 2. How many 9-acre fields in 63 acres ? 72 acres? 81 acres? 54 acres ? 450 acres? 3r}o acres? 945 acres? 3. How many eggs 0^ 9c. a doz. are worth 270. ? 36c. ? 18c.? 45c.? $.63? $.72? $.54?S4.5O!'*3-6o?$i8?$30? 4. How many times must 9 be taken to make 45 ? 63 ? 36? 8i? 9181* 927? 999? 909? 936? 864? 756? 567 f 5. How many times must 9 be added to itself to make 36? 54? 45? 63? 27? 72? 18? 81? 108? 396? 468? 6. At 3 lambs for $27, how many would I get for $iS ? $81 ? $27? $72? $45 ? $54? $369?' $396? $963? $936? 7. Find the average of 6 l])s., 8 lbs., 9 lbs., 5 lbs., 6 lbs., 6 lbs., 7 lbs., 4 lbs. and 3 lbs. 8. How often can you subtract 9 from 63? 72? 81 f 99? 54? 45? 270? 450? 3O0? 405? 648? 873? DIVISION. 7S Analysis. Exercise 168. What is the price if : - 1. 4 sheep cost $2>? $24? ii2} $40? $36? $64? $73? 2. 3 Iambs cost $15? $24? $V>? $j6? $45? $''>3? $37? 3. 5 calves cost $20/ $j-f ^45? $4"? $3"? $6o?$ic»? 4. 7 lbs. roHt 3IC. ? 35c. ? 28.:. ? $.63? $.42 ? $.49? S.56? 5. 8 yds. cost 32c. ? 64c. ? 4Sc. ? $.72 ? $.88 ? $1 .28 ? 6. 6ei,'yscost 18c. ' 12c.? 54c.? 3f>^- ? $48? $24? 7. 7 quarts cost ;' . .' iSc. ? 45c. ? $.36? $ ^3 ? $'-o8 ? txeiclse i^). 1. If 2 sheep cost $S ($10. ^'.), uh.it will 3 sheep cost? 2. If 2 books cost l6 (1 JM n.-. '. V"m<\ cost of 5 lbs. 4. What arc 3 stamps worth if 5 < osi 25 (15, 20) cents? 6. 4 parcels weigli 20(12, 10) lbs.; what will 6 weigh? 6. What will 8 pens cost, if 6 pens cost i3 (6, 18) cents? 7. If 2 (4, 5) yds. cotton cost l«) (20, 30) cents, wh.if will 3 (5, 4) yds. cost? 8. If 6 (9, 12) tons of coal cost .$42 ($40.50, $78), what must be paid for 7 Ions of coal ? Exercise 170. What is the remainder when you ilivide each of the following numl)ers by 2 ? 4? 3? 6? 8 ? 9.? 7 ? 5 ? 1. 359,648,721. 53>%462,97i. 187,369,524. 2. 432,7'/^ 185. 284,396,157. 642,183,975. 3. 875,364,912. 962,471,538. 537,814,296. 4. 768,419,253- 375,246,819. 863,451,792. Write down the quotient as it is obtained. Write down each successive remainder. 76 MENTAL Alv'ITHMETIC. I' Exercise 171. Ibs^'cos??'''"' '^"^^ ""'' '^ ^^°"^5) c, wluit will 4 (5, 6) llicoLV'' ''''''' '^"'^ ^' ^''' -»"> '••' ^'^''^^ -'» 3 (5. 9) shfepUsfr "" '°'' ^'5 ^^^5. $4S). What will y (6, 8) 4. I paid $r6 ($r2, $::o) for 4 cords wood. Find the cost of 5 (7, 9) cords at the same ,,rice. 5. I paid 18 (30. 24) rents for 6 bottles of ink What should I pay for 8 (7, 9) bottles of ink ? ** 6. If 7 (8, 9) sheep sell for $35 ($64, $t^) what will I get for 9 (1 3, 1 1) sheep ? -^^ ^ " •*' '>54A wnat will I Exercise 172. woulcll'f ^l ^^ "'^" ''° '"^ Y"'-'' •" '^ (^' «) f'avs, how long would It take one man to do it ? ^ 2. If 8 (3, 4) I)oys can saw . ord of wood in ^ (- -\ hours, how long would it tak. , •. boy to saw ii" ^ ^" '^ wood "r /""fxr"'^'' .^^!^^ °"? '"■'" to split a cord of wood, If 2 (s, 8) men do it m 20 (16, 8) minutds? 4. If 4 (6, 9) men do a work in 3 (4, 4) hours ho«- long should It take 6 (8, 12) men ? ' lon^* slfould 6Vx^ S''' ,'T ^ ''""* '" ^ ^'^' =) '^«"'-^' »«»"•• long siiouiu (8, 6) girls be sewing it ? 6. If 2 (6, 7) men do a work in 10 ra cWla, « k.v,. long >s needed by 5 (8, 5) men ? ^^' ''* ^ ' ''"^^ 7. If it requires 8 (9, 6) days for 6 (4, 7) men to do 1 work, ,n how long would 16 (12, 3) men do it ? 8. If 18 (17, 16) lbs. of tea cost $.7? ($r.7; $- -r,\ rnore^than,5(i3, .0) lbs., how much wil^a^bsfohuch DIVISION. ~7 Exercise 173. 1. If 5 (6, 8) yards flannel cost $1.00 ($1.80, $2. jo). what will 7 (9, 6) yatds co.t ? ' -^ t h 2. If 7 (9, 8) yanis tweed cost $2.80 ($4.50, $3.60), what must I pay for 8 (7, 1 r) yards? i^'i!'^ / ^l\?^ '^''"'"^ '-■''''' ^'•5'^ (^'-"5. $-36), what should 5 (9, 8) books cost ? 4. If 52 70 90; cents pay for 4 (5, 6) books, how mucli should I pay for 6 (7, 4) books ? 5. If $i.8o($3.2o, $4.50) pays for 5 (8, 15) do/, buttons, liou' many can be bought for $1.50 (.{4, $9, ? 6. If 15 (20, 21) calves cost $75 {Uo, $126), how many calves ca 1 I buy for $ioo ($200, $150)? 7. If i6(iS, 13) dozen eggs cost $1.28 ($2.70, $1.41), how many can be bought for $.S ($4. 50, $22)? Exercise 174. 1. If 16 (24. 32) men Iniild a barn in 8 (10, 4) days how long would it take 4 (6, 8) men to build it ? 2. If 12 (15, 25) boys saw n pile of wood in 12 (20, 20) days, in what time would 6(12, 20) boys saw it ? 3. How long would it take 7 O2, 8) men to complete a work 21 (24, to) men could do in 10(5, 9) days? 4. If 12 (15, 50) boys can do a work in 7 (5, 4) days, in what time would 42 (25, 40) boys do it ? 5. How long should 3 (40, 9) bovs take to d > a work 9 ('6, 27) boys can do m 9 (20, 10) hours? 6. In how many weeks would 14(20, 12) men do a work tiiat 7 (5, 18) men can do in 6 (8, 4) weeks ? 7. If 9 (15, 40) bovs do a work in 12 (lo, 12) davs how long will it t ike 6 (25, 48) boys to do it ? ' ' 8. If 3 ducks are worth 4 hens, and 5 geese are worth 10 clucks, find the price of agoo^e, if hens arc worth 75c. i I \ I 78 MENTAL ARITHMETIC Exercise 175. 1. 1/6 (7, 6) men earn S24 ($21, $60) in 4 (3, c) days. how miK-.h should 5 (9, 1 1) men earn in 5 (2, 3) days ? 2. 1 earn $rs (SiH; $42) in 3 {4, 6) days. How much should 9 (7, 5) men Kurn in 5 (6, 7) days? 3. 3(5, 6, men earn $6 30 ($25, $15) in 2 days, how much should 8 ^4, 5) men yet for 5 (3, 6) days ? 4. It 3 (^, 3) fields, each 5 (lo, 9) acres, cost $300 ($4cxj, $1 o.Su), find cost of 5 fields, each 4 (6, 8) acres. 6. 1/4(7, 9) Ijaskets, each 7 (9, 8) lbs. grapes, cost $i.4o($4.4i, 15.76), what will 5(6, 8) baskets, each 8 lbs., cost ? ,^^Ji,'^i^\^^'^^^''^'''^^'^^ 5(^ 5) il>s- tea, cost $8 (*9, $16), find cost of 5 (6, 9) ( addies, each 8 (4, 6) lbs. 7. If 5 men working 8 (9, 7) hours a day, do a worV in 3 days, how many day^ of 10 hours would it lake 4 men? Exercice 176. 1. Find the cost of 16 (24, 32) pears @ 4 for 5 cents. 2. Find the cost of 9 (15, 24) sheep @ 3 for $10. 3- If 3 (4. 8) pens cost 10 cents, what will 12 cost ? 4. If 5 (10 20) cents pay for 12 pens, how many will 1 5 cents pay for ? 5. If 3 (7, 9) boys earn $10, how much will 12 (14. ^6) boys earn ? \ •»» j / 6. I can walk lo miles in 3 (4, 6) hours. How far can 1 walk ni 12 hours ? 7. If 3 (5. 7) men do a work in 5 (8, 10) days, how many men could do it in 15 (5, 14) days? a If ij (2, I) of my money is $10 ($12, $16), how much have I ? ^- ^[ ? (i §) of my flock is 15 (20, 25) sheep, how many sheep have I ? .»/ r» 10. If I (}, 2) of a pound of butter cost 12 (8, 9) cents, what wiU 2 pounds cosi ? DIVISION. 79 Exercise 177— Sharing. 1. Divide 24 (36, 84) cents equally between A and B. 2. Divide 48 plums equally among 3 (4, 6, 8) boys. 3. Divide $36 between A and B, so that A may have 2 (3, 5, 8) times as much as 15. 4. Divide $48 between B and C, so that C may have ^ (3. i ^) '^s 'T^"ch as IJ. 6. Divide 12 (42, 48) cents amonj( A, H and C, giving B z (3, 3) times, and C 3 (3, 4) times, As share. 6. Divide $21 ($49, $63) aujong A, H and C, so that B may have twice as much as A, and C twice B's share. 7. Divide $40 ($64, $96) amon^ A, B and C, so that Bs share may equal C s, and As may equal both. 8. Divide 28 (63, 84) cherries equally among 4 boys and 3 girls. 9. Divide 56 (66, 63) plums among 2 boys and 3 girls, giving a girl 2 (3, h) times a boy s share. Exercise 178. 1. Divide $5 ($15, S25) equally between P and B. 2. Divide $25 ($50, $75) between A and B, so that A may have 3 times as much as B. 3. Divide 21 (24, 36) sheep between A and B, so that A will get 3 15, 2) as often as B gets 4 (3, 7). 4. Divide 54 cents ($.72, $12) among A, B and C, so that A will have 2 cents as often as B gets 3 cents, and C gets I cent. 5. The sum of two numbers ie 45 (88, 90). (3, 4) times the other. Find each. 6. The sum of three numbers is 77 (Si, 99). is 2 (3, 4) times the second, and the se( ond is great as the third. Find the three numocrs. 7. Find the wages of each, if 2 men, 3 women and 4 boys earn $9 ($10.80, $36), and a man earns twice as much as a woman, and a woinin twice as much as a boy. One is 2 The first 2 times as M, 80 MENTAL ARITH.%fETIC. # Exercise 179. 1. Diviue$9($i;;, $27) between A and ?>, so that B \vill have $3 more than A. 2. L»i»ide 28 slieep into 2 flocks, one having 4 (^;, 6) sheep irore than llic other. 3. Divide 47 apples between Will and Rob so that Rob wdl hav : 5 (9, 11) less than Will. ,.'^- •'^.^"^ '^ ^•'^'■""^ ^'5 (5=7, $45). A earned $5 (J3, $13) more than B. How nnuh diil each earn? 5. Divide S2S ($38, $54) anion- A, IJ, and C, so that A may have $3 ,$2, $3) mure than B, and B may have $2 ($3, $3) more than C. 6. Divide $31 ($64, $91) a :ionK' A, B, and C, so that A may have $5 more than B and $5 less than C. 7. The sum o( three numbers is 16 (46, 57). The first is 3 (4, 2) less than the second, but 2 (3, 5)'greai.r than the third. Find tlie three numbers. Exercise 180. 1. I bought an equal number of 2-cent, 3-cent and 5-cent stamps, paying $.80 ($3.60, $5). How many of each kmd did I l)uy ? * ^; ' •''V^^''^4('h2o, $144) in an equal number of $1, $2, .^4 and S5 bills. How many bills iiave I ? 3. I have an equal number of 5-cent, lo-cent and 25-cent pieces. If all are worth $1.60 ($2.80, $8) how many coins have I ? 4. For 15 (22, 3G) cents I can buy 4 peaches and 3 pears, paying two cents more for a peach than a pear rind price of each. 5. Divide 3s (48, 65) plums amon^ 5 bovs and 4 girls giving each girl 2 (3, 5) more than each boy. 6. A man gets $2 a day more than a boy, and 4 men and 8 boys get $20 (J14, $26)a day. Find wages of each. 7. Geese are worth $r more than ducks. Find price of each, if 4 ducks and 2 geese cost $5 ($8, $6.50). DIVISIOW. 8i 1 Exerctee i8i. 1. 2. 3. 4. 5. G. 7. (6 + 4) + (3 + 7)-(5 +''')= 7xS + 9H-3-^JX4- (9-3) + (8+4)-(7-2)-= 5x6 + 8x3-284-4-= (7+^')-(7-3) + (8-^-)= (9x8)-^(7-3)-=-(45^9) = 7x6-7-3 + 8-6= i6x i2~3X4x(36-:-4) = 7 4(8 -6) (9 -4) - 15 = (6 x9) + (9 + 3)+(i2 + 2)- 9-6 + 7-(3+^')+9= (6 + 9 + 3) (14x12 + 84)=: 8-(3 + 4)-(8-7) + 5^ (.8- 12 -3) (27 + 36+ 12)^ Exercise 182. 1 1 r f ! 1. A man is 4 limes as old as his son, and ihc sum of Uicir ages is 30 (35, 45) years. P'ind a-^e of tlie son. 2. .\ man is 5 times as old as his son, and the sum of their ages is 42 (48, 60) years. Find the fathers age. 3. A man is 6 times as old as his son, and the sum of their ages, is 21 (35, 42) years. Find age of each. 4. I am 7 times as old as my son, and the difference in our ages is 30 (36, 48) ye;us. Find our ages. 5. A boy has 3 (7, 5) sisters and 4 (5, 9) brothers. How many children are in the family? 6. I bought the s unc number of lambs (^ $4 and calves @ $5. How many f each di I I buv Uy $1 S ? $V) ? $ >! .> $450.? $720.? $900? $963? S072? $954.? $828? $756? How many animals did I buy .'' 1. (2+3)X2^ 2. (7 + 4)x4 = 3. 4. 5. 6. 7. (7-4)xS- (9~ 3)X7== 6x4+3- 6+4+2= 8-6+2- Exercise 183 (2-r2)x(3 + 3)- (5 + 2)x(6-4) = (7 -4)x(9-5)- (9xS)+,8 + 4)- (8x6) + (9 -6) = (8x6) + (6x4^=: 6x4+8+2-5= 9x5 + 9 :-3- 8--- 8 — 2 X 3+ 16 + 4 - (9x8 -6x5) + 7== (6x7) (|X I2) + I4-= (9-3)(6f4)+i2 = (9X.2)-(6x6)= (9-5)(8 + 6) + 28 = mm 83 AfENTAL AI 6. Sam gave away 6 apples. What part did he give* .fhehad ,2 apples? ,8 apples? 36 apples? 24 apples ? «..TrK '*''''/ ^"''''- '^^'*'«' P'-^'-t "f his farm did he sen. ,f he has ,6 acres left ? 24 acres ? 32 a, res ?74 acles' ■^Z S'.'''^'; ''^.^""'T /■'" "^«^l 24 shoe* ? 48 ' ioes ? 64 shoes 1- 54X7-m8 = 2. 63x5-21 = 3. 72 xg-i-27 = 4. 48-M4i-42 = 6. 96X I2-r64 = 6. 56x5-^70= 7. 84x7=^-49 = 56 shoes? 96 shoes? Exercise 186. 28 X 1 4 f 56 ^ 3r)X7-F43^ 51x8-34- 35x9-^45- 32X7-F56 = 40x24-1-84 = 72X l8-r8l-= 88 shoes? 35x24-^60 = 48x25-=- 30 = 48x27-32^ 56x15-^35 = 56x15-1-40= 64x9-^-96 = 75x33-^55- .T-I-C-Cft.lBEE DIVISION. «3 ExerciM 187. Fill the blanks properly : — Dividend 1. 36 (40, 45) 2. 35 (40, 45) 3. 50 (56, 63) 4. 45 (37, 49) 6. 36 (45. 50) 6 7 Divisor 2 (3, 4) 5 (6. 7) 7 (8, 9) Quotient Remainder 3 ( '44. '21, 400, 900. 1.600, 2,500, 225, 65. 2. I paid $.64 ($1.44, $2.25) for a number of ImkiUs @ as many cents each. Find the iumil)er and the pin «. 3. What is the square of 99? 97? 49? Sg? (n.)': 101 ? 102.' 103? 201 ? 202? 35? 45? 85? 75? 115? ii-~: 195? 395? 999? 9999? 4. Give all the numbers less than 100 which a«r per- fect squares. 5. If 6 (5, 8) times the square root of a number ih 42 (66, 72), find the number. 6. I divide the square root of a number by 4, and the quotient is 2 (3, 5). Find the number. Exercise 189. Add, subtract, multiply or divide in order. 1. 7x8 + 4-r5x6-2X2 + 4-r l2X5+4-r8= . 2. 9X7+i-f-8x9 + 3-f-5X2-»-6-r6x7 + 7 + i-4-2 = 3. 5X7-|-I-i-4X9- I^IOX6 + 2-r5T-2X9-r3 = 4. 8x4-2 X4+ r -ri I x6^2- 1-^8 x7-8-r 10x9= 6. 6x7 + 8-1-2x4-10-9-^9x54-4-^7x4 + 2 = 6. 5x9-1+4x6-2+8x9+8+4+5x6+1x4= 7. 8x9+5+7x4-2+7x3+7+5x9+3+8-6- 84 MKNTAI, AUIIflMKTIC. i 1, 2. 3. 4. 6. 6. Exercise 190. Coinpaic in as many ways as you can 3 ;ind 5. 4 and 7. 6 and 8. 5 and 9. 7 and 9. S 'd7. 3 and 4. 3 ii«ui 9. 4 and 8. 2 and 8. 3 and 6. 3 and 9. $4 and |6. S3 anil $7. $4 and $9. S5 and $S. $6 ami $9. $3 and 38. 58 and $24. $7 and $28. $9 and $18. $6 and J30. $5 add $35. $4 and S28. Exercise 191. had 7^r.^-n.f? ^'^n''^ "'"' '" "'.'.''."f 5 (8, 7) lx)ys, and nai» 7 U, j) left. How many could have received 3 nuts > 2. A walking 28 miles a day, is 27 {33, 63) miles ahead ot n. How fast must H walk to overtake A in 3 days? 3. A train 56(98, F26yyards long is moving 14 yards a second. How long will it be passing a point? 4. I Iwiight 2| sheep for $140 ($17:, $-.76) and snlrl the-n for $.64 ($.33, S.88). Fitd .u'e?;ge"'gain Sf loss wf; ^ ^I'-'^Va?/''!",' ^^'"^ Will was 3(9, 8) times as old as Mary, t md Will's age, if Mary is now 12 years old. 1, ? "jI: ^'''^ "5 /^ "P' ^"'^''^ ^-f-So. find the cost of 4 hats and 6 caps, 16 hats and 1 2 caps, . 5 hats and 1 5 caps 7. If a barrel of flour lasts 8 people 6 weeks, how many i>eople would it last one week ? 2 weeks' ^ weeks? 4 weeks f 8 weeks ? 1 2 weeks ? 16 weeks ? 24 week. ^ 1. 2. 3. 4. 5. 6. 7. .J of I 2 + 4 — ?{ of 15+6 = ; of 24 + 7 .. i of 25 + 8 = .! "<"35 -3 = iof45 C> = H of 72 - 5 = Exercise 193. fj of 15 4-6 = ^ of 16 f 7 = ^ of 20 + 8 = § of 42 -7 = i of 42 -6 = A of 3: -9 = i' of 81 -7 = •3 of $20 + $8 = j; of $28 + $6 = ij of $40 + $7 = fl^ofJ45-$9 = .; of J63 J4 = •2of$9r'-$8 = ^' of $96 - $7 = DIVISION. 85 Exercise 19,1. 1. What are the factors of a numlicr ? Write down 8 numbers, less than 20, which have no factors, 2. Resolve 15 (21, 36, 60) into its prime factors. 3. Write down the «(>iiiposite numbers less tlian 20. 4. What number taken from 25 will kavc a remainder exactly divisible by 4 ? 6? 8? 7? 9? 6. What number added to 37 u ill give a multiple of 3? 7? 8? 6} 9.? 5? 4? 10? 6. ,"0 of a scores how many times \ a dozen } 7. The product of two numbers is 175 (jco, 7'>n\ One of them is 5(15, 9). Find the other. 8. What numi)er divided b/ 5, and the i|uotient divided by 6, and that quotient divided Ijy «, yives a result of 12 ? Exercise 194. 1. How many strokes does a clo( k, striking the hours, strike in 12 hours? i day? ( week? 2. How much frinj-e will be needed for a table-cloth 9 (8, 12) feet long and 6 {7, 8) feci wide ? 3. H's age is 7 (5, 8) times C'sage. Find age of each if the sum of their ages is 32 (42, 54) years. 4. How old am I if 4 times my age + 7 times mv a<'c IS 44 years ? ' " 6. A runs 10 (15, 20) yards while B rm-s 8 fi2, 19) ywrds. How far will B be behind in a loo-rod race f 6. A has $7.50 (^4.80, $15) and B has § (J, I) as much. How much have the two ? 7. If 4 (5, 6) men ran mow a field in 5 (8, 7) dajS, how many men can mow 4 fields in lo 18, 2c) days? 8. Charlie shares 30 (36, 66) cherries equally with his 3 brothers and 2 sisters. Find share of each. 9. A boy !)uys apples at 5 cents a dozen and sells them at 3 (3. 6) for 2 (5, 5) cents. What is his gain on 3 dozen ? 6 dozen ? 84 apples ? 108 apples ? 8c MENTAL ARrTHMKTTC. Exerc3«e 195. 1. 36+4-9. Name each ofthe parts of this question, and show the relation of each to the other. 2. VVhen can subtraction questions be worked by division ? Show that addition and inulliplicaiion are the converse of subtraction and cr is of one denomination. A Compound nuniljcr is composed of more than one denomination of the sume nature. Similar mmiltets are tiiose of the same denomination. An Aliquot Part of a number is a factor of it : as6Jscfij; 25 cents is of $1 ; 53. is of ^^"i. Reduction is the process of reducinj; a number to one of some other denoniiafclion. Reduction Descending is the i)rocess of reducing a nundier to one of a lower dcnominatioji vvi1liiM.11 altering the value. Reduction Ascending is ilie piocess of reduoing a numlicr to one of a hij^her denominatiun. Simple ad'lition, subtraction, multiplication or division is the proc ss of adding, subtracting, nudtiplying or dividing simple luiinbers. Compound addition, 'subtraction, multiplicuion or division, is the process of adding, sublraciiiiij, multiplying or div ding, compound nuinljcrs. The dimensions of anything is its measurements according to the standard unit of lenj;ili. The multiplier nuist always be an abstract numlier. The divisjr may be a!»s'ract or denominate, simple or coinix>und. 87 ■ i MICROCOPY RESOLUTION TEST CHART (ANSI and ISO TEST CHART No. 2) 1.0 I.I |i.O US ■ 2.8 |2.5 1^ 12.2 13A L4.0 I III 1.8 1.6 ^ APPLIED IM/IGE Inc S^ 1653 Eosl Mgin Street r^ Rochester, New York Ufi09 USA ^= (716) 482 - 0300 - Phone S= (716) 288 - 5989 - Fax 88 M KNTA f , A U FTH M KTIC. Exercise 196 - Canadian Money. 1. What is i!ie val.10 of a cent ? a dollar? a mill? 2. 1 low m.inv cents in $1 ? $:: ? $3? $5? $20? $25? $1.25? $1.75? $2.45? $3.65? Szo.y^f $io.oy? 3. How many mills in 3 cents ? 5 cents? 8 cents ? 4. How many cents in 10 mills? 20 mi Is? 51J mills ? 45 mills? 55 mills? 7^ mills? 94 mills? 643 mifls ? 6. llxprcss 8345 mills in dollars and cents. 6. Will has 45 c cats ; May, :^7 cents ; Rob, 56 cents, and Alice 75 cents. How muili moaey have they ail? 7. Find the sum of .$1.75, $1.38, $2.47, and $6.99. 8. Krom$iotake $(.23, $3.43, $2.87, $3.54, $4.99. 9. P'ind cost of 4 (6, 5, 8, 9, 7) books (<]- $1.25 each. 10. 4 (5, 6) books cost $1.20. Find cost of 7 books. Exercise 197. 1- •} (h ]) I'i- suyar costs 3 cents. Find cost of 4 lbs. 2- If fi (p :,) lb. butter costs 12 cents, find cost of 2 lbs. 3. How many lo-ccnt pieces equal 201-. .'' 30c. ? 80c. ? $.70? $1.50? $2.40? $3? $7? $9? $15? $25? 4. How many books @ 25 cents can I get for $r.25 ? $1.75? $3.25? $3.75? $4.23? $5.5or $10.25? $35.25? 5. What part of $1 is 50c. ? 25c. ? 75c. ? 20c. ? loc. ? 6. How many books $.75 ($.48) can I buy for $ro? 7. How many lambs at $2.25 can I buy for $4.50? $6. 75 ? $9 ? $36 ? -1=7 ? $8 ? $ 1 5 ? $20 ? $40 ? 8. I have 40c. and Will has i (', J) as much. How much has Will ? How much have both of us ?* 9. A book cost $.75 and a pen ^ (J, |) as much. Find the cost of both. 10. I have $12, in an equal number of 5-cent, lo-cent,* 20-cent, and 25-cent pieces. How many coins are there? .... X4 = $r. 75x12. $4.5oxS = $2.25x ... . .... X I2 = $3.75x8. $7-5ox6 = $3.75x .... \VKK;HTS AM) Mt-ASURKS. 89 Exercise 198 -United States Money. 1. Name the Ameri<:;in coins— },'oUl, silver, other. Give value of each. What other money is used ? 2. How many cents in 2 dimes ? 3 dimes ? 8 dimes ? 3. How many dimes in 20 ccmUs ? 30c. ? Sdc ? Soc. ? 25c. ? 35c. ? 75c. ? 83c. ? 64c. ? 97c. ? 4 How many dimes (cents, mills) in $1 ? $3 ? $5 ? $9 ? $1.35? $1.65? $2.25? $3.25? $S.(>3^ $1-375? $2,875? 5. How many dollars in 2odimes? 30 dimes? 60 dimes? 35 dimes ? 45 dimes ? 85 dimes ? 54 dimes ? 69 dimes ? 6. How many dollars in 2 eagles ? 4 e. ? 8 e. ? 10 e. ? 7. How much must I act for a hat that cost $4.25 to gain $1.50 ($2.75, $3-35)? '^'^ 'o^^ $.35 ($.28, $.69) f 8. I buy fruit for $7.25, and sell it at a loss of $1.50 ($2.75, $3.35)- How much do I get for it ? 9. I earn $9 ($ 1 5, $2 1 ) a week. Find my daily wages. 10. I spend $3.50 ($10.50) a week ; how much a day? Exercise 199. 1. From $20 take $9.74, $4-35. $6-99, $'2.33. $i4-87- 2. How much do I gain or lose bv buying for $15 35 and selling for $13.85? $17- '5? $16.73? $1448? 3. Find my weekly wages @$i. 75. ($---5> $3-45) 'ifl'iy? 4. Find my years wages @ $45 ($75. $'-5) ^^ i»onlh. 5. 15 lbs. sugar @ 20 (25, 24) lbs. for $1 = iQ. 12 (18, 20) lbs. rice @ 15 lbs. for $1 = 7. Find ^ (1, f, h i ?. ?, h h R. A) of $'• 8. Find cost of 24 books @ ${, (^' $h ® $«. ('^ $8' ^'^ $M- 9. Find cost of a book @ 35c., and a lamp @ 4 (7, 9) times as much. 10. How many letters can I post for 24c. ? 36c. ? 75c. ? 11. How many times can I spend 75c. from i eagle. 12. A has $3.75 more than R, and together they have $8.25 ($12.35, $12,45). How much has each ? 90 MENTAL ARITHMETIC. Exercise 200 -English Honey. 1. What is a penny? a shilling? a pound? a farthing? a sovereign ? a guinea ? a crown ? 2. How many farthings in w/. ? 2>/. ? v/. > m/. ? zd ? IK ? i-^/- ? 14'^- ? 2^'^- ? 3]'/- ? 61^/. ? 7.y. ? 3. Kow many pence in 8 far. ? 16 far. ? 24 far. ? 25 far. ? 30 far. ? 21 far. ? 35 far. ? 50 far. ?' 75 far. ? 4. How many pence in I5. ? 2.?. ? 5.?, ? 4?. ? q.s- > io.j ' I/-? 2/-? v'-? 2/6? 3 '4? 5/9? 6,3? 13/4? J 7/6? 5. How many shilliii;^s equal \2cf.? 2.\d.> 48^.? 72^^.? 2or/. ? 3o £S^ /12 ? ;^i I05 ? ^2 io.y.? /3 5.9.? ^4 ,5.?. ? ^8" 12.9. ? 7. Find the sum of gd.,6(l., 8d., -jd., \d., ^d. and io.v. 8. How much is,2; 2^. bd. ? 4 yds. (^ 13/4 ? 7 cows (^ £^ \os. ? 9 cans @ 7.V. 6rt'. ? 5 yds. @ 17/6 ? 8 cows (?/} /,5 i i.v. ? 7 cans (V>) 3.y. 4^/. ? g yds. @ (,8 ? 6 cows @ £6 ^S-^- ? 4. Multiply ^i 65. 8]r/. by 2 (3, 4, 5, 6). 6. Find .] (J, f) of \d. ; \s.; £1; I cr. ; i sov. ; i g. 6. Divide ^16 i6j. 8.W. by 2 (4, 3, 5, 6). 7. Mow manysi.x-pencesin i5? 3,?. ? 3i,-. 6^^. ? 7.9. 6(/. ? How many crowns in £1} £j ? 10 sov. ! 5 g. ? 8. How many books ® 25. 6^^. can I buy for 7s. bd. ? .2S. 6d. ? 175. Gd. ? 105. ? 155. ? j^ I 10.V. ? ^^2 155. ? 9. If a herring and a half cost a penny and a half, how many should I get for 15. ? 55. ? ^i ? £1 los. ? WEIGHTS A\D ^MEASURES. 9« Exercise aoa - Liquid Measure. 1. Give the table which shows the relation between gills, pints, quarts and gallons. 2. How many gills in 2 pints? 3 pts. ? 5 pts. ? 8 pts. ? 3. How many pints in2cniarts? 3 qts. ? 5 (jts. ? 9qts. ? 4 qts., ! pt. ? 6 qts., I pt. ? 8 qts., I pt. ? 9 ql^-' ' P^- ? 4. How many ciuarts in i gallon ? 3 gal. ? 5 gal. ? 9 gal- ? 3 gal., I qt. ? 4 Kal., 2 qts. ? 6 gal., 3 qts- ? 9 gal., 3 qts. ? 5. How manv gallons in 8 qts.? 12 qts.? 24 qts.? 10 qts. ? 15 qts. '? 25 qts. ? 35 q^^- ? 45 qts- ( 5° qts. ^ 6. How many quarts in 6 pints? 8 pts.? 12 pts. ? 7 pts. ? 9 pts. ? I 5 pts. ? 25 pts. > 35 pts. r 49 pts. ? 7. How many gallons in 1 5 pints ? 25 pts. ? 35 pts. ? 8. Reduce 3 gal, 3 qts-, i pt- to a simple number. 9. Compare i gal. and i qt. ; i qt. and i pt. 10. I drink a pint of milk a day. How much milk do I drink in a week ? 2 weeks ? 5 weeks ? Exercise 203. 1. One cow gave 3 gal. 2 qts. i pt., another 4 gal., 3 qts. and a third 3 gal., 1 pt. Hdw much: did all give ? 2. A mil'.man had 12 gal, i qt., i pt. of milk and sold 9 gal. 3 qts. How much has he left ? 3. Find the cost of 4 (5^ S) g:iHons (?» 2c a pt. 4. Find the cost of 16 (32, 48) P'nts ('^ 25c. a gal. 5 At 6c. a qt., what is the cost o*" 4 gal, i pt- ? 3 ga'-, 3 qts., I pt. ? 9 gal., 2 qts. ? 7 gal-, • qt-, • Pt- ? 6v\nA 1 <"' -i 1 •' ■'"' ^. AH^f a gallon. 7 \ r ler holds 2 gills. How much milk wouW fill 20Uin.,..ers ? 30 tumblers ? 45 tumblers ? 4S tumblers ? 8 How many pint bottles will hold 4 gal, 3 qts., i pt. ? 5 gal, 1 qt., 1 pt. ? 7 gal, 2 qts., I pt. ? 9 gal, i pt- ? 9. Find the weekly cost of i pt. (« qt., i gal.) of milk each morning (a 3c. a pt. 92 MKNTAI. Ainrf-MKTIC. Exercise 204 Dry Heasure. 1. How many gallons in . peck? 3 pks. ? 5 pks ? 3 pks., I gal. ? 4 pks. , gal. ? 9 pks ,1 gal. ?^ 2. Mow many peck a i bushel ? 2 bu. ? 6 bu ? 2 bu., , pk. ? 5 bu., 2 PKS. ? 8 bu., 3 pks. ? 16 bu., :t pics. ? 3. How many gallons in i bushel ? 3 bu. ? 6 bu. ? 4. How many quarts in i peck ? 2 pks. ? 8 pks. ? 5. What simple numljer equals 5 gals., i qt. } 5 bu ' ^-l 5 pks., r gal., 3qts. .' i bu.,'i qt. i^ pV, fpt ? O. How many pints in i qt. ? i gal. ? , pj-. p , ;-,„ p 7. Hovv many qts. in i Q, J, J, ., |) of a peck.^ ». F ind value of a bushel @ loc. a gal. @ 4c. a qt a Fmd value of a bu. of cranberries at 6 pts. for ->4c 10. Find cost of 1} (2j, 3^3) bu. beans at 5c. a qt. 11. How many quarts of chestnuts should I get for $.72 when sellmg Cm $1.28 ($2.56, $1.92) a bushel? Exercise 305. 1. In two ways, compare 1 gallon and i pint da?s wil!' W^ ^^^1 ' Pi- ?^ "''I!' ^^^'^ f^^d- "°^^ >"any aays will 3 (5, 8) bushels last him ? How many pecks will he eat in a week ? 3. Find the sum of 5 bu., 3 pks., r gal. ; 2 bu., 2 pks 1 gal., and 3 bu., i pk., i gal., 3 qts. ^ ' 4. From 8 bu., 2 pks., take 5 bu., i pk. ; 3 bu., 3 pks • 2 bu., 2 pks., I gal. ; 3 bu., 3 pks., , gal.; 2 qts. ^ ^ ' iuf-^ hu'\ 'TV'T ■' '" 5 (7, 8) bags, each contain- nig _ .)u., T pk., f gal., 3 qts., i pt. ? 6. Divide ,6 bu., 3 pks., I gal., 3 qts., i pt. by 2 (4, 8). K ^?.7 n-^"y ^''^^' ^'"^^"'i containing 2 bu. ^ pks canbehlledfrom22bu.? 33 b.,.? 13IH.., 3pks^> ' 8. If 8 busheL apples are worth $4.80, what is the cost of 3 peck= f 1 bushel ? 1 bushel ? 9. Find the gain or loss on buying 5(8, 12) bu nuts @ 8 cents a quart, and selling & 5 cents a pint WEKIMTS ANP MF.ASURKS. 93 Exercise ao6 Table of Time. 1. How many scrnnds in 2 minutes? 3 niiii. ? 5 niin. ? I niin., 5 sec. ? 3 tnin. 10 sec. ? 6 inin., 25 sei . ? 1 hoMi? 4 Ills. ? 8 Ins. ? min. 2. How many mnuites m 2 hrs., 10 min. ? 4 lirs., 20 min. .' 7 Ins., 35 3. I low m;iny hours in 1 20 min. ? 240 min. ? 420 niin. ? 160 min. ? 255 min. ? 625 min. ? 76^ min. t 8.S5 min. .' 4. How manv hours in i (l;iy .'' 2 d. ? 5 d. .-" (> d. ? K d. ? 2 d., 3 hrs. ? 2 (1., 8 hrs. ? 3 d., 10 hrs. ? 4 d., 12 hrs.? 5. How many days in 48 hrs.? 72 hrs.? 120 hrs.? 55 hrs. ? 80 lirs.'? 115 hrs. ? 140 hrs. ? 258 hrs. ? 6. How many days in i week ? 3 wks. ? 8 wks. ? 2 wks., 3d.? 3 wks. 5 d. ? 4 wks., 6 d. ? 7 wks., 4 d. ? 7. How many weeks in 14 days ? 28 d. ? 49 d. ? 77 d. ? 30 d. ? 40 d. ? 67 d. ? 88 d. ? 75 d. ? y2H d. ? 7^>3 ^1- ? 8. How many months in i year? 3 yrs. ? 5 yrs. ? 2 yrs., 3 mo. ? 2 yrs., 7 mo. ? 3 yrs., 8 mo. ? 6 yrs., 9 mo. ? Exercise 207. 1. Find the sum of 6 hrs., 20 min., 3ocec.; 5 hrs., 30 min., 50 sec; and 8 hrs., 29 min., 35 sec. 2. Find the sum of 5 wks., 6 d., 15 hrs.; 4 wks., 5 d., 12 hrs.; 6 wks., 4 d., 9 hrs.; and 3 wks., 6 d., 12 hrs. 3. From 9 wks., 4 d., 15 lirs., take 4 wks., 3 d , 12 hrs.; 5 wks., 5 d., 9 hrs.; 7 wks., 5 d., 20 hrs. 4. What time does a person work a week, whose daily time is 5 hrs., 20 min. ? 6 hrs., 15 min. ? 8 hrs., 25 m'in. ? 5. How much sleep would a person {^et a week, from 10 p.m. to 5 a.m. a day? to 5.30 a.m. ? to 5.45 a.m. ? 6. How much is .1 Q, J, h }, h h ,V) "f ^ ^^'cek? 7 Divide 6 wks., 4 d., 8 hrs., 24 min., by 2 (3, 4, 5). 8. How many times is 3 hrs., 20 min. contained in 6 l.rs., 40 min. ? 13 hrs., 20 min. ? 23 hrs., 20 min. ."■ 9. .A. person is awake 15 hrs., 45 i"'"- <'i ^^V- ^" '^^^^ many days does he sleep 24 hrs, 45 min. ? 16 hrs., 30 min. ? 41 hrs., 15 min. ? 49 hrs., 30 min. ? 33 hrs. ? 94 MKXJAI. ANfTflMKi-ic. Exercise ao8. 1 ■ low mud, less than a year is 3 ,no. ? 9 mo. ? 7 mo ? 3. How n.-.n., .„ I • r' ^' ^' •'' •'• «) "'^ ^ y^Arf 4. H yr ? 1 ,,- ? ^« ? Q. F md my yearly „,,.es (,. $,0 ($8. $24) a week ' ►7 IT - 4 »K->. . 3 Wks. ? h Wks. ? II wks 3 atteiuiluK^'^' -^ ''^^' •" ^ ^7' ' '> --^-ks' school. Find my 9. Find my weekly wages rr. $..35 ($,.5^^ j,.^^ ^ 7 ln«., 45 mm. .> ^^ """• ' 9om,„..P ,5o„.in.? Exercise aop. Name the leap years in, his S„. ^- How manv davs finm Tin » »^ t- l -Ap.^5PMay33tJ^n/-p^:;,^^;5^^Maj.4 3. How many weeks from Jan. 15 to Feb. 5 ./ ' 4. \\ h.cl, two successive months have 63 (60) days ? August "TsTv?' ''^f"?^^^ '" '^'^ "^""^'> 'f ■- w,.Apr:,r(^i;^,^^;;occ^^:';,,fsL?l;tr"^ WEIGHTS AND iMEASURKS. 95 Exercise aio -Avoirdupois Weight. 1. In a table, show the relation of tons, hundred- weights, pounds, antl ouui es. 2. How many o/.. in 2 IIjs. ? 3 lbs. ? 4 lbs. .•* 6 lbs. ? 3. How many Hjs. in 32 0/.. ? 64 oz. ? 80 oz. ? 12S oz. ? 25 oz. ? 750/..^ a^ oi. f 100 oz. .'' 165 oz. .'' 3300/.? 4. How many lbs. in i cwi. ? 2 (3, 5, 7, y, 1 1) cwt. .' 5. How many twt. in i ton .'' 2 (4, S, 12, 6, 3, 9) Ions ? 6. How many Ujs. in i ton.' 3 (6, y, 12, 4, 8, 5) tons.'' 7. Express a-, simple numbers :— 2 t., 3 twt., 18 li;s. ; St., 15 cwt ') t., 14 cwt., 20 lbs. ; y cwt., 3 lbs., 8 oz. 8. Find the sum of 3 t., 15 cwt., 26 ll)s. ; 2 t., 14 cwt. ; 5 t., 24 11)S. ; 4t., 10 cwt., 18 lbs. ; and 3 t., ') cwt., 36 lbs. 9. From 8 tons take 3 t., 14 cwt., 48 Jbs., 10 oz. 10. Find weight of 5 bars each lO cwt., 75 lbs., 12 oz. 11. What is .J (i, 2, J, ;;, I) of a lb ? a cwt. ? a ton ? Exercise an. 1. Whai part of a lb. is 8 oz. ? 4 oz. ? 2 oz. ? 6 oz. ? 2. Find cost of 4 (8, 12) lbs. sugar at 16 lbs. for $!. 3. How many 2 (4, 8) oz. packages will weigh 2 cwt. ? 4. How many packages, each 2 lbs., 8 oz., in 15 lbs. ? 5. 4 qts. oats weigh 4 lbs., 4 oz. Find weight of 1 bu. 6. Which is the dearer, 3 cents a lb., or ij.75 a cwt. ? 7. Bought hay @ $15 a ton and sold @ 85c. a cwt. What is my gain on i cwt. .'' i ton ? 10 tons.'' How much did I buy if my gain was $30? 8. If 5 oz. tea cost 15 cents, find the cost of 10 lbs. P. A grocer's pound-weight is i oz. light. How much is any loss on 64 lbs. ? 4 cwt. ? 80 cents ? $48. 10. Find cost of: — 6 tons, 1250 lbs. coal @ $4.80 ($3.60, $4.40) a ton. 9 cwt., 25 lbs. flour @ $3 (.$3.20, $4.80) a cwt. 3 tons 3 cwt. bran @ $10 ($15, $12) a ton. 7 lbs., 4 oz. cheese @ i2 (16, 20) cents a lb. 96 MKNTAL ARITHMKTK:. 1. 2. 3. 4. Exercise aia-Troy WelKht 6. K«l„,c 2( • '"• '^'- "'""^"- ""I"- '<-'• '>.CUIK C 40 (Co, ho, I Jo Co n- t^-i I 7. low .nany il,. i„ . , ( "^ V ""i' ^^^ ''"' "' '''■'^'^^ a !,m::?;;;:: ■;:'•'■;-- V"-r'^ ■-- Exercise ai3^ Apothecaries' Weight ^. me clown the u.I.lc of Apothecaries' w It 3- KMlure , lb. Apot!,. to 0/ todr, > ^ O- How many sc. in 5 d,-, -, «,., p o , ' ^ *''^^' ' 611,, , 3 <■"■•>•, -bLi..'' X cirs., I sc ? • 'low many ( rs. in ^ 0/ - ,? o '• Ilo\vn)any v-r nnuvlp-. , ''"'"'" "'^- ? O T; -in^ r -^ ^^' -^ l">^^^lers, ea. h i sc 1 c ,.r^ W- I'md co.st of 2 lbs., 8 0/ at c /"A s^ ^«^-. '>srs. 10. Find value of .. . 6 Latf: ?"'' ' '''•'"• WKIC.HIS ASD Ml AMM'.S, ';7 Exercise ai^ L near Measure. 1. IFow I11.IMV inclirs iii i foot? 2 ft.? 3 ft ? ; f t ? 2 i' ? 3' 4 " ? 4' W ? 5' r," ? 6' 9 ? s' 7 ■ ? ,/ 5- ? 2. I low many foot in 24 indies ? 3^, in. ? rnaiii. ? 72 in. .> 40 in. .^ 5(i in. ? 65 in. ? 75 in. ? 43 in. ? 94 m. '; .S7 in. ? 3. How 111,111/ feet in :i y:v\\ } 2 \iU ? 4 vds. ? S yds. ? 2 \(is., 1 fl. ? 3 yds., 2 ft'. } 4 ydv. 2 ft. .'' 5 y 50'.^ 70'.? 80'? 5. How many ^ards in r rod.' 3 ids. ? 4 rds. ? 6rds. ? 3 rds. ? 5 rds. > 7 rds. .' 9 rds. ? 1 1 rds. .' i 5 ids. t 2 1 rds. ? 2 rds., 3 yiis. ^ 4 rds., 5 yds. ? 3 rds., i yds. ? 6. How 11-any rods ill 11 yards? 22 yds.? ^3 yds.? I 5 yds. ? 25 yds. ? 35 yds. ? '48 yds. ? 5; )ds..? '70 yds. ? IZyils. ? 18 yds. ? 20>ds. ? 30 yds.? 40 yds. ? 42 yds. ? 7. How many rods in a mile 2 ivii. ? 3 mi. ? 4 mi. ? I mi., 50 rds. ? ! mi., So ids. ? i mi., 160 rdi. ? Exercisj 315. 1. What simple 1. timber is equal to : — 3 yds., 5 in. ? 4 ids., 2 yds., 2 ft. ? i mi., 240 yds. ? 5 yds., 7 in. ? 5 ids., 4 yds., 2 ft. ? 2 mi., 150 yds. ? 2. Afield is [30 ids. X4ords.]. Explain fliis e\|)ression. 3. How much fringe would trim a tablecloth f6'x4'l? [S'xi2'J.^ [4'6"X5'6"J: [5'4"x7'«"J? 4. How lonpr a fence \.onld enclose a field : — [.^ords. x3ords.]? [24 ids. x 36 rds.]? [25 ids. x 45 rds.]? 5. How many posts S' apart will be needed for a st.aight fence of 64 ft. ? 96 ft. ? 40 yds. ? 80 rds. ? i mi. ? 6. How many posts 8 ipart will be needed for a fence for a field [64' x 80'] ? [96 yds. x 1 20 yds. ] ? 7. How much wire will be rec .ired for a 6-strand fence around a field [64 yds., i ft., 9 in. X35 yds , i ft., 3 in.]? 8. How many 3" pickets placed 3" ap?»ti will be used to f( enre a riel( [236 ' y ^r, 4']? Lf44y< d..]: 9^ MKNTAI, AKriMMIfTir Exercise ai6. 1. HoxvI..ngisasuc? a l)..n.l ? a sp.ui ? afatl.om* a pare? a U-a^Me? What is ,a. I, „s..,| to ineasuu.? 2. How .nany teN-KMaph ,x,les, ,r, lo.ls apart, will rca(hamile? 2 milos.^ 3iml»^? 5 miles? 3. How many rovolntions will a wheel i6'^ feet in circumference make in jjoinK I (2, 3) miles? 4. A fence around a f.cl.l 20 (_v^, ,5),o<|.s wide, is ,00 rods lonK. How lon^ is the field ? 6. How many strips of carpel ,5' (2' 5') wide is needed for a room 9 (18, 27) wide? '"^ci.lu 6. Rooms are [9' X 1 2'J ; ( , 2' X . 5'] ; [ , 5' ry X , , • 3"]. How much niouldinK i« needed for walls of each room > How many strips of ,8" wall paper will each room need > Howmanystripsofcarpet2'3"widewill ra. h room take? Fmd cost of the carpet at $.50 ($.75, $,.35) a yard. Fuul cost of border carpet r- $.75 ($,, $,.35) a yard. Exercise 317. 1. Multiply 5 rds., 3 yds., 2 ft., 9 in. by 2 (3, 4). 2. Divide 12 re's., 4 yds., i ft., 6 in. bv 2 (3, 5) stet; ^.T\ '""'^ 7'-P<^t."iIl he needed for a stairs of 18 steps, each 12 inches wide and 8 inches high ? 5. If 16 rds., 3 yds., 3 ft., 8 in. of a 60-rod fence was blown down, how much remained standing? o ^.k^Tfl'^'V" '''^''" "?"'*' '^^ '''^'^^ «<■ »'^'-ee chains 2fr,7'in ./ '"• ' ^^■'''•' ' '"'•• 9 i"-. and 8 yds., 7. Find in lower denominations 1 (f . 5) of a mile. 8. An nch is what part of a foot? of a yard ? 8 v^ds^'"ft '^ '";'' "^ ^^^^' "> ^^''P^ "'^ ^^'•P^'^ each » yds., 2 ft., 6 m. long, @ 75 cents a yard. WEir.ins ANt) MF.ASUR. ^. 99 ExercUe a 8 -Surface Measure. 1. What is a square? a square inch ? a s.|uare lo'»t ? 2 How many hlotks an inc li square woi.d rover si paperh'xi']? li" x 4 J? 1-" ^ f' 1 ' l> = ' ^ . v ] ? [i' x . J? 3 How nuiny stones one foot square would cover a spacel5'x6j^ [/ x 8'] ,' [f/xyj.' JV -I' 4 How many square feet of lum ci will make a floor [8 X9'i-[9'xi2']?[i2'xi5 ]t[i2.\-x\(>\? ly.l.x i yd. ? 5. What is the Icn^'lh of a floor 8' wide, «(.nt;»ining 96 sq. ft. ? 128 sq. ft. i" M q. ft- ? i(>^ ^'1- ''• ^ 6. How much land is in a field [10 r.ls. x 16 rd-s.l ? [.6nU. x2ords.l? [2ords x 24 rds.)? [40 rds. x 40 rds J? 7 Two wcil-|)ro|H)rlioned fields of different meas.ir^- mcnts contain 300 sq. rds. What arc the dnnenbious of eai h ? 8. I have 1 1 pieces of paper of different sizes, ea« h having a -urface on one side of 3^)0 sci. in. Find the sizes. 0. Find the area of a scpiare 6 " (9', 8 yds. , 1 2 rds. ) long. Exercise ai9> 1. How many sq. in. in 1 scj. ft. ? 2 sq. ft. ? 3 sq. ft 5 sq. fl. ? I sq. ft., 36 sq. in. ? I sq. It., 44 sq. m. ? 2. How many sq. ft. in 28S sq. in. ? 432 ^M- .'"• ? 200 sq. in. ? 300 sq. in. ? 400 sq. in. ? 600 sq. m. ? 3 How many si\. ft. in i sq. yd. ? 2 »M- '^- ■ ^9 sq- ft- ? ^'^ '^'l- "• ? 5. How many sq. yds. in i sq. rd. ? 4 s(|. rds. ? 5 sq. rds. ? 9sq. rds. .? 2 sq. rds. ? 6 sq. rds. ." 3 sq. rds. ? 6. How many sq. rds. in 1 acre ? 2 ac. ? 3 ii<;. ? 4 ii'^- ? 1 ac, 40 sq. rds. ? 1 ac, 80 sq. rds. ? 2 ac, 1 20 sq. rds. ? 7. How many sq. rds. in 121 sq. yds. ? 242 sq. yds. ? 70 sq. yds. ? 85 sq. yds. ? 40 ^4- V'^s- ? S^ sq. yds. ? 8. How many acres in 10 sq. chains ? 30 sq. ch. ? 25 sq. ch. ? 75 sq. ch. ? 125 sq. ch. ? 225 sq. ch. ? lOO MKNTAL AIUTHMETIC. Ill I Exercise aao. 1. Flow many square yards in the ceilin- of a room [9x15 J-- [i2'xis)? Ii5'x'3j? [24'X27']? 2. How many square yards in tiie walls of a room [.ox.2X9'J.. L':: xis'xio'J? f 16' x 20' x .2'J? 3 I low many acres in a field [lords xiGrds.l? [i6rds.X2ords.J?[2ords.X4ords.]? [32rds.X4ords.i? 4. At $25 an acre, what is the value of a field • - Lioch.xi2ch.]? [i2ch.x,5ch.]? [I5ch.xi8ch.]? 5. What is the width of a field that is 40 rods lontr and rontams 4 acres ? 5 acres ? 7 acres ? 6 acres ? 6. Plow many acres in afield that is 20(24, ^-) rods wide, and needs a fence 120 (128, 144) rods long ? 7. A road is 4 rods wide. What length of the road conlams I acre ? 2 acres? 5 acres / 8 acres ? 8. How long a fence would enclose a field of 4 (7. g) acres, it it is 16 (_'8, 36) rods long ? ^ ^^ Exercise 33 1. 1 . Find the value of a field 40 rods square @ $27 an acre. 2. Find the value of a field 20 ch. square @ $25 an acre. 3. How many acres in a mile of road i chain wide.? 4. Reduce }. (], •') sq. yd. to sq. ft. and sq. in. 6. Fhid the difference between 15 sq. ft. and 15' square. 6. Find the outside surface of a box 6' x 4' x 2'. 7. Find the cost of painting a brick 2"x4"x8" @ o cents a square foot. ^ [66 ft. X 55 yds.] ? [44 yds. X 55 yds.] ? ^ 9. It cost $35 to fence a field 20 rds long at 50 cents a rod. I'ind the width of the field. 5" i-enis 10. How many bricks 2" x 4" x 8", laid on edg^ will be requi red for a walk [4' x 20 J ? [3-4" x 40'] ? 11. Find the cost of painting a S-foot close board fence around a lot [84' x 126'] @ 9c. a square yard. WRIGHTS AND MKASURES. lOI Exercise 23a— Solid Heasure. 1. What is a cube ? a cubic inch ? a cubic foot ? 2. How many bloc ks, each one cubic inch, will cover I i,u hot om of a box [3' x 2"] ? [4 " x ?"] ? [6" x 8"] ? 3. How many cubic-inch blo( ks will form two layers in the bottom of a box [3" x 4"] ? [5 " x 6'J ? [9' x 1 2 "j ? 4. How many blocks, each i cubic inch, will fill a box [2" X 3" x 2"] ? [3" X 4" X 5"J ? [4" X 5" X 6"] ? ri2"XI2"x6"]? [12"X12"X12"J? [I'Xl'xi']? I Cub. ft. ? 5. How many cub. feet of water will fill a rectangular trough [6' X 2' X 1'] ? [8' X 3' X 2'] ? [i yd. x i yd. x i yd.] ? 6. How many cul)ic feet of air in a room [i 5' x 1 2' x y'] ? [!5'XI8'XI0']? [l8'X2l'XI5'J? [24'X25'X2l']? 7. How much timber is in a beam [20' x 2' x 1'] ? [3 [4'x4'x8'].? [4'x5'x8'].^'[8x8'x8'].?' 7. How many feel of lumber will a stick of timber 3' square and 12' long make, if J is lost in the sawing? 8. A plate of copper 3 (4, 5) feet long and 4 (6, 8) feet wide IS an mch thick. How thick would it be if made 6 (16, io feet) long and 2 (3, 2) feet wide ? Exercise 335. 1- If 2 (3, 4) in. is the unit of length, find unit of volume. 2. Find the volume of a cube whose edue is 1"? ->"? 3"f 6"? 9"? 4'? 5'? 7'? 8'? 10'.? 12'? 3. How many cub. ft. in 23 cub. yds. ? ^^ c. yds ? 25 c. yds. ? 21c. yds. ? 230 c. yds. ? 99 c. yds. ? 4. How many cul). ft. of stone in 122 cords.? 132 cords ? 25 cords ? 1 25 cords? 250 cords ? 375 cords ? 750 cords ? 5. Find the number of bricks 2" x 4" x 8" required to build a wall 2' x 8' x 20' if J of the wall is mortar. Length. Height. Thickness. 5(8, 1 2) ft. 4 (^',35) ft. 4 (5, 9) ft. 9(8, 10) ft. 5 (6, 35) ft. 6. Volume 90 (240, 700) c. ft 96 (270, 7 :o) c. ft 8 (9, 1 5) ft 3 "(6; 24) "ft. 20(175, 672)c. yds 5(7,8)ft. 4(5,6)ft. 7. Find the volume of rectangular solids — [r6"xi'x8"]; [2'6"xi'3"x8"]; [4' 2"x I'S-'x 2' 6"]. WEIGHTS AND MEASURES. 103 Exercise 226 - Qrain Measure. How many pounds in a biislul of : — wlieat ? rye ' potatoes ? beets ? peas f oats ? onions ? apples ? baile) .' corn ( beans ? carrots ? clover seed ? timothy seed ? flax seed ? buckwiieat ? 2. 3. 4. 5. What is the cost of: — 1. 30 (15, 45) Is. wheat @ 64 (72, 80) c. a bu. ? 12 (24, 36) lbs. peas @ 45 (65, 75) c. a bu. ? 10 (40, 50) lbs. clover seed @ $i.So a bu. ? 24 (12, 36) lbs. barley (T" 60 (72, 96) c. a bu. ? 28 (14, 42) lbs. corn @ 48 (52, 64) c. a bu. ? 6. 6(18, 36) lbs. timothy seed Of: .?2.4o a bu. ? 7. 40 (30, 42) ll)s buckwheat @ 96 (88, 72) c. a bu. ? 8. 8 (32, 40) lbs. rye @49 {^^3, 7°) c- ^ 'jn- •' 9. 42 (57, 62) lbs. oats @ 34 (68, 17) c. a bu. ? 10. 6 (20, 48) Ills, onions @ 90 (96, 75) c. a bu. ? 11- 58 (39> 84) lbs. barley @ 96 (48, 24) c. a bu. .' Exercise 227. Find the cost of: — 1. 20 bu., 30 lbs. wheat at 66 (80, 96) c. a bu. 30 bu., 36 lbs. barley at 60 (64, 72) ( . a bu. 25 bu., 14 lbs. corn at 48 (60, 96) c. a bu. 32 bu., 17 lbs. oats at 30 (38, 40) c. a bu. 24 bu., 15 lbs. peas at 40 (60, 80) c. a bu. 30 bu., 28 lbs. rye at 40 (48, 60) c. a bu. 45 bu., 45 lbs. beans at $1 ($1.20, $1.60) a bu. 28 bu., 36 ll)s. clover seed at .$1 ($2, $2.50) a bu. 40 bu., 50 lbs. onions at $1 ($1.20, $1.30) a bu. atoes 2. 3 4. 5. 6. 7. 8. 9. P' 5" (75» 90) 11. 25 bu., 24 lbs. buckwheat at 36(48, 64) c. a bu. 12. 75 bu., 12 lbs. timothy seed at $1.60 ($2, .$2.4o)abu. 13. 20 bu., 21 ll)s. linseed at $ I. ;o ($2.50, $1.60) a bu. 104 MKNTAL AkITHMKTIC. Exercise aa8. How many pounds in : - 1. 4bii.peas? 4 ini., 15 lbs. corn ? 6 bu., 24 lbs. rye ? 2. 8 bu. rye ? 7 bu., 48 lljs. wlieat ? 3 bu., 36 lbs. beans } 3. 9 bu. oats? 5 bu., 56 lbs. peas ? 8 bu., 35 lbs. beets ? How many bushels in : — 4. 144 lu... barley? 200 lbs. wheat ? 600 lbs. rye? 5. 136 lbs. oats? 350 lbs. onions ? 700 lbs. oats ? 6. 168 lbs. rye? 500 lbs. buckwheat? i ton of peas? Find the cost, at the given price per bu., of : — 7. 360 lbs. wheat (^ 75c. 8. 480 lbs. peas Oj) 63c. 9. 720 ll)s. beans ('» .f 1.25 10. 560 lljs. rye ('" 95c. 1 1. 680 lljs. o.its 49c. 12. 960 lbs. barley O -j^tC. 485 lbs. barley @ 48c. 676 lbs. corn @ 56c. 593 lbs. oats @ 68c. 747 lbs. rye @ $1.12. 268 lbs. wheat @ $1.20. 354 lbs. oats @ 17c. Exercise 329. 1. What is the diflferenre between the wei^-ht of 41: bushels of peas and 45 bushels of corn ? ° 2. Find the weight of a load of ?5 bushels of barley and 25 bushels of wheat. • 3. What is the difference between the weight of 60 busliels of oats and 34 bushels of onions ? 4. How many bushels of wheat will weigh as much as 30 (25, 45) bushels of barley ? 5. How many bushels of corn will weigh as much as 28 (42, 70) bushels of wheat ? 6. How many bus' els of oats will veigh as much as '7(j4, 51) bushels of peas ? 7. How many bushels of clover seed will weigh as much as 30 (43, 60) bushels of r\ e c 8. How many bushels of oats will weigh as much as I tnn, 14 cwt. ofcariotb? WEIGHTS AND MEASURES. 105 Exerciise a30-ni5cellaneou8. 1. How many ejjgs in i doz. ? 2 (3, 5, 7, 9) doz. ? 2 doz. and 6.? 3 doz. and 8 ? 7 doz. and 9 ? 8 doz^. and 1 1 ? *A. How many dozen in 24 .!* 36? 84? 9O ? 120? 168? 30.' 40.? 50.? 63.? 75? 100? 150.? 200? 700? 3. How many doz. in i gross ? 2 (4, 6, 8, 10, 12) gr. ? 4. Find cost of a gross of books (?$ i (2, 3) c. each. 5. Find cost of a gross of pens @ 2 (3, 4) for a cent. 6. How many make a score ? 2 (3, 4, 6, 8, 9) score } 7. How many score in 40 ? 60 ? 80 .' 76 .'' 38 .' 99 ? 8. Find cost of 3 (5, 8) score marbles at 4 for a cent. 9. Bought marl)!es @ 3 cents a score, and by selling them ^ 4 for a cent, gained $r . Find how many I bought. 10. How many sheets in a quire ? (2, 3, 6, 9, 12) qrs. ? 1 1. How many reams in 20 quires .? 40 qrs. } 80 qrs. ? 25 qrs. ? 45qis. ? 75 qrs. ? 95 q's. ? 135 qrs. ? 157 qrs.? 12. Find cost of 2 (3, 4) reims of paper® 3 (4, 6) sheets for 5 cents. 13. My hens lay 2 doz. and 8 eggs in a day. Find the value of the eggs laid in a fortnight @ 12 cents a dozen. Exercise 331. 1. How many lbs. in i bl)l. flour? pork? beef? salt? 2. Find cost of a bbl. pork @ 8 (9, n) cents a pound. 3. Find cost of 2 (3, 5) bbls. beef® 7c. a lb. 4. Find cost of J (J, f) bbl. of flour at 3 cents a lb. 5. Find value of .J (J, % 2) bbl. salt at 2 lbs. for ic. 6. I bought beef at $9. 75 a bbl., and sold it at 8c. a lb. Find my gain on 2 i3, 5, 8) bbls. 7. I paid $11.25 ^ '^l^l- f"i" pork, and sold ("19(10, 11) cents a pound. What is my gain on 2 bbls. ? 4 bills. ? 8. How many bbls. of pork ® $12.50 must I sell, @ IOC. alb., to gain $30? $45? $75? $37.50? $67.50? 9. Find my gain or loss on buyinnf 20 bbls. salt ® $.75 ($.90, $1.25) and selliuq^ On 2 lbs. for a < cut. io6 MICNTAL AKITHMKTIC. Exercise ajz— Analytic, 1. Find cost of 3 tons hay 5 lbs. for 3 (4, 6) cents. 2. Find cost of 20 doz. bananas @ 3 (4, 6) for 5 cents. 3. At 2 (3, 4) oz. for 5 cents, find cost of 10 lbs. tea. 4. Find cost of 12 (15, 18; bu. wheat @ lolbs. for iSc 5. 5 pis. cream cost 45 (55, 75) c. Find cost of 20 gal. 6. At 2 (4, 8) oz. for 5 c, find cost of i ton of spice. 7. Find cost of 10 (15, 25) yds. ribbon ® 4 in. for 5c. 8. $40 is paid for a lot (4 X 20) rds. Find cost of 10 ac. 9. If 48 yds. of road cost $144, find cost of a mile. 10. i3 (24, 36) sq. in. cost 72c. Find cost of i sq. yd. 11. 500 ibs. coal last 7 days. How long will 4 t. last? 12. How many %d. ($d.) stamps can be bought for /i ? 13. Find tl.^ cost of a section of land @ $25 an acre. 14. 3 (5, 6) bu. oats cost $i.So. Find cost of 680 lbs. Exercise 333 -Review. 1. How many panes [9"x 12"] can be cut from 36 sq. ft. of glass ? From a glass [8' x 6'] ? 2. How many lots [33' x 99'] can be made of a field [i2rds. x2ords.].? [36 rds. x 12 rds.]? [40 rds. x 12 rds.]? 3. How many cent pieces can be placled side by side on a surface [ 1 5" x 24"] ? [6' x 8'] ? [5' 6" x 5' 4"] ? 4. What are the dimensions of a square field which contains 64 sq. rds. ? 100 sq. rds. ? 400 sq. rds. ? ! ac, ? 5. What are the dimensions of a paper 3 times as long as wide, and containing 75 sq. in. ? 300 sq. in. ? 6. How many lo-acre fields make a sq. mile ? 2 mi. sq. ? 7. A field is 40 rods long, and contains 4 (5, 9) acres. Find its width. 8. How many furrows 1 2" wide must be made to plow a field whose width is 4 rods ? 8 rods ? 20 rods? 12 rods? 9. Find the distance travelled in plowing a 10 acre field which is 40 rods long, if the furrows be 12" wide. WKIOHTS AND MKASUKKS. 107 Exercise 334 Sharing:. 1. Two parcels weiyh 6 lbs., 8 oz. (5 lbs., 6 oz. 9 lbs., 4 oz.). Find the average weiylit. Two parcels weigl) '5 Ihs., 8 oz. One weighs 60Z., (Slbs., 12 oz. ; 5lijs., looz.). Find the other. Two strings reach 75 yds., 1 ft., 6 in. One is 12 2. 7 lb 3. yds., 2 ft., 8 in. (28 yds., 1 ft., 7 in.). Find the other. 4. Divide ^4 155. dd. between two men, giving one 2 (3, 5) times as much as the other. 5. V.'hat is the average size of 3 (4, 5) fields, which together contain 75 ac, 96 sq. rds. 6. One field contains 3 (7, 4) times as much as another. Find each if botii contain 32 ac, 120 sq. rds. 7. The average weight of three pipes is 7 cwt., 45 lbs. One weighs 2 lbs. as often as the others weigh 3 lbs. and 4 lbs. Find the weight of each. 8. Divide ^45 \()S. 6d. .unong A, B, and C, giving A 2td. as often as li gets zd. and (-", \d. Exercise 335. 1. Divide 15 lbs. sugar into two parcels, one 4 (8, 12) ounces heavier than the other. 2. Two parcels weigh 16 (20, 25) lbs. Find the weight of each, if one weighs t 1 >., 8 oz. (3 lbs., 4 oz. ; 2 lbs., 10 oz.) more than the other. 3. A pole 34' 5" long is broken into two parts, one 4' 2" (j' 8 ", 8' 4") longer than the other. Find each. 4. Two sheep cost ^3 i5a\ dd. One is worth \our, down stream, and 6 5, 6) miles an hour up strea. . How far will I row in still water, in 4 (7, 6) hours ? Exercise a37. 1. How many cub. ft. in .} (;1, ij) of a cub. yd. ? 2. What part of a dozen is 6 (4, 8, 3, 9, 2)? 3. Find 25 cents' worth of peaches @ loc. a dozen. 4. If 2 quarts fill 8 glasses, find size of the glass. 5. I paid 1/6 for ij doz. eggs. What is the cost of 15 eggs ? 24 eggs ? 36 eggs ? 50 eggs ? 75 eggs ? 90 eggs ? 6. A earns $4.50 a day and B earns Find the weekly wages of the two together. 7. If a gallon of milk costs 20c., what will be the cost of 1 qt. ? 3 qts. ? 7 qts. ? 9 qts. ? 20 pints ? 36 pts. ? 8. How many g.illons will fill one dozen pint bottles ? 2 doz. ? 4 doz. ? 8 doz. ? 6 doz. ? 10 doz. ? 9. What part of a bushel is i peck ? 2 pecks } i gal- lon ? i quart ? i pint ? 2 pks., I gal. ? 3 qts., i pt. ? § as much. WEIGHTS AND MEASURKS. 109 Exercise 338. 1. The average weight of 5 (7, 9) sttcl plates is i t(.n, 16 cwt., 75 lbs. Find their aggregate weight. 2. Find the average size of 8 (6, n) fields, each of which contains 4 ac, 120 sci- rds., 16 sq. yds., 3 sq. tt. 3. I sold 4 cows for $175-25, ;»nd 6 others for $224.75. Find the average price I rci eivcd for them. 4 I sold 2 horses for lyj 16-v. 8rf. ; 3 horses for C^^ 125. 9^., and 5 horses for jjbz io5. id. Find average price. 5. My wood-shed is 20' x 8' x 8' and contains 5 cords of wood. How much more would it hold ? 6. How many lots 2 rds. x 10 rds. can be made if 4 fidds, each 12 acres, \i\{h I) '» "^^d for street:^ ? 7. Three loads of wheat average 36 bu., 15 lbs. \ ind their value @ $.80 ($1.20, $.96) a bushel. 3. Find gain or loss on buying 240 bu. oats ^ 24 bu. for $10 and seUing @ 8 bu. for $5. Exercise 339* 1. How much water must be added to 6 (8) gals, of wine @ $3 to make a mixture worth $2 ($1.50) a ?»'• 2. A man bought 10 gals wine (^f) $3, and after putting in enough water to make it worth $2 ($1.50, $!) he sold it @ $2 ($3, $4) a gallon. Find his total gain. 3 A man earns twice as much as a woman, and a woman twice as much as a boy ; and i man, 2 women and 3 boys ea.n $8.80 a day. Find weekly wages of each. 4 A man l^ought a number of Iambs ® $2.25, and the same number @ $2.75. How many did he buy for $750 i 5. I paid $7,600 for two farms, one ® $28 an aci .-, and another twice as large @ $36 an acre. Find size of each. 6. It cost $36 to make a fence. If it had been 4 rods shorter it would have cost $32 ($28, $24). Find the length. 7. A fence around a field cost $426. Had the field been 6 rods longer, the fence had cost $438. Find the length of the field. no MENTAL ARITHMETIC. Exercise 340, 1. Read $4.56, $5.08, $6.40, $63, $.75, $2,875. 2. .Show thut 9 sq. ft. -- i sq. yd. 3. Show thai I M|. rd. - 30] !,(|. yds. 4. .Show tlic nuinlKT of cuh. h. in i cub. yd. J). Give the standard unit of measure for scMing : — milk su),Mr egys coal wood grain oranges chsrrici: Uimljer paper potatoes wheat 6. Give the standard unit for measuring : hay cloth bricks Jarms rivers cental quip.tal roads boards population mountains fences grain j^i evinces distances 7. Name some articles sold by the ; — oz., lb., ton. bushel do/en bajj qt., pi., gal. barrel ^iross ream 8. What are the dimensions (^f a line .' of a surface ? of a solid.'' 9. If I foot '-ere the unit of length, what would be the unit of surface ? of volume ? 10. What I.' a cord fool ? Mow many are in a coid ? 11. Distinguish a short ton from a long ton. 12. Which is the heavier- 1 Ih. gold or i lb. feathers.' An ounce of gold or an ounce of lead ? 13. In reducing 55., exf. to pern e, what is your multi- plier ? Is it abstract or denominate .-' 14. 6d. is what part of 15. ? 2.v. ? 55. ? 20s. ? 15. !n what country is the franc (the mark) the standard unit of value ? 16. $1 a pint is what price a gallon ? a gill ? 17. Find the \yeight of a peck of wheat, barley, oats. Find the weight of a gallon of peas, corn, potatoes. 18. What are the aliquot parts of ^i? $1? i week.? I bushel ? I yard ? i square yard ? x cubic yard t I pound ? I gallon ? -SCHOOL HELPS SERIES - rOR THIRD OLA8SI8 ^anadlaa History Notes By u. £. Henderson and C. Q. Fmser. Price, 11 centi. aoography Notes Revised By C. U. Fnser. Price, 16 conts. Physiology and Hygiene Notes By 0. £. HendenoD and C. U. Fraser. Price, 12 centi. •Tonior Langrnage Lessons By G. £. Henderson and C. G. Fraser. Price, 15 cent*. ■aceroises in Orammax By Q. £. Hendenton and C. G. Fraser. Price, lA cents. How We Are Governed By Geo. A. Fraser. Price, 10 cents. Mental Arithmetio Xxeroises— Part I. By C. 6. Fraser. Frioe, 16 cents. ■xeroises In Arithmetio for 3rd Classes By G. E. Henderson and E. W. Bruce, M.A. Price, 15 centc. Teachers' edition wiiti answers. Price, 20 cents. Summary of Canadian History in Verse By G. W. Johnston. Price, 10 cents. FOR SeCOKD CLASSES Junior Language Lessons By Q. E. Henderson and C. G. Fraser. Price, 15 certi. ■zeroises in Arithmetio for 2nd Classes By G. E. Henderson and E. W, Bruce, M.A. Price, 12 cents. Teachers' edition with answers, 15 cents. Mental Arithmetio Xxeroises— Part I, By C. G. Eraser. Price, 15 oentd. FOP FIRST CLASSES Bxeroises In Arithmetio for 1st Classes By Miu R. Church and Miss A. Hardiug. (For Teachers only). Price. 20 ceats. ' Phonies, Vocal Expressions and Spelling By Miss B. Church and Miss. A. Harding. Price, 80 centr Me ntal Arithmetio Exercises -Part L By C. a. Fras«r. Price, 15 cents. 3mU pottpaii on ruetipt tf priet er Ihroui^