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McLELLAN, M.A., LL.D., Principal of School o/ Pedagogy and Director n/ Normal Schools, FJ^TIT I- Authorized for utte in the Srhonlg of Nova Scotia. Authorized, for u/te in the SchotUs of Manitoba. Vxed in a. large numlter of the hfttt Schnnlg nf Ontario. Authorized hg the Minister of Kducotion for use of Model School StndentH. liecommended for use of Teachcrn in Ontario, FlI'TRr<.Nr![ ElUTION. PUK^K, 80 ClONTS. TORONTO : W. J. GAGE «fe COMPANY, 1H9l>. ?!»■ i 'S Entered aooording to Act of u>e Parliamenii of Ganada, in the year one thousand eight hnndred and seventy-seven, in tha * office of the Minister of Agrioulture, by Adam Millbb & Oa ^-1 ^*^eE: ^^^K^*?*^^"-- "■ ' ,7'*'' "'>!■■!■■': i Pi'' ■" "WJB*"' ^ ■■ ■ " ,V- ^ ,-3., ^.'**- ■"«-,' HINTS TO TEACHERa ??■ 1. Use natural objects (numeral frame, etc.) to give first notions of numbers. First, teach carefully the ana- lysis of elementary numbers (with their notation) up to nine inclusive — ^so as to give clear notions of addition, subtraction, multiplication and division. 2. In addition etc., let the pupil have plenty of drill in small numbers^ till he thoroughly comprehends t'le ele- mentary processea Types of easj/ questions are given in the book — let similarly easy questions be framed by the teacher, and by the pupils for mutual drill. 3. Give many practical questions, so that ultimately when a problem is prepared the pupil will be able to know in an instant which of the fundamental ruleSi or what combination of them, is to be applied in the sola* tion. 4. Always proceed from the known to the unknown. The pupil learns subtraction from his knowledge of additionf etc., etc. : knowing that 4 -f" ^ = 7, he knows that 7 — 3 = 4, and that 7 — 4 = 3; knowing that 4 X 3 = 12, he knows that 12 contains 4, 3 times, and 3, 4 times, eta 5. In the " simple rules," prepare the way for fractions ; make young scholars familiar with /actors, multiples, measures. The pupil having become thoroughly familiar by proper training in the simple rules, with the notion of dmtion into tquBl parts, and with the language expreti HINTS TO TBA0B1R8. «ing saoh division, wiW find but little difficulty in ilio nrhole lubject of fractions. 6. In general, pnp'Js should not be permitted to use * text-book during recitation — ^yonng pupils need no book ; those who have advanced to division, an^.lysis, etc., will do better to prepare assigned lessons, and at the same time, should have additional questions proposed corres- ponding to the given types. 7. In addition to daily oral work, there should he/re- quent written examinations ; the pupils are furnished with pencils and Email slips of paper ; they are directed to turn to certain questions, to write down on their slips the numbers of these questions, and are then allowed a given time to solve them mentally, using the pencil only to writOj opposite its number^ the answer they have found tor any question. 8. The pupil should commence mental arithmetia vvbftn he enters school, and should continue it so loner as it is thought necessary that arithmetic should be one of his Stttdkft OONTBNTS* Chap. L— Simplb Rulii, Bionoir 1 ••• flionoir 8 Ssonoir 8 ... ••• ... ••• ••• .•• #•• .•• *•• ••• w *•• ••• .•• .• • ••• ••• ••• .•• • • Jo .«• .•• .•• ••• .•* *•. ... ••• ••• ZD OKvlAOn V ... ... ... ••• *•• ••• ••« ... .«. .•• OS OMTTIOM O ... ... *■« ... ... ... ... •«. ... *•• vO D*wllOW O ... •■• *•• .•• ••• .. ( •«• ... ••• ... 4U SSvTIOa f • • ••• ••• .•• • • ••* ... ••• #•• • • 4# Chap. II. — Fractions. SlOTTOK 1 ... SionoN 8 Stctiok 8 ... KCOTIOV 4 .•* *•• .•• ... .•• .a« MM ... ... ... •«• ... .•• **• ... .•* ... ••« ••« ..• ... ... *.. ... ... (»• «•( *«. ... ... *•• «.. ... #•• .•• *l BionoN . .. ... ••* ... ••• ... .•* .*• •• Chap. IIL — Rbduotioh ahp Compound Rvlu. SsonoN 1 • —m ... SlOTION 2 .•••.. ... M aWnoii 8 ... M* ... ... .•• • •• ••• Ow* ... •.• ••• ••• ••• aat .•• ^V* Chap. IV.-^^msTioNS for Ezaminatiov. ft? k t JPi|"|l!ll|*!^4.^^!W|^jPISP^PIlW*im|!,* . ii"^Jf?lf?J«f»Bf^'|jpp;^ ' "^Wi'^-Plii CHAPTER I. FUNDAMENTAL RULES Section I.— Addition. Examples. — 1. 1. Charlie had 2 cents, and he found 1 cent : how manj had be then 1 Ans. — 2 cents and 1 cent are 3 cents. 2. John has 2 dollars, and his father gives him 3 : how many has he now 1 8. Harry had 2 marbles, and Charlie gave him 6 : how many had he then t 4. Mai'y had 9 pins, and found 2 : how many had she thent 5. Sarah paid 3 cents for a pen, and 8 cents for a holder : how much did she pay for both f 6' In a class are 9 boys and 5 girls : how many art there in all t 7* Mary paid 7 dollars for a dress, and 4 dollars for a bonnet : how much did she pay for both t 8. Harry shot 5 pigeons, and Willie 7 : how many did both shoot t 9* How many are 2 and 11 1 and 21 2 and 21 2 and ^1 3 and 21 2 and 41 4 and 2 1 2 and 5 1 5 and 21 2 Mid 61 6 and 21 2 and 71 7 and 21 2 and 8 1 8 and 2 1 2 and 9 1 9 and 2 1 2 ponoe and 9 pence 1 2 days and 9 days 1 10. How many are. 3 and 2 1 2 and 31 3 and 31 8 ^f^ejHf^TJWWWP! 10 MINTAL ABITnUBTia >. and 41 4 and 3 1 3 and 5 1 5 and 31 3 and 6 1 6 an^ 3 1 3 and 7 1 7 dollars and 3 dollars 1 3 hours and 8 hours t 8 tons and 3 tons 1 3 tons and 9 tons 1 9 thousand and 3 thousand 1 11. How many are 4 and 31 3 and 41 4 and 414 and 51 5 and 41 4 men and 6 men 1 6 boys and 4 boysl 4 yardaand 7 yards 1 7 inches and 4 inches 1 4 tons and 8 tons 1 8 tons and 4 tons 1 4 hundred and 9 hundred 1 9 hundred and 4 hundred 1 12> A man paid 9 dollars for a coat and 5 dollars for a vest : what did both cost him 1 18* James spends 6 cents in apples and 9 cents iu oranges : how much does he spend in all 1 14' A V)oy found 8 eggs in one nest and 9 in another : how many eggs did he find 1 15* Willie caught 9 lobsters in the forenoon and 9 in ^•he afternoon : how many did he catch in all 1 16. How many are 6 cents and 8 cents 1 6 dollars and 8 dollars 1 6 dimes and 8 dimes ) 6 shillings and 8 shil- lings 1 6 pence and 8 pence) 8 farthings and 6 farth- ings 1 8 pears and 6 peai's 1 8 tenths and 6 tenths 1 8 thirds and 6 thirds 1 17. How many are 5 and 414 and 515 and 515 and 61 6 and 5 1 5 and 7 1 7 and 5 1 5 and 8 1 8 and 51 5 months and 9 months 1 9 tens and 5 tens 1 18. How many are 6 and 5 1 5 and 61 6 and 6 1 6 and 71 7 and 61 6 and 81 8 and 61 6 and 91 9 and 61 19. How many are 7 and 61 6 and 71 7 and 7 1 7 farthings and 8 farthings 1 8 drams and 7 drams 1 7 grains and 9 grains 1 9 grains and 7 grains 1 80* How man^ are 3 and 71 7 and 81 8 and 8 1 8 ■ '"'.iflJ^-l: t «.^^ai>M4W&< J ADDITION. 11 and 9 1 9 and 81 9 fourths and 8 fourths ? 8 tenths and 9 tenths 1 21. How many are 9 and 61 6 and 91 9 and 71 7 and 91 9 and 81 8and91 9 and 9 1 9 thousand and 8 thousand. 22. How many are 10 and 21 10 and 31 10 and 41 10anl51 lOandei 10 and 7 1 10and81 10 and 9 1 10 and 10 1 28' A man travelled 9 miles by coach and 10 ini!ea by rail : how far did he travel in all 1 24. John caught 7 haddock and £dward 4 more than John : how many did both catch 1 25. How many are 11 and 31 13 and 31 16 and 31 22and31 24 and 31 12 and 51 16 and 51 18 and 6 1 21 and 5 1 Examples. — 2. 1. Row many are 11 and 81 13 and 81 14 and 81 18and81 19and 81 |21 ahd 81 lland91 12 and 9 J 13and91 15 and 91 17 and 91 19and91 21 and 9*1 2. How many are 2 and 2 1 2 and 12 1 2 and 221 2 and 321 2and421 2and521 2and621 2and721 2 and 821 2 and 921 $2 and $92 1 2 pence and 92 pence 1 2 tens and 92 tens 1 8. How many are 3 and 31 3 and 13 1 3 and 23 1 3 and331 3and431 3and531 3and631 3and731 3 and 83 1 3 and 93 1 96 and 4 1 - 4. How many are 4 and 41 4 and 141 4 and 24 1 4 and341 4and441 4and541 4and641 4and741 4 and 841 4 and 94 1 98 and 2 1 6* How many are 5 and 516 and 15 1 5 and 25 1 S 18 ■^^T*'f'?5'rTT^Tf?^5p^^pPirs^^ MENTAL ABITHMBTIO. iind 35 1 5 and 45 t 5 and 55 ? 5 and 65 t 5 cents and 75 cents 1 5 pence and 85 pence! $5 and $95 9 5 tens •ad 95 tens t 6. Susan paid 7 cents for needles, 10 cents for threaa, and 9 cents for pins : how much George buys 9 marbles at one time, 6 at another, Wdd 12 at another : how many does he buy in all \ ,0. A farmer sold 8 bushels of oats, 9 bushels of peas, and 9 bushels of rye : how many bushels in all did he •elll 10* The head of a fish is 6 inches long, the tail 9 inches, and the body 12 inches : find the length of the fish. 11. Har\'ey pays 5 dollars for a pair of boots, 17 dol lars for a suit of clothes, and 4 dollani for a hat : wha* does he pay in all 1 12' A man had 95 dollars in a savings bank, and do posited 5 do'!ars more : how much money had he then ii \)ank1 18. How many are 6 and 61 6 and 16 ? 6 and 26 \ 6 and 36 1 6 and 46 1 6 and 56 ) 6 and 66) £6 and £761 6 and 861 $6 and $961 14. How many are 7 and 7 1 7 and 17,1 7 and 27 1 7and371 7and471 7 end 571 7 and 671 7 and 771 7 and 871 7 and 971 15. How many are 9 and 8 1 8 and 18 1 8 and 28 1 8and 381 8 and 48 1 8 and 58 1 8 and 681 8 and 781 8 and 881 8and 981 16. How many are 9 and 9 1 9 and 19 1 9 and 29 1 9 and 391 9 and 49 1 9 and 59 1 9 and 691 9 cents and 79 cents 1 9 farthings and 89 farthix^t t9 and $991 9tMUiuid99tens. IS 17. How many are 10 and 11 1 10 and 21 1 10 and 81 1 10 and 411 10 and 51 f 10 and 61 1 10 and 71 1 10 and 811 10 and 911 10 hundred and 91 hundred t IC tenths and 91 tenths 1 18. How many are 10 and 131 10 and 22 1 10 and 321 10 and 421 10 and 62? 10 and 62? 10 and 721 10 and 821 10 and 921 19. I used 8 rolls of paper for a bed room, and 28 for A parlor : how many did I use for the two rooms 1 20. A' farmer has 7 acres in forest and 67 acres cleared : how many acres has he in all 1 21. Herman's grandfather was 73 yeara old 8 yean ago : how old is he now 1 22* A man travelled 9 miles by stage and 89 by rail : how far did he travel 1 28' A carter pai I 10 dollars for a cart and 92 dollars for a horse : how much did he pay for both 1 24* Jane paid 5 cents for ink, 7 cents for pens, and 92 cents for an arithmetic : how much did she pay out 1 25. John gave his brother 5 cents, his sister 6 cents and hail 19 cents left : hiw much had he at first 1 26. Richard had 9 marbles, and Harry and Thomas hod together 79 marbles : how many had all three f Examples. — 3. 1. How many are 10 and 41 lOandUl 10and241 10 and 34 1 10 and 44 1 10 and 54 1 10 and 64 t 10 and 741 10 and 841 10 And 941 2. How many are 11 and 31 11 and 231 11 and 331 11 and 431 lland531 11 and 631 lland7df 11 cents and 83 cents 1 $11 and $93 1 a Howmanyarelland41 llandUt llMidlAI mm PPiP mwmmmwm wm mk^im 14 MIMTAL ABITHXinO. 11 and 341 11 and 441 IT and 541 11 and 641 11 and 74 1 11 minutes and 84 minutes 1 11 houis and 94 hours 1 4. How many are 10 and 51 10 and 15 1 10 and 25 1 10 and 351 10 and 451 10 and 55 1 10 and 651 10 and 75 1 10 guineas and 85 guineas 1 £10 and £95 1 5. How many are 11 and 51 11 and 15 1 11 and 25 1 11 and 351 11 and 451 11 and 651 11 and 651 11 seconds and 75 seconds 1 11 francs and 85 francs 1 11 crowns and 95 crowns 1 11 fourths and 95 fourths 1 "^ 6. How many are 3 and 81 3 and 18 1 3 and 28 1 3 and 381 3 and 481 3 and 581 3 and 681 3 and 78 1 3 gallons and 88 gallons 1 3 pints and 98 pints 1 3 tens and 98 tens 1 7. How many are 8 and 41 8 and 141 8 and 241 8 and 34) 8 and 441 8 and 541 8 and 641 8 and 74 1 8 and 84 1 8 and 94 1 8 tenths and 94 tenths 1 94 twelfths and 8 twelfths 1 8. How many are 7 and 7 1 7 and 171 7 and 271 7 and 37 1 7 and 47 1 7 and 57J 7 and 67 1 7 and 77 1 7 and 87 1 7 and 97 1 0. How many are $8 and $61 8 shillings and 16 shillings 1 8 pence and 26 pence 1 8 pounds and 36 pounds 1 8 ounces and 46 ounces 1 8 yards and 56 yards 1 8 miles ahd 66 miles 1 8 hours and 76 hours 1 8 days and 86 days 1 8 years and 96 years 1 10. How many are 11 and 7 1 8 and 9 1 10 and 9 S 7 and 141 6 and 121 9 and 15 1 11 and 18 1 15 and 121 11. How many are 14 and 13 1 16 and 14 1 21 and 121 24 and 131 25 and 151 27 and 131 23 and 171 lil How many ar« 29 and 11 1 30 and 20 1 34 and 101 aswidist ADDITIOM. 1ft 18 Find the result of 8+2+5+7+9+6+4 +7 ^ Of 3-j 4+2+7+8+5+9+3+6+? How many ar« 8+9+3+6+7+5+4 1 Add 1, 2, 3, 4, 6, G, 7, 8, ft. 14. How many are 7 inches and 4 inches 1 4 miiei and 7 miles ? 7 pounds and 4 pounds 1 4 ounces and 7 ounces) 4 tons and 7 tonst 7 hundreds and 4 hun- dreds 1 5 tens and 4 tens % 4 tens and 5 tens ) 7 tens and 8 tens) 15' Find the sum of 40 and 50. Ana. — 40 is 4 tens, 50 is 5 tens; therefore 50 and 40 are 9 tens, or 90. 16. P»id 20 dollars for a cart, and 70 dollars for a horse : what did I pay for both 1 17. Peter gave away 20 marbles, and had 80 left: how many had he at first 1 18. Eliza paid 30 cents for a pen case, and 50 cents for a geography : what sum did both cost her 1 19. A farmer sold 20 bushels of turnips, 30 of barley, and 50 of wheat : how many bushels in all did he sell 9 20. What is the sum of 26 and 37 1 Arts, — 26 is 2 tens and 6 units ; 37 is 3 te.\25 and 7 units ; 2 tens and 3 tens are 5 tens ; and 6 units and 7 units are 13 units, or 1 ten and 3 units ; which, added to 5 tens make 6 tens and 3 units, or 63. 21. What is the sum of 33+441 35+151 36+121 40+361 40+291 44+201 48+321 45+351 22. 4+8+6+2+7+12+10+9 are how many 1 28 16+12+6+18+4+10+24+16+12 are how many 1 24. 22+23+11+15+16X2+28+12+15 are how many I % / t*ui„ ^m^mimm^ pgi^^^(|wu,ii,ru(|»ui«ljji. . H MOTAL AKITHmfHl EZAMPLU. — i, 1. Jane has 13 pins In one cushion, and 37 inaiicther bow many has she in boUi ? 2* Alfred gave 8 pears to Willi::m, 12 to Ghutei 9 u James, and had 11 left : how many had he at fintt 8* A woman paid 18 cents for a pound af ehe^^Be, 6S cents for a pound of tea« and ir» cents for nutmegs: hoix much did bhe spend in all? 4- From Halifax to Shubenacadie (he distance is 4) miles, and from Shubcnacadio to Truro the distance t> 19 miles : fino the distance from Halifax to Tima. 6. A prrocer paid 47 dollars for com meal, and 75 dol- lars for flour : what did both cost him1 6. A farmer has 12 acres in oats, 17 in tjg, and 27 in wheat : how many acres in gi-ain ha3 het 7. A fisherman caught 13 cod on ^Tonday, 28 on Tues- day, and 59 on We-Inrsday : how many did lie catch in the three days t 8. 73-j- 174-3 4-7-1- 10 are hiw many 1 9. Willie gave 57 cents to lis sister, and had. 65 cents left : how many had he at first t 10> Brampton is 28 miles west of Toronto, and Bow- manville 43 miles cast: find the distianoo between Brampton and Bowmanville. 11 A man began business with 28 thousand dollars, and in 10 yeara cleared 68 thousand dollars : how much was he then worth J 12. A man bought a cow f r 25 dollars, a calf for 5 dollars, 3 lambs for 8 dollars, and a pig for 2 ddlani : what did he pay for all 1 18- A horpe is worth 85 dollars, and a waggon Ift irilara : what ia tlia ralua of both t ADDRIOir. 19 14. Luoy bought a bonnet for 3 dollars, a silk dren for 19 dollars, and a shawl for 29 dollars : what did she pay for all t 15* Thore are 31 days in January and 28 in February : how many days in both t 16. An orchard contains 15 cherry-trees, 37 plum- trees, and 45 apple-trees: how many trees are in the orchard t 17* A lady bought some tape for 10 cents, some pins for 18 cents, and a pair of scissors for 30 cents : how much did she pay for all t 18. A merchant bought a horse, saddle and bridle; for the horse he gave 75 dollars, for the saddle 25 dollars, and 7 dollars for th 3 bridle : what did they all cost him 1 19. From Toronto to Whitby is 29 miles, and from Whitby to Port Hope is 33 miles : what is the distance from Toronto to Port Hopel 20. Bath is 18 miles from Kingston and 36 miles fronr Belleville : bow far from Kingston to Belleville 'f 21. Cobourg is 72 miles from Toronto and 103 miles from Kingston : how far from Toronto to Kingston I 22. From Montreal to Cornwall is 68 miles and from Cornwall to Kingston is 105 miles: what is the distance from Montreal to Kingston 1 28. Oshawa is 33 miles from Toronto and 300 miles from Montreal : what is the distance from Montreal to Toronto 1 24. John hoes 19 rows of potatoes, James 31 rows, and William 48 rows : how many rows do they all hoe I 25. A grocer mixes 3 pounds of tea worth 12 shillings, with 4 pounds worth 20 shillings : how many gondii ac<% there in themixturel HBifPr 5rw< jyiim^liippp il^i "WW ■n* ,. J ,^i..JJ .. ,ii| I iLW?PW!|f!fPPWfW^^^!P(P3^^ ■..-y. 18 KBNTAL ARITHMETIO. 26. A person sells 6 apples for 12 cents, and 9 otlien /or 15 cents : how many apples does he sell, and wha^ does he get for them 1 27. James and Robert ha»l equal amounts of money in the mjrning ; during the day, James lost 6 dollars and Robert gained 9 dollars. In the evening, who had the larger amount, and how much larger ? 28* A father divi.led a certain number of oranges be- tween his wife, 2 sons and 3 daughters. He gave to the youngest son 5, to his wife 7, and the rest he divided equally between his three daughters and eldest son. The eldest son's share was 5 more that his mother's. How many oranges were divided ? 29> A father divide'l a certain number of apples between his three sons; to the first he gave 11, to the second 4 more than the first, and the third 7 more than jihe second : how many apples had he 1 Section II.— Subtraction. Examples. — 5. 1. John had 3 cents and gave his brother 1 : how many had he left 1 ^7i^._Thc diffe ence between 3 (that is l+l-j-l) and 1 is 2, therefore he had 2 left. 2. A boy had 5 apples and gave away 3 : how many had he left 1 8. Jennie had 8 needles and lost 5 : how many had she remaining 9 4. Rufus caught 9 trout and gave Charles 3 : how many had he le^* 8UBTBACTI0N. 19 5. How many are 3 and 21 2 from 51 3 from 5 t 6. How many are 5 and 41 4 from 91 5 from 9 1 7. How many are 6 and 3 1 3 from 91 6 from 9 1 8. How many are 6 and 51 5 from 111 6 from 111 9. How many are 4 and 71 4 from 111 7 from 111 10. How many are 4 and 101 4 from 14 1 10 from 141 11. How many are 8 and 5 1 5 from 131 8 from 13 1 12. How many are 5 and 91 6 from 141 9 fi'om 141 18. How many are 7 and 101 7 from 171 10 from 171 14. I paid 15 cents for oranges and 9 cents for ap- ples : how much more did the oranges cost than the ap- ples 1 15. I had 17 dollars, and paid 12 dollars for two barrels of flour : how much had I left 1 16. Jane is 16 years old : how old was she 7 years agol 17. How many are 4 from 121 4 fi-om 131 4 from 14 1 4 from 15 1 4 from 16 1 4 from 181 4 from 20 1 4 from 24 1 18. How many are 5 from 121 5 from 14 1 5 from 151 5 from 171 5 from 20 1 5 from 22 1 5 from 24 1 19. James has 20 marbles and sells 6 of them : how many has he leftl 20. Bought a cart for 24 dollars and sold it foi* 17 iolhirs : how much did I lose 1 21. Bought a cow for 28 dollars and sold it for 40 doUai-s : find my gain 1 22. How many are 12 — 91 15—91 19 — 91 16 — 61 14 — 41 25 — 51 30—71 27-.-71 l^ -6t 14 — 81 20 IIXNTAL ABITHMina 28. How many are 16 — 31 24 — 4! 16 — 5t 17—81 19 — 91 29—81 34 — 31 35—61 6Qt _81 67 — 61 24. How many are 69 — 61 53 — 71 16 — 1011 36 — 161 26 — 121 20 — 141 30 — 121 29 — 1011 39 — 201 26. How many are 24+2 — 3 1 19-f 6 — 6 1 30+ 45—121 37+13—151 45+16 — 101 40+1+3 — 6! 26. Howmanyare40-f 1+3 — 61 37+3+10—81 26+16+5 — 91 27. Begin with 67 and count back to 3, by su1>tract- ing 4 successively. 28* Begin with 50 and count back to C, by subtract- ing 2 ; thus 5'\ 48, 46, Two men bought a horse, the one pays Tftdrllars, and the other 29 dollars less : how many dollars did both pay! 14. From Toronto to Thomliill is 1 2 miles, from Thorn- hill to Richmon 1-hill is 5 miles : how far from Richmond- hill to Aurora, the distance from Aurora to Toronto being 31 miles! 16« John bought a watch for 15 dollars, and a chain for 9 dollars. Ho sold them both for 29 dollars : ho¥^ much did he gain 1 16. William and James start from the same point ana travel in the same direction, the one at the rate of 13 miles, and the other at the rate of 7 miles : how far apart will they be 1 17. On January 7th, how many days yet remain in the month 1 18. Mary was bom 6 years before Ann; Mary is 21 years old : how old is Ann 1 19. How many is 90— 60 1 Aru. — 90 is 9 tens, and 50, 5 tens, 9 tens — 5 tens are 4 tens, or 40. 20. How many is 75 — 26 1 92 — 60t 87—401 98 — 701 67 — 421 84 — 431 96 — 361 86 — 551 21. How many is 75 — 37 1 ^n«.— 75 is 60+15 and 37 is 3r 8^ is 4^, and 45 -> 7 is •UBTRAOnOV* fS. How manj is 46 — 89t 57 — 881 89 — 19t 89 — 741 43 — 281 52 — 271 67 — 391 84 — 651 S8* To the number 10, add 10 and subtract 5, add 5 and subtract 10, add 12 and subtract 6, add 6 and sub- tract 12, add 20 and subtract 10, add 20 and subtract 10^ and give the result. 24. There are 65 scholars in a school, and 30 of them are girls : how many boys are there 1 25* A merchant bought 67 quintals of codfish^ and in ft week had sold all but 35 Quintals : how many did he sein 26* A man began business with 42 thousand ilollarB, and in 5 years lost 22 thousand : how much had he lefbl 27* Edgar had 19 peaches, he gave 7 to Mary and 6 to Minnie : How many had he left 1 28' Bought goods to the amount of 29 d .llan : for how much must I sell them to gain 13 dollars 1 20. A bin has in it 55 bushels of oats, 23 bushels are taken out of it at one time and 9 bushels at another : how many bushels are left 1 . 80. Pindresultof22 — 8+13 — 6+4 — 1+7+9 — 20, and also of 86+14+20 — 15+10 — 30. 81. Johnoarned 80 cents one ilay, and spent 30 centa of it, the next day he earned 50 cents : how much had he «hen1 82. 9 tenths- 3 tenths? 8 twelfUui — 4 tweUUuil 38 fifteenths— 15 fifteenths 1 wmwm^ ^m^ flWnWMWfiwp" 26 MENTAL AAITHHETia Section III.— Multiplicatioiu Examples. — 8, 1. Wliat will 2 apples cost at 4 cents each S Arts. — 1 Apple costs 4 cents, therefore 2 will ood** 4-f-4 that is 2 times 4 cents or 8 ceiita. 2. What will 2 oranges cost at 5 cents each 1 8- A man earns 8 dollars. a week, how much will he earn in two week si 4. How many is : 2 times 1 2 times 4 2 times 7 2 times 10 5 times 2 2 times 2 '2- times 5 2 times 8 2 times 11 8 times 2 2 times 3 2 times 6 2 times 9 2 times 12 10 times 2 5. l^^ind the cost of 2 barrels of mackerel at 12 dollars a barrel, 6. What is the cost of 4 yarTs of tape at 3 cents m yai-d ] at 4 cents 1 at 6 cents ] 7. How many is : 3 times 1 3 times 4 3 times 7 8 times 10 8 times $ 3 times 2 3 times 5 3 times 8 3 times 11 11 times 3 3 times 3 3 times 6 3 times 9 3 times 12 12 times 3 8. What will 3 barrels of flour cost at 7 dollars a barrel 1 9. A man earns 3 dollars a Jay, how much will he earn in a week 1 10- Find the cost of 12 yards of calico at 3 pence per yardi 11. What will 4 pounds of rice cost at 6 ots. a pound I at 7 cents 1 at 8 cents t How many is : 4 times 1 4 times 4 4 times 7 4 times 10 2 times 4 4 times 2 4 times 5 4 times 8 4 times IT 5 times 4 4 timeM 3 4 times 6 4 times 9 4 times 12 8 times 4 ^lULTIPLICATIOir, S7 1^. What will 4 pounJs of sugar cost at 11 cents a [K und 1 13. Mary bought 4 yards of cotton at 9 cents a yard > what Old it cost her 1 14. I paid 4 dollars a day for a team and kept it 10 days : what did it cost me 1 16. How mivay ia 6 times: 1? 2? 3? 41 61 61 71 81 91 10 1 111 12 1 How many is 8 times 5 1 6 times 61 7 times 5 ) 9 times 6 tenths 1 4 times 5 tens 1 7 times 6 hundredths 1 16. Find the coso of 5 cordf of wood at 6 dollars a cordi 17. 6 boys received 11 apples each : how many did they all receiv o1 18. At 5 cents a pound, what will 7 pounds of rice cost 1 8 Bbs. 1 9 lbs. 1 10 lbs. 1 12 lbs. 1 19. How ma.iy is 6 times 1 1 21 31 4t 5f 61 71 81 91 11 111 121 2 tensi 5 tensi 7 thirds 1 8 fourths 1 20. I paid 6 dollars a ton for 9 tons of coal : what was the whole cost 1 21. Jane bought 11 yards of cotton at 6 pence per yard : what did it cost her 1 22. How many is 7 times 1 1 2t 3t 4t 61 61 71 8? 91 101 HI 121 2 pencel 3 shillingst 4 tenths 1 23. A merchant averages a profit of 12 dollars a day : how much is that a week 1 24> A merchant bought 7 quintals of codfish at 5 ddl- lurs a quintal : what did he pay in all 1 26. How much will 8 yards of silk cost at 9 shillings a yard 1 9 inches of gold wire at 7 pence an inch 1 86. How mimy is 8 timos 1 1 21 31 41 01 6t j^MMM^^f^^^m^:^^. <•'* u. m wHarw ^'W^m- " tt MKirtAt hmtuutno, 7t 8t 9f lot in 12t Howmaclii8l2time8 8t 7 times 89 27- Find the cost of 9 lbs of sugar at 10 cents per pound 1 Of 8 barrels of flour at 7 dollars a barrel 1 28- A steamer sails 12 miles an hour for 7 hours : what distance does she make 1 29^ What will be the cost of 9 lbs. of cheese at 8 pence a pound 1 9 yards of cotton at 8 pence a yard 1 80. How many is 9 times 1 1 2? 3) 41 6t 6t 7f 8t 91 10? 11) 129 How many is 8 times 9 1 7 times 91 81. How many inches! are in 9 feet, there being 12 inches in one foot 1 X 82. A farmer makes an average profit of 11 dollars an acre : what profit has he off 9 acres of land 1 88. How many is 10 times 11 21 31 4t 51 61 71 81 91 101 111 121 How many is 9 times 101 8 times 10? 84. What will 10 lbs. of butter cost at 9 cents a pound 1 at 10 cents 1 at 11 cents 1 85. What will 9 yards of muslin cost at 11 cents a yard 1 86. How many is 11 times 11 21 31 41 5t 61 71 81 91 101 111 12i 12 times 111 9 times 111 7 times 111 87. Find the cost of 11 yards of ribbon at 11 cents a yard 1 10 quintals of codfish at 4 dollars a quintal 1 88. I bought 11 fi>s. of halibut at 9 cents a pound : what did it cost me 1 89. How many is 12 times 11 21 31 4^ 51 6f 71 81 91 101 111 121 2farthing8l 4 ounces! fttenal 7twelfth8l %^s '■wii^irr-'^r'^'i-' ''* tl.ai:.''. -^..^iLi^i t: jLMjestr.i'^.-Tecai.iyste ;'!.' '':'■■ ':^l*^gii4M MULTIPLICATIOH. 40- What will 12 dozen of eggs cost at 12 cents a dozen t 41> What will 9 topB cost at 5 pence each t 42' What will 8 knives cost at 6 dimes each t .48 -At 12 cents each, what will 9 primers cost) 44 What will 8 yards of broadcloth cost, at 4 dollars a yard 1 45. If a boat moves at the rate of 11 miles an hour : how far will it go in 11 hours ) 46' Mr. Finkle's stage, moving at the rate of 6 miles an hour, takes 4 hours to go from Newburgh to Kingston : how far from Newburgh to Kingston % 47* If A steamer sails 7 miles in an hour : how far will she travel in 7 hours) In 9 hours) In 11 hours t In 12 hours 1 48- At 7 cents a pound : what will 8 ponnds of beef oosti 10 pounds 1 6 povndsl 12 pounds) 49- How much is 8 times 2-fifths ? 9 times 3-tenths t 12 times ^twelfths 1 6 times 3-elevenths 1 50' How much is 7 times 5 pence ) 5 shillings t 5 hours? $51 Xdl 5-tenths1 5-twentieths ) 5 hun- dreds % 5 thousandths 1 G SAMPLES 9. 1 What are the factors of 6 1 10 f 16 t 21 1 36 f 2. When 10 is a factor, with what figure does the pro- duct always end 1 8. When 5 is a factor, with one of what two figures does the product always end 1 4* How much greater is 11x9 than 10X7 1 5> A farmer sold 8 sheep at 5 dollars each, and 9 pigs tX 6 dollars eaoh : how much did he receive in all t SjBf'^'SP^P'^ MM!-,\ ,-i, A wf^^s^m^mif^mm io MBNTAL ABITBKETia 6. How much is 12X61 5Xllt 7X91 12X81 7X7? 9X71 7X91 10X111 9X1^1 7. A man*s wages is 13 dollars a montlj. he flpenda 5 dollars a month : how much does he save in a year 1 8. 10 men can mow a field in 12 hours : how loiif^ would it take one man to do it 1 Sol. — It will take one man ten times as long as 10 men — 10 times 12 is 120 hours 1 9- If 6 men reap a field in 7 days, how long will it take 1 mani 10* A quantity of provisions will last 8 men 12 days : how long would it last 1 man 1 11. 9 horses eat 80 bushels of oats in 20 days : how long will that quantity last 1 horse 1 12« It takes 8 men 8 days to do a piece of work : how many men will do it in 1 day 1 iSol. — 8 men do it in 8 days.*. 64 men will do it in one day. 13- How many men must be employed to do a piece of work in one day, which it takes 11 men 12 days to do 1 14 • A tailor has 43 yards of broadclotli ; if he sells 23 yards of it, what will the remainder be worth at 6 dollars a yard 1 15. If 6 pipes of equal size can fill a cistern in 12 hours, in how many hours could one of them fill it 1 16. 12 men dig a ditch in 11 days: how many men would dig it in one day 1 17. Three times 26 are how many 1 Sol. — In 26 there are 2 tens and 6 units. 3 times 6 units is 18 units, or 1 ten and 6 units, and 3 times 2 tern is 6 tens, which with 1 ten and 8 units maka 7 tens And 8 units, or 78. ..'tiilt.Laii. .^'■J.r .■\t)JlAjSi^i:^..Jujit^jJi'ft^i'(^^i .^t>Uilij. MULTIPLICATIOM. 91 18. How many is 4 times 181 239 259 18 1 329 5 times 75 9 6 times 84 9 i times 92 9 S times 16 tens 9 19. Wbat are the factors of 89 15 9 22 9 90 1 %\S 149 169 329 969 849 100 9 1209 20. Find as many sets of factors as you can for 94. For 30. For 48. For 16. 21. How much is 14 times 139 Analysis. — The factors of 14 are 7 times 2.'. 14 times 13 is equal to 7 times 13, multiplied by 2. 7 times 13 is 91 ; twice 91 is 182. 22. How much is 18 times 23 9 15 times 38 9 16 times 26 9 14 times 72 9 21 times 17 9 35 times 139 25 times 19 9 32 times 269 23. Five times twelve, less ten, plus 15, is how manyl 24. How much more is 8 times 8 than 7 times 9 9 25. If fc^o nien start from the same place and travil in opposite directions, the one travelling at the rate of 9 miles an hour, and the other at the rate of 4 miles an hour, how far apart will they be at the end of 5 hours 9 26. Two men start 60 miles apart and travel towards each other, the one at the rate of 4 miles an hour, the other at the rate of 3 miles : how far apart will they be at the end of 5 hours 9 27. Find the result of 6X20X15 ; and of 21 X7— 3 xii. 28. For how much must I sell 25 barrels of mackerel which cost me 8 dollars a barrel, so as to gain 50 dollars 9 29. Bought 5 cords of wood at 6 dollars a cord, and handed in payment 4 ten-dollar bills : how much change gaouid I receive 9 80. A farmer sold 7 8hee|) at 9 doilaro eaoh| and 9 r^v j;"'f>n^RS^35P7s n MENTAL ARITHHETia lambs at 2 dollars each : how much did he get for them aUI 81* A tailor has a piece of cloth containing 23 yards ; if he should cut from it 13 yard^, what will the remain- der be worth at 4 dollars a yard 1 82* A and B travelling toward each other met in 12 hours: how far apart weretluir starting points, it' A went 10 miles an hour, and B 12 1 88- Find first the sum, then the difference, and then the product of 10 and 35. Of 11 and 36. 84* How many yards m 14 pieces of cloth, each con- taining 37 yards 1 86. Bought 23 cows for $48 each ; sokl them at $60 apiece : what was the profit on each and on the whole 1 86' Two men start at the same place and travel in the same direction; one at the rate of 7 miles an hour, and the other at the rate of 3 miles an hour : how far apart will they bo in 9 hours 1 87- A man bought a horse for $dO, paid |3 a week fo' his expenses, and received $5 a week for his work ; at the exi)iration of 8 weeks he sold him for $80 : did he gain or lose by the operation, and how much 1 88' If a traveller, starting from any point, travels 10 hours, at 4 miles an hour, and then returns at the rate of 6 miles per hour for 3 hours, how far is he then from Mio place of departure 1 Section IV. —Division. Examples. — 10. f. At 2 cents each, how many apples can be bought M. — STM7 2 c«nt8 will bur an ap]^ ; S it sivisioir. .ained in 6 3 times : therefore 3 apples eui be' bought for 6 cents. 9. At 4 cents each, how many oranges can be bought for 12 cents 1 3- ^or 24 cents how many pounds of sugar can be bought at 8 cents a pound] 4. Paid 32 dollars for 8 cords of wood : how much ia that a cord ? 5' 3 times 2 are 6 ; how many times is 2 contained in 61 3 in 6 1 6. 15 is how many times 3 ? how many times 61 12 is how many times 2 1 how many times 6 1 how many times 4131 7. How many times 4 are 81 161 121 201 24! 281 8. John spent SO cents in pencils, at 6 cents each : how many did he buy 1 DIVISION TABLE. 1 In 2 in 8 in 4 in 6 in 6 in 1, once 2, once 8, once 4, once 6, once «, once 2, twice 4, twice 6, twice 8. twice 10, twice 12, twice 3, S times 6, 3 times 9. 3 times 12. 3 times 16, 3 times 18, Stimei 4. 4 " 8, 4 " 12, 4 '• 10, 4 " 20, 4 •• 24, 4 " 5, 6 " 10, 5 " 15, 6 " 20, 6 •• 25, 5 " 30, 6 " 6, 6 " 12, 6 " 18, 6 " 24. 6 " 30, 6 " 36, 6 •• 7, 7 " 14, 7 " 21. 7 " 28 7 •* 85, 7 " 42, 7 '• 8. 8 " 16, 8 " 24. 8 " 32, 8 •• 40, 8 " 48, 8 " 9, ft " 18, 9 '• 27, 9 " 36, " 45, 9 " 54, 9 «• 10, 10 " 20, 10 " 30. 10 " 40, 10 ** 50, 10 •• 60, 10 » 11, 11 " 22, 11 " 33, 11 " 44, 11 «« 55, 11 '• 66, 11 •• 12, 12 '• 24, 12 " 30, 12 •• 48, 12 " 60. 12 •• 72, 11 •* 9< A boy paid 12 cents for pens at 2 cents each : how many did he buy 1 10. At 3 dollars a yard, how many yards of silk caa be bought for 27 doUaisI 11. A horse trotted 48 miles in 6 hours: how many miles an hour did he average 1 w^ l'>?r,'^.m *V^ •^^^^f^J^-^aJ^^T S4 ■KNTAL ARITHMETia 12. A fiEirmer gave 60 dollars for sheep, paying 6 dollars a head : ho'vv many did he buy t 13. A carpenter exms 12 dollars a week : how long will it take him to earn 72 dollars 1 14. A bag contains 3 bushels : how many such bags will be required to hold 36 bushels 1 15. One man can do a piece of work in 66 hours : in how many hours can 6 mon do the work 1 16- It takes 50 men onn week to «lo a certain work : how many weeks would it take 10 men 1 Division Table — Continued, • m 7, onoe 14, twice 21, 8 times 4 " «, B6, 6 42, 6 49, 7 08, 8 68, 70, 10 77, 11 84, 12 «< u u 8, 16, 24, 40, 48, 66, 64, 72,. 80, 88, 96, 8 in once twice 8 times 4 6 6 7 8 9 10 11 12 <4 • < « «< (I M «« «< 9 in 9, once 18, twice 27, atimes 86, 45, 4 6 54, 6 63, 7 72, 8 81, 9 90, 10 99, 11 108, 12 « « •< M ought for 63 dollars ) 18. How much will 70 yards of cotton cost at the rat* of 10 yards for 1 dollar 1 19. How much halibut at 12 cents a pound can bi bought for 96 cents 1 20* A freight train is moving 12 miles an hour : hoi» long will it be moving 84 miles ? 21. How much la 6 times 10 divided by 5 1 by 12 1 by4t 82. 9 times Mary's age is 108 : find her age f 28- If one horse can eat a quantity f oats in 144 dayi| bow long will it take 12 horses to eat an equal quantity t ^t.f. ;•■■;■' ■:. V'-"'p- '^^SS^f^ ■ ?■ DIYIfllOlf. 84> How long will it take 11 men to do a eertaio work, if 55 men can do it in 1 day 1 Note. — ^The sign of division is +, thus 15+5 meau tliat 15 is to be divided by 5. 25* At 3 cents each how many apples coald yoa bay for 8 cents, and how many cents would you have leftl 26. What is the quotient of 40-5-51 40-J-81 40-f-lOt 27. 45 are how many times 51 91 101 111 15 1 28. If you had 63 dollars, how many sheep could you buy at 6 dollars each, and how many dollars would yon have leftl 29- How many times is 4 contained in 28 1 5 in 15 1 $6 in $241 3 cents in 27 centsi £2 in £161 1 hour m 9 hours 1^ 5 dimes in 35 dimes 1 6 tens in 36 tens f 2 fifths in 12 fifths 1 3 ounces in 36 ounces 1 5 tenths in 55 tenths 1 80. How many times is 7 contained inl41 9in36t 10 in 401 8 in 561 11 in 331 9 in 541 12 in 721 7 in 701 10 in 701 £11 in £991 8 guineas in 40 guineas! 81. How many times is 2 contained in 24 1 12 in 24 1 3inl81 6inl81 12 in 1081 8 in 961 9 in 991 11 tens in 121 tens 1 12 hundred in 144 hundred 1 10 tenths in 120 tensi 9 thousand in 45 thousand 1 82. What is the quotient, and what the remainder in the foUowingl 14-f-5 1 68-*-71 9-5-21 39-J-41 112-*- 111 62-f-lOI 61-^71 61^81 19-f-2 1 63-i-61 140 days-^12 daysl 150 pence-f-12 pence 1 |133-i-$ll t 27 ounces+lO ounces 1 Examples. — 11. 1. 3 times a number-]- 4 times the number — twice tint aumber-|-7 times the number — 5 times the numlMt •quak 90 : what is the number t M V. MENTAL ARITHMETIC. 2. Jolin being asked his age replied : if you add 20 to 8 times my age the sum will be 100 : find his age. 3. What number must be taken from 95 so that the remainder may be exactly divisible by 10 ? 4. What number must be added to 129 to get a sum exactly divisible by 12 1 5. Divide 38 tens by 2 tens ; 64 tenths by 3 tenths j 65 by four ; 87 weeks by 5 weeks ; 136 by 4 ; 121 shil- lings by 11^38 days by 3; 308 months by 6; 150 guineas by 12. 6. Bought 12 yards of broadcloth at 6 dollars a yard, and paid for it with wood at 4 dollars a cord : how many cords did it take 1 7. The remainder is 4, the dividend 148, and the quotient 12 : find the divisor. 8. A house was bought for $1200, and sold for $1500. The profit was divided between 6 persons : what was the share of each ? 9. What number multiplied by 7 will give the same product as 14 multiplied by 9? 10. What number must be added to 29, so that it may be exactly divisible by 9 1 11. If the sum of 9 and 7 be multiplied by their dif- ference, and the product divided by 8, what will the quotient be 1 , 12. W^hat number must 4 be multiplied by, so as to produce twice 32 1 13- The sum of the product of two numbers and 6 is 94, one of the numbers is 7, find the other 1 14. What number subtracted 11 times from 456, leaves remainder 5% 15- A man gave $12 each to a certain number of men, and hiid $5 left of $125 : how manv men were there t OIYISIOV. 87 16* Charles said : — if you multiply the number of dollars I have by 12, and subtract $15 from the product the remainder will bo $69 : how much money had he t 17. 6 times 12 is how many times 48-f-6 % 18. 9 times 1 is h w many times 54-J-9 1 19. I received 30 yards of tweed for 5 tons of hay at $12 a ton : what was the clotL a yard 1 20' Willie having been asked how many dollars he ha«l, replied : if you add 9 to the number and multiply the sum by 8, the product will be $160 : how much had he) 21. Minnie having been asked her age, said : 9 times my age 6 yiears ago is 81 : find her age. 22' 6 times my present age is 9 times my age 5 years ago : how old am 1 1 28' At 15 cents a yard how much wincey can be bought for 300 cents ? for 400 1 24. If a quantity of provisions last 1 man 48 days, how long will it last 4 meni ^ men 9 8 men? 12 men 1 25. A woman sold 12 dozen of eggs at 15 cents a d -zen, and with the proceeds bought raisins at 18 cents a pound : how many pounds did she get ] 26. At 15 dollars an acre how much land can be bought for $1801 $300? $450? $6001 27. If 6 times Mary's age is divided by 12, the quotient, multiplied by 1 5, will be 75 : find her age. 28. A man paid $220 dollars for 10 months board : how much did he pay per month ? 29. A merchant's expenses are $12 a day : in how many days will ihey amount to $900 ? r^. wmw If '. . "". I fm'Wr^^^'mmww" MENTAL ABITHMETIO. Section V.— Miscellaneous Questions. Examples. — 12. I. Multiply 30 by 4, subtract 50, add 10, divide hy §, multiply by 7, and what is the result 1 2 Subtract 10 from 6 multiplied by 8, to the remainder add 4, divide the sum by 6, multiply the quotient by 11, subtract 7 from the product, divide the remainder by 10, add 30 to the quotient, and what will be the sum 9 8- 70 barrels of pork cost $5.60 : what was the price per barrel 1 4- One man can do a work in 55 days : how long wiL it take 10 men ) 5. A number multiplied by 8, divided by 6, multiplied by 10, and the product increased by 5, equals 45 : what is the number 1 6) Multiply 15 by 6, add 5, divide by 8, multiply by 6, subtract 10, divide by 5, add 2, multiply by 11, and what will the product be 1 7. The divisor is 5, the dividend 39, the quotient 7, Fin J the remainder. 8. The remainder is 5, quotient 6, divisor 7. Find the dividend. 9. How many sets of factors in 24 1 in 481 in 601 in 1251 10> By what number must the product of the sum and di£ference of 9 and 7 be increased so that the result may be exactly divisible by 7 1 II. A man bought an equal nuDiber of pigs and sheep for $63. Each pig cost $3. and each sheep $4 : how many of each did he buy 1 MISCELLANEOUS QUESTIOJTI. 39 12« A woman bought 26 yards of dross g:^ods at 30 cents a yard, and 22 yards of cotton at 10 cents a yard : how much change did she receive out of a $10 bill 1 18* There is a i?umber which, when divided by 4, and the quotient increased by 9, the sum multiplied by 3, and the product decreased by the difference between the arith- metical complements of 4 and 7, gives 33. Find the number 1 14' If 3 corJs of wood are worth 18 dollars, and 10 cords are given for 12 thousand shingles, how much «iro the shingles a thousand 9 16. If 3 j)Ounds of ^lour are worth 1 pound of sugar, and 6 pounds of sugar are worth 1 pound of tea, h^yw many pounds of flour are worth 2 pounds of te 1 1 16- A boat sailed up river for 10 houra at the rate of 3 miles an hour, but returned over the same distance in 6 hours : how fast did it sail down stream 1 17. When wheat is sold at the rate of 6 bushels for 12 dollars, liow many bushels must be given for 4 cords of wood, at 5 dollai's a cord i 18. A. steamboat can run 8 miles an hour down river, and cnly 6 miles an hour up river ; after running down liver for 3 houra, how long will it be in returning 1 19. Twenty acres of land are bought for 8'}0 : how many dollai*s per acre must they bo sold for, that the pur- chaser may double his ni(.ney1 20. I divide 26 oranges between two boys, giving om 7 more than the vther : h w many will each hnvef 21* If four barrels of flour are worth $36, how many yards of cloth worth $3 a yard will 2 barrels of the flour Imyl 22* A boy OB MB way to market with 17 lobstors, lost 1.1, I II f'l}' « } • vm. 40 MENTAL ARITHMETia 3 of them; tKc rest he sold for $1.12 ; how much was that apiece 1 23' Bought 6 barrels of pork for 120 dollars : at how much a barrel must it bo sold to gain $2 a barrel ? 24. Divide 15 cents between John and James so that John mav have 3 ct^nts less than James. 25' At 2 dollars ii bushel, how many bushels of wheat must be given for 4 barrels of flour at $8 a barrel 1 \ \3 26' A man can do a piece of work in 4 days when the days are 12 hoiu's long : how long will he take when the days are 8 hours Jong 1 27« Exchanged 11 tons )f hay for 15 yards of iloth at 6 dollars a yard, and 4 yards at 5 dollars a yard : how much was the hay worth a ton 1 28- A man can do a piece of work in 5 days by work ing 8 hours a day : how many hours a day must ho work t ' do it in 4 days f 29* Two men are 96 miles apart, and are travelling toward each other, one at the rate of 5 miles an hour, and the other at the rate of three miles un hour : in how many hours will they meet 1 Section VI.- Analysis Examples. — 13. 1. When a number is divided by 2, the quotiont is one of the two equal parts which compose the number, and is called one-fialf of the numl)ery thus : — 6 divided by 2 gives quotient 3, which is one of the two equal parts (34-3) that compose 6, and is therefore uno-hal^ offi. AVALTSI8. 41 % So, when a number is divided by 3, the quotient is one-third of the number ; when divided by 4 the quotient is one-fourth ; when divided by 5, one-fifth ; and when divided by 6, one-sixth. 8. What is one-half of 6? of 8 1 of 24? of 8 tens? of 16 hundred? VJ hat ia the one-third of 3? of 6? of 9 fifths? of 27 tenths? What is the one-fourth o{ S 1 of 12? of 36 ? of 60 twelfths? What is the one-fifth of 6 ? of 15 ? of 20 ? of 40 ? What is the one-sixth of 12 ? 18 ? 30 ? 42 ? 54 ? What is oncsixth of 36 pence ? 36 ounces ? 36 minutes? 36 tons? 36 tenths? 36 twentieths? 4. how many halves are there of any number ? How many thirds ? fourths ? fifths 1 sixths ? 5. How much is one- third of 9 ? 2 thirds of 9 ? How much is one-fourth of 12? 3 fourths? How much is one-fifth of 15 ? 2 fifths ? 4 fifths ? How much is •ne-sixth of 24 ? 3 sixths ? 5 sixths ? 6. When a number is divided by 7 the quotient is called one-seventh of the number ; when divided by 8, one- eighth ; when divided by 9, one-ninth ; when divided by 10, one-tenth j when divided by 11, one-eleventh; and when divided by 12, one-twelfth. 7. How many sevenths are there of any nnmber? How many eighths 1 ninths ? tenths ? elevenths t twelfths t 8. How much is one-seventh of 14? 21 ? 421 How niucfi is 2 sever.f's of 3r» ? 3 sevenths ? 4 sevenths ? 9. How much is oue-eiglith of 40? 3 eighths! 7 eighths. 10. How much is one-ninth of 9? of 18? of 81 f How much is 4 ninths of 27? ftninlhs? 7 ninths 1 ■.-;' T^Sl'JtS"-' ■ ^"i!r-"'^'-.r ■?;■■■. ,;^;:^ -,-. ; . .. .«;"':',»!!• JSW 49 MBIITAL ABITHlfETia Br,. . If-. How much is one-ninth of 27 pounds t 36 farthings! 45 days ) 54 grains 1 63 tens % 72 tenths ? 72 fifths f 11. How much is one-tenth of 10 1 of 301 of 70! How much is .2 tenths of 501 3 tent'*-'* 6 tenths! 10 tenths 1 12. How much is one-elcvonth of 22 1 2 elevenths ! 4 clevcnthsl 7 elevenths ! elevenths 1 10 elevenths! 18. How much is one-twelfth of 1 2 1 of 36 1 of 72 ! of 841 of 961 How much is one-twelfth of 1081 3 twelfths % 7 twelfths 1 9 twelfths 1 1 2 twelfths 1 14. One-half a number is 10, what is the number ! Hoi. — Since ona half is 10, two halves, or the whole number, is 2 times 10 or 20. 15. One-fifth of my ago is 6 years : how old am I ! 16. What is the number whose sixth part is 10 1 The aumber whose seventh part is 8 1 The number whose ninth part is 9 1 The number whose tenth part is 10 1 17. The rent of a house for a certain time is $60, what is the rent for one-sixth of the time 1 for 2 sixths! for 5 sixths 1 18* A man has $36 a month, and saves 2 ninths of it : how much does he save in 1 2 months 1 19> One-seventh of the money I have is $12 : how much have 1 1 20. If 22 is one-sixth of the value of a horse, find his value 1 21. What is 5 eighths of 16 yards 1 of 16 dollars I of 16 cents 1 of 16 years) of 16 daysl of 16 pence? of 16 farthings 1 of 16 hundredths 1 22- There are 12 months in a year, how many in one* sixth of a yearl in 2 sixths 1 in 5 sixths? 28' One pound oi cheese costs 18 cents, what will un*- srr- balf pound oott ? one-third of a pound t 5 sixtiui of t pound. 24> Five-sixths of 72 are how many times 6 1 how many times 121 how many times 10 1 25' James is 16 years old, and 3 fourths of his age k 6 sevenths of Harry's : how old is Harry t EZAHPLBS. — 14. 1. If 3 oranges cost 15 cents, what will 7 oraaiges coat f JSol. — 3 Oranges cost 15 cents, one will cost on^ third of 15 cents, that is 5 cents, therefore 7 will cost 7 times 5 cents, or 35 cents. 2. If 7 apples cost 14 cents, what will 11 costt 8. If 9 mackerel cost 81 cents, what will 12 costt 4* If 15 yards of tape cost 45 cents, what will 8 yards cost 1 5. $84 are paid for 12 barrels of herring : what would be the price of 10 barrels ? 6* If six men can mow 12 acres of grass in. a daj, how much can 13 men mow in the same time) 7. If 3 apples are worth 6 oranges, how many oranges are 20 apples worth t 8. If 8 dollars will buy 80 yards of cotton, how muok will 11 dollars buyl 9. When 60 cents are paid for 4 dozen of eggs, how much must be paid for 7 dozen 1 10. If 50 cents will pay for 5 lbs. of sugar, how mnoh will 120 cents buy/ Sol. — 5 pounds cost 50 cents, 1 pound 10 o^iiia, and if 10 cents buy 1 pound, 120 cents will buy 130-i-10| that is 12 pounds. D yittiiiiiliiEiiteMMiiii W""""' 14 MENTAL ARITHMETia ■ 11. If 8 men build a wall in 6 days, hoT.' many would build it in 12 days) 12> When $80 is paid for 8 barrels of mack&rel, how II limy barrels will $110 pay for ? 18. If 8 yards of calico can Le bought for 96 pence, how much can be bought for 132 pence 'i 14- If 4 ziien do mow a field in 12 days, how long would it take 6 meni JSol. — 4 men do it in 12 days, therefore 1 man will do it in 48 days, and 6 men will do it in cue- sixth of 48 days, or 8 days. 16. How long would it tako 11 mt^n to do what 10 men would do in 11 days'< 16. If 10 cents will buy 6 herrings, how much will 40 herrings cost 1 17. When five yards of broadcloth can be bought for 20 dollars, how much will $56 buy ? 18. If 8 copy-books cost 80 cents, w hat will 40 copy- books cost. Sol. — Since 40 is 5 times 8, 40 books will cost 6 times what 8 cost, or 5 times 80, thau in 400 cents. 19. What will 15 oranges cost, when 3 cost 11 cents'* 20* How many dozen of eggs can be bought for 90 cents, at the rate of 2 dozen for 30 cents ? 21. What will 21 pounds of rice cost, If 13 pound& cost 65 cents 1 . * 22. How much will 40 barrels of fiour cost, \7hen A barrels cost 26 dollars 1 28- How much honey at 12 cents » pound must be g^ven for 4 pounds of coffee at oJ cents a pound 1 S4. What is the cost of 30 yards of cloth at the rate of5yAixkfbr9doUM«t AKALYtm, 41 26* If 12 men de a piece of work in 10 hoari, how iong would it take 8 men to do the same work t 26' If a steamer make 48 miles in 4 hours, how long will it take her to make 72 miles 1 ^ -K^ 27> If 3 fourths of a number is 12, what is 5 times the number ? Os^ % (j 28. If 4 fifths of a pound of tea cost 60 cents, what will 2 pounds cost 1 /^^O C^^^

A lot and house cost $900, the house cost 8 times 48 much as the lot : find the cost of each 1 / ^^^ 40* Ed^'ii twice as old as Edgar, and their united ages is 30 years : find the age of each ? / 41' A horse and cart cost $108 ; the horse cost 5 times u much as the cart : find the cost of each 1 42' 72 ceD* . d -Tided between Harry and Charlie, for every 4 cents ^' '7 receives, Charlie gets 6 : how many does each receive 5 , ,^ Sol.— Ot •^:^n ^ ^ ' Harry gets 4 and Charlie 6, but 9 is con^»^Lle - times in 72, therefore Harry gets 8 times 4 cents and Charlie 8 times 5 cents. 48* Divide 60 marbles between Willie and Eddie, so Ihat for every 2 Willie gets, Eddie shall get 3. ^^ Cy^ On a certain holiday William caught 11 trout as often as Charles caught 7 ; William caught 55 : bow many did Charles catch 1 49* ^BVv^ lud out 60 cents in apples, giving 5 cents ^ 9WUJ app ie e; ke kept a number lor kuuaelf and pare 7- AVALTBIl. 4^ Ml equal number to each of 8 gImb mates : how many di^ each receive 1 < 60* I^ 9 barrels of flour are worth $63, how man) barrels of apples at $3 a barrel can be had for 6 barreb of flour % 51* A newsboy bought 9 papers at 3 cents each, and 8 others at i cents each; he sold all the papers at a uniform price, and gained altogether 26 cents ', find what he re- ceived for each paper 1 52' If $100 will support a family of 7 persons for 8 weeks, how many persons would it support for 14 weeks f 68- Two-thirds s)f 36 are 3 times what number 1 4 times what number 1 6 times what number 1 8 times what number ? 54« Eight-ninths of 81 are 6 times what number ) 8 times what number 1 9 times what number 1 12 timet what number 1 55* Four-fifths of 60 are how many times 6 1 how many times 8 1 Ten-elevenths of 65 are hour many times 5f 109 251 Section VII.— Highest Common Factor, &c Examples. — 15. 1. What numbers multiplied together will produce 8 1 101 161 351 481 401 451 511 421 2. Kesolve into factors, 15, 20, 25, 33, 36, 40, 50. 8. What factors have the following numbers : 2, 8^ ft, 7,11,13,17,19,22,23, 27,321 4* Name the prime and ihe componte numbers in Iii0 iKUowing, 24, 26, 27, 28. 29, 30, 31, 34, 3ft^ 37, H M^ 41.47,541 ■J^ Wfc?i'^y .: ■■^*^^^''' ^^*WfW 48 MKMTAL ABITHXinO. 5. What are the factors of 61 91 12 1 16 1 lOf 181 211 321 331 361 391 491 611 6. What are the prime fadars of 44 1 641 661 60 1 671 681 701 761 761 7. Name the divisors which are common to 8 and 10 ^ 12 and 16 1 10 and 30 1 9 and 36 1 24 and 36 1 8. Find the highest common factor of 8 and 24, 36 and 27, 32 and 48, 37 and 68, 18 and 80 1 9. Find a common multiple of 2 and 3, 6 knd 6, 4 and 8, 9 and 12, 32 and 481 10. Find the least common multiple of 8 and 12, 9 and 12, 12 and 20, 16 and 48, 10 and 36, 48 and 96 1 11. What is the «^war(j of 1 1 21 31 41 61 61 71 81 91 101 111 121 131 161 141 201 12. Find the cube of 1, 2, 3, 4, 6, 6, 7, 8, 9, 10, 11, 12. 18. What is the square roo^ of 11 41 91 161 261 361 491 811 641 1001 1441 1211 14. 6 times the square of a number is 320 : find the number 1 15. If the square rort of a certain number be divided by 6, the quotient is 2 : find the number. 16. If 11 be added to Harry's age, and 1 is added to 6 times the square root, ^ of the sum will be nine : find his age. Highest Common Factor and L. CM. Examples — 16. 1. What is meant by Common Factor, Highest Com- mon Factor t S. Find the H.C.F. of 4 and 6, 7 and U, 8 and 13 17 lyia 86, 06 and 14. HI0HB8T OOMMON FACTOR AKD L. 0. M. 4f le to >iii- U 3. Find the H.C.F. of 2, 4, 6, 8, and 12 ; of 5, 16, 26, and 39. 4. What is meant by the multiple of a number f what by the L.C.M. of two or more numbers 1 6. Find the L.O.M. of 4 and 6 ; 9 and 12 ; 8, 16, and 32; 4,6, 9, 18, and 36, 6. Find the L.O.M. of 2, 4, 6, 8 and 12; 6, 16, 10, 20 and 30 ; 3, 6, 9, 24 and 36. 7. A farmer wishes to put 24 bushels of wheat and 86 bushels of silver chaff into the least number of bins that shall contain the same number of bushels without mixing the two kinds of wheat : what number of bushels must each bin hold, and how many bins will be required 1 8. A gentleman has a triangular plot, the sides of which are 63, 84, and 105 feet, wishes to enclose it with k)ards of uniform length and greatest possible : what via oe the length of each board 1 How many boards will be required if it be 4 boards high all round) 9. A, B, and agree to purchase pigeons at the high- est price each that will allow each to invest all hia money ; A has 45 cents, B, 60, and C, 76 : how many can each purchase I 10. A can dig 4 rods of a ditch in a day ; B, 6 ; and C, 8 : what is the least number of rods that will furnish a number of whole days' work to any of ^ the three men* 11. The fore wheel of a perambulator is 3 feet in cir« cumference and the hind wheel 5 : what distance will be passed over before they are in the same relative pos ition as at first 1 12. The H.O.F. of two num>»ers is 2, and the L.C.M. is 12 ; one of the numbers is 4 : what is the other) 18. The H.C.F. of three numbers is 2, and thflii -.i} iiliiiiiffi'iitiiitfiii^^^^^^^^ iMiiMiiiirii .'* V'.-^|!r«.-.'^*rT A « .. ..iw^v^^vi^^^ppf^pvpiinfi^^ 00 MENTAL ARITHMITIO. L.O.M is 60; the first number is 4, the second 2 more ihan the first : what is the third 1 14* f^d the least number which, divided by 3, 5 and ", leaves 2 for remainder in each case. 15* What is the smallest sum of money with which I can buy rabbits at 25 cents each, pigeons at 15 cents each, and hens at 30 cents each 1 16< A boy can dig X2 post holes in a day ; his brother can dig 18 : what is the smallest number which will fur- nish exact number of days' labor for either alone or both together t 17. What is the least number which, divided by 3, 5» 7, 9 and 15, will leave 1 for remainder 1 18* What is the greatest and what the least number that can be subtracted an exact number of times from 55 f 19. What is the greatest and what the least number that can be subtracted from 153 an exact number of times f CHAPTEB n. Section i.— Fractions. INTEODUCTORY. Examples. — 1. 1. If anything, as a foot, a dollar, a pound, a number, dsc., is divided into two equal parts, each part is one-Aa{/ of the thing divided; if it is divided into three equal parts, each is one-third, and two of the parts are -fourtlis, and three of them tAr«»-fourthB ; if it is divided into five equal parts, each is one^J^, two FRACTIONS. 1^1 «f them are ^o-fifbhs, three of them ^e^-fifths^ foar of them fowr-fifths ; and so on for other divisions. ISbw, instead of wordsy we may ase figures to express one or more of the equal parts into which the thing has been divided, thus : — One-half is represented by ^, two halves by | ; one- third is represented by ^, ^ti70-thirds by |, ^A?'ee-third8 by I ; one-fourth is represented by |, o. In these expressions the lower ligure shows the number of parts into which the thing is tivided, and indicates the fractional unity (one-half, one- «hird, one-fourth, How much does | lack of 1 1 How much does ^ lack of 1 1 How many twentieths must be added to j^j^ to make it equal to 1 1 14. Take f from 1 and what is leftl Take y*, from 1 and what is leftl 16. Which is the greater, one-half or one-third 1 One-sixth or one-fifth 1 One ninth or one-twelfth 1 One twentieth or one-thirtieth 1 16. A horse cost $100, and a sleigh f as much : Find the cost of the sleigh. 17- A man sold ^ of a piece of cloth which contained 40 yards : How many yards were left 1 litch in twelve dig days, part il can he dig in 1 day 1 in 5 days 1 in 7 days % -I ] 'VS.. I rRAOTIONS. m i' 19* If B can dig a ditch in 10 days, what part of it can he dig in one day ? in 5 days 1 in 9 days t 20. If a peraon leaves his property, worth $1800, to his wife and 8 children, in equal parts, what fraction of the whole will each have, and how many dollars ? 21. What is the ^ of 181 of 18 shUlingsl of 18 pence 1 of 18 days 1 of 45 farthings 1 of 45 hours. What is the j\ of 36 seconds 1 of 36 ounces 1 of 36 tens % of 36 tenths] of 36 twelfths'! of 36 fiftieths? 22- I owned || of a ship, and sold 4 of my share : how many sixty-fourths had I left 1 23* If you put up ten pounds of tea in packages of one pound, what part of the whole do you put in one pack- age 't in 3 packages ? in 7 packages ? 24. 1 is what part of 101 of 51 of 15 1 of 9t •One-seventh is what part of 2-sevenths 1 4-sevenths t 5- sevenths 1 6-sevenths ? of 5 1 of '61 One-nineteenth ' is what part of j% 1 /, 1 jj 1 |^ 1 |f 1 3 is what part of 1 1 25. A person having $85, earned $115 more, and then gave away one-fourth of what he had : how much did he give away : how much did he retain 1 26. Jane has | of a dollar, and Harry and James have each I of a dollar : how much more have these than J ane 1 27. If ^ pounds of almonds cost 80 cents, what pari of 80 cents will one pound cost 1 2 pounds 1 3 pounds! 5 i>ounds 1 7 pounds 1 What part of 12 is 7 1 91 15 1 28. What is 1-seventh of £j^ 1 ^^ 1 29. What is 2-sevenths of ^f 1 S-seventhst Rnthsl 6-sevenths 1 13-sevenths1 80* If 12 oranges cost 36 cents, what part of 36 cents i-i U^ iS< lit 6-a0v- ! !•■' ^^Wiw T"^^, IIP"* §4 MINTAL ARITHMETIC. 11 pi I will 1 orangnoostl 2 oranges) 3 oranges? 5 oranges 1 b oranges 1 81* Ii^ <^ certain Sigh School tiiere are 12 boys and t as many girls ; required the number of girls, and the Aumber in the school. 82- What do you understand by 3-fourths 1 5-sixths 1 r-eighths? j%'i iJI ifl 88> A cow was bought for $60, and was sold for J of the c st : what was the gain 1 84- Tz ^^ ^^^ number of hours in a day is the number of hours I work , how many hours do I work ? 85* 3-ninths of 18-f5-sixths of 18 is how many? 6- ninths of 54 are how many times | of 20 ? 86> 3 sevenths of 21 are how many times 3 1 Sol. — 1 -seventh of 21 is 3 ; 3-sevenths of 21 is 9, which is 3 times 3 ; therefore 3 sevenths of 21 is 3 times 3. 87* 3-eighths of 24 are how many times 6? 4-fit*ths of $15 are how many times $3 ? | of 15 tenths are how many times 3-tenths? ^ of 15-twentieths are how many times jj'^ 1 7-ninths of 27 are hew times 9 I 88 Fred had $60 ; J of it he spent for a watch, and ] of it for a suit of clothes, how much had he remaining 1 39. A pole whose length is 15 feet is in the air and water, and } of the whole length, less 3 feet, is the length in the water, required the length in the air 1 40. The interest on $600 for 6 years is equal to J of the principal : how much was the yearly interest ? 41. What will 3-fourths of 8 pounds of coffee cost at ao cents a pound ? 4Jl \ is worth $2,400, and 5 sixths of A*i fortune u 10 times the interest on B's fortune for a year : what ia the inftirest on B's fortune t VRAOTIONt. W9 48* -A road 160 miles long is composed of 10 equal aections. What fraction of the whole road are 6 of these sections, and how many miles do they contain ? 44* If the rent of a house for 30 days is $90, how much will it be for 17 daysl 45- "^^o site of a sch ol cost $700 ; and 4-seventh8 of this $100 is 1 -eighth of the cost of the building : required the cost of the building t Section II.— Reduction and Anal]rsis. ^Examples. — 18. 11 M liM M ! f Hi! 1. How many fourths in 4| 1 Sol. — 4}=4-j- j ; in 4 there are 16 fouiiihs, there- fore in 4-|-| there are 16 fourths-]- 3 fourths, or 19 fourthly that is Jj*. . . 2. How man> thirds in 3i 1 4§1 6 J 1 6f1 13J1 8. How many fifths in 4^ 1 3| 1 7| ? 8§ ? 4. How many sevenths in 7^ 1 in 8f ? in 10| 1 in lljf t 6. How many ninths in 1 J 1 in 2| ? in 4| 1 in 5f 1 6. By how much is 4| greater than 3^ 1 than 2| 1 7. What is the resuH, in fiA.- l/--f Gy-t— 4/7 ? 8. How many tenths in 3j^ 1 in 2^^^ 1 in 4j^ ? in 9. How many twelftbg in 2y\; t in l^\1 S^l is 10> How, then, are mixed numbers reduced to improper /Tactions ? 11. Reduce to improper fractions 3^, 44, 6|, 6j, OJ, iOtV '■■■if'* ■ 5*1 M- ."•II :;^!i lit ih^i^u} '•^f—w'^mf^^^^^^^mfi M MBNTAL ABITHMBTIO. m. Reduce to improper fractions 1^^^, 2j\, 3,^*2, 1^^. 18- How many fourths of a dollar will 7 yards of cloth cost at $2| a yard 1 Sol.—2i=\^ and 7 times -V-=¥- 14:. How many thirds of a dollar will 9 barrels of flour cost at $6| a barrel 1 16. What will ten yards of cloth coj«t at |2| a yard ! 16- What will 10 lbs. sugar cost *t 6| cents per pound 1 at 7 J cents 1 5| cents 1 17. What will 7 yards of cloth cost if 2 yards can be bought for $6f 1 18. If 9 felt hats can be bought for $11 J, how much will 8 hats cost 1 19. If 3| tons of coal cost $60, what will 4 toui^ cost at the same rate 1 20. How much will 14 lbs. of raisins cost when 3^ lbs. oost 50 cents 1 21. 2^ yards of muslin cost 48 cents : what will 10 yards cost at the same rate t Fractions. —Reduction. UNITS. Examples. — 19, 1. How many imits are there in J 1 tSol. — 2 halves make one unit, and 7 halves contain 3 halves 3 times with oTie-half remainder .*. in J there are 3^ units. 2. How many units in {1 in ) 1 in^^ ^t^ ^ j,it iiijyii FRACTIONS. — REDUCTION. 57 a kre 8. How many units in ^^- 1 in 5^'*- 1 in $^ t in 4. How many units in %^ 1 in ^^- 1 in y- 1 in f J 1 5. How, then, may any improper fraction be rednced ifo a mixed number? 6. Reduce to mixed numbers -y-, y, %^-, $\% £-\i, K' Bhillings, 'v^-. Reduce to mixed numbers ^^^- pence, ^^^ hours, ^/ seconds, f^ farthings, f g, ^f^-, -Jf, J-,^^- 7. At $6 J a barrel, what will 12 barrels of flour cost 1 8. If 2 dozen of eggs cost 28| cents, what will 3 dozen cost 1 9. I paid $9 for 2| l.arrels of apples, what will 5 J barrels cost at the same rate 1 10. If I of a pound of tea cost 48 cents, what will 1 ib. cost? 2 lbs. 1 3 lbs. ? 4 lbs. 1 3 J lbs. 'i 4 J lbs. 1 5| IbH. 1 11- If I of a ton of hay is worth |4|, what will 7§ tons cost 1 12- A man walks 7 miles in 2 J hours : h w far will he walk in 4| hours'? 13. Find the number of bows, each containing J of 8 yard of ribbon, that can be made out of 7| yards. 14- At a church collection 43 dollars, 24 half dollars, and 32 quarters were received : what was the whole amount ] 15. a pint is one eighth of a gallon : how many pinti? in 133 gallons'? How many gallons in 141 pints] 16. If a boy can split | of a cord of w od in a day, how long will he take to split J of a cord 1 J ? 1 cord 1 2 cords 1 8 cords 1 17- How many quarter-pound weights will it take to 5 • f •! ' u r a' in i m ^^ •P«PPBPP«I«B "^■^^^P" 58 MENTAL ARITHMETIC. tMdance 56 pounds weight! How many half-pcund weights 1 18. How many lots -^^ of an acre in size can be laid out of 5 acres 1 from 7 acres 1 from 2 ,'j 1 19* If a man can do ^ of a piece of work in 2 hours, hew long will it take him to do the whole 1 20. If a boat is 3 hours in performing ^ of its trip, how long at that rate will its whole trip take 1 21. If a locomotive can go six miles in ^ of an hour, how many miles can it go in one hour and a half 1 22. With $24 collected from one customer, $16 from another, and $11 from a third, a person paid | of his taxes : what did his taxes amount to *) 23. 74-8+6+4 is 1 of what numberl /j+.s^+J^g + j*2 is J of what number 1 24. 5 is a third of how many times 6 ? Of what num* ber is 5| one-seventh 1 One-ninth 1 One-twelfth 1 25. If A fifth of a yard of carpet cost two-fifth of a dollar, what is that a yard) How much would $27^ buy] 26. If A ninth of a pound of raisins cost 2 cents, what will 4 ninths of a pound cost 1 What will 3 j poun>li cost H 27- A roan being asked the value of his horse said^ $-3/- is one-tenth of its value : what is its value 1 28' 9f is a seventh of what number ? 5f is l-fourtli of what number ] 7 J is 1 -ninth of what number I 29- 1 8 is 1-half of 6 times what number 1 80- 15 is 1-sixth of 5 times what number 1 81. A wagon cost $60|, which is 1-fourtb the cost of the buggy : what was ^he cost of the buggy 1 82. 7| is j of what number) i of ^hat number t l» ♦« »« FKAOTIONS. — RBDUCTION. 88> A man being asked his age, said his youngest son's age, which was 15 years, was just one-eleventh of 3 times his age : what was his age 1 84« A lady's shawl cost $9, which was 1 -eighth of 4 times the cost of her dress : what was the cost of the di*ess 1 85. A house cost $800 which was 1 -tenth of 4 times the value of the farm on which it stands. Required the value of the farm 1 86. 2 thirds of 21-|-3-fourth8 of 16, are how many times 71 87* 3 sevenths of 21-}-3 eighths of 40, are how many times ^ 1 88. Tf 3 j lbs. of butter cost 60 cents, how much can be bought for 360 cents 1 89' I of 21 is ^ of what number 1 | of what number I 40. 2+8 — 3 is J of what number 1 41. 4 o^ ^6 **^® ^ow many times 8 1 42. How many fifths in 41 In 4|1 How many sevenths in 3 1 In 3 J 1 How many ninths in 3 1 In 3^1 How many tenths in 4 1 In4|1 In 2^1 In 3^1 ijii ? , ! I L Fractions.— Reduction, &c. Examples. —20. 1. In j how many twelfths 1 Sol. — In 1 there are 12 twelfths .'. in f there »r« 2 thirds of 12 twelfths, or 8 twelfths, that is ^. S. How many sixths in ^ 1 ^1 } 1 § 1 8- How many eighths in 1 1 ^1 |1 ft 1)1 3|1 4. How many fifteenths in ^1 jt 2}1 |1 ft ^^ 4ii Wf^ ^^^P^pP?Pr^^^v^^ 60 MSNTAL ARIT9MBTI0< ft »« 5* How many twenty-firsts in ^ t ft 9J 1 6. Reduce J, f, }, f , 1 j*jj, 2| to twenty-fourths. 7. Reduce }, §, f, H, 2 J, f^, 1 Jg, 2t1j to thirty-sixths. 8* Since |=-J |, how may the latter fraction be derived from the former i 9. Since ^ |=} how may the latter fraction be obtained from the former t 10. How many fifths in /^t ^^ t A? A^ iV W 11. How many ninths in f|1 ||1 iJt ifl J| 1 12. How many fourteenths in if 1 |g1 J|1 f^V 18. Reduce to eighths ^^ |J, Jf , 4|, |J. 14. Reduce to their lowest terms ^i^f -j^^, j|, § J, jj^, ||. 16. Reduce to lowest terms ^f, |i f|, §f, | J, |f , -j-V,. 16. Reduce to lowest terms §|, ||, yViy* f §» Jl* n 17. If 2} barrels of fiour cost $20, find the cost of 3} barrelft. 18. John has $40 a month, which is { of half of what James has : how much has Jamesi 19. 16 is Y^^ of three times some number: finl | of the number. i 20. $43 is f of A's money, and B has § as much as A : how much has each f 21. A h rse cost $100, which is g of 10 times what the saddle cost : fin 1 the cost of the saddle. 22 Re-luce ^, '|, |, j^9 to sixteenths. 28- Reduce ^, |, -,3^, ^J to twentieths. 24- Reduce |, |, g, j\[, ^^ to twenty-fourths. 26. How, then, may fractions be changed to equal ones having a common denominator ? 26. Reduce }, ^, ^, yV> ^ ^ common denominator. 27. Reduce J, i, «3, i, } (( i< « »»pti-7 nuoTiovs. — B^ucTioir, no. fl it « 28. Reduce f , /q, f , j^jf to a ccmmon deno m inatoi^ 29. Reduce i, I, t, } ^ .• 80. Reduce §, i, 1 J, f " « « 81. Reduce t\j, j^, y^, J 32. Reduce IJ, 2J, 3f , f 88. Reduce the following mixed numbers to improper fractions : bj% Ty^, 12^ 10|, 20§, 8?, 7/^. 84' Change the following to mixed numbers : f }, f > V-, ¥-. -V» ¥-» f f » W» ft. ii ¥» W. 86. Reduce to their lowest terms : / , jg, ||, yTjj<5jj 83 1 1 1 46 3> lSTJ» 3^ A'*» 16 78 g^> 3?» 55» ??> 86. Harry gave his sister $40, which was | of all he had : how much had he 1 87. John being asked his age said : 3 fourths of my present age equals my age five years ago : how old is he 9 88. Findthesumof J+J+J+J+f 89. I gave $120f for a horse, and $19| for a saddle: find the cost of both. 40. Mary says that ^ her present age is | of her age three years ago : find her present age. 41- James being asked how much money he had. saM : If I had $20 more, { of the sum would be ^ of what X now have : how much had he % 12. What is the result of ^j— /^ 1 J J— /^ t 4f — ^\ 1 48. i- owned || of a ship, and sold ^ of the ship ; what part had I left f 44. John gave § of his money to Charles, ^'^y of it to Ida, and had 20 cents left : how many cents did John «nd Ida each receive t I m i^lW'^^^i^'^^^^^l^^^^^'v^ MINTAL ABITHMKTIO. Fractions.— Section III. ADDITION AND SUBTRACTION. EXAMPLltS. — 21. 1. John had } of a dollar, and his father gave him | mor^ : how much had he then 1 2. One man had | of an acre of land, a second hao {, and a third had } : how much had they all f 8. Bought a barrel of flour for $7|, aAd a cot-d of wood for $42 • ^^^ much did he lay out t 4. Find the lesult of ft + A— /u4- A- -A- 6. Find the sum of f and f . 5o?.-|=:A, i=,%, and A4-A=l?» or 1^; 6' Find the sum of } and | : of | and |. 7. Find the sum of } and j : of | and |. 8. I had f of an acre of land, and bought J of ab acre : how much had 1' then t 9. Find the sum of 8H-2i+3J. 10. Add i, I, i, f Add 2J and 3f. 11. Find J+J+2j+3}+7f 12. Add /g, J, j% and ^. 18. Find the sum of 2j4.3i-f 8f 4 12i. 14. i of a number increased by | of the number k equal to 70 : find the number. 15. Willie being asked how much money he bad, said : if the amount were increased by i^ of itself, I should have $84 : how much had he t 16. { of A*s money increased by } of his money, equals $81 : how much had he) 17. A man gave $80 for a watch, and $404.{ of tb» 6 9 fBAOTIOire. — ADDITION AHD STTBTRAOTIOV. 63 oo0t of the watch is 4 times what his chain cost : find iits cost. 18* I had 3 of a dollar, and paid f of a dollar for a pound of coffee, how much had I left ? 19* A man owned f of a ship, and sold j'^ of the ship : what part had he left ? 20- Find the difference between ^ and }, j and |y I and y*^. 21. What is the result of 6|-f 8f— 3J t 22. Subtract J from J, ^ from ^, ^ from }, ) from J, 23. Subtract | from f, } from |, | from {, { from §. 24. Subtract ^ from ^, ^ from J, 2^ from 3}. 25. Subtract 31 from 4^, 2J from 3J, 3J from 5J. 26. What is the result of J+ J~J 1 of i+|— J 1 27. What is the result of J+J— Jl of J— .s^-f-Jt 28. What is the result of 2^4-4^— 4J1 of lJ-f-1} 9 I i — -5 * 29. What is the result of 3J+2J— 6J? of 2J— IJ 80. What is the result of 4J— 4J+6Jt of 2i-f2» _ 9 I ? 81. What is the result of 1 J-|-2§--3J ? of 7§— 5 J ? 32. From the sum of Wj and 4| take ij — ^\. 83. Findthevalueof*3j4-4f— 2j~fi. 34. A can do a piece of work in 5 days, and B in 4 days : what portion of the work can both together do in one day ? in 2 days ? in 3 days ? 85. i of a post is in the ground, and there are 7 feet of it above ground : find its entire length. 86. The difference between ) of my money, and ^ of it, is $16} : how much have I Y wmm lVlt^'_"-',il>,'ii^ ■ ■ -W W^"f^^'-'.W^ ■■■'' 64 MIRTAL ABITHlllTia 87* Bought a coat for f ll/^, and a vest for fSjr, and handed in payment 2 ten dollar bills : how much change did I receive? 88. From 18} subtract 7{. =17— 7+1— |=10J=10J. 89. Find the results of 4}— J, of 12— 6|>^, of 36) -24|. 40. I bought two articles, one costing $15|) the othei $20 J, and gave in payment a $50 bill : how much change did I receive ? 41. J J of the candidates at an examination failed it arithmetic, { in other branches, and 20 passed: hoiv many candidates were there 1 42. How do you add two or more simple fractions 1 two or more mixed numbers ? 43. How do you find the difference between twc simple fractions ? between two mixed numbers t Fractions— Addition, &c Examples. — 22. 1. A can do a work in 4 days and B the same work in 5 days : what part of the work ca^ both together do in one day 1 2. John can do a piece of work in If days and Jamec ill 2 J days : what part of the work can both do in a day 1 8. A grocer sold } dozen of oranges to one man, J of a dozen to another, and | of a dozen to a third, aad had 3) docen left : how many dozen had he at first f FRACTIONS. — ADDITION, ETa )rk in Ifa 3J 4> Sold I of an ucre of land to one man, f to anotlitr, and y^3 to a third : how much did I receive at 60 cents an acre 1 6. A can do ^ of a piece of work in a day, B \ and C I : how much can all three do in a day 1 6. If a boy who had $4}, earned $2| more, and had $1 j^^ given him, how many dollars had he then 1 7' If a person buy a razor for f of a dollar and a strap for § of a dollar, for bow much must he sell them both in order to make half a dollar 1 8. If 6 is J of some number, what is } of 3 times the some number 1 9. 8 is f of some number : what is } of the same number 1 10. Henry's horse cost 90 dollars, which is ^j^ of 5 times the cost of the cart : required the cost of the cart. 11. A watch cost $90, which is | of 10 times what the chain cost : required the cost of both. 12 What number added to j will make J 1 18 A gave 48 cents, and | of this is 4 times as man? as he had remaining : how much had he at first t 14 Jane having 50 pins, lost J of them and then found as many as remained : how many had she then 1 16. What fraction is that which exceeds f^ by /^ 1 16 What number is that from which if 4| be taken, the remainder will be 3|| 1 17. A beggar met four persons ; from the first he ob- tained J of a dollar, from tjjp pAcond J, from the third ^, and from the fourth ^^ : how much did he get from alii 18. Thomas spends 6^ cents for sweets, 12} cents for a top, and 5} cents for a slate : what did they all oost t iil ff.^" ^^pii^Pi!^^^ P!lip^^|i^"PP"P«l^PifWpp 66 MEKTAL AKITHMBTIO. 19 • James Spent | of a dollar for a book, | of a doUai for half of a ream of paper, and had J of a dollar left : how much had he at first Y 20> A man paid 2^ dollars for a hat, 3} for a Test and 9^ for a coat : what did the whole cost 1 21> A man travels 2 J miles the first hour, Z^ milek the second, and 4^ the third : how far did he travel in the three hours 1 22* The sum of two numbers is 16{, and the less ii i^\ : what IS the greater 1 28> What number must be added to the sum of 3^, 2y'\j, to make lOj^^ 1 24* What number is that which added to the sum of h T2» and y»5 will make f |1 25* A grocer, having a bushel of potatoes, sold } of it to one customer, ^ to another, and ^^ to a third ; what part remained unsold 1 26. What number added to the sum of 2)- and 3| will make the result a whole number ? 27* A stage, after making ^ and | of its trip, had 7 miles yet to go : how long was it J trip 1 28. From two remnants of calico, containing respec- tively 4 J and 8| yards, were cut 12 j J yards for a dress : how much did what was left lack of a yard 1 29. Bought some paper for $12y^^%, (sold it for ^ISi^^i^ : by how much did the cost exceed the profit f 80. A can do a piece of work in 12 days, and B i ^ days : what part can each do in one dayl How m . can both together do in 3 days. After they have worked 2 days, how much will then remain to be done t 81. ^ can do a certain job in 9 hours, and F in 6 hours. After they have worked together at it one hour and a half, what part of the job remains to be done t rHAOTIONS. — ADDITION, STa 67 82- A can do a piece of work in 6 days, B in 8, an \ ^j in 1 2 : how much more work does A do in a day than B, and B than 1 83> } of a certain number increased by | of the same number, equals 34 : required the number ? 84> A. certain sum of money diminished by its \ and \y equals $15 : required the sum. 85. What number is that which diminished by its J, equals 36 % 86. Find the difference between 9-|-12f and 8|4-4a. 87. If 2 of James's age increased by ^ and \ of his age equals 57 years, what is his age ? 88. j of B's money increased by the difference between { and I of his money equals 190 dollars: required his money. 89- $40 is 4 times what A paid for a chain, and the cost of the chain, increased by its 1 1 tenths, is \ of the cost of his watch : required the cost of the watch. lilli Section IV.—Multiplication. Examples. — 23. 1. What is J of J 1 Sol,-i=l and.i of §=J.\i of J=i (or i^J/. What is I of J 1 ^Z._J=J§ 1 fifth of this Is jS^, and 2 fifths 5iy of|=-Vu(or|^|). 2. Find the result of J of J, J of J, i of J, f of 1, J of 8 1 f5> ff of. T3* 8. Fin. he result of J of 2}, ? of J|, J of ^, | if 4 J 4. I o^ ed f of a ship and sold } of my share : what part of V ship did I sell t ,^wm n-jmrn 68 MENTAL ARITHMETIC. 5- f of ^} cf $50 is -^^ of the cost of a watch : find its costi 6. Find the result of f of f of 24, of | of 2|. 7> 7^ of the candidates at an examination failed in English grammar, § of the remainder failed in geo- graphy, and 10 passed: how many candidates were there t 8. An orchard has 60 fruit trees, j^^ of these are apple trees, and | of the remainder are pear trees, and the rest are cherry trees : find the number of each kind. 9. John's age is | of Henry's, and the difference of their ages is 4 years : find the uge of each. 10. Find the results of | of j^^ of |, of | of V, off of 3*. 11. I paid $500 for a building lot, and j^^ of its price is J of the cost of the house built on it : find the cost of tlie house. 12. How many is 3 times J ^ |1 J? f? «1 |f 13. How many is 7 times f ? | ] 1 1 1 1 /^ 1 ^^ f 14. How many is 8 times J| ? 9 times /^^ 1 10 times 1^ ] 15. How many is 11 times fV? j%i 3^? ^y,? ^\1 16. Multiply I by }. ^oZ.— |X3=f ; J is the J of 3.-.|Xi ia J of j= Examples. — 24. 1. If a family consume | of a barrel of flour in 1 week, how much will it consume in 6 weeks 1 2. What will cost 6 yarcis of cloth, at j of a dollar a yard 1 8. At j of a cent a piece, what will 12 eggs costt 4. If a man earns } of a dollar in a day, how mvicb will ho earn in 12 days! MUI^TIPLIOATIGir. 5. 5 times 4 and f of 4 are how many 1 6. What will 5| barrels of flour cost, if a barrel cost 7. 7 times 6 and J of 6 are how many ? 8. If a barrel of flour cost $6, what will 7} barrels cost 1 9. At 6^ cents, what cost 9 pounds of ricel 12 pounds? 15? 181 10. If a peck of corn cost ^^ of a doii&r, how much will 2 bushels cost? 11. Find the cost of 20 bushels of wheat, at $2| a bushel ? At $2^ ? 12. How many are 4 times 2^ 1 6 times 3| t 13. How many are 8 times 5| ? 9 times 6§ 1 14. If a horae can trot 9| miles in 1 hour, how far at tliat rate can he trot in 8 hours 1 15. How much can be earned in a year at $11} a m nth ? At $1 Of a month ? 16 If 8 men can do a piece of work in 3j dayB, how long will it take 1 man to do the work ? 17. If J of a bushel of oats is worth $|, what is a bushel worth ? Analysis. — If | of a bushel of oats is worth $|, J or 1 bushel is worth 6 times $^, which is $| or $|. 18. When J of a barrel of flour is worth $lf , what is a barrel worth ? 19. If & man can reap /g of an acre in ^ of a Jay, how much can he reap in a day ? 20' If i of a melon is worth as much as 6{ apples, how many apples are worth as much as 1 melon 1 21. 5 J is I of what number? -f^ of what number ^ ^ of what number t p«'flpp"^*^*'^^'«lif '"PPWJP^ if""^ PPS^ TO MINTAL ARITHMETIC. 22. 5 times 2j*^ is } of what number f 28* 2 times 3| is } of what number 1 24* If 20 pipes of a certain size can fill a cistern in y^^ of an hour, in how long will a single pipe J as large ai each of them, fill the same cistern ) 26. Two and 3-fifths, is one-fifth of what number 1 26. One and 3-seyenths, is one-eighth of what number 1 27* If the current of a river be ^^ of a mile an hour, how far would it carry a boat in 8 hours 1 28. How many are 5 times 3'j,X^'i 29* How many are 8 times 12f — f 1 80* How many are 9 times 10| — 1 1 81. 7 times 20 and | of twenty are how many 1 82. Multiply 4J times 10 by | of 15 1 88. Multiply 2 times 9 J by 2 J times 4 ? 84- Emma is 3J years old, Laura is 5 times as old as Emma. In how many years will Laura be 2 11 85. What two ways are there of multiplying a fraction by a whole number 1 fori bu^ Division. Examples. — 25. 1. Divide 4 by 2. Sol. — If we divide 4 units of kny kind by 2, we get 2 units of the same kind^ therefore 4- sevenths divided by 2 give 2-seventhB, that is f . 2nd Sol.—'To divide anything by 2 is to take } of it, and J of 4=j\=§. 2. Divide i by 3, j\ by 4, jj by 6, if by 6, f f by 7, II by 9. DIVISION. n re 3. Find the quotients in the following case* : |^-3, J . II, 2-T-6, 2 J^4, 3|-f-7, 8j-^34. 4. Since 4-i-2= f , or y*^, what are the two ways of liiv iding a fraction by an integer 1 5. If 100 lbs. of flour cost $4, how much can be bought for $i ? how much for 7 dimes ? for 60 cents ? 6. I gave $3| for silk at $4 a yard : how much did I buy? 7. Divide 4 by J. Sol. — In 4 there are 20 fifths, and 20 units of any kind divided by 3 of the same kind=2^o-_g | 8. How many times is ^ contained in 3 J ? in 4J ? in 5f ? in 6 |. 9. Find the quotients in 3-j-J, 4-i-J, 6-5-J, 44-f-4. 10- If a yard of cotton costs | of a shilling, how much can be bought for 6 shillings ? for 8 ? for 10? 11. If a man can earn J of a dollar in J of a day, in how many days can he earn $10? 12. Find the quotients in 24H-y^g, l?-i-y«g, lys-^/s. 13- How much will 10 boxes of herring cost, if 3 J boxes cost $5 J ? 14. 3 men can do a work in 6§ days : how long will it take 12 men to do it ? 15. If 3J barrels of apples cost $14, how many barrels can be bought for $20 ? 16. If John can walk 2 J miles in | of an hour, how far can he walk in 3 hours ? in 5 J hours ? 17. A man paid $30 for a piece of linen, at $J per yard : how many yards were there ? 18. How often is } gallon contained in 7 gallons ? ^ week in 8 weeks? f penny in 9<2? J of a mile in 4 miles % f of an inch in 1^ feet 1 |'*f,yi1 , ii t- ;!■!■ ! il:,' mmmmm 72 MENTAL ABITHMETia 19. If } bushel of potatoes will last a family 6 dajs how long will 3 bushels last them ] 20. Divide J by |. Ist Sol. — The divisor is fifths ; and the dividend reluced to fifths=f X5=y fifths and ^ units of any kind, divided by 2 units of the same kind ==J of y=V> which may be got by multi- plying} by f. 2nd SoL — 1=2 J and |=2®^ ; but 15 units of any kind divided by 8 units of the same kind-=y* ;.} (or ^g) divided by | (or ^%)=\^ (or JXf). 21. How many times is § contained in 1 1 | in J ? |in|? JinV ginfSI T'^in^fl 22. How many bags of oats can be bought for | dol- lars, at I of a dollar a bag 1 Analysis. — As many bags can be bought for { dol- lars, as I of a dollar is contained times in | dollars ; f is contained in |, Jg® times=l| : therefore IJ bags of oats can be Vought for } dollars. 28- If a man can mow J of an acre in an hour, how long will it take him to mow | of an acre ? 24- At I of a dollar each, how many knives can be bought for 1 J dollars 1 26. If a horse can run j of a mile in 1 minute, how many minutes would he require to run | of a mile ? 26- If John saves § of a dollar, rid James J of a dol- lar in a week, how long, at that rate, would it take them to save 1} dollars? 27. How many yards of cloth at $li^ a yard can be bought for $2} 1 •SB. li a horse eat j of a peck of oats in a day, how long will 8| pooka last hio^l DIVISION. n S9- A yacht was hired for 10| dollars a day ; if each person paid | of a dollar, how many persons were thure in the company 1 If each were charged | of a dolla**^ how many then in the company 1 80* In order to raise 6| dollars, how many contribu- tors must there be at j^^ of a dollar ? at | of a dollar each? 81* If ft miller takes for toll, jf^ of a bushel of every bushel of wheat that he grinds, how many bushels must he grind, that he may receive 9| bushels 1 82' If the cars run | of a mile a minute, how long will it take them to run 25 miles ? 83> If a man walks | of a mile in ^ of an hour, how long will it take him to walk 12 miles 1 84- A boy having 12 quarts of berries, sold | of them for $i : what was that a quart? 85. Amongst how many boys can you divide | of 1§ oranges, if you give J of J of an orange to each 1 86< If a turkey cost $1|, how many can be bought for $9 ] 87* How many times will 4| gallons of oil fill a lamp that holds J of f of 1 gallon 1 88- If a stage run 24| miles in 3 J hours, how far does it run in one hour 1 89- Bought § of 4} cords of wood for ^ of 54 dollars, what did it cost a cord 1 40. Divide J of J of 14 by | of 3 J. 41. A farmer divided 213| acres of land among hia three sens ; to the Arst he gave | of it, and the remainder he divided equally between the other two : how many acres did each receive ? 42* A farmer bought | of a farm which was | of what 6 Ji*. n m mmmmmm'^ 74 MENTAL ARITHMETIC. his neighbor bought : what part of a farm did his noigh* bor buy 1 43' Bivide $42 in dollars, half dollars, and quartet dollars, and of each an equal number 1 44* Hew many gallons, quarts and pints, arid of each an equal number, are there in 44 gallons t 45- A man met some beggars, giving to the women 20 cents each, the boys 10 cents each, the girls 5 cents each. He gave to all $3.50 : how many beggars were there ? fl' Examples. — 26. 1. What part of 3 is 1 ? of 3 is 2 1 Sol—1 is J of 3. -.2 is I of 3. 2. What part of 7 is U of6is2^ of9is7? 3. What part of 8 units of any kind is 9 units of tli9 same kind ? of 11 is 5 1 of 12 is 4? 4. What part of | is | ] Sol. — 1=73 and 4 = f%f because 1 twelfth is l of 8 twelfths/. 9 twelfths is the | of 8 twcl'thb. 6. What part of | is ^ 1 of | is J 'i of J is | ? What part of 5 is § 1 of | is y*^ ? of J is J ? 6. What part of ^hjl of 3 J is 3 H of 4? is 6 ? 7. What part of {\, is 6 1 off is 41 of g is 3i 'i 8. What part of a foot is 4 inches i 3J inches 1 and 9 1 inches 1 9. What part of a mile is 140 rodnl is 160 rods'* 10. What part of an hour is 15 minutes 1 is 40 niin.v 11. What part of 10 miles is | of 8 miles ] is 2*. Qd. of £2.58. ? 12. A man having $12, gave $2 J for a hat and $3 J for a pair of boots : what — *" '*' *"^* ••^ney did he use I DIVISIOH. 75 'i Ma 18. If the interest on $100 is $4, what part of the principal is the interest 1 14> If a man buys a horso for $60, and sells him for $75, what part of his outlay is he gaining 1 16. If a vessel sail 60 miles in 5 hours, what part of 5240 miles will she sail in 9 hours 1 16. One man walks 4J miles while another walks 3 J : what part of the distance that the first walks does the second walkl 17. What part of 3 J acres is J of 4 J acres 1 of IJ gallons is 1 qt. 1 pt. 1 18. A merchant gained on a hogshead of sugar | of 46 1 dollars, which was J of two times what it cost him : what did it cost him 1 what part of the cost was the gaini 19. John earns 9 cents as often as James earns 12; when John has earned 63 cents, how much has James earned 1 20. Two men start from different points and travel towards each other, the first travels 6 miles while the other travels 3 miles, and when they meet the first hat travelled 20 miles more than the other : how far apart were they when they started 1 21. If 4 men can do a piece of work in 8 days, how many men can do a piece of work 6 times as great in half of the timel 22. If 5 horsei eat 1^ tons of hay in 1 month, how many tons will six horses eat in 2| months 1 28. How many days will it take 5 men to earn $11 1, if 3 men earn $| in ^ of a day 1 24. Beduce 1 year and 4 months to the fraction of a year. '■';'l i h Bl ^^ 76 MENTAL ARITHMBTIO. 25. Keduce 1 year and 3 monthi to the fraction If a man can cut 8 cords of wood in { of a wt9k| kow much can he cut in 2^ weelui I ^mmm 78 MENTAL ARITHMETIC. 8. If a man can walk 7 miles in 2 hours, how far cui he walk in 3 days, by walking 10 hours a day ? 9. If 3 J barrels of apples cost $5^, what will | barrel cost] 10. A carpenter worked 11§ days, and after paying his board and other expenses with | of his earnings, had $20 left : how much did he receive a day. 11. If 3 men incur an expense of $2 7 J, how much more than ?7J must each pay. 12. If 3 pair of socki cost ^f^, how many pairs can be bought for $2rf'jf 1 18. If 8 men can build a wall in 5 J days, in how many days could 5 men do it 1 \ 14. If 9 men can perform a piece of work in 9 J days, how long will 7 men take to do iti 15. A is three score years and ton ; if J of B*s age i^ 4 of O's, and J of C's is y'ly of A's, how eld is B 1 18. If to I of the number of sheep in a flock you add 70, you will double their number, how many sheep are there in the flock 1 17. James is 18 years old, and J of his age is | oi half his brother's age : how old is his brother 1 18. If from a certain number increased by 7 yOu suV tract 3, and multiply the remainder by J of 20, the pro duct is 80 : what is the number 1 19. If a pole 6 feet long casts a shadow of 6f feet, what will be the length of the shadow a pole of 9 feet will casti 30. If 5 gold pens cost $7}, what will 7 gold pens oostt SI4 What is the length of a pole, the shadow of which is 10 feet long, at the same time a pole 6^ feet long casts »iht4ow If* (DAn earns 1 10]^ in 4 days, how many dollan irill he earn in 14 days ) 23. If I of 9 be 6, what will a fifth of twenty be ) 24. If i of 10 be 3, what will ^ of 20be1 26. If 8 yards of ribbon coat f 1], how mnny yardt can be bought for $3} ? 26. If 2 apples are worth 1 orange, 2 pears are wortli 3 apples, how many pears are worth 6 oranges 1 27. If J be 9, what will 7 be] 28. How many yards of cloth f of a yard wide are equal to 12 yards J of a yard wide 1 29. If UO exceed by $10 ^ of } of what I gained by the sale of a house and lot, how much did I gain 1 30. If i of a yard of cloth cost ^, what will g of a yard cost % 31 A man being asked his age, said that were he 3 times as old, ^^ of his age would be 8 years : how old was hel 82. If J of A's age is § of B's, and } of B's age is } of C's, how old are A and B, if C is 81 years old ) Examples. — 28. '. 1. 7 is § of what number ) Sol. — J of some number is 7, 1 third is ], and 9 thiris, or the whole is 3 times }, or ^^-.sslOh 2. 6 is I of what number f 3. 25 is I of what number 1 4. 14 is J of what number t 6. 9 is I of what number 1 6. I of 20 is J of what number! 7. 18 is I of what number ) 8> 10} IB ) of what number ) I,.,; 1^ ao MENTAL ARITBllina 9> { is I of what number f 10> f is 73 of what number t 11. J of I is { of what number t 12: James gave 9 cents for a slate which was ^ of bii money : how much had he 1 13* A man bought a horse for $90 which was | of hifl money : how much had he 1 14> A gentleman was married at 30 years of age which was J of ^ of his wife's age : how old was the wife] 16. Two men agreed to build a wall, one man built 15 rods, which was J of what the other built : how many did the second build, and what was the length of the wall 1 16. A man sold 3^ cords of wood at $3 J a cord, which WAS 3 of what he received for a ton of hay : how much did he receive for the hay 1 17. Paid $3 for a neck tie, which was § of what my vest cost : what was the cost of the vest 1 18. A son's age is 20 years, and it is j^^; of the father's age : what is the age of the father 1 19. 15 is f of how many times 7 1 Sol. — I of some number is 15, 1-eighth is 3, and 8-eighths is 8 times 3 or 24, 24 is 3| timet t* 20. ^9 is I of how many times 8 1 21. 36 is 4 o( how many times 6 ? 22. 35 is I of how many times 5 1 ' 23- 28 is I of how many times 51 24. I is 7 of how many times 31 26- T% is 9 of how many times j 1 26. H is ^^'^ of how many times 2| t 27. f of 21 is I of what number 1 Sol—^ of 21 is 15, 15 is f of 25 .M( of Si li | of 25. ANALYSIS. 28. ) of 27 IB 4 of what number t 29* j of 64 is } of what number 1 80. if ^'^ 1 of how many times l^t 81' f of 36 is J of how many times 6 1 82. 4 ®^ ^^ ^^ f ^^ ^^^ many times 7 1 I of 48 is I of how many times 9 1 j*Q of 72 is J of how many times 6 1 81 38 84 86 4 of 56 is I of 3 times what number 1 ^/._3 of 56 is 24, 24 is f of 27, which is 3 tunes 9 : therefore 9 is the required number. 86. I of 54 is I *of 9 times what number] 87- I of 81 is j\ of 4 times what number 1 88. I of 36 is { of 1 times what number? 89. I of 108 is y'lj of 8 times what number 1 40' 4 ^^ I ^ I ^^ ^ times what number 1 Examples. — 29. 1. A horse cost $80, and J of the cost of the horse is I of four times the cost of the carriage : what was the cost of the carriage ' 2. A watch cost $60 ; and | of the cost of the watch is f of 6 times the cost of the chain : the price of the chain is required. 8. A cow cost $40, and | of this is f of 8 times the cost of a sheep : what is the cost of a sheep 1 4. A house is worth $12,000, and J of its value is | of 100 times the value of the lot : what is the value of the loti 5. What number added to 4 times | of 21 will make 521 6. The insurance of a house amounted to $80, and J of that is Jjf of 3 times its value : what is the value of the boiisdt pi ;f.' i Mii m 92 MENTAL ARITHMETIC. 7. A horse cost $180, and | of the cost of the horse is I of 6 times ibe cost of a cow : what was the cost of a cowl 8. The distance from Montreal to Prescott is 112 miles, 4 o^ ^^^ distance is ^\ of 1 6 times the distance to Kingston : what is the distance from Montreal to King- ston, and from Kingston to Prescott 1 9. Kingston is 48 miles east of Belleville, and J of 11 times this distance is £ of f times the distance between Montreal and Cobourg : what is the distance from Mon. treal to Cobourg 1 10. Port Hope is 33 miles from Whitby, which is J the distance between Napanee and Cobourg, and j'y oi this distance is | of J of the distance from Montreal to Ottawa, and of 6'> miles more : wlat is the distance from Montreal to Ottawa 1 11. A yard of a certain kind of cloth, 4 quarters wide, is worth $4 : what will a yard and a-hali^ of th same kind of cloth, 5 quarters wide, be worth 1 12. I of i of 60, is i of how many times f of | of 24 1 13> A man had | of his money stolen from him ; the thief was not caught until he had spent | of it, the re- mainder, 50 dollars, was given back : how much money had he at first 1 14. A farmer dividing his farm between his two son» gave the elder 10 acres more than § of the whole, and th6 younger the remainder, which was 22 acres more than } of the whole : how many acres in the farm 1 15. Bought a piano for $240, and | of the cost wa« } of what I received of 8 young ladies for the use of it how much did each young 1 ady pay 1 16. A shoemaker's tools are worth $80 ; | of this is ono year ▲1NALYBI8. 83 } of J of 2 times the value of the stock : what is the value of the stock 1 17. A farmer, alter selling $200 worth of his stock, finds that § of the remainder is equal to | of three times the amount sold : what was the value of his stock at first? 18. Two boys comparing their money — one said he had 60 cents, the other said, j'^g of your money is just j\ of 6 times my money : how many cents had the latter ? 19. A boy being asked his age, said that 18 years was 2 years less than J times | of his age : how old was hel 20. A man pays $600, and f of this is just § of J o^ twico his annual income : what is his annual income 1 21" A gentleman is 64 years old, which is 2J times the age of his eldest son, and the eldest son is 2| times as old as his youngest brother : what is the difference in the ages of the two brothers ? 22- A and B engaged in play ; A had § as much money as B, B gaining $16, which was | of IJ times as much as he commenced with : how much did he com- mence with, and ho\? much had he left ? 23- A farmer gave § of 1 i times his ready money for a buggy, I of what was left for a harness, and had re" maining $12 : what did he pay for the buggy ? 24- A does a piece of work in 4 days, and B in 5 days : ki what time could both together do the work ? A71S. — A in 1 day does J-, and B j^/.both do 5^5 in 1 day, ^'g in ^ day /.the whole in ^^-=2^ days. 25. One tap fills a cistern in 3 hours, another in 5 houra : in what time would both running together fill it ? 26. A does I of a work in 4 days, when B comes to help him, and they finish it in 5 dnvs each by himself take to do ♦• -». m how long would ^;pn|npiipp 84 MENTAL ARITHMETIC. 27. If A can do a piece of work in 6 days, and B J as much again as A in a day, how long would B take to complete the wojk after A had worked 1 J days 1 28- A can do a piece of work in 6 hours, and B in 8 hours : how long would B take to finish the work after A had worked 3 hours ? 29. A does I of a piece of work in 16 days, he then calls in B, and they do the work in 4 days more : how long would B take to do the work t 30' A does a piece of work in 3 hours, which is twice the time B and C together take to do it, and A and C could do tlie work in IJ hours : how long would B alone take to do it 1 31. A, B and C can dig a ditch in 20 days, A and B in 40 days, and A and C in 30 ckys : how long would each take to do it 1 32. One shoemaker makes a pair of boots in } of a day, another in | of a day : how many pair can both make in a day 1 33- A, B and C can do a piece of work in 5 days. B and C can do it in 8 days : in what time can A do it alone 1 34. A and B can do a piece of work in 30 days, B in 70 days : how much more of the work does A do than B 1 35. If 5 men can do a work in 10 days, how many men could do 4 times as much in one-fifth of the time 1 36- If a barrel of flour supply 4 persons 5 weeks, how much will supply 3 persons 2J- weeks 1 37. ^f 3 furnaces consume 12J tons of coal in 2-5 days, how long ^ill 8} tons lait 5 furnaces 1 A and B qsm do a piece of work in 1 ^ days, A and ^ ANALYSIS. 8ft in 1 J days, and B and G in 2| days : in what time could B alone do it 1 89- A. can do a piece of work in 3 days, B in 4, and C in 6. A leaves off I a day before the work is finished, And B § of a day, C finishes the work : how many days did A, B and C work ? 40 • A. crew can row down a stream a certain distance in 3U minutes and back again in 32, what fraction of the distance is the rate of the stream an hour"? If the rate of the stream be half a mile an hour, what will the dis- tance be 1 41. A crew rowed down stream 7 miles Iii 30 iiiuiutes and up stream the same dist^Qoe in 35 minutes : find th« rat-^ of the stream per hour. 12' A crew can row down a stream In 20 minutes and back again in 30 : find the distance, the rate of the stream being 1^ miles an hour. CHAPTER III. REDUCTION AND OOSflPOUND RULES. Section i.— Currency. Examples. — 30. 1. How many farthings in 1 half penny ? in 2 pence 1 in 3 pence 1 in 6 pence ? in 5 J pence 1 in 7 J pence ? 2. How many ponce in 5 cents'? in 101 in 20 ! in 2o 1 8. How many 5 cent pieces make a dollar 1 how many 101 how many 201 4. How many cents in 3 pence 1 in fid 1 in 9 pence t la 12 pence 1 in 30 pence 1 in G01 in 15 pence) \ 'i- 86 MENTAL AKITHMETIC. 5. How many farthings in 8 pence 1 in 12d1 in 60d' in 7 Jd 1 in 9 Jd t 6. How many shillings in $1 1 in $21 in $4 ? in $10 1 in one-fifth of a dollar 1 in 3-affchs 1 in 4-fifth8 1 7. How many sixpences in 1 shilling? in 2 shillings? Ie 3 shillings! in 4s. 6d1 in 7s. 9d ? in 33. lldl 8. How many 5 cent pieces are equal in value to 60 pence 1 12 pencd 10 shillings? 7a. 6d ? 9. How many dollars in 1 pound 1 in £2 1 in £5 1 in.^ll2s1 in £2 13s? English Money. EXAMPLBS. — 31. 1. How many farthings in 1 penny? in 9 pence? in 6 pence? in 20 pence? in 12 pence? in 5jd ! in 6Jd? in 7Jd? in lOjd? 2. How many pence in 4 farthings? in 12 farthings I in 36 farthings? in 48 farthings? in 63? in 50? in 47? 3. How many pence in 1 shilling ? in 4 shillings ? in 7 shillings? in 10 shillings? in 20 shillings? in 48. 6d? inVs. 9d? in 8s. lid? 4. How many shillings in 12 pence? in 48 pence I in 36 pence ? in 60 pence ? in 240 ? in 50d ? in 69d I 5. How many shillings in 1 pound? in £i ? in £7 t in £10? in£l lOs? iA£16s? in £3 15s? in £*] 19a 1 6. How many pounds in 20 shillings? in 40s? in 80h ? in 120s ? in 30s ? in 49s ? in G7s t in 75s f 7. How many pence in 4s. 6d ? iu 5s. Gd ? in lOi. 3d? inl2s.6dt iu £L 13d. 6df di] "^'•^ 1 BN6L1SH MONEir. 87 8 Blos/ \-iaiiy sliillings in J£2 6s ? in £3 98 1 in XG lOsI 9- At 3 Jd a pound, how many shillings will 24 pounds jf rice cost 1 10. At 5 shillings and 6 pence a yard, how many :)ounds will 16 yards of carpeting cost? 11. How many crowns in £1 1 in £5'i in £10 5s 1 n£ll 10s 1 X2>. In reducing £3 10 shillings to shillings, which is :,lie multiplier, the 3 or the 20 1 Give reasons for your mswer. UNITED STATES MONEY. Examples. — 32. 1. How many mills are there in 8 cents? in 12 ct»1 in 15 cts 1 2. How many cents are there in 60 mills 1 in 80 mills ? in 40 mills ? in 45 mills ? in 57 mills ? 3. How many cents in one dime ? in 3 dimes ? in 7 dimes? in 14 dimes? 4 How many dimes in 10 cents? in 2'J cents? in 43 cents ? in 90 cents ? in 85 cents ? 6. How many dimes in $1 ? in $3 ? in $7 ? in $8 1 in 2-fifths of a dollar ? in 3-fifths ? in 4-fifths ? 6. How many dollars in 1 eagle ? in 2 eagles 1 in ^ eagles? in 11 eagles? 7. How many eagles in 10 dollars? in 20 dollars? in 70 dollai-s ? in. 1 20 dollars ? 8. How many dollars in 100 cents? in 200 cents t in 700 cents ? in 125 cents? in 235 ? in 510 ? 9* Bought 20 yards of cloth at one-half dollar a yard : 'low nr.xny dollus '.li«l I pay ? irt^ftit^itf^- ,:^:i>^m' How many ounces in 20 penny- weights 1 in 40 penny-weights? in 100 penny-weights? 5. How many ounces in 1 pound 1 in 2 lb. 1 in 5 lb. ? in 9 lb. 1 in 12 .1 in 3 lb. 8 oz. 1 in41b. 9oz1 6* How many ouuds in 12 ounces? in 36 ounces 1 in 60 ounces ] in 144 ounces ? in 65 oz. 1 in 90 oz. 1 7. How many penny-weights in 2 oz. 10 dwt? 8. In 6 lb. 7 ^»z., how many ounces ? 9. Find the value of 4 oz. of gold, if 3 dwt. are worth 18 shillings ? 10. In 1 pound how many grains ? 11. How many spoons, weighing 35 dwt. each, can bo made out of 1 lb. 2 oz. of silver '\ 12. A jeweller bought 7 dwt. of pure gold, 9 dwt. of MEAIUBIB OF WBIOHT. — APOTHECARIES* WEIGHT. 89 gold coin, and 16 dwt. of silver :»how many ounces did he buy altx)gether 1 13. If 1<^ dwt. of silver are worth 70 cents, find the value of 3 pounds of silver. Reduction. — Apothecaries* Weight. Examples. — 34. 1. How many scruples in 5 oz 1 in 1 lb.1 2' In 95 gr. how many drams? in 4 lb. 5 oz., how many drams') 3. How many grains in 3 dr. 5 sc.1 4. How many grains in 1 oz. 1 in 2 ounces 1 in 5 ounces 1 6. How many drams will it take for 20 powders, each containing 20 grains 1 6. How many powders of IJ sc. each can be put up from an ounce of soda 1 7. If a druggist charges 50 cents for ten powders con- taining 15 gr. each, at what rate is that per ounce 1 b- A druggist charges 8 cents for 4 drams of opium : what rate is that per pound 1 9. How many scruples, drams and ounces, and of each an equal number, are there in 7 pounds 1 10. Two-thirds of 18 scruples of a certain drug cost 36 cents : what will 4-sevenths of 1 4 pounds cost t Examples. — 35. 1. How many drams in 4 oz.1 in 8 oz.1 in 10.oz.> in 5 oz, 10 dr.1 in 7 oz. 12 dr.1 3. How many ounces in 2 pounds 1 in 5 pounds ? ia -■#- 9v MENTAL ARITHMETIC. 32 drams) in 3 lb. 5 oz.1 in 4 lb. 9 oz.1 in 2 lb. 1] 0Z.1 ' 8. How many pounds in 2 quarters 1 in 3 quarters : In 4 quartei-sl in 48 ounces? in 96 ounces) in 2 qr 12 1b.? inSqr. 15 1b.1 4. How many hundred-w ^ht in 4 quarters) in t quarters) in 16 quarters) in 20 quarters) 5. How many hundred- weight in 2 tons ) in 3 tons 1 In 2,000 lb. ) in 4,000 lb. ) in 2 tons 3 cwt. 6. How many lbs. in 1 cwt. 2 qr. 13 lb.) 7. How much will 2 cwt. 1 qr. of beef cost at 10 cents a pound ) 8. How many four-ounce weights can be made out of 2 J pounds of brass ) 9. How many 7 l'*. packages of sugar can a grocer put up from 2 cwt) from 2 qr. 13 lb.) 10. Bought 1 cwt. of meat for $17.50 ; sold it at 22 cents a pound : what was the whole selling price ) What was the profit ) 11. I gave 3 cwt. 2 qr. cf hay worth $20 a ton, for butter worth 25 cents a pound : how much butter did I get) Section III.— Measures of Length, Surface, and Volume. Examples. — 36. LONG MEASURE. 1. How many inches in 1 foot) in 2 ft. ) in 5 (1.1 in 2 ft. 6 in. ) in 5 ft. 11 in. ) in 8 ft. 4 in ) 2. If 4 inches make a hand, wliat is the height in feet of a horse 16 hands high ) CLOtB. MEASURE. 91 8' How many feet in a yard f How many in a fathom 1 in 2 yds. 2 ft. 1 in 12 yds. 1 ft. t 4- How many times will a stick 5 yards long be con tained in a mile ) ^ 6. How many yards in 4 furlongs 1 in 7 fur. t in 6280 feet? in 272 feet 1 6. How many chains in a milel in 160 rods) in 6 furlongs 1 in 136 in., how many yards) 7. How many inches in 3 yds. 2 ft. 10 inches 1 8* What will it cost to dig a ditch a quarter of a mile long, at 50 cents a rod 1 9* The roads in Ontario are 1 chain wide, what is the width in rods 1 10> If it takes 5 minutes to travel a furlong, how long will it take to travel a mile ) 11. A man travels 50 rods in 5 minutes, how long will it take him to travel one mile 1 12> How many steps, each 2 feet long, will a boy take ii4 walking 110 yards) Cloth Measure Examples. — 37. 1. How many nails in 2 quarters ) in 5 qrs. f in 18 inches ) in 24 inches ) 2. How many quarters in 4 yards ) in 3 yards ) in 12 yards ) in 5 yds. 2 qrs. ? in 6 yds. 3 qrs. ) 8. What cost 10 yards of velvet, at $10 an ell, Eng- lish) 4. What will 18 yards of cloth cost, at $12 a French •11) 5. How many dresses each containing 12 Flemish i PIPP 92 MEHTAt AEtTHlfEtia ells can be m&de from a piece of doth containing 18 French ells 1 6. How many nails in tbree jds. 3 qrs. 3 nails 9 in 75 nails, how many yds. &c, % 7. How many dresses each containing 10 yds. can be made from a piece of cloth containing 40 ells, English 1 8. A coat requires 3 yds. of cloth : how many coats can be cut from 40 Flemish ells ? 9. In 7 yds. 2 qrs., how many E. B. f how many E. Fr. 1 how many E. FL 1 10. If 5 yards of cloth cost 7 dollars, how many yards can be bought for 56 dollars 1 Square Measure. Examples. — 38. 1. A black-board is 4 feet wide and 12 feet long : how many square feet of furface has the board 9 2. A slate has a surface of 80 sq. in., it is 8 in. wide : find its length. 8. How many sq, in. in one-sixth of a sq. fb. 9 in S-sixthsl in 5- sixths) 4. How many square inches in a board 4 inches long and one inch wide 1 in 4 inches long and 2 in. wide ? in 4 inches long and 3 inches wide 1 6. A board is 3 yds. long and one yard wide : how many square yards in it 1 6. How many square feet in 3 square yards 1 in 8 square yards 1 7. A yard of ::arpet is 3 ft. long and 3 ft. wide : how many square feet in iti OTBIO 1IEA8URI. 9i 8. How many square feet in a yard q{ oloth 2 feet wide t in 5 ft. wide 1 9. How many square feet in a room 12 ft. by 15 ft.1 now many sq. rods in 1 ac. 20 rd. of land 1 10. How many yards of carpet 2 ft. wide will bo re- quired to cover the floor of the above room 9 Cubic Measure. Examples. — 39. 1. How many cubic feet in one ninth of a cubic yard 1 in 4-ninths ? in 7-ninths ? 2. How many cubic feet in 3 cubic yards 1 9 cubic feet ? 8. A brick is 2 by 4 by 8 inches : find its solidity ? 4. How many cubic feet m 1 cubic yard 'i in 3 cubic yards 1 in 4 cubic yards 1 6* How many cubic yards in 27 cubic feetl in 81 cubic feetl in 100 cubic feet? 6. How many cubic feet in 2 tons of timber $ in 5 tonsi 7. How many cords in 32 cord feet ) in 24 cord feet ? in 80 cord feet ? 8. How many cords in a pile of wood 24 feet long, 4 feet wide, and 4 feet high 1 9. How many loads of earth, each 1 cubic yard, mus» be removed in digging a cellar 21 feet long, 18 feet wide, and 6 feet deep 1 10. How many cubic feet are in a stick of timber 16 inches wide, 9 inches thick, and 21 teet long 9 «>, IMAGE EVALUATION TEST TARGET (MT-S) :/. 1.0 I.I |[^ IS i? us 110 1.25 U 1.6 •• 6" ► p> A 7 /J ^ Photographic Sciences Corporation 33 WIST MAIN STRUT WIBSTIR.N.Y. 14580 (716) ara^soa ^ V -q'^" <^ « or #5' <^ o^^' ^ Mjl u .1.11 .1 . |,>1.PJ '»^l»Vlf^^T|f #« MBHTAL ARI'M^MBTia Liquid Measure Examples. — 40. 1. How many gills in 4 pints f in 8 pints) in IS pints 1 in 11 pints, 2 gills 1 in 13 pints 3 gills 1 2. Howmany pints in 16 gills) in 32 gillst In 86 gills 1 in 47 gills) 8. How many quarts in 3 gallons ) in 8 gallons ) in 15 gallons) in 10 gallons 3 quarts) in 13 gallons 2 quarts ) 4. How many gallons in a pipe) in 1 hogshead ) in 1 tun) in 4 barrels) in 6 barrels) 5* If a tumbler hold half a pint, how many times will 1 gallon of water fill it ) ' 6 Bought 6 gallons of oil for $10, what is the prioe per quart ) 7« Bought a pint of milk for 4 cents, at what rate is that per gallon) 8. 3 pints of molasses having been sold out of 2 gal- lons, what is the remainder worth at 80 cents a gallon S 9. A merchant bought a hogshead of molasses for $40 and sold it at the rate of 30 cents for 6 pints, how much did he gain by the bargain) 10. How many pint bottles will be required to hold 4 gal. 2 qta. of tomato catsup ) Dry Measure Examples. — 41. 1. flow many pints in 2 quarts) in 6 quarts) in 7 quarts ) In 8 qts. 1 pt ) in 9 qts. 1 pt ) S. How many quarts in 1 peck ) in 2 pecks ) In ft peeks ) in 4 pks. 3 qts. t in 6 pks. 2 qts. t lOIB TABLE. 96 S. How manj pints in 1 peck 9 in 3 peoksf in 7 pecks t in 2 pks. 1 gal. 2 qts. t 4. How many pints in S bushels, 3 pks, 3 qts. f 5. If a chaldron of coal costs |12, what is the price per bushel t 6. How many baskets, holding 2} pecks each, will 5 bushels of apples fill 1 7. If a horse is fed 6 quarts of oats a day, how long will i( take him to consume 6 bushels 1 8* If 8 pints of strawbernes cost 32 ccntp, what will 1 bushel cost at the same rate 1 9. A sold to B 1 bushel and 1 peck of currants, at 2 cents a pint, and received in payment 1 bushel of rasp- berries at 4 cents a pint : who pays the diffiTcnce, and how much % 10. A farmer sold 2 bushels 3 pecks of clover sned at $6 a bushel, receiving in |)ayment 5 bushels 2 pecks of wheat at $1.50 : what is yet due him 1 11. A boy gathered 3 bushels 4 quarts of chestnura : how many times would they fill a pint measure 9 TIME TABLE. Examples.— 42. 1. How many seconds in 2 minut'es 1 in 4 minutea 1 2. How many minutes in 2 hours 1 in 4 hours) in 120 seconds 1 8. How many hours in 2 daysl in 4 daysl in 360 minutes t in 3,600 seconds 1 4. How many days fram 1st January to the 17th of \f arch 1 from 3rd February to 1st July t II. How many months from August 9th to Novembit £ EM 'Jf «' ^!P" H imrtAL ABITHlfSTia 9^ 9tli t fifom June 2nd to November 2nd t from Apiil 6tk to October 6th 1 6. Which years are leap years t Which of the months have 31 dayst How many days has 5 th month t the 11th month 1 7. What are the natural divisions of time 1 how are the year and day divided 1 8. If a man can do a piece of work in 30 minutes, how many hours would it take him to do 15 times as much 1 9. A can do a piece of work in 20 minutes: how many hours would it take him to If a man earns $12 a week, and pays for expenses $12 per month of four weeks, how much will he save in 40 weeks t 18. A man walks one-fourth of a mile in 5 minutes, how long will it take him to walk 10 miles? 14. If 12 men can do a work in 1 hour 45 minutes, how long would it take 1 man 1 2 men 1 5 men 1 MISCELLANEOUS TABLE. Examples. — 43. 1. How many units in a dozen 1 in 4 dozen t 2. What is the cost of 4 dozen of peaches at 2 cento • piocti 1 . 8* What cost 1 gross of writing books at 10 cts. eadlif 4. How many score in 60 1 in 80 1 in 100 1 5* What cost a ream of paper at 10 cents a quire t 1 gross of pens at 5 cents a dozen 1 '•«,'■•<- OOMBOUND BULM. W 6* At $11 a hnndred-weight, what oosta 1 bam,] of beef 1 3 barrels of beef f 7* Bought a barrel of pork at 12 cents a pound, an«l ■old it at $15 a cwt.: how much was made by the sale) 8* Bought wheat at 3 cents a pound, and soU it at $2 a bushel : how much was made on a bushel 1 9. Paid 5 cents a pound for flour: how muoh was that a barrel t 10* Bought 170 lbs. of oats : what was the cost at 62 cents a bvshel 1 11. Bought 300 lbs, of wheat at 2 cents a pound, and sold it at $1.50 a bushel : how much lid I gain) ..,? 'f'V* Compound Rules. Examples. — 44. 1. Add 7 bushels 2 pks. and 8 bushels 3 pks t 2. A grocer sold on Monlay 5 gals. 2 qts. of m lasses ; on Tuesday, 2 gals. 2 qts., and on Wednesday 4 gals. 3 qts. : how much did he sell in the three lays 1 8. How many acres are there in two fields, one con- taining 9 acs. 70 rds., the other 8 acs. 9C rai. 1 4t' A fore quarter of lamb weighed 7 lbs. 9 oz., and a hind quarter 8 lbs. 12 oz. : how much did both quarters weigh t 6. Find the sum of 3 yds. 2 ft. 9 in., and 4 yds. 2 fL 6 inches. 6* A farmer sowed 1 bushel 4 qts. of clover-seed, and 1 bushel 2 pks. 3 qts. of timothy-seed : how much did he low of both kinds t 7* Ad I together 50 cubic yds. 13 cubio ft. aii4 10 oabio yds. 17 cubio (i t '•v'\'"i"'3;i'A ^■^^ mmi^^m^»mi9^^ *""l*iiP'' 98 MENTAL ARITRMITIC 8. A coal dealer delivered 12 tons id cwt. of coal to one man, and 8 ions 15 cwt. to another : find the whole quantity soM to these two men. 9. A man had 9 bushels 3 pks. of potatoes, he sold 6 bushels 2 pks.: what quantity had he left ? 10* A grocer had 13 lbs. 8 oz. of castile soap, he sold 8 lbs. 10 oz. : how much Lad he leftl 11. From 16 ft. 5 in. take 11 feet 7 inchest 12. From a cask containing 16 gals. 2 qts. of vinegar, 10 gals. 3 qts. were drawn : how much ivas left t 18' I have 9 weeks vacation and 6 weeks 4 days have already passed : how much of it is left 1 14* A crock with the butter in it weighs 34 lbs. 8 os., the crock alone weighs 7 lbs. 12 oz. : how much butter does it hold 1 15- From a piece of land containing 7 acras, 3 acres 70 sq. rods were sol I : how much is left) 16' It takes one hour 45 minutes to go by rail from Toronto to Hamilton, and 3 hours and 20 minutes to go by b- at : how much time do I save by rail I Examples. — 45. 1. How much tea will it take to fill 6 canisters, each containing 1 lb. 8 oz. 2. If a horse eats 2 pks. 6 qts. of oats in 2 days, how much will last him 14 daysl 8. Multiply 3 qts. 1 pk. by 10. 4> It takes 7 yds. 3 qrs. of cloth to make one salt d clothes : how much will be required for 5 suits t 6* If 3 cows eat 3 tons 18 cwt. of hay during tbe winter, how much would keep 6 cows t wfKif^:- t^ w^^ n ^ m I ^ nim^^, , .^ uii . . . .^j|||||ijgu^4:^ i |p^ OOMPOUIID BULm 99 6* If it requires 2 bushels 1 pk. 2 qts. of wheat to sow an acre of land, how much will be required for 5 acres f 7' J ennio is 9 years 7 months olic feet of granite, when 1 foot weights 1 cwt. 1 qr. 15 lbs. 1 10. Multiply 2 gals. 1 qt. 1 pt. by 7. 11. If 11 bushels 3 pks. of grain sow 5 acres, how much is required for 1 acrel 12. Bivide 21 miles 40 rds. by 4, 18' If a cooper can make 4 barrels in 5 hours, how i >ng will it take him to make 3 barrels 1 14. Four bags weigh together 8 cwts. 2 qrs. 10 lbs : what is the average weight of ench bag 1 15. Divide 3.5 years 6 m nth s by 6. 16. If one barrel h Ids 2 bushels 3 pks. of apples, how many barrels will be required to h id 5 bushels 2 pecks 1 17. I divided 12«. 6cZ. among a number of boys, giving each 2«. ^d. how many boys were there 1 18. A stationer sold 21 gross 7 dozen of copy books in r. days : find the average daily sales. 19. A farmer cut 15 tons 5 cwt of hay from 5 acres: what was the average per acre 1 W i Examples.— 46. 1. What 18 the sum of 10s. 9d. and Ss. 6d. 8. What is the sum of £1 38. 9d. and £5 98. 4d.1 8. A boy throws 9 pW 6 qts. of potatoes into a bsnel '^^ f.,' '^'^i^^W^'^WW'^^''^'^^- ^v^^' 100 MBM TAIi ARITHMETIC. all oady containing 2 pks. 3 qts., how many bushels, Ac, are then in the barrel 1 4> A grocer mixes three kinds of tea ; 5 lbs. 11 os. of the finit kind, 6 lbs. 7 oz. of the second, and 3 lbs. 10 os. of the third : how many |>ounds in the mixturel 5> From a bin containing 10 bush. 3 pks. 1 qt. of oats, a person took 3 bush. 9 pks. 6 qts., how much was left) tj. How much of my fence remains to be built, if there is 15 rods 5 yds. to be built in all, and 11 rods 2 yds. 1 ft. is completed 1 7. What are the contents of 8 pitchers, if each hold 1 qt. 1 pt. 1 gillt 8. If 1 man can do a piece of work in 4 hours 45 min., how long will it take 6 such men to do it? 9. How many quart boxes will 2 pks. 6 qts. of befiies filll 10. How much must I pay for a I'iece of land 10 roll by 12, at the rate of $160 an acre t 11. A school walk conta^ining 240 sq. fb. is 12 ft. wide, what is the length ) 12> How long must a box be that is 4 ft. wide and 3 ft. dec]) to contain 1 8 cubic feet 1 13. What will 3 gross and 6 buttons cost at 10 cents a dozen 1 14. At 40 centu a square foot, what will be the cost of a piece of land 30 ft. by 50 ft.1 15. A boy observes that the fore wheel oi his little wagon makes 55 revolutions more than the hind wheel in goint^ 20 rods : what is the circumference of the fore wheel, that of the hind one being 3 feet 9 16. The difference between the product of two num- bors and 9 is 171. One of the numbers is 12, what is ih«otlisrt sjt^Bstogjg-w^^^g^ CWXPOUND LUS. 101 17. A room 15 ft. long by 12 ft. wide oostB $30 to carpet it : what would it cost to carpet a room with the same carpet if it were one yard less in length, and 2 feet less in yridth 9 18. How many days of 6 hours each will it take 16 men to do a piece of work, if 5 men can do it in 9 days of 10 hours eachi 19* How far will a locomotive, moving at the rate of 6 miles in 15 minutes, go in an hour and a Ifalf 1 20> At 3 cents an inch, how much will 2 yards, 2 feet, 2 inches of silver wire cost ? 21. How many bricks 9 inches by 4 will bo required for the bottom of an oven 8 ft. by 6 ft. I 22. The divisor and quotient are the same, the re- mainder is 7 inches, which is tw i less than the divisor : what is the dividend ? 28* A room 12 feet wide costs $30 to carpet it, but if it had been 3 feet less in length it would only have cost $24. Find the length of the room. 24. A owes B $25.20, and gives him on account $17.75. If he pays the balance with a teu-dollar bill, how much change should he receive ? 26. Divide 20 bush. 7 pks. 3 qts. of potatoes into 10 equal heaps : how much have we in each heap 1 26- At $2 a square rod, a man paid $960 for a build- ing lot : how much land did the lot contain t 27 > From a pile of wood containing 7 cords, a man sold 4 loads, each 12 feet long, 4 feet wide, and 4 feet high : find how much remained. 28. When peas are worth $1.60 a bushel, what will 6 quarts cost 1 29. Find the cost of 12 lbs. 16 os. of ham, at 1$ omim apouad. 'ja' Ml ■M W. '^np^w'^f^ ';^'.i ^y^wf rm^'^'%^j!fnfr^'^ 102 MENTAL ABITHMBTIO. 80- It coHtfi $20 to carpet a bcdroc m with carpet cost ing $1 a squara yar:!; the room is 12 feet wide : how long is it 1 81' Find the cost cf fencing, at $3 a rod, a field which is 60 rods long and 40 rods wide. 82' How much clover seed will be required to sow a field of 8 acres, one acre requiring 1 peck, 5 qts 1 8d> A stationer paid $3 a ream for paper, and sold it at 27 cents a quire : find his gain on 5 reams. 84- A market woman took 6 dozen of eggs to mar- ket, broke 9 of them, and sold the remainder at 28 cents a dozen : how much did she receive 1 85- What is the value of a load of oats weighing 1037 lbs. at 40 cents a bushel ? 86' Find the thickness of a block of stone containing 360 cubic feet, its length being 30 feet, and its width 4 feet. 87' A floor is 21 feet long and 6 yards wide : what will be the cost of painting it, at 30 cents a square yard 1 88. What will be the cost of 17 cwt. 3 qrs. 10 lbs. of iron, at $60 per ton 1 89- How many bushels of wheat are there in a load of 32 bags, each bag containing 92 pounds 1 40 • How many pint and quart bottles, of each an equal number, can be HUed from 19 gals. 3 qts. 1 pt of omv r%nt winat Tjc^:a'^E'**T^-% ^tTESTIOKS rOR BXAltINATIO]r& CHAPTER IV. lOS Questions for Examinations. (1) 1. John had 26 marbles, lie won 32, and then sold 40 :' how many had he left 1 2' A drover bought 25 sheep at $5 a head, and 5 cows at $36 a head : find the cost of the whole. 8. A farmer sold 35 barrels of apples at $4 a baricl, and bought with the proceeds pork at $6 per cwt.: how much pork did he get ? 4. If I bought 80 turkeys at the rate of 10 for $6, and sold them at the rate of 16 for $14, how much did I gain? 6. A boy bought a book for half a crown, a slate for 6d.: how much hange did he get out of half a guinea 1 6* How many lbs. of sugar at 4d. a pound, can be bought for a crown and a shilling piece Y 7. The L. C. M. of two numbers is 24 and their G. C. M. 4 ; one of the numbers is 8 : find the other 1 8. I own f oi j% of a ship worth $30,000, and I sell } of my share : what is the value of my remaining interest in the ship 1 9. If the four-pound loaf is worth 10 cents when wheat is $1 a bushel, what should be charged for it when wheat is worth $1,10 per bushel 1 10. Susie being asked her age, said : If the difierence between i^^; of my age and | of it is multiplied by 12, the product will be 20 : find her age ? 11 Multiply 16 by 12, add 8, divide by 400, multiply m ■V. I.. 1?^ Ft I 1 ipipniUiLiJpi IW^SKW^TV^ p*i»jtw«i^^f»J!!P»iittW| I. m MINTAL ARITHMETIC. by 128, take the square root, and multiplj by 50 : what is the result t 13. A can do a piece of work in 4 days, and B in 4} days : in what time will both working together do f of the work t 18> } of 56 is } of how many times 16 1 (a) 1. I bought a horse for $175, kept him 7 weeks at i ooHt of $35, and sold him for $275 : how much profit had It 2. The dividend is 285, the quotient 17, and the re* mainder 1 3 : find the divisor. 8. Bought 10 reams of paper at 20 cents a quire, and sold it for $4.50 : what was my gain on each quire t 4« I divided £1 78. 6d. among a number of children, giving Is. 3d. to each : how many were there t 5. Divide $75 between A and B, giving B $15 more than A. 6. T^T of the candidates at an entrance examination failed in English grammar, y^ of the remainder failed in arithmetic, and 15 passed : how many candidates were there 1 7. The distance from Yarmouth to Boston is 240 mile», and twice the distance from Yarmouth to St. John is 30 miles less than J of the distance from Yarmouth to Boeton : find the distance from Yarmouth to St. John. 8. A man working 9} hours a day can do a piece of work in 8 days : how many days will it take him if he works only 6j^ houra a day 1 9* A and B can do a work together in 2} days, A can do 3 times as much in a given tim<^ as B : find the time would take to do it QUHTIONB FOB BXAMlKATIOMt. 105 10' A boy spent } of his money, and then found that $] was ^ of what he had remaining : how much had he at first 1 11. It costs $72 to carpet a room 24 feet long and 18 feet wide : what would it cost if the room were a yard wider 1 12- If to my age you add { of it and 15 years, the sum will be 39 years : find my age. (3.) 1. A farmer sold a horse for $132, and a eow for $68 : how much had he left after paying $85 for a waggon 1 2. $450 is divided between Harry and James ; as often as the former gets $8 the latter gets $7 : how much does each receive? 8. When $400 is paid for 25 acres of land, what will 1 acre and 1 rood cost 1 4. A market woman sold 4 lbs. 4 oz. of butter, at 32 cents a pound, and took her pay in cotton at 8} cents a yard : how many yards did she have 1 5. Find the least number from which 17, 34, and 51 can be subtracted an exact number of times. 6> A man after paying an income tax of 2} cents in tlie dollar, had $1,560 left : find his income for a yearl 7. A can do /^ of a piece of work in 9 hours, and B in 15 Iioura ; after A has worked 3 hours B comes to work : in what time will the work be finished ? 8. A boy being asked how much money he had, re- plied : if you add 1 to 5 times what I have, 13 times the square root of the sum will be 1 17 : how much had he t 9. How many yards of carpet 27 inches wide will it take to carpet a figor 18ft. 9in. long and 12ft. wide t $ li ■4 106 MENTAL ARITHMBTIO. 10. A man failing in business was able to pr } of 7 is { of how many times 3 1 11. A garrison in a state of siege is put on short allowance : each man receives 12 oz. of bread, which is 4 of a full ration, and 10 oz. of meat, which is | of a full ration : find the daily rations. 12. A horse cost $1,200 and | of its value is | of 2^ times the value of the farm on which it stands : find the value of the farm. (5.) 1. A man bought a pig for £1 15s., a sheep for 15s. more than he gave for the pig, and a cow for twice as much as he paid for the sheep and pig : how much change did he receive out of a £20 note 1 2- If a man take 3 steps in going 10 feet, how many- would he take in going a mile 1 8. Find the L. C. M. of 3, 17, 51, 1021 4. Charlie and Willie had each the same number of cents; Charlie spent 10 cents, and then they together had 70 cents : how many had each at first 1 5. If A can do a work in 3 days, B iu 4 days and C in 5 days, in what time could all working together do the work 1 6> A has a certain amount of money, and B has 1^ times as much, both have $180 : how much has each 1 7. A man owns | of a ship and sells J of his share for $1,275 : find the value of the ship. 8. The length of a room is 18 feet 6 inches, and its breadth is 12 feet : how many yards of carpet 27 inches wide will oover the floor % 'III 108 MBNTAL ABITHMBTIO. 9* i of 40 is /<; of how many times 10| 1 10* A boy being asked how many cents he had, said 4 times the number is 18 less than 7 times the number how many had he 1 11. If 3 pints contain 114 cubic inches, how much will be contained by a rectangular boiler 2 feet 6 inches long, 1 foot 7 inches wide, and 18 inches deep 1 ' 12* If } of a yard of cloth cost 80 cents, what will | of a yard cost 1 18* 7 men can build a wall in 8 days of 10 hours each : in how many days of 12 hours each could they do it 1 ' (6.) 1. Findtheresult of 75+85— 27-4-12. 2. A man undertook to split 400 rails at the rate of 1 rail in 3 minutes, agreeing to pay 5 cents for every rail he was short of the 400, he worked 10 hours and gave up : how much had he to pay 1 t 8* A boy being asked his age replied : if you add 5 to my age, take the square root, multiply by 5, add 5, and take the square root, the result will be 5 : how old waF hel 4- A man bought some apples for 88 cents, at the rate of 5 for 11 cents, and divided them among his 5 children : how many did each receive 1 5. A and B can together do a piece of work in 2^ days, B can do 2J times as much as A in a given time : find the time required by each alone to do the work 1 . 6. If 6 persons spend $36 in 3 days, how much will 10 persons spend in 5 days 1 7. A farmer sold 12 sheep which was | of } of hii flock : how many were in the flock after the sale t QUSSTI0N8 FOR EXAMINATI0K8. 109 8- $500 is to be divided between A and B so that me often as A gets a dollar, B gets f of a dollar : what will each receive 1 9. A quantity of sugar was sold for 12 cents per pound, the gain being J of the cost price, the total gain was $3 60 : find the quantity of sugar. 10- If one-third of a shilling were 6d.f what would } of£l bel 11. J of 64 is I of how many times | of 32 1 12. A flag'StaffSO feet high was broken into two parts by the wind, it was found that Af of the longer part was r^^ of 9^ times the shorter part : find the length of each part. 18. 4 of 72 is J of how many times J^, of 60 1 ' (7.) 1. A man bought two building lots, one for $246 and the other for $328, and sold the two for $1100: how much did he gain 1 2. If a machine can cut 100 rails in a minute, ho\/ many can it cut in 10 days of 10 houi-s each 1 8. A teacher having a school of 100 boys and 120 girls, divided the scholars into the largest possible num- ber of classes so that each class of girls should number the same as each class of boys : find the number of classes. 4. Bought a gold chain 18 carats fine, weighing 2ob. 14dwt. 10 grains, at $24 an ounce : find the cost. 6. I of 27 is { of how many times j'^ of 90 1 ♦6. At what hour between 3 o'clock and 4 o'clock will the hour and the minute hands of a clock be together t r I * Sm *' Bzaminaiion Papera in Arithmetic," pa^ 9fti mm^ ( mmm§y no MHNTAL ABITHMETia 7' A horse cost $80, and } of his cost is | of four timet the cost of the carriage : find the cost of the carriage. 8. If the ten-cent loaf weighs 4 lbs. when flour is $6 per barrel, what should it weigh when flour is $7.80 per barrel] 9. A drover bought a number of sheep at $3 J a head, and lacked $7 of the amount required to pay for them ; had he bought them at $3^ a head he could have paid for them and had $3 left : how many sheep did he buy ? 10* A woman gave $1.20 to some children ; each boy received 9 cents, and each girl 7 cents; thrjie were 3 times as many girls as boys : how many Wdre there of each class 1 11. I sold a farm for $4800 by which I incurred a loss of ^ of what it cost me : how much did I lose 1 12< If 8 men in 6 days of 10 -hours each can do a cer- tain piece of work, how many men will be required to do the work in 8 days of 7^ hours each ? (8.) 1. A boy can pick 3500 stones off a summer fallow in a day : at 20 cents a thousand, how much will he earn in a week 1 2. A farmer exchanged 10 bushels of wheat at $1.20 a bushel for 20 bushels of oats and $3 cash : what were the oats a bushel 1 8. A goldsmith manufactured 2 oz. 5 dwt. of gold into rings each weighing 9 dwts., and sold the rings at £1 4s. each : What did he receive for them 1 4> A and B can together do a work in 6 days, and B oan do /j- of the work in a day and a half : how long would it take eaoh working alone t I, '. qUmiONS FOB IXAIIIHATIOV. Ill 6. If { of an inch on a county map correspond to 6 Kiles, what distance will represent 3| miles ? 6. f of 32 is I of how many sixths of 18 f 7. In a drove of 120 animals there are 50 cows and the rest are horses : how many horses must be sold chat there may be left 4 horses for every 5 cows 1 8. How far may a person ride in a stage which maKes 6 miles an hour, so that he may drive back at the rate of 8 miles an hour, and be gone only 9 hours t 9. I sold a hoase for $2800, by which I gained J of what It cost me : find the cost. 10. Harry is 10 years old and Mary 15 years: in how many yeani will Mary be 3 times as old as Harry t 11. After losses in two engagements a cavalry troop was found to consist of 950 men , in the first engage- ment they lost 1 in 12, in the second j^^ of the remainder : find the number of men in the troop at first. 12- In a municipality the assessment is 18 mills on the dollar : for how much is a man assessed whose taxes are $63 ? (9.) 1. What number must be subtracted from 3050 to get a remainder exactly divisible by 55 1 2. Hannibal won the battle of Cannse, B.C. 216, being then 32 years of age ; he was defeated at Zama, B.C. 202 ; he died at the age of 65 : how many yeai-s before his death was the battle of Zama fought? 3. Emma bought a book and slate and a pencil for 3s. 8>1. ; t^e book and slate cost 3s. 4d. ; and the slate and pencil cost Is. 4d. : fin I the cost of each. 4. A man agreed to work for 30 days on the conditions that for every day he worked he should reoaivef 1.50, bul wm^^w^ "Pff ts imrTAL ABITHllinO. ■hould paj 50 cents a day for his board every day h« should be idle ; at the end of the time he received $40 v How many days did he work t 5 The dry goods in a certain store cost $1,200, anil | of their cost is -^ of three times the cost of the groceries : find the c^st of the groceries. (I. By selling cigars at 70 cents a 'lozen -^ of their cost was gained : find the price at which each cigar should have been sold to gain { of their cost. 7. A farmer sold Jj^ of his farm at the rate of $40 an acre, and received $2,800 for it : what was the remainder of the farm worth at the same rate 1 8. A boy said : if from the square of my age you sub- tract 48, j'j of 5 times the square root of the remainder will be 15 : find his age. 9. Divide $192 among Harry, John and James, so what John may have twice as much as Harry, and James 1} times as much as John. 10* How much cloth at 5s. 3d. per yard can be bought for 21 guineas 1 11. If T receive $12 for the use of $150 for 1 year, how much should I receive for the use of $375 for 18 months f (10.) 1. Bought 26 barrels of mackerel at $8.25 a barrel, paying $100 cash, and giving my note on three months for balance : find the face of the note. 2. Find the greatest number that will exactly divide both 38 and 59, leaving 6 and 11, respectively, as re- mainders. 8* Two towns A and B are 45 miles apart ; a persDii ■ets out from A to B at the rate of 3 miles an hour, and f^- ■!!• 9UI8TIOMB FOB IXAMIKATIONS. 113 two hoars Ufter, another sets out from B to walk to A «t the rate of 9j^ miles an hour : how far from A. will the/ meet % 4. SimpUfy \ (72+82)-2 |. X \ 93+45x3 }, 5. Fin4 the cost of 7,200 yards of cloth at 9s. 6.1. ])er yard. 6* W))at is the length of the longest stick that will ex- actly mmsure 3 yards, 2 yards, and 9 inches % 7> Qpw maay yarvls of carpet 27 inches wide will be requir^^ ^or a room measiriag 18 feet by 25 feet 6 inches f 8. find the L. C. M. of 126, 225, 630, and 900. 9» If ^om a certain number 5 less than its half be tako|i, and from the result 4 more than \ (of this result) be taken, the remainder will be 22 : Find the number. }0. A cistern has 3 pipes ; the first alone can fill it in 19 minutes, the seconl in 16 minutes, and the third can ^pty it in 8 minutes : if the cistern is empty, and all ^ree pipes be opened, in what time will it be filled f U. Reduce 2'* lbs. 2 ozs. to the fraction of 1 quarter, and 9^. to the fraction of 7s. 6d. 12. Eeduce to lowest terms //g, and yiylg. (U.) 1. The River St. John is 450 miles long, and the Miramichi 225 miles ; the sum of these lengths will give the length of the St. Lawrence, lacking 87 miles : find the length of the St. Lawrence. 8* A boy bought a lot of lead pencils for 80 cents, anl lold some of them for 36 cents at 3 cents a piece, losing (hereby one oent on each : for how much eaeh mint he seU Um remainder t; gain 4 cents on the lot I ■It I IP ■»F¥'wpfi^ipiW!i^»pii^s«»wiw^lpprj 114 MBBIAL ABITHMETfO. 8* ABtaiioner sold a dozen articles for a certain price ; his gain on 5 articles was his selling price for 3, and ha ■old 4 for 40 cents : fin.l the whole cost. 4. Two men bought a quantity of flour for $40, thb first paying $3 for every $2 paid by the second j the flour was $6 a barrel : how much will each have 1 5. T^tf My horse is worth } as much again as my buggy : what fraction of the price of the horse is the buggy worth less than the horse? 8> Having laid out } of my money, and lent | of the re- mainder, I have $24 left : how much hai I at firat 1 4. A man has to be at a railway station at a certain time; if he walk 2} miles an hour he will be 12 minutes too late, but if he walk 3 miles an hour he will be 12 minutes toe soon : at what rate must he walk to be just in timet 6* A number which is divided into 3 parts, which are as 1, 3, 6 ; the ecoond part is 24 : find the number. 0b A merchant bought wheat at $1.20 a bushel bj Ifc 120 MmrTAL ABItHMBTia measure, and just gets his money back by selling it al $1.10 a bushel by weight: how many pounda to the bushel did the wheat over-run 1 7* If to ^ the cost of my horse you add $80, the sun will be 1^ of the cost : find it. 8. 10 square yards of cloth are required, the cloth selected is one yard wide, but when sponged will shrink Jjf in length and -^^ in width : how many yards must be purchased 1 9. If 40 lbs. of sea-water contain 2 lbs. of salt, how much fresh water must be added so that 3 lbs. of the mixture may contain 1-^- ounces of salt 1 10. A boy sold 2 dozen oranges, | of his gain on 12 was his selling price for 4 : what fraction of selling price h cost 1 11. Three men or four boys can do a work in 12 days : in what time can 3 men and 4 boys do it ? 12. A school is allowed 1 ^ houis for dinner ; a boy walks home at the rate of 4 miles an hour, takes 20 minutes to eat his dinner and is back in time, walking at the rate of 3 miles an hour: how far does he live from the school 1 (17.) 1. The latitude of St. John is 45** 18', that of Toronto, 43** 40' : allowing 70 miles for a degree, how many mileu is St. John north of Toronto 1 2. 5 men or 8 boys can do a work in 6| days : in what time will 3 men and 4 boys do 2^ times as much t 8. A man sold a horse and gained j'g of the selling price ; if he had bought him for $12 less, he would have gained J of the cost : find the cost. 4. A and B do a piece of work, A receiving $2 a daj 6 a i a t 5 $ w ■.ii- ■■*■ qUESnONQ FOB BZAMINATIOVB. ISl g le and B $3 a day ; A works twice as many days as B, and f70 is paid for the work: how many days did each work? *5' The sides of a right angled triangle are 6 ft., 8 h, and 10 ft. respectively : find the length of the pei-pendi- cular on the hypothenuse. 6. Find the cost of | of ^ of 40 bushels of wheat at $1.1 2J per bushel. 7. What is the first time after 1 2 o'clock at which the hands of a clock form an angle of 60° ) 8. A boy being asked how much he was worth said: add $17 to the number of dollars, take the square root, multiply by 5, add 5 to the product, extract the square root and multiply by 80| ; the result will be 402 : how much was he worth 1 9- An agent sold $2700 worth of goods, receiving for hia trouble $3| on every $100 : how much did he receive in all? 10 • A brakesman is noticed running in the same direction as the train, on the top of a freight train going at the rate of 10 miles an hour, and is observed to take J a minute to pass 2 telegraph poles which are 20 rods apart : at what rate is the man running, iadependently of the train 1 (18.) 1. Bought 10 chickens at 60 cents each, 6 ducks at 60 cents each, and 4 turkeys at $1 each, paid on account $6.80 : how much is still duel how man^ ten cent pieces will pay the balance 1 2> A teacher being asked how many scholars he had, -fj! *Note thai the produot of the perpendicular on the hypothenoM equate < fffodael «f the other two lidee. mm^ 122 MENTAL ARITBMETia answered that 30 of them were boys, and J of them^ l€M 20, were gii»ls : how many scholars were there in all 1 8. If 7 of my age has passed since I was 36 years old, how old am I ] 4. An equal number of geese, chickens and turkeys were sohl for $11.40 ; each goose brought 60 cents, each chicken 30 cents, and each turkey ^^- of the cost of a goose and a chicken : how many fowls were soJld 1 6' How much water must be added to 30 gallons of brandy, at $4 a gallon, to make it worth $2.50 t. gallon? 6. A man went to market and bought a turkey and a goose weighing in all 24 lbs., the goose at 8 cents a pound and the turkey at 12 cents a pound ; the whole cost was 12 cents more than if he had bought both at an average price of 10 cents a pound : what was the weight of the turkey 1 7. What o'clock is it if the time past 10 is J of the time past 9 1 v 8. One number is 7 J times another: if the difference between them is 65, what are the numbers ] 9. How many boxes 9 inches long, 6 inches wide and 3 inches deep, can be packed in a space 3 ft. each way ? 10. A owns I of a lot of land, and B the remainder. The lot is sold, A receiving | of his share of the money and B J of his. B afterwards received $40 from the pur- chaser, and the balance then due was divided equally be- tween A and B : what was the lot sold for t (19.) 1. A waggon is going at the rate of 8 miles in 1 hour and 20 minutes, and a buggy in coming up behind at th* QUBBTIONB FOB BXAMIMATI0N8. 123 rate of 6 miles in half an hour. If the buggj overtakes the waggon in 1^ hours, how far was it behind at first 1 2. The product of two numbers is 48 : if one of the factors is ^ of 27, the other is 4 of what number ? 8. A and B hire a livery at Brampton, to drive 12 miles, each to pay in proportion to the distance he rides. A calls at B's residence which is 4 miles from Brampton, and leaves him there on their return : what should each pay, if the hire of the rig- cost 3 dollars! 4. A*8 and B*.s ages together are 48 years, 4 years ago B's age wtcS | of A's : required their present ages 1 6* A pole is 51 feet long, is broken by the wind, § of the length of the longer is equal to J of the length of the shorter : find the length of each. 6- If J of a piece of work can be done by three men in 2 days : how many men will it take to finish the re- mainder in three da-ys 1 J. What o'clock is it, if the time past 3 is J of the time from now to 4 ? 8. Which is the cheaper, a hat that costs $1.40 and lasts 7 months, or one that costs $2.70 and lasts 9 months 1 What is saved in thr*)e years by wearing the cheaper hat 1 9. Two blocks of wood, each 6 ft. long, contain the same number of cubic feet, the fii*st is 2 ft. by 1 J, and the lecond is 9 inches one way : what are its dimensions the other! 10. The expense of carpeting a room with carpot is $20, but if it was 3 ft. wider it would cost $26 : find the width of the room t ■■ip ■m 12^ MENTAL AKItllUETta (20.) 1. A iDarcel of 1 2 lbs. weight is carried 26 miles tot SO cents, and the rate for the distance over 10 miles is ) of the rate for the first 10 miles : how far can a parcel of 9 lbs. be carried for 20 cents 1 2. Two hens and 3 ducks cost $1.15 and 3 hens, and 5 lucks cost $1.85 : how much more does a duck cost thaji a bent 8. A does f of a piece of work in 4 hours, 6 does ^ in an hour, and finishes it in J of ira hour : how long would it have taken all working together to do the work t 4. B travelled 102 miles in three days ; the first daj he travelled } as far as on the >!ist two days, and on the last day J as far as on the first two days : how far did he travel on the first day f 6. A dishonest milkman adds a quart of water to every gallon of mile and then sells the mixture at i'^ more than it cost him : what is his profit on an expenditure of $10 1 6. A farmer having bought a certain number of sheep for $100, when a dog killed 8 of them, he sold } of the remainder for cost and received $20 : how many did he buy I 7. Two men, A and B, enter into partnership and gain $300 ; A owns | of the stock, lacking $40, and gains $180 ; required the whole stock and share of each 1 8. A thief has 220 yards the start of an o£Scer, in the next half mile he gains 10 rods more, after which the officer runs 3 to la while the thief runs 2 rods : how fur had each run when the thief was overtaken t 0. One-^Mh' of the pupils in a class are girls, f he other QUESTIONS FOR EXAMINATIONS. 12d half are boys; the girls own G5 books, the boys 91, each having the same number. What is the largest number of pupils that could be in each class 1 10. How many flowers can be planted along tlie borders of a flower bed 12 ft. long by 9 ft. wide, tlie flo^ drs being 6 inches apart 1 .11* What is the value in cents of the largest coin with which I can pay the following three bills : 2 crowus. i sov«rei|p[i, and 1 guinea 1 Bnd of Part L