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Those too large to be entirely Included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent §tre film6s d des taux de reduction diff^rents. Lorsque le document est trop grand pour dtre reproduit en un seul clichd, (I est film6 d partir de Tangle supdrieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'images n^cessaire. Les diagrammes suivants illustrent la mithode. rrsta to pelure. T a 3 32X 1 2 3 1 2 3 4 5 6 GRAFTON'S GRADED ARITHMETIC BOOK IIL BY E. W. ARTHY, SUTEBINTENDENT OF CITY SCHOOLS, MONTREAL. Authorized for use in the Promnce of Quebec. FRIOE, 15 OEITTS- MONTREAL: F. E. GRAFTON & SONS, PUBLISHERS. 1899, \ Entered according to Act of ParUament of Canada in fl,, one thousand eight hundred and ninety-d. bv F TZl' IV" in f Iio nffl r i.1 , . . "luety six, by H.h. GrAJTON & SoNS. m the Office of the Minister of Agriculture. ^ I ^ \ 5^ .' NOTE TO TEACHERS. This collection of exercises has been arranged and compiled for the use of young pupils. It is intended to furnish a sufficient number of easy and easily graded examples. It has been prepared for inductive teaching. New work is introduced by easy sight examples, the object being to lead to an almost unaided perception of processes and principles. Too often young pupils have to grapple with numerical difficulties when attempting to grasp a new principle. Many of the problems are new; others have been collected at various times during the past twenty years from sources too numerous to sj^ecify. The merit of the work (if it has any) does not consist in the originality of its matter, but in its arrangement and grading. Nothing is so discouraging to teachers of arithmetic as the ease with which pupils forget. For this reason, though the ordinary arrangement by topics has been adopted as best calculated in the first instance to impress upon the mind a new principle and rule, one-third of the book is taken up with review and test examples, and with exercises intended to secure rapidity and accuracy in the simple rules and other computations. These exercises should be taken as occasion demands. The author desires to express his indebtedness to Mr. Nevil Norton Evans, M.A.Sc, Lecturer in Chemistry, McGill College, for revising the section on the Metric System. A Teachers* Manual, giving full directions in using this book, as well as Answers to examples, may be procured from the Publishers. Price, 35 cents. ii '"A CONTENTS. Common FRAcrrroNs . . • . Denominatk Fractions Practice .... Cancellation ... Proportion .... Metric System .... Mensuration . • . 24 Circular Measure .... qq Percentage ,, ^ 36 Profit and Loss Simple Interest Discount .66 Present Worth _ •••••... 69 Compound Interest -o A •••••... 60 JttAPiD Arithmetic Miscellaneous Examples (\Vi:i'"ti:n-) h/» Test Exercises (Mental) ' • * 79 Test Papers (Written) . Review Exercises (Theory) «„ ' • • • • . .93 X. Work by shortest method : — 1. i + 2. i + 3. i + 4. i + 6. i + f--fi; 17. I Q at' 13. 14. 15. 16. 6. 7. 8. O. 10. 11. 12. i + i + 1 + i + 18. *", 19. 20. 1 !¥• 1 1 J.-- ^21. T* - ' 1:' 22. 1 IT'; 1 ;, J/ 23. ;; 24. + + + i + i + i - 1 __ "6" i- rV. h. TIT- ,^ 1 ^** 1 w X XT' • _ll 1 . i" 25. J 26. J 27. I 28. ^ 20. J 30. I 31. i 32. i 33. ^ 34. tV 35. ^ - 36. tV 1 -i- 1 7* f ^ 1 '* .. J XT' _ 1 XF- ^ _ 1 XX' J'i^ B (%7ijf;. 1. i + 2. J + 3. J + 4. J + 6. f + 6. f + 7. f + 8. § + 0. i + 10. 1 + 11. 12. !■ ^(? 13. |..»'' 15. l^j 16. i^!i 18. 1.:" 19. 20. 2. 4_ 8 2 5 i- .j'l + f + i + f 4 -L. 5 IT T- T- f -i- f - I i-i- i-i- ■u 21. i 22. f 23. ^ 24. f 25. f 26. f 27. f 28. -y- 29. I 30. i _ iJ -i- -i- -i- _ 5 "8 -J 5 M a /To FRACTIONS. •t- ■ \ 2. Sry^ 4- ITJ.-^, ; 12. 35 _ ;' 4 6. 3G 21. .^^ - .2f 22. 9| - 8|. • f 3 + 281 -0^14. 3G ^ V J.^^^' 'I " 2f. 1. I X 5.- 2. f X 10. 8. A X 5. 4. tV X 2. fi- A X a '«ii. f X 7. ^12- iV X 6. 15- f X 16. - V 10. i X 18. - \^ 1'7. i X 20. ' !l.^ i X 18. 19' il X 90. 6. ft — 9 V» 1 O , i - _ o * *='. 4 J A 0. " X 11. 14. f X 21. IS 21. , ^ ^2_ 1. A 2. T% 8- tV 3. 6. - xg^ - 9. 4. e -^ 3. 6. li -r 7. " ^' -2. 3.^ 11. If ~5. 12. If -f- 7.- ^ 13. 8J -f 5. ^, 14. 8J ^ 10. 7 JLl • ,± J. 8. f -f 8. i -r 2. 10. f -r 5. 16. 2jV ^ 9. . (, 16. 2rV.^4. )-^ 1'7. oj -f 7. 18. l^V -r 10. ^ 4. 8.-^ 3 ^ V 19. 3j?j. i 20. 3i ■ \* IT 21. T*r ^ 9. 22. I- -f 2. 23. f -f. 4. 24. § -:. 6. 25. f ^ 6. 26. f ^ 9. 27. 6,1 4- 4. .28. 3| ^ 7. 29. 6| 4- 5. SO. 2^- ^ 3. ^^^ V 'S 1 «ft F n. 1. 8} X 3.'^ -.11 16 X i 21. 101 X 2J. , a. 7i X 9^ 12 18 X f 22. 305 X 3i. 8. 6§ X 8. 13 20 X *. 23. 201 X ^. 4. 9i X 7. 14 17 X f. 24. 224 X \\. 5. 6i X 6. 16 89 X \' 25. 340 X 8^ 6. 4| X 5. 16. 78 X «. 26. 100 X 9f 'i 7. ^ X 8. 17 83 X I' 27. 32 X 11§. 8. 8J X 6. 18 51 X f 28. 40 X 16J. 9. 6^ X 5. 19 . 63 X f 29. 36 X Ln. XO. 5J X 4. 20 42 X G f 30. 20 X V^\. 1. 19i - r 3. 8. 22J 4- 5. 15. 230^- -r a 2. 16| ^ - 4 9. 65J -f 9. 16. 321i -r 8. 8. 16§ ^ - 7. 10. 57f -r 2. 17. 101 f -r 9. 4. 12t ^ - 5. 11. 315i -^ - 2. 18. 2161 ~ 7. 6. 24f H - 8. 12. 213^ - - 3. 19. 321f -f 8. 6. 191- ^ r 6. 13. 321i - r 3. 20. 514f -r 5. 7. Vl% -i r 9. 14. 622i - r 5. 21„ 213*- -r 5. II. A oomplex fraotion has a fraction in either its numerator or denominator, or in both. Keduce to simple fractions : — 1. 3J 2. 4i 3. 12 4. 15 6. f 6. 3 7 34 IJ 34- "6 T ^ / w ■ ■ ■ I COMPLF^^X FRACTIONS. 7 » 8. 6 9- I 10. « i^ 11. -«- 12. 9j 1^ //- ^2. ^.nd the quotient of the 8th divided by the 9th 23- |_X_,\ f 24. 1 K 6 -^ H 27. 8 X 9| ae. I of 2j 30. . „f .^ ITT TVof5i 32. 33. 23 21X21 35. 31- j-j^i fioflf 33. I3|^12f 39. 7f-^3f 25. f of 13| 28. U\x3?jI, 81- f of 1^ 14 1^ 34. 12f on^ 37. ^0^ .40. 3|o .A.A_ Q^i i I ■Uix^Pip^iV^ractice the v|lue of :-f "" ' I. 508 articles at 50 f. -i :;^'^-^ :5' 4^ 1 f / ■^ 2. 305 3. 576 4. 704 6. 198 6. 648 7. 211 « (( f< ti « « at 25;^. o. 440 at $1.33^. 10. 506 at $3.20. 11.409 at$416f. 12. 316 at$1.12|. 13. 127 at $2.10. 14. 209 8. S6(i ari&l^s^^ ^^^^.^\ « te te tt it at $1.06| at $2.37J, at $3.75. at $4.40. at $1.87i. at $10.05. 16. 17 chests of tea. each 59 lbs., at SSJ/ a lb ^r 10. 158 tons of coal at «f^ ^qi 4. "; 17. 170 lbs. soap at 8^^ a lb. / . \ "i.^ '^' f-iOchX 1 ^>i.^.Vl..u,Vy'i;^.; J ^•Hf'.'XKO I X^^ 1 87. >vvj'^.0'i..^,,^ 1 88. 1^ ba^^l 89. %0. $1.06i 1 41. $2.37J, 1 42. $3.75. 43. $4.40. 44. $1.87i. 45. 46. M^48. $10.05. ' 1 49. 1 60. CANCETXATION. 5 yds. 1 ft. 9 in. at $1.G2 per yard. 17 acres 2057 sq. yds. of land at $18.72 the acre. 18 yrs. 5 mos. 1 wk. salary at $1000 per year. Salary for a year at £1. Is. ll|d. per day. Rent of 29 houses at £13. 14s. 2d. each. 1309 roubles at 2s. 6Jd. each. 706,500 fire bricks at £3. 13s. 6d. per thousand. 90| dozen pairs of boots at 12s. 9d. a pair. 107 shares at £93. 15s. 8d. each. ., /. 27 yds. 1 ft. 5 in. at $0.45 per yardT 15 acres 2662 sq. yds. at $1.10 per acre. 154 bu. 3 pks. at $1.00f the bushel. 24 yrs. 5 mos. 3 weeks at $150 per annum. ,/ 25 tons 155 lbs. at $16.80 the ton. j^u-.^^. VI. Find the value by cancelling of : — 1. 3 X 15 X 4 2. 7 X 25 X 16 3. 8 x 14 x 24 20 X 12 X 9 8 X 30 X 14 32 X 12 X 7 4. 28 X 5 X 12 5. 2x5x7 6. 5 x 21 x 32 20 X 7 X 32 10 X 11 X 11 48~x 35 x 3 7. 2 X 50 X 11 8. 56 X 42 X 9 9. 30 x 6 x 16 33 X 4 X 10 7 X 8 X 27 3 X 8 X 40 10. 17 X 85 X 4 11. 5 X 81 X 77 12. 90 x 40 x 42 20 X 3 X 3 11 X 55 X 63 100 X 63 X 24 \ I ■i) 13.5-5 X •081x4-9 14.2-1 x-.^-c.; 12-6 15.4-2 x 14-3 x '66 CO v^ /j.O -- -oo uu ^ 4-2 A OO Ox x=5G Art O r\ -4 A -4 <--\ -« oU XUJ4X i'ili /'> 2-S ^: On -^ •J S-'o «) c - 10 PROPORTION. VII. PROPORTION. 1. If 12 yds. of cloth cost $15 wliafc w,']] q ^ 2. If 57 cwt. of surrar cost toia f ! H ^ ^^'- ^^^^ ? 3 Jf tlm , 1 ^^^' ^^^^ will 95 cwt cost ? <*. It the yearly rent of a farm of 1«9 a ^ i^ ! what is the rent of a mrt of .> . ^''''^^ ^^ ^^^3, 4 T* oor ^ ^* ^^ contamincT 49 aprp« ? 4. If 385 yards of linen cost ^Cv^ I can be bought for $18 ? ^^^^ ^63, how many yards Vlf 96 men reap 40 acrp«^ nf r^ - - ■ 2f -n Win reap i ^..Ti:]."! z:z: r'' ''-' '7. If 84 sheen r.n 1 '''''' P^"^^^"^ ^^ 266 days V^rnj. for 9-wtf:rirr!.r'™^^"^^-^* «- ■ong wai the p.oviZ: Cf""'"^"' "^ ^O" -- : h w w^'l'a s^r"'. '"" °' ' ""''' "-■^■^ - «4.75. what additional n,en „,ust he empLy ? ^^'' ^°^ ""^"^ 11. What will 10 hnvpo .f cost $5i ? ''°'"^' "^ °'^^'g«^ «o«fc, if 3J boxes walif in" J :* ? """ '' ^ °^ ^" '^-' '^o- fer can I 14. If 3h barrels of apples cost tlA i. can be bought for $20 ? ' """^ "^^"^ ^^^^^^s 15. i of a race is 500 yards, how long will /, be ? \ PROPORTION. 11 16. ^ of a city contains 9000 inhabitants; what will ^ of it contain ? ^ 17. If 7| acres be ploughed in GJ hours, how long will it take to plough 3|- acres ? • 18. In how many hours can a field of 3 J acres be reaped, if one of 5 J acres is reaped in 6 hours ? ti ' , -, . . 10. If 100 dinners can be paid for with £3 J, how' many can be paid for with £7^ ? .:!'.;• ^^ 20. If a certain quantity of corn feeds 12 horses for Hi days, how long will it feed 45 horses ? 3 ' - - ■ . 21. How many men can perform in 1-68 days a piece of work which 120 men perform in 2-66 days ? ' ' . - 22. If 1^ yards cost 17^ cents, what will 3-^ yaKff^ cost r • 23. If 11 J cwt. cost $5|, what will 4} cwt. cost ? . - ' '> 24. If 3-75 cwt. is carried for ^0-875, what weight should be carried for $2-625 ? ' :^ ,— ° 25. If 2-875 cwt. cost $16-1, how much can be bought for $19-75? V J) . V'- ' 26. What is the rent of 21 acres 140 sq. rods of land If the rent of 36 acres 120 sq. rods be $42 ^^ :S- 27. If a person walks 17 miles in 5 hours 12 min. 31 sec, how far can he walk in 3 hours 40 min. 36 sec. ? 28. If the earth moves 69,000 miles in its orbit in an hour, through what space does it move in 16 min. 48 sec. ? ^^ 29. If I lend a person $100 for 12 weeks, how long ought he in return to lend me $175 ? 30. If f lb. cost $1, what will f of 14 lbs. cost ? a^-:^-;^ /" 31. If a field of IG acres produces 440 bushels of wheat, how much will be grown on 22 sq. yards ? 32. The shadow of a man whose height is 5 ft. 3 in. was 4 ft, G in. at the same time that the shadow of a steeple was 156 ft. Mnd the height of the i 3pl e. 12 PfiOPOBTlON. C^ 33. How long would an icebem h^ fl«„*- breadth bei„g 20 feet ? '^"' "'^''' »''« ' 35. Wiiat will 33i dozen of A,.„ii- • rate of $49 for 82 do/en a'd 8 itUes' "" '"' ^' ^"^^ ^ wo:m /c;;:^f ::;/^^^ >-^^ »^ ''- -e le,., what 37. How many yards of carpet 175 feet wid» w ]^ cover a floors yards long and llfeet broad' ^°"" i-"\iirf::it:.::fr ^^^'^^^^^^^^ ->>- being 35J feet ? '" '""" ''^«' ">« length irteoif'' '""^ *=°^' ^'-''^ -'>''' -IJ 31-5625 ttitiscifhor/^^^^-'"^^'^"--'-- rate per hour dnp* if f i .. "^^"""^^s to 8; at what forstoppaS"? ' ""'""'^^ '^'"S allowed ^ 43 From | of 5 cwt. 28 lbs. take i of 4 cwt 5fi lb« , £nd the cost of the ren.ainder at $0M forlcwt 28 il 44. How long will it t^l-„ t„ ° ^^ ^'^^• long. 12 ft broad Z Oft ''^''' ^ """^^ ^^ ft, yards 5 ft in it:: 26 ir/"^' ^' "^^ ^^'^ "^ ^ -"^^^ ^^fqs^;s3-5-^--.Ht reri„irtS,Srf:f;oif'---va.neofthe METlilC SYSTEM. 13 vm. METRIC SYSTEM. Metric Weights and Measures are those whose units increase and decrease regularly by the Decimal Scale. The metre is the base, and from it the metric system derives its name. The metric system has three principal units : the metre for measurements of length, the litre for capacity, and the gram for weight. The ?iigher denominations are formed by prefixing to the name of the unit the Greek numerals : Deca, signifying 10;^ Heoto, 100; Kilo, 1000; Myria, 10,000. Tho lower denominations are formed by prefixing to the name of the unit the Latin numerals: Deci, signifying iV or -1 ; Oenti, t^tf or -01 ; MiUi, i^jht or -001. JK^.,)Kilometre = 1000 metres. /Centimetre = Tff^ of a metre. Money. 100 centimes = 1 franc (fr.) Length. 10 millimetres* (mm.) = 1 centimetre (cm.) "^ 10 centimetres 10 decimetres 10 metres 10 decametres 10 hectometres 10 kilometres 1 decimetre (dm.) 1 metre (m.) 1 decametre (Dm.) 1 hectometre (Hm.) 1 kilometre (Km.) 1 myriametre (Mm.) Only units printed in blacic letter are in common use. 14 if ill METRIC SYSTEM. Si^RFACE Measure. 100 square millimetres = i •au.i* «««♦. ^ f 100 square decunetre.s = 1 «,„^ „.„. ^^^_ \^^ 100 ceiitiarcs (ca.) = i ,„ („) 100 ares — i ,. » /tt » — 1 hectare (Ha.) A ccnhan is the same in size as a sj. mHn. mnn ,• •„• Solid Measpke. l— 1000 cu ,.e luillnnetres = 1 cub.c ce„«.™e,™ (ou. em ) 1000 cubic decimetres = 1 .„„. m.t« (cu. m ) In measuring wood tlie o«i;c viHrc is called a Stere. Capacity. = 1 centilitre (cl.) = 1 decilitre (dL) = 1 litre (1.) = 1 decalitre (Dl.) = 1 hectoiitre (HL) Weight. = 1 centigram (eg.) = 1 decigrai'i (dg.) = 1 arram (g.) = 1 decagram (Dg.) = I hectogram (Hg.) = 1 kilo«rram (Kg.) 1000 kilograms make a metrio ton. Equivalents. 1 metre = 39-37 inches. 1 litre = 176 pints. 1 ki ome re = -6214 mile. 1 hectolitre = 22-01 gaL 8 kilometres = 5 miles (nearly). 1 gram = 15-432 graLs. 1 sq. meti^ = M96 sq. yds. 1 kilo = 2-2046 lbs. 1 hectare = 2-471 acres. l a,etric ton = 1-1023 tons 10 millilitres (ml.) 10 centilitres 10 decilitres 10 litres 10 decalitres 10 miilig^rame (mg.) 10 centigrams 10 decigrams 10 grams 10 decagrams 10 hectograms * v (' METRIC SYSTEM. A {Length). Tlie metre is the principal unit, and is usee',, like yard, for measuring lengths of materials, such as cloth, for short distances. For long distances, as along roads railways, the kilometre, like the 7iiile, is used. 1 metre = 39-37 inches. 1 kilometre = 0-6214 mile. 1. How many metres in a decametre? Hectometre ? Kilometre ? i ^ J" M 2. What part of a metre is a decimetre ? ^ Centimetre ? Millimetre ? 2 3 3. Read in terms of the metre (or kilo- S- metre) and one other denomination : — 11 17-5 m. 41-625 m. 9-327 Km. 1 m. ? 32-2 ra. 54-886 m. 643 Km. -01 m. §; 64-25 m. 29-7 Km 5-68 Km. -001 m. I 23-62 m. 99-9 Km. 0-563 Km. -001 Km. 2 15 the and and 4. Express in terms of a metre : — . 5 m. 3 dm. 24 m. 49 mm. 2-3090 Km 17 m. 24 cm. 64-38 Km. 27-056 Km, 6. Change:— 5747-3 m. to Km. 58-5 m. to cm. 5335 m. to mm. o 3 9471263 cm. to Km. 4-8735 Km. to m. 372-7575 m. to cm. 6. What is the total length of 5 pieces of cloth measuring respectively 12-6 m., 9-75 m., 26-08 3-56 m., 31-5 m. ? f-;/-^?^^^"- 7. If the work done by two men measures 18 m. cue has done 8-75 m., how much has the other done ? m., and /'^y- ?,> IG METIirC 8Y8TEM. ■I 7^ o * V T - 8. I ow ,m.„y Kn,. i„ 8,r72 m. niulliplieil by 2036? e. C».,t of ; 7 „,. of silk „t "■50 francs tl,o uLe ? ^ V^' ^' 10. A luerclmnt ina.lo a profit of 1200 fn.ncs ),v my.ng n ,„oee of cloth at the mte of 7-50 franc, for 5-30 >"•. nnd s.. l,ns it at the rate of 24 francs for 15 n>. How niiicli did he buy ? t 5 .' . .->fj, Uo 1 walk in 7 days, going to and fro once a day ? ?. 9 4 / 13 At 7-056 Kin. a,, hour, how far shall I go i„ 6 ''^ hours 24 mm. ? >/ S ' . / S" 5i cy /U>, , B (Surface). J 2 3 ^ 5 6' 7 fl .9 10] 20 JO 50 00 1 ■ 7/?j ao 90 0. — m the next l,iri,„r W '"""°' "■ '""=■■ ••''"''■nmation nmko a u„it V The sjw. metre is used in measuring ordinary surfaces as floors, ceilings, etc. It is equal to about 10-| sq ft \ 2036 ? tre? ^^i^' '^ 'an OS by for 5-30 1. How my Km. go in 6 length, unit .1 lacea of rfaces, tfc. cd in MKTKIU aYSTKM. 17 1. 7Tf Ldw many sq. nietrus in a sq. Dm. ? A s '■ 15. Cost of 1-5340 Ha. of land at $2*385 an are ? 3 6 S 16. What is the length of a court whose breadth is 15-5 m. and area 2-945 sq. Dm. ? \^ ry-t-w 17. What is the area of tlie walls, floor and ceiling of a room which is 11 m. long, 8-25 m. wide and 6-75 m. high? j.a tX '%)%' -^i vrx^ 18. If 21-45 Ha. of land can be rented for-486-75 francs, what will be the rent of 2800 Ha. ? . [ -7 i uU>rX.^ 10. Cost of covering the surface of a box 1*2 m. long. • SVJ' I •6 m. wide and -25 m. higli at -006 fr. per sq. cm. ? ) (/ . ^ {^. 18 !■■ METRIC SY3TE31. C {Solid Measure), Cubic metres 1000 (10 x 10 x 10) cubic decimetres. i^O^'o:^;J^^^ ^^ *^e -its of length, .., 100. 1. In a cu. metre how many cu. dm. ? Cu. cm. ? 2. What part of a cu. metre is a cu. dm.? Acu.cn.. 3. Jixpress m terms of a cu. m. 27 cu dm • i «? V7 ' Lr;- '' ^"^ '-■ ■' '' - - '"^ - -.: ,> -4. Eead 4-406 cu. m. ; -004017 cu. „,. ; -46 cu m Q.ocr 1 ^ " "" ^" ** room Wt 8 25 m. loner, 5-64 m. wulo o^rj 9.«r ^. , . , , it- Y ^ .) / Ve^ci, \ METRIC SYSTEM. 19 D {Capacity). s., lOOti !ie next ? . cm i 3U. DP long svooc y '•^.ci. Litre. Cubic deoimetre. The Litre is the principal measure, and holds about a quart It has exactly the same capacity as a mhic decimetre. The Hectolitre is equal to about 22 gal. or 2f bushels. 1. How many litres in a HI. ? A cu. dm. ? A cu. m. ? 2. How many cu. cm. in a litre ? In a HI. ? 8. Eead and express in terms of the litre 6-049 Kl. ; 24-5705 cl. ; 1567-009 Dl. ; 630485 dl. 4. 364 dl. leaked out of a cask containing, 73-0025 HL How much was left ? V p • (- o d 1? ' '^ ' '-" 6. A gentleman buys 1-48 HI. of wine at $0.55 a litre, 72 1. at $0.45 a litre, and 3 HI. at $1.05 a litre. Find the cost. /^ rj y- \ . ^ (•: 6. Find tho value of 1180 Kl. 6 1. of barley at 20-05 francs a HI. !) , ,\ ' ^^j' / ^ 7. Divide 203 1. of soup among 18 men and 22 women, giving each man double a woman's share. 8. How long will 215792 1. last if 674-35 L is con- sumed weekly ? ^/, OTiyf->^ ;-. / •j'^ / ciX-ATr-K-L 0. A person allows 18*948 cu. m. of water to run from a tank containing 27,875 cu. dm. How many litres are left in. the tank ? »i 20 METIIIC SYSTEM. 10. A wine merchant boufrht fi'?". wi t • francs DPr Hi i ^"I'o^ic ^m 111. of wme at 60 rancs per HI., and a certain number of HI. of brandy at 1 / 5 francs per HI. He miVI f^q onn 4^ . oranay at TTr^,„ I, ' P ^ od,900 francs for the wholp How much brandy did he buy ? * 1 1. How deep is a tank to hold 9000 1. if the bottom IS a square measuring 1-5 m. on a side ? ^ E {Weight). • i Cubic centimetre. Gram. A cubic centimetre of water weighs a gram. ^ ■fffram is used to weigh gold, sUver ana drugs. Akilogmm (called kilo) h used in Kilogran,: we.g .ng all common articles, as groceries, etc. A .«» ,s used in weighing coal, hay and heavy articles. Akilo=2-21bs. A metric ton = l-l tons Av. 1. How many ^ams in a kilo? In a Hg. ? 2. W liat part of a ton is a kilo ? ' 3. Weight of 1000 cu. cm. of water? ' 4. Weight of a cu. m. of water ? 6. Weiglit of a litre of water ? -f^rof^^::^^-^^:--*-- 7. Change 20-426 kilos to grams; to tona 8. Change to Kg. 553-273 g. ; 48-03 g ; -094 g. \ METRIC SYSTEM. 21 ine at 60 brandy at >he whole. le bottom tides. v. rill be 0. A butcher buys one bullock weighing 382 kilos at 1-35 fr. a kilo, another bullock weighing 341 kilos at 1-25 fr. a kilo, a cow weighing 280 kilos at 095 fr. a kilo, and a calf weighing 59 kilos at 1-75 fr. a kilo. Find the total cost. 10. What quantity of tea at 8-75 fr. a kilo ought to be given in exchange for 700 kilos of sugar at 1-35 fr. a kilo? 11. At 1-5 cents a kilo, what will 3*25 tons of hay cost ? 12. At $8 a ton, what will the coal cost to supply a factory for a week, if 250 kilos are burned each day ? 13. If 7-25 kilos cost 399 francs, find the cost of 43*5 kilos. 14. How many loads of earth, each equal to a cubic metre, will it take to fill an excavation 4 Dm. long, 8 m. wide and 2*4 m. deep ? 15. What is the value of a nugget of gold 2-6 cm. long, 2*3 cm wide and 0-65 cm. thick at $15.40 a cu. cm. ? 16. What is the length in metres of a gravel walk which is 2-4 m. wide and covers an area of 89 1 sq. m. ? 17. What is the height in metres of a wall which is 180 m. long, -625 m. thick and contains 562*5 cu. m. ? 18. Make out the following bill: — 52-25 HI. of wine at 245 francs a litre, 18 HI. of wheat at 18-25 francs per HL, •1 ton of sugar at 1-05 francs a kilo, 135*5 m. of plank at 1*20 francs a metre. 22-5 steres of wood at 1750 francs a stere. 10. The wheel of a locomotive is 4 J m. in circumfer< ence; owing to the state of the rails it loses 15 turns in every 100 revolutions. What distance is gone over in Ou,i.uv uilriiS ui tiie wTiuel f 22 METRIJ SYSTEM. Metric System :- "*" ^"'^"^^ ^'^^ ^'^rioua meaaures inThe Each side of this square measures 1 decimetre, or 10 centimetres, or 100 milhmetres, or 3*937 inches. which has the dimensi: ons A litre is a cubic measure, each side of of tliis figure. A cubio centimetre of pure water at 4" C. weighs a gram. 1 cubic decimetre = i „»,« = iMo^ram 1 cubic centimetre = 1 milliiitre = : gram. -1-2 -1-4 —1-5 1-6 X^ ,^1 WEIGHS i'lii —1-8 inches. .10 1. How many litres iu 6-5 cubio metres ? of wate!"' ""°" " '"°="^""^ °^ -^^56 cubic metres \ METRIC SYSTEM. ^ emistry," rea in the sions rram 3 4 5 — -6 — -8 .10 I tains tres 3. What is the weight of water required to fill a cistern 90 centimetres long, 64 centimetres wide and 36 centimetres deep ? 4. A litre of a certain gas weighs 1-675 grams. How much does a cubic metre weigh ? 6. How many litres in a vessel whose capacity is U cubic metres ? r j ^ 6. How many cubic metres in a rectangular tank 125 cm long, 80 cm. wide and 60 cm. deep ? How many litres? What weight of water would be required to fill it ? 7. How deep must a cistern be to hold 8000 litres if the bottom is a square 2-5 metres on a side ? 8 Find the weight of a bar of iron 50 centimetres long, 4 centimetres wide and 1 centimetre thick if iron weighs 7-8 times as much as waten n-i ,1' ,^^^V' ^^^ ""'^^^'^ ^" ^''''"^^ °^ 2J cubic metres of OU that weighs ^V as much as water ? 10. Find the weight in metric tons of the volume of water contained in a cistern 4-35 m. long, 3-64 m. wide and ^ as m. deep, supposing the water to be at 4^ Centitrrade Change from the English to the metric system, o^r from the metric to the English system, using the equivalents given on p. 14 :— 1. 35 yds. 2 ft. 9 in. to metres. 2. 3-75 metres to yds. ft. and inches. 3. 3 mi. 130 rods to Km. ^. 18-25 Km. to mi. and rods. 6. 6 lbs. 4 oz. to Kg. 6. 36,000 eg. to oz. 7. 356121 kilograms to cwt. and lbs. 8. 4 sq. ft. 72 sq. in. to sq. m. 9. 45 sq. m. to sq. yds., etc. 1 0. 2 ac. 140 sq. rds. to Ha. 1 1 . 3-5 Ha. to ac. and sq. rds. 12. 3 gal. 2 qts. 1 pt. to litres. 13. 36-7125 HI. to gal. 14. 1800 gallons to cubic metres. 15. 47-S7o cubic decimetres to gal. qts. pts. 24 MExXSURATlON. ;v 1 Pi IX. MENSURATION. -face nlZil'!,2;r' '"" '' "'■ "™^''- Knd its 4. Wl,at will be the cost of fln "'""' ^"' ' ^ '7. Cost of carpeting a room 1« ff ^\ ^ inches wide at $1,871 perylrZ '^" ""'^^ '"'P^' ^7 8- How many yards of carDef- 97 ' ^. -cover a iioo. .. ,, 3 ,, ,„„^„ J^^ ^S^.tUt ^^" '4i«,.s?;iririX^^^^ ,/ 10. How many bricks each q : ^' ^"'^ ' ^wiu CO tbe z o. atcr .3-^7rh;y;^-' V"eJetreottratr'^\^:"-f^i-».. Knd the length of the floor '"'^'' '^ ^^^'^O- 12. How many tiles Pinh o • i. the floor of a hall 20 ft.' 3 i„ by ntl "^""'' ^'" ''"^^^ ea "fofAr i ;u;i'ri:s^^^^^^ t^ ^. - - ^ --^ the hall. ^' '' ^^^•-^- ^ind the width of . \\ MENSURATION. 25 -0 ft. by 13 ft. 9 in. Find the cost of staining the border oi the hall at 27 cents a sq. yard. ^ 1 6 If the length of a rectangular field is 15 rods, what must be Its breadth so that it may contain exactly an acre ? ^ 16. How many acres of ground are occupied by 100 miles of a road, 63 feet wide ? 17 How many yards of fencing will be required to go :^ i^und a field 40 rods long, which contains 5 acres ? ^ 18. How many inch cubes can be cut out of a cu yd ? , . ^o .!^; ^^'""^ '" ^^'^ '''^'^ '^^''^^"^ ^^ "" blo^^ of stone 3 yds. ^ 1/^2 ft. long, 2 yds. 2 ft. broad and 1 yd. 2 ft. thick ? lA u^-°/ .^r ""^^"^ ^"^^^ ^^- ^^ ^^^^^ will a cistern contain ^which IS 7 ft. 6 in. long, 4 ft. 6 in. broad and 4 ft. deep ? 21. How many gallons of water will the cistern hold if a gallon contains 231 cubic inches ? 22. The content of a cube whose side is 2 ft. 3 in. ? 23. What will be the weight of a brick wall 10 ft. W t^'u ?• ^'^^' ^""^ ^^ ^^' ^^^^^' '^ ^^^^' ^^^- foot weighs IzO lbs. ? ° 24. How many cu. yards of earth will be cut out of a dram 420 ft. long, 2 ft. broad and 4 ft. deep ? In what time will a man complete the excavation, allowing that he can lift 500 cu. ft. of earth per day ? 25. A canal is 300 yds. long, its breadth is 5 yds 1 ft and Its average depth is 5 feet. What weight of water does It contain, a cubic foot of water weighing 62J lbs. ? 26. A cubic foot of water weighs 1000 ounces. What weight of water can be contained in a vessel, the length width and depth of which are each a yard ? ' n\ "^T "^^""^ ^"""^^^^ ''^'' ^^ P""^ '"^° ^ ^^^ ^ ft- by tt. by -x ft., if a bushel measures 2150-4 cu. inches ? 6 26 MENSURATION. !■ •v i An angle is the opening between two str.,m),'f r ./ meeting at the same point. ° ' ''°^' ^^ The siw or ■magnitude of an angle deDenrl, „n, • i the extent of oveninn «„H „ ,f aepencls entirelyupon If the two Z rinnilTh "^°", "'! '''"^'* "^ ''« ^"'« extent of openil ITl T T^ ^ J''"'""""'^''' "^'^ angle willT; I e 1" d'^ t^f ' "^^ f " ^'^'^ °^ '"^ movable and the ot f.;d he siL" ft' '"" " opening will increase or aZ " °^ "'« ""«'« or (^) An Obtuse angle is greater than a right angle 0^) An acute angle is less than a right !Jle When one Ime meets another line so as tn f square opening or right angle, the one iL Ts idTb' perpendicular to the other. ^^ A Area of Parallelograms. opposrsr:;ran5p:r:u:r^ ''"- '-^^^ ^- -' Parallel lines are equally distant from each other -.r every po.nt If produced, they will never mee a he rails of a ■■ail.oad .-un parallel to eac], other ) pa.tlll!l:. '''''"'''' ^ *"'*- «-' -^ rn.nMd are (For area of square and rectangle see Book IL , p. 79. ) MENSURATION. 27 Rhombus. Rhomboid. A rhombus is a four-sided figure having all its sides equal, but its angles are not right angles. A rhomboid is a four-sided figure having its opposite sides equal, but its angles are not right angles. 1. In the above figures point out the obtuse angles and the acute angles. Point out two right angles formed in each by the dotted line. The dotted line is the perpendicular height, or altitude. 2. The above figures are parallelograms. Why ? Cut '/rom paper figures of the same shape. Draw the perpen- dicular height (dotted line) and cut through it. Adjust l;he piece cut off to the other end of the figure so as to form a rectangle. 3. This is now a rectangle. Why? Measure the length and breadth. Find the area. Observe that the breadth of the rectangle is the same as the perpendicular height of the parallelogram. 4. How, then, can we find the area of a parallelogram? Ans. Area = length X perpendicular height. ^ 6. rind the area of a rhombus 12 feet long and 6 ft. 6 in. in perpendicular height. 6. Express in acres the area of a rhomboid 605 yards long and 32 yards in perpendicular height. 7. Find the he Ight of a parallelogram 3 sq. yds. 4 ft. 36 in. in area and 7 ft. 6 in. in length. 8. A diamond-shaped lawn 53 ft. 4 in. long and 28 ft in perpendicular breadth is to be sodded. How many sod*^ '^"'^^ 1 /3 ^„ •■11 1 . - >' k->, tJctV ;h 16 in. square, will bo required ? (Uratv plan.) 28 •MKNSUlUTfO.N. B 'HI' m Area of Triangles. fc tnangle. triangle. A trian^^ie is a figure bounded by three straight lines l*f ^^^^ M..,/. has a right angle. An .^.,/«,,,,^ ,,,-^,^^^ j^^^ ^j^^^^ equa! sides An ^ w.. w^,, has two equal sides "^ c Line EB = perpendicular height. T — = ^ ^>^e BD = diagonal. parts b, ^:tt:Zo^rt'z:S''r'' ^-'^ ' '^^ kind of a figure ts each ;art ? ° ^'"' ""• ^''''' a. Compare the two trianelea thii» ^v.^ ■ j they equal to one another? wla part „f .f" ' , ^'^ gram is each triangle ? ^ °' """ parallelo- 3. What can you say of the si^e «(>„*■ , parallelogram having the^ameterL^hTr^'^ ^"' ^"■"",r 7'' '° '^"'^ ">« «^^ °f a trianale Base, V ft. 2 in.; perpendicular height, 12 ft. 8 in MENSURATION. 29 e. Tlie base of a triangle is 13-24 chains and its height IS 8-50 chains. Find the area in acres and rods, 10 aq. cluiina being equal to an acre, t . xC /j;^ ■ <^ ' 1 7. Find the height of a triangle whose area is 27A sq yards and base 5 yards. . . 8. What is the ])ase of a triangle whose area is 40 acres and i)eri)endicul;ir height 100 rods ? ;' ^ • - • 9. What will it cost to dig a triangular lot of ground whose base is 45 rods and height 20 rods, at 5 cents a sq. rod ? 10. What will it cost to fence a piece of ground in the shape of an equilateral triangle whose sides are 8 rods each , at 12} cents a foot l^ ' •/ ■ ' c^ , J' Ci*f^"*/'-fOe, Area of a Circle. A circle is a plane figure bounded by a curved line, called the oiroum- ferenoe, every part of which is equally distant from a point within, called the oentre. The diameter is a straight line drawn through the centre and termi- nating at each end in the circumference. The radius is a straight line drawn from the centre to the circumference, and is equal to half the diameter. 1. This circli has been divided into a number of triangles. If the number of triangles should be indefinitely increased, what can you ^ ^ say about the relative length of the side and perpendicular height of each triangle ? Circle. I 30 MENSURATION. 'ill \ ^^,J^-^U.t will constitute the sun. of tl^ bases of the 3. Jfow, then, find the area of a circle ? diviJ^lX ''"''''''-' ^''^^-^^f-'--^ h the ra^nu. and circltnM'r"''; '^'" ^"•-•"^f«r«"^o nn,l diameter of any eirclo and divide one ])y the oflior ir /. ^ cli-oter do you , ;!f „ ,,,, a-U16. di..l.^ r.l ;^,.-™""f-nce of a drcle whoso uianiLttr is L, feet ? 4d yards ? 100 rods ? 7. What is the circunifercneo of a circle when the radius IS ecjual to 2-5 miles ? 7r, yards ? 10. Find tlie urea of the following circles •_ (a) IJimneter, 10 ft. ; circumfercuce', 31-416 ft g I),,™ete,. 20 feet. (-) ])ia„,eter, 100 feet 11 Fin l,r "',"''• <'■) r.adi„s, 7 ft. 6 in. ;n yard! ""' °' ' "'^'^"'" 1'°"^ ^''»« 'l'''"'«ter is n,v!^,' ■^'?'' /".'""■"' '""' ■■«'« t*"^ =P"ce covered by a c.r ,dar plantahon 5(i-.5 rods iu circumference. ^' ^\ 13. What 13 the surface measure of a round tahln whose diameter is 5 ft. 8 in. ? '® 14 A horse is tied in 'a field by a cord 7i rods in length,one end of which is attached to a fi.ed Imn Fmdu. acres and rods the area on which he canlr^e'' 13 indf ^'"' "^ ' '""'^ '"^ ^''"^ 'li''"'«ter is MENSURATION. D Solids. 81 n Cube. i A Cube 13 asiilid with ■ ■■.| . SIX eqiiul sciuaru faces. 'J'ri»"gular I'linm. CyUudor. A Mem is a solid that has two equal and parallel pa„« %„res for it.s cn.Is. Its si.les are paralleh'^,. Vs A Cylinder is a round solid having cinmlar ends. (Book it; ir"''''''''^"'''"''^''"''^''"^"'^' cylin^defr '^" ^'°" "'"^ "' '""* '"""^"" "^ " P™" «' Ar^B. MalUply the arm of the. lase hy tlu height. 3. Are these two rules really the same ? it oui f "''%^~' V"'I'«>^* " 'ri""Sular prism and spread It out flat Its three upright faees hecon.e a figure of what kn,d ? Its two ends are figures of what kind ? How fim tl,e area of its three upright faees ? Of its two bases ? ui the whole ? • 6. Ptepeat the above process with a cylinder cylii?der^"' ' '"^' ^'' '"^'"^' '^' '''" "' " "^^^' P™^ «- ^ • 7. ^l^' ^''^^'V^y i^^^ perimeter of the figure hy its surface) add the area of the two hoses, .^ ^ aoxxc by wrapping paper round a wooden model N'i' 32 i^i (/ I T^TFini MENSURATION. Find solid content and total area of: (a) A cube whose side is 6 feet. (h) A square prism whose base is 2J yards by 2|- yards, and lieight 4 yards. (c) A triangular prism whose height is 20 feet, and whose base is an equilateral triangle with sides 12 feet in length and perpendicular height 10-4 feet. (d) A cylinder whose height is 15 feet and the diameter of its base 3 feet. ^^ ^ 8. What is the upright surface of a cylinder whose diameter is 20 feet and height 65 feet ? O. Find the cubic content of a log of wood whose height is 6 ft. 6 in. and itj diameter 3 feet. V 10. A cylinder is 3 feet long and li feet in diameter. How many square feet of canvas will be required to cover its upright surface ? Its entire surface ? 11. How many cubic feet in a triangular prism the area of whose base is 920 sq. ft. and height 20 feet ? 12. Find the cubic content of a prism whose heigT fc is 25 inches and base a rectangle 3 by 5 inches. 13. Find the upright area of a triangular prism 5 feet high, whose base is an equilateral triangle with sides each 30 inches in length. 1^14. Express in cubic yards, feet and inches the content , of a cube whose edge is 100 inches. ^16. Ex-^ress in square yards, feet and inches the surface of the above cube. j^^l6. How many cubic feet of stone in a rectangular «^lock 18 inches square at the end and 3 ft. 8 in. long ? ,17. A round tank is 16 feet deep and 8 feet in diameter. How much will it cost to cement the sides and bottom of it at 25/ a square foot ? 1 Q TT.,,,r ^.-..-.-.-.,. y^|^|0 £gg|^ q£ ^Q_i_.^jj. ^ XT -iiUVV iiiU-i the tank hold CIRCULAR MEASURE. 83 XI. CIRCULAR MEASURE. 60 seconds (") 60 minutes 360 degrees 1 minute Q. 1 degree (°). 1 circumference. For purposes of measurement the circumference of a circle is divided into 300 equal parts called degrees. 1 . How many degrees in half a circumference ? 2. How many degrees in a quadrant (J circle) ? 3. How many degrees in J of the circumference ? ^ of the cir. ? |- of the cir. ? yV of the cir. ? 4. Through how many degrees does the hour-hand of a clock move in 12 hrs. ? In 6 hrs. ? In 3 hrs. ? In 1 hr. ? 5. Through how many degrees does the minute-hand of a clock mo'^^e in 1 hr. ? In I hr. ? In 10 min. ? In 1 min. ? did 6. In making a journey round the world through how many degrees would you pass ? 34 CIRCULAR MEASURE. 1. Eeduce 51° 23' 4V to seconds. 2. Ill 20,836" how many dcfTees ? 3. Find f of the circumference of a circle 4. Multiply 67° 23' 17" by 15. 6. Divide 84° 19' 45" by 15. 6. From 57° 4' 29" take 41°* 17' 54''. 7. What is latitude ? 8. If one place is situated 59° north of 'the equator and ano^ier 34° north, wh.t is their difference in latitude; 9. it one place is situated 26° north of the equator an another ir south, .Jat is their difference in latSe; of ^^^^^^^^ ^"T," ''° ''' '^' ""■' -^d that 1 1 Tb 1 . . 1 ; r^'"'^ '^''^ ^^^^^^^^« "^ latitude. 1 1. ihe latitude of London is 51° 30' 49" K nrwi fi. ^- of New York is 40° 42' 43" N ^J\ ll ?* latitude. difference in of 'cle ""oVf '1' ^^ ^"^^^ ^'^P^ ^« ^1° 10^ N., and that ot Cape of Good Hope is 33° 55' 15" S. Find their difference in latitude. B Longitude and Time. 1. What is a meridian ? 2. rn^t is the English standard meridian ? How is ' It marked m degrees ? Ans. Greenwich 0° 3. mat is longitude ? What is East longitude ? Wes longitude ? If two places are on opposite sides of Ldl ""''""' ''" " ^^"^ ^^™ - Witude 4. How many hours does the earth take to turn on' Its axis, or describe a circumference ? CIRCULAR MEASURE. 35 equator, ititude ? equator, Ltitude ? lid that itude. id that 3nce in id that I their low is tude ? les of jitude [•n on* Bi 24: hours in time = 3G0° longitude, 1 hour in time = — ° longitude. 1 minute in time = £' lon^dtude. 1 second in time = -l^" longitude. 6. How express longitude in time ? Ans. Divide the number of degrees, etc., hy 15. 7. How express time in longitude ? Ans. Multijply the nurriber of hours, etc., hy 15. 8. If the difference of time between two places is 19 min. 12 sec, what is their difference in longitude ? 9. If the difference in longitude between two places is 20° 36' 15", find the difference in time. 10. The difference of tune between Albany and San > Francisco is 3 hrs. 14 min. 47f sec. Find their difference ^ in longitude. 11. The difference in longitude between St. Petersburg and Washington is 107° 19' 45". Find their difference in time. 12. Montreal is 73** 25' and St. Paul 93** 4' west of Greenwich. What is the difference in clock-time between the two cities ? 13. Montreal is 73° 25' W. and Paris 2° 20' E. of Greenwich. Fhid their difference in time. 14. How much earlier does the sun rise in Montreal than in New York,, Ion. 74° ? In Chicago, Ion. 87° 37' 45" ? In San Francisco, Ion. 122° 26' ? 15. When it is 9 a.m. in Montreal, what is the time in New York ? In Chicago ? In San Francisco ? (Time will be later in places east ; earlier in places wtsL Why ?) 1 6. When it is 3 o'clock in tlie afternoon at Greenwich, what will be the time^ in Montreal, Ion. 73° 25' W. ? In Constantinople, Ion. 29° E. ? In Calcutta. 88° 27' E. ? Ill 36 PBHCENTAGE. XII. PERCENTAGE. Per cent, moans in every hundred. Tlie sign of per cent, is %. Tlius, 5/ means 5 nor cent, or 5 in every liu,„Ired. "^ ^ Percentage i« the process of computing by tl.e Imndred. coijuter' " ■"""'"■■ °" "'"•=" "- P--"'%- - ^ Jhe ««mfe. 0/ hundredths taken is called the rate per I. When a num),er is divided into 100 equal parts what .s one of tl.e parts called ? Two of the paS F^ of the parts? Twenty of the parts ? 2. A man ha,l $500 and lost $10 out of every hun dred ; how n.„.y dollars did he lose ? How n^Z cent^? *'"''' '"""'^ '''""Jredths of 100 is 5 ? What per 5. What fraction of 100 is 5 ? Wliat decimal ? 6. Read and verify the following tahle :— 1% = -01 5% = -05 10% = -1 20% = -2 25% = -25 60% = -5 ^5% = -75 100% = 1-0 _ 1_ 100 1_ i; o 1 1 0^ — . .1, 5 = J 4 — 1 = i = 1 1 my = •Vo I2|% = «'7i% = C^'J% = •^'i% = 617 = •i/o 8,17 = I ■ ~ ' --f •33J = •GG| = •125 = •375 = •025 =- •875 = •0025 = f i 8 5 8 i Jl TF 1 ^ CO PERCENTAGE. ^ 1 ^ ^ A (Sight). 1. Read the following deciinuls as rates per cent •— 2. Find the decimal and per cent, equivalent to :— 3. Find the per cent, equivalent to 7 in eyery hundred; 1 in every hundred; 3 in 20; 5 in 8- Mn SO- TS in_ 1000 ; 225 men out of every thousand ; 2 in a dozen ;' uine in a score ; 12 in a gross. 4. Find the fractions (in lowest teims) and decimals equivalent to :-^ ^0% 25% 5% 4% .33^-7 12r/ 8iy 45% 6G|% 4% 4% I75I 325^ l^y - 6. What per cent, is :— ° ° ^ 13 cents of $1? 800 lbs. of a ton ? 9 in. of a yd ? H dys of 1 wk. ? 89 lbs. of 1 cwt. ? | doz. of a score ? 1 qt. of 1 pk. ? 1 pt. of 1 qt. ? 1. J of 850 ■^"- 2. I of 396 3. xV of 550 4. I of 30 6. 1| times 16 6. 2^ times $1.20 7. 2^^ of 1000 3. -5^^ of 2000 9- tV of $4.80 10. f of40 Id. of Is. ? 1 cwt. of 1 ton ? B (Sight). •5 of 86 •33^ of 240 •1 of 384 •75 of 20 1-25 times $40 2-5 times $6 •005 of 400 •002 of 500 / •0625 of 32 '.y •375 of 64 30 inin. of 5 hrs. ? 1 pt. of 1 gal. ? 50% of 124. 33J-% of 333. 10% of 175. 75% of 50. 125% of 60. 250% of 100. i% of 600. i% of 200. 6i°/ of 80- mx «f 100. -^7,. 38 PERCENTAGE. 1. 2. 3. 4. 5. 6. Percentage 35% of 846. 92% of 1004. 1G% of $4.35. er/o of $1000. 37|%of$1568. 421°/^ of $4820. 7. 9% of $3465. a 10% of $250. 9. 8% of $600. ^ 10. 257^ of $120.' 11. 6f/^of$320/ 12. 20% of $250. 13. 100% of $350.' 14. 6% of 400 men. ^ 15. 7% of 300 acres. 20% of 275 gaL 87„ of 50 days. 137, of 300 sheep. D {Questions 1-10 at sight). 1. In a school of 700 children 10% are absent. How many are absent ? 2. A teacher receiving $50 a month has her salary increased 20%. What was the increase per month ? 3. A house and lot cost $4000. The lot cost 37J% of the whole. What was the cost of the lot ? . • 4. In a school of 600 pupils 66|% are girls ; how many are girls V How many boys ? What per cent, are boys? 6. My income is $720, 1 lose 12|%. What is my loss? 6. Of a regiment of 960 men 6^% are killed ; how many survive ? 16. 17. 18. = Base X Rate. 10. I037, of $34.78. 20. 1137, of 784-1 miles. 21. 47^ of 8-845, 22. 8|7^ of $748.02. /-' 23. 1-17^ of $1477.75. ' 24. 17^ of 24900 . . 25. 87^ of -000^ 26. 75% of 244 tons. 27. 607^ of 350 marbles. 28. 33L% of 393 eggs. 29. ]6|7^ of 624 soldiers. SO. 83^7^ of 672 yards. 31. 12|7^ of 848 boys. 32. 37^7, of 960 rods. 33. 87|7, of 800 bricks. 34. J7o of 690 oranges. ^ 35. 17^ of 500 bushels/-- 36. 1207, of 60 lbs. PERCENTAGE. 39 V 7. I had $750 in the bank and drew out 4% of it. How much was left ? a A town of 10,000 inhabitants increased 25% in 5 years. Find its population. -^' \ / O. In a sclmol of 300 pupils 7% study ,Latiii, 15% yAlgebra, 66f^^ench and 75% Arithmetic; 'How many pupils study each of these subjects ? iO. I have 40 cent-pieces, 20% more quarters than cents, and 8J% more dollars than quarters; how many dollars have I ? i •w 11. I had $875 in the bank and drew out 15 per cent, of it ; what remains ? 12. In a village containing 330 people 13yV per cent are under 10 years of age. How many are under 10? What percentage are 10 or over ? 13. Which is greater, 7% of $6300 or 6% of $7200 ? 14. A farmer raised 5972 bu. of grain and sold 65 per cent, of it at $0.65 per bushel. How much did he receive ? 15. I spend 18f per cent, of $950. How much have I left ? 1/^ 16. If I buy a cow for $64.50, at what must I sell it to gain 10 per cent ? 17. The prime cost of some goods is $3.75; for what must they be sold so as to gain 15| per cent. ? 18. I buy a fariii for $2225 ; for what do I sell it if I lose 8 per cent. ? 19. What is 11 per cent, of £10. ? 20. What is 55 per cent of 12 cwt. 90 lbs. ? 21. The population of a city in 1880 was 100,384. During the following ten years it had gained 113 per cent. ±md its population in 1890. w 40 PERCENTAGE. XIII. A (iiiyht), 1. What fraction of 4 is 2 ? 80 is 15 ? 12 is 6 ? 20 is 5 ? Jb is 50? 100 is 3? 100 is 25 ? 100 is 89? 60 is 40 ? 2. What per cent, of a number is tlie whole of it ? I of it? iof it? I of it? l of it? J of it? 4/ §? 3. («) What fraction, {h) what decimal, (c) what per cent, of 20 is 12 ? 25 is 12?^ 25 is 7 ? ■ 200 is 50 ? 25 is 5 ? 15 is 6 ? 10 is 3? 25 is 15 ? 2 is J? 2 is J ? , 3 is I iy^^({ • What per cent, of 1. 100 is 12p B (Sujht). 2. IGfisO? 3. 3:.]^ is 10? 4. $300 is $12 ? : 6. $450 is$90?o^^ 6. 7. 8. 0. 10. i is I? Is. is 4id. ? 66 days is 11 days f 66 men is 6 men ? 2 days is 8 hours ? $1 is 6| cents ? 4, •i' 11. I had 400 sheep and sold 120. What per cent, did I sell ? 'Vo ^^i''^ 12. I had 400 sheep; I now have 500. What is the per cent, of increase ? >0^/ o '^^-^ 13. I had 400 sheep ; I now have only 260. What per So'cent. of decrease ? What'^er cent, have I left ? 14. raid $25 for a chest of tea and sold it for $6 more than I gave ; what per cent, of profit ? ^--'i «, , w* [ what 'D'"." ■/ PERCENTAOa 41 16. Bought a horse for $25 and sold him for $50; what per cent, was tht profit? /' ^^''■\, 16. I lose J of my money. What per cent, still remains to me ? r 17. If a pint of water is added to a gallon of milk, what per cent, of it is water ? ' / 18. I lost 16f% of my money; what per cent, had I left? 'c'<3'-^" 10. 40 marbles; gave away 15 ; wliat per cent, did I V^glve away ? What per cent, did I keep ? /.-i' r 20. 6 oranges in a box containing 5 dozen are bad; what per cent, are good ? ' Bate = PevQentage -j- Base. 1. What per cent, of 2. What per cent, of n is 2f ? '. ; , :^ 63 miles is 10-08 miles ? / ^ $5i is $4f ? -^<6 I „j ^ 154 lbs. is 7 lbs. 11-2 oz. ? J ' S420 is $60 ? , ^ ti. 4yds. is 9 inches ? U {; $1600 is $96 ? /, ^ 142 yds. 8 in. is 32 yds! ? ^ ^1- 3. If 24 apples are spoiled in a barrel containing ^^ 288, what per cent, is spoiled ? j ^ 4. In a school of 180 pupils 153 pass an examination ; what per cent, fails ? ' - °/o 6. If the rent of a house is reduced from $375 to $350, how much is the reduction per cent. ? L '-: 6. If the rent is increased from $425 to^$459, how much is the increase per cent. ? % 7. How much per cent is Is. 6d. in the J^l. ? r ^ 8. I pay $1 for a book of which the published price IS $1.2© ; what per cent, is the reduction ? / /^ f" O. From a cask containing 90 gal., 4 gal. 2^qts. leaked out; what per cent, leaked out? -$" 8 ^ *2 PKRCENTAQE. 10. In a vilk^cre containing 2088 people 87 die of fever- what is the death rate per cent. ? ^ ^ ' 1 1. To 72 gallons of milk 3 jrallons o^ water are added; what per cent, of the mixture is water ? / 12. An article bought for $2.50 is sold for $2.75 ; what is the gain per cent. ? 13. If I gain 1^ cents on every 12 cents, what do I gam on the dollar ? > ^ , 14. Bought eggs at 16 for a quarter and sold them at lu tor a (piarter ; what is my gain per cent. ? -^ - - 15. A fruit-dealer bought oranges at 25 cen^sl score, and sold them at 25 cents a dozen ; what did he gain p c ? - 16. If I buy at 30 a dollar and sell at $0.75 a dozen what IS my gain per cent. ? '^ ' . 17. In dictation I spell 235 words correctly out 5f 250 ; what per cent, of the words are correct ? '/ ^ 18. What per cent, of 75 bu. 3 pk. are 50 bu. 2 pk ? ; 19 Sugar whicli cost $4.37^ a cwt. is sold at the rate ot JO lbs. for a dollar ; what is tlie gain per cent. ? 20. If the population of a town increases from 8624 to 9702, what is the increase per cent. ? /^c; XIV. ^^. ^H A (Sinht). s 1. 8 is J of >vhat number ? |? J? |? 4^ 2. 24 is 1 4)f what number ? f ?^^4 ?^ « u A ?^'^ jl ? a t) 3. 12 is 507^-of what 307^'' 407^y 607^^' number? I07 ? 207 ? 257 ^ 707^ f 757.1° 807jr 1007 V (^' . i. 1 n t a I ii\ ^ ■. r\ , - i> _ _ . 4. 16 is I7i of what number? A7 '^ "4-7 ?'' V/ ? PEKCENTAQE. 43 Find tlio nuinl)er of which 6. 48 is 07^. 6. 24 is 47° 7. 32 is 5°/° 8. 48 is 20°%. O. 12J is 107^. 10. G| is 257/ 11. 5 is 8iyJ 12. 50 is 62l7^. 13. GO is 607," ^14. i is 16i7°. B 15. J is 507^. 16. 20isr/o. 17. iif;40 is 207^. 13. S(58iH;u7° 19. 25 (!(,.;. is l'2f /^. 20. 15 is 1257^.*' 21. 750 mi. is 507^. 22. 40 yds. is 57^.° 23. 75 is lG6f // 24. 15 days is 17^. '.V^ 2x^" Base = Percentage -f- Hate, 1. 85 is I of what number ? />J ^ 2. 225 is -025 of wliat number ? 3. 555 is 62^7^ of what number ? - 4. $495 is I of what sum ? 1807^ of what sum ? '^ ^ ^ 6. $9820 is 85 per cent, of what sum^^^.^— | j j . .X- ^ 6. 210 tons is G07^ of what quantity ? :,• " ' 7. £2000 is 11 5 per cent, of what sum ? 173^^. ' a. $873.25 is 4^ per cent, of what suip ?^ ./ ,^ ^^•''^ ^^'-j' 0. $476 is I per cent of what sum ? ^ •, b o'^-o o ' 10. $175,420 is 11217^ of what sum? '" ' i c? >S , 9 ^ rho 0. 12r/^ofr>30is6|7^ofwhatsum?/y /; ■ 10. 8ohl Roods at a piiii of 227^. The profit was $47.80. For how much were they sold ? ^ i* -^ \ •- ' , XV. ^ A (Sii/ht). 1. 10 is I more than what nund)er? -25 more? 257 more? 2. 10 is J more than what nund)er? 3.3^7 more? 3. 8 is 'J less than what number? | less? 4. 70 is 12^7o ^^''^^ <^^»'^^i what numl)er? 507 less? 6. 36 is 12r/o more than what number? 10°/ less? 6. What number increased by 257^ of itself is°100 1 7. Wliat number increased by 6|7 i« 08 ? 8. What num1)er increased by 25°/ is 35 ? 9. What number diminislied by 207^ is 60 ? Is 48 ? 10. What number diminished by 307 is 70? Is 49? 11. A horse was sold for $40 which°was 33^7^ more than his cost ; what was paid for him ? 12. A jeweller sold a watch for $110, gaining 107 What did it cost ? ^°' 13. A pupU answered 24 questions correctly, which was 207o less than the total number. How many ques- tions were asked ? 14. A pig cost $21, which is 16|°/ more than the price nf n. nnlf "Fhul fhp Torino f\f o oolf/ii ' ) fl.-i PERCENTAGE. 45 B 10%. What number incroasal What numlxir diminished 1. liy 107^ is $2750 US<^ e. By 1^7^ is 5100 9^ ^^' a. By 107^ is $i)r,r,2 ? ^^.^^ 7. By Vr/' is G475 't^y „^^ 3- % 207^ is $.S720 ?^. ^ 8. liy my is 13125 ?^. -v^) 4. By 28^7 Js $8095 ?7^- 0. By 67 i« 2100?^ *. J /y ^ ^ ^^y,':^Vo ^'« *»«-«0 » '^'^■•'^^ 10. By 127^ is 1200 ?''*** V' 11. My flock of shoep in^jreased 8 per cent.; I had then 324. How many Imd I at first? S^^ ' ol-v>^ 12. I lost 8 per cent, of my flock of sheep and had 276 remaining. How many had I at first? ^<' t- 13. A town after decreasing IV /^ has 4539 inhabitants. How many inhabitants had it at first ?oV^i) 14. If after decreasing 22 per cent, the population is ii003, what was it before the decrease ? J" ^^"5 -' 16. What was the original price pf a book sold for $1.20 at a loss of 36 per cent. ? /^ h 7-£ nolo' ^Z^'"'' i"creasing 11 per cent, the population is 5883 ; what would it be if it has decreased 11 per cent. ?>2'V' 17. What percentage of a regiment survive, if ^ die m battle, J of their wounds, and ^ of fever ? ? S i / / 18. A shepherd loses J of his flock and then 207 of the remainder, and has 384 left. What was the original number?:' \tiu^J^.iJ^, (1^^ 10. By selling 500 sheep for $2695 I gain 10 per cent • (^ what did each sheep cost f/'^ >9 O ^^ 20. I lose 207^ of my money and then 12^7 of the remainder, and have $2240 left; how much had {^^"^^^ , 21. Of the eggs sold by an old woman 3f per cent, axe bad and 154 are good. How many were sold ? v ': ^ -^JT- : 22. A grocer sold 950 barrels of flour for $5760, which was 207^ advance on the>st ; what was the entire cost ^7 .9^ and the cost per barrel ? ,t5 I '■^ yi (-4- i ) $10 loss? ^"^ 0. Goods sold at double the cost ?? 1 J times the cost ? Wliat was the cost price in the following : 10. Selling price $120, {a) 20°[gkm, (b) 20% losstc^' 1 1. Selling price $150, (a) 25% gain^ (b) 25" f loss?" 12. Selling price $300, (a) 50°/^ g^indh) 50°/ loss? ^o^ __13.^elling price $140, (a) 40% gain, (5) 307° loss % ' '' 14. I buy a cow for $25 and sell her for $30. What have I gained per cent. ? ^^^fo 15. Sugar costing $150 is sold for $165. Find the gain per cent. ) ^^ N 16. If the gain on $9 is $2, what is the gain 7 ? J f PERCENTAGE. 47 17. Bought goods for $25; for how much must they be sold to gain 8 per cent. ?^"\ 18. What must a table. costing $57 be dold for so as to gain 5 per cent. ? si -CiS ' 1 9. What nmst be the selling price of goods which cost $32 to yield 25°/^ profit ?"^ HO 20. If the gain on $24 be $3, what is that per cent. ? J:^ ^21. A person bought goods for $64 and sold them for ^ $72 ; how much was gained per cent. 1/^^ 22. A picture costing $75 was sold for $60. Find the loss per cent, ^-o V,, 23. By selling goods for $5, 25% is gained on the cost price. Find the cost price. 24. Selling price $48, gain 20%. Find cost price. V (^ 26. Selling price $48, loss 20%. Find cost price. -^^^^ <5 26. Cost price $80, selling price $60. Find loss p.c.^ 5 1^ 27. Cost price $10, selling price $12. Find gain p.c. . ^ ' ^ B 1. 2. 3. 4. cy Cost price $96.50, profit 67^. Find selling price. ' f^^^ ^ ^ Cost price $2750, loss 35%. Find selling price.)7 ^V^'^ i Selling price $675i, profit 10i%. Find cost price^r ti'M Selling price $2750, loss 157^. Find cost price.. ^^:->i^ 6. Cost price $3584, selling price $4175.36. Gain 7 f 6. Cost price $8500, selling price $6970. Find loss % / &fi, 7. If I lose 5 per cent, by selling a watch for $47.50, at what must I sell it to gain 8 per cent. ?%-// , qq 8. If I lose 8 per cent, by selling a machine for $23, at what must I sell it to gain 157^. ,5 §'76'^ 9. If I gain 10 per cent, by selling for $45, how much per cent, should I lose by selling for $36 ? /(^ ^/o 10. If I gain 8 per cent, bjr^^selling for $63, at what must I have sold to lose 167^ ? ^'/jl Q 43 PEBCENTAGE. m 11. If I lose 10 per cent, by selling at $40, how much per cent, should I gain by selling at $52 ? ' =:/ 12. By charging $15.75 for an article 5°/^ is gained; how much 7^ would be gained by charging $16.50 ? / 0% 13. Selling cheese at 16| cents I gain 10%; at what mu.§t I sell it to gain 20 per cent. ? ; i v'^ ^14. By selling an estate for $15,000 a man gains 20 'per cent. ; how mucli did he give for it ? > ' c) ;: »> •'• 15. By selling an article at a profit of $2.50 I gain 16 per cent. ; what did I give for it ? r ^S, h ;> - 16 Sold goods at a loss of 20% and ac'tual loss of ^o / .50. Fmd the prime cost. ''' ^ p J. j . 17. What is received for 30 yards" of cloth costing 55 cents a yard, when sold at an advance of 20%? /f, ^6 18. Bought apples at 3 for a cent. ; how many can be sold for 5 cents to gain 6f per cent. ? '' ^ //, 19. A merchant sells 95 bags of rice L $35f, thus gammg 12J per cent. ; find the prime cost per bag;/^ 20. An agent sold a lot of ground 25 feet front by 75 feet deep, at 80 cents a square foot, and charged the owner 2 /^ of the money received for his services. What was the agent's commissionitp What did the owner receive ? ¥ .- 21. A commission merchant sold 150 barrels of flour \^ at $5.80 a barrel ^nd charged 4% commission. What was " his commission ? ' -^ - ' ' ^ ^ 22. A commission of 57^ is charged by an agent for collecting an account of $49.80 \ what sum does he pay to his employer ? /M ' J / 23. If $420 are paid annually for insuring a property for $18,000, what is the rate per cent. ? ^- > 24. If $72 are paid for insuring $4800, what is the rate ? / ' 25. How much must be paid for insuring a store and ' goodsvaluedat$7500, if therateis ir/ ? i « - ^ y\ \ INTEKEST. 49 JOf^ by 75 )wner b was flour t was perty * rate?/'-^ >> and XVII. INTEREST. Interest is money paid for the use of money lent. Principal is the sum lent. Rate of Interest is the rate -per cent, of the principal payable annually. Amount is the sun^ of the principal and interest. A {Sight). 1. If the interest of 100 is $6 for a vear, what would be the interest of $50 for the same timel-^ Of 200 ?^'' Of $300 ? Of $400 ^ V Of $150 ? Of $250 ? 2. If $6 is paid for the use of $100 for a year, how much should be paid for 6 months? 3 months? 4 months? 8 months? 9 months ? 1 month ? 11 months? 3. What part of a year is 6 mos. ? 4 mos. ? 3 mos. ? 2 mos. ? 8 mos. ? 7 mos. ? 9 mos. ? 10 mos. ? 11 mos. ? 4. What part of 1 year's interest is the interest on the same sum for 1 mo. ? 2 mos. ? 3 mos. ? etc. 5. Reckoning a month as 30 days, what part of a month is 15 days ? 10 days ? 6 days ? 5 days ? 2 days ? 6. If the interest on a sum of money for a month is $24, what is it for 15 days ? 5 days ? 3 days ? 20 days ? 7. What is the interest |or 1 year at 5% on $100 ? $300? $500? $450? $50^ $1200 1 ^^^ 8. What is the interest; for 2 years at 5% on the above sums ? ■ yi( i -^ , -a O. Interest for 2 years 6 mos. at 4% on above sums ? 10. Interest for 2 years at 3|°/„ on the above sums ? 60 INTEREST. B 1 1 Interest \l '^^icipal X Hate x Time, (Express rate decimcdhj, e.g., 6% = j§, = -qq,^ Find the simple interest on :— 1. $627 at 5 per cent, for 2 years.'^/, i • > o 2. $203 at 6 percent, for 3^ years >. ^ ,/ ^ a $910 at 5^ per cent, for 3 JeZ ^ 4. $825 at 3^ per cent, for 31 years. ^ 5^ t^ 5. $/7o at 21 per cent, for 4 months.^ ^?^5 y i 6. $64 at 4| per cent, for 15 months. A3 /^ ^ 7. $607 at 4 per cent, for 7 years, y ^^ ■ - 8. $144 at 1} per cent, for If years. '5 . VI U 0. $510.62^^ at 4 per cent, for 4 years X ; 1 ^ 13' «20- 9. ll ?f •=""' '""^ " ^'^"'^ 2 month. Tilt 13. «20o.25 at 5-75 per cent, for 18-375 years.^^" I « i • 3 J: W900-875 at 4-45 per cent, for em~i '.' ' ?A" $280.14 at 3-86 per cent, for 5-19 yeaJJ.^^ ' ^ ' " ' 18. $3000 at IrV per cent, for 1 year 11 months. ■" '' Tind the shnple interest and amount of :_ 19. $248.60 at 6 per cent, for 3 months.' ?■ •) p i 20. $275 at 6 per cent, for 2 months. ^ 1 y 21. $5000 at 5 per ce5it. for 1 monthji' SVr . $2835.20 at 6 per cent, for 2 months. $850 at 6 per cent, for 73 days. $«70 at 5 per cent, for 146 days.-: . #1^ ) at 5 per cent, for 75 days. ' . f 3c 75 at 6 per cent, for 130 days: INTEREST. M 28. $1864 at 7 per cent, to- 2 yrs. 245 days. 3 ^^^ ■ ^ ^ 29. $1G84 at 6 per cent, for 1 yr. 280 days, i, / y^-:. -' 30. $0500 at 7 per cent, for 3 yrs. 73 days. / / Lj ) ; . u b 31. $1156 at 7 per cent, for 219 days. -^ ^''^ ' -^^' ^-32. $4470 at 4 per cent, for 292 days. - 7^ J. 6 t/ . 33. $1250.26 at 6 per cent, for 1 yr. 146 days.X'"*:> '^' Find the interest, reckoning even months only, of: / 34. $165 at 6 per cent, from Jan. 4 to April 4, 1890. v/35. $270 at rijxota June 19, 1890, to Apr. 19, 1891^^. ) y ^36. $1234 at ^1^ from Apr. 10, 1894, to Oct. 10, 1894:' ;, cv v/37. $1895.23 at 6% from June 25, '88, to Mar. 25, '89; <<5 "> / 38. $560.60 at 7% from May 5, 1891, to Dec. 5, 1892. y 30. $275 at 6% from Jan. 12, 1893, to Nov. 12, 1897.- ' Find the exact interest of : — 40. $100 at 5% from May 1 to Aug. 10. 41. $500 at 4% from April 2 to June 4. 42. $1375 at 37^ from Dec. 1, 1890, to May 1, 1891. / 7- ^ i- c^Z, $4596.50 at 3% from Dec. 30, '91, to Mar. 31, '92. ' 44. $1200 at 3% from Jan. 3 to March 15. 7. ^: , - 45. $4380 at 3 J7o from Dec. 3, 1885, to Mar. 21, 1887. //46. $3625 at IJV^ from Oct. 2, 1885, to May 17, 1887. C Bj(d6 = Interest ^ {Principal x Time). (This will give rate expressed decimally. ) 1. (Sight) At what rate of interest has the principal been invested in the following cases : — If $100 in 1 year gives $10 interest ? $7 ? If $500 in 2 years givfes $60 interest ? $25 ? If $200 in 3 years gives $24 interest ? $60 ? If $250 in 8 years gives $25 interest? $150? If $400 in 3 years gives $60 interest ? $45 ? If $200 in 2| years gives $30 interest ? $135 ? ^ 52 INTEKEST. '■'' I ;i Find the rate of iterest : — u^ 2. When the interest on $700 for 8 yrs. is $168. ^ ^ 3. Wlien the interest on $375 for 4 yrs. is $56.25.^ J/ 4. When the interest on $956 for 2i yrs. is $119 50 <3' " ^6. When the interest on $1421 for 7^ yrs. is $355.25. J i 6. A\hen the interest on $1000 for 12^ yrs. equals ^ the principal V ^ ^ 7. When the interest on $300 for 9 mos. is $18. § ^-^. When the interest on $8450 for 3 mos. is $147.87} 7 O. When the principal doubles itself in 5 years. r>D ' 10. When the interest on $652 for 15 years is $440.10. Vi 1 1. When a sum of money is doubled in 16 years. , '^' 12. When the interest on $1728 for 3 months is $84. % -" 13. When an investment in 5 years yields a sum ^ equal to | of the principal. 6^ V, 14. When $490.62} amounts to $686.87} in 8 yrs. 6'^) 15. When $500 amounts to $562.50 in 4 years jl ) 16. When $105,700 amounts to $116,270 in 10 ylars*^ i eJ 17. When $213.50 amounts to $266.87} in 64 years u. ^ " 18. When $328.80 amounts to $356.20 in 2 years ' u' ' ^ 19. When $311.50 amounts to $336.42 in 1 yr. 4 mos"^ // L Time = Interest -^ (Principal x Hate). (Express rate as a fraction, e.g., .5% = ^s^.) 1. (Si^hf.) For how many years has the principal been earning interest in the following cases:— $20 interest, $300 principal, 2°/^ rate ? 3°/ ? $90 interest, $400 principal, 3°/° rale ? 5°/ ? $48 interest, $400 principal, 4°/° rate ? 6°f ? $45 interest, $450 principal, 10°/^ rate ? 2}-°/ ? $60 interest, $200 principal, 2}°/° rate ? ny° ? $250 interest, $5000 principal, 2}//^ rate ? '^ 4°/ ? INTEREST. 63 Find the num})er of years in which : — 2. 3. 4. 6. l^ The interest on $1100 at 3f /^ will be $115.50, The interest on $1250 at 6°/^ will be $1^7.50. - -^ The interest on $390.62^ at 4% will be $46.87J.3 The interest on $4209 at 5% will be $52.61i. 3 The interest on $750 at 4% will be $20. -T /^ 7. The interest on $50 at 5% will be $100. ^ b^ The interest on $840 at 21% will be $161.70. 7 The interest on $4212 at 4i% will be $277.87|. $4900 will amount to $5292 at 4°/^. ' ^ $210 will amount to $252 at 21°// 7 A sum of money will double itself at 3^/^. ^ ^ "^^ $50 will amount to $85 at 6%. '^ ^ $1650 will amount to $1782 a°t 4%. "s^ 15. $3745 will amount to $3932.25 at 2|%.-^ 16 $2416 will amount to $3050.20 at 5|7°.^ ^ IV. $500 will amount to $606.66f at 51°// ^ c-^ 8. 9. 10. i-ll. 12. 13. 14. Principal = Interest -f {Rate X Time). (Express rate as a fraction, e.g., 5^% = WVV-) 1. (Sight.) What is the principal in following cases? Interest $100, rate 1°/^, time 1 year. Interest $450, rate 57^, time 2 years. Interest $300, rate 2|7^, time 6 years. Interest $300, rate 37^, time 4 years. Interest $60, rate 117^, time 2, years. Interest $270, rate 37^ time 2 years. Find the principal which will produce : — 2. $63 interest in 3 J years at 4 per cent^ d ^ L^3. $60.12 J in 5 years at 5 per cent. ^^^^' <>' ^ 4. $70,31 J in 3 years at 6 per cent. 3 '^ 6. Jf 2.50 in 5 years at 2 J per cent.^ o-d , ir'i^ ^-€: $101.50 in 71 years at 3i per cent.^ ^- ^^ 64 Hi INTERKST. I> 7. 6 cents a day at G% per annumf ji" ^ J- 8. $4r>0.G6 ill 3 yrs. G mos. at G7>' ^ ///^ Find the principal which will miunmt to:— O. $5292 in 2 years at 4 per cent? u '^ trO 10. $2G7 in 2} years at 5 per cent. 1 1. S55G.25 ill 2 yrs. 3 nics. at 6 per cent. .$ ^-^-6n.os.at4percer^.J ^., . 16. $287.50 m 2 yrs. 6 mos. at 6 per cent. 'O ^o. / Problems in Interest. 1. Find the amount of $140.G2J for G years 73 days at 4 per cent. / ; -', ^-^ ^ 2. In what time will $1263 double itself at 4i per cent, yearly? ,-; . - c^>j ^^ 3. At I per cent, monthly, find the simple interest on 5lf2a for 1 year 11 montlis;'^,:* . / j- - 4. In what time will $370 gain $123,334 at 3i per cent, per annum ? r '^ 11 ^* "^i""^ ^^'^ ^"'''''''* °^ '"^^^^^^^ ^« ^e paid on $200 for 11 mos., $250 for 9 mos., and $300 for 6 mos., at 5°/ - ^ y^ \^<,%f^'''of ''^' P'' "'^^- ^'^^ '^'0.95^ amount to/ 3P7«.()OiV in 3^ years ? ? ^ <.QoJ\n^^ ^I"" ''''''''"'^ ^^ ^^^ ^"^ ^^ 4 «^o»ths at 2^7 is ^JJ2.40, what was the principal ?* ? - ^o, o"ro-^^ *1'^ ^''^''^ "^^"'"'^ ^^^'^ ^ y^^^rs at 4 per cent, is 3^ol.J0g, what was the principal? // ., , 9. Ill how many years will the interest on $G90 become $87.97i at 3 per cent. ? - 10. A professorsliip was founded with a salary of $1250 a yr. ; what sum was invested at G7^ to produce it ? Xo- H- h U' INTEUKST. 65 1 1. A man has $8000 wliioli ho wishes to invest so as to proihice $500 a year ; wli.at rate inu.st he cliarge ? <> .^ ^^ 12. At wliab rate of interest must $450 be loaned to gain $50.50 in 1 year 6 months? ^ V t /. 13. What sum invested at 1% a month will amount to $500 in a year % ^ -' - ^/ : , ' 14. How long will it take $350 to gain $1350 at 6°/ ?/^ - h.,j 15. Find the interest o| $150 from January 1 to^ ^"^ November 20 at G per cent;'/ , q ^ 16. Find the simple interest of $000 for 93 days at 6 per cent. - 17. Find the interest of $420 for 73 days at 47'^.J'<^ 18. Find the interest of $1425.20 for 219 days at 3 per cent. 1 0. What is the interest on a loan of $5800 from Jan 15 to July 4 at per cent:t / & .J ■ .^ '^ y 20. A girl is 1 9 years old. What sum of money must be invested for her at 4% simple interest, that she may receive $405 when she is 21 t'S ^6 21. January 1, 1894, $036 was put out at interest. On September 1, 1895, it had amounted to $078.40. Find the rate of interest. V -4 22. On May 1, 1890, $300 was borrowed at 21°/ interest. It remained on simple interest until it amounted to $405. When was the debt paid ? ' ,.^v^i J, , y: 23. A certain sum of money was placed on simple interest at 4% when a child was born. In 25 years it had amounted to $520. What was the original sum ? j 24. When was $500 put at interest at 5^0 if on July 1, 1894, it amounted to $G00.00|? ./^^-; • / > ' 25. How much must be put at interest at 5°/ to have a monthly income of $100 (^ A daily income of $5r.> ■ ^ \X-, i K.i>^.'j^ 66 DISCOUNT. XVIII. DISCOUNT. Diooount is a deduction from n stated price, or from a debt paid before it is due. Bank discount is simple wtrrcst paid in aihance. Wliolesale business bouses usually sell goods on time and take notes from tlie retailers in payment. Wben tbe bolder of a promissory note sells the note to a bank the sum paid by tbe bank is called the proceeds of the note. I lie amount deducted from the face of the note is the discount. $000. Montreal, ^r)th January, 1896. Forty (Jayfi nficr date Ij^romise to pay Gault Brothers or order nine Imndred dollars, value received. Diseounted at cy^, Feb. 4th. JOHN MARTIN, » Who is tbe maker (,f tbe above note ? Who is the payee ? What is the face of the note ? Is the note negotiable ? K\^; rind the da^y on which it will mature, allowing 3 days' grace. Who discounted the note ?/ How many days had thejiote still to run when it was discounted ? Find the amount of discount which tbe bank will deduct from the face of the note. rind the proceeds of the note. To whom paid ? Who will be responsible to the bank for the payment of the note at maturity ?. -If the note is not paid, what must the bank do ? -^ ^ %h/^ t .A DISCOUNT. 67 Bank Discount. 1. Find the day of maturity of the followiTig notes, the date of the note and time being given: — Sept. 7. Time, .M mos. ' ISfay 18. Time, 6 mop. Anglo. Time, 4mos. Nov. 20. Time, 11 mos. July 27. Time, 5 mos. i May ^0. Time, 13 mos. 2. Find tlie day of maturity of the following notes, reckoning exact days : — Feb. 10. Time, 10 days. '^June 7. Time, 47 days.^ Kov. 23. Time, 20 dafs'/^ April 0. Time, 70 days.' Aug. 10,. Time, no day's/' _;,^ July 3. Time, 60 days. 3. Find the number of days that the following notes have to run from date of discount to date of maturity:— Date of note, Aug 3. Time, 3 mos. Discounted Sei)t. 15. ^ Date of note, July 7. Time. CO dys. Discounted July 7.4 j .. Date of note, Sept. 15. Time, 4 mos. Discounted Sept. 21. ; ; ^^ Date of note. May 21. Time, 00 dys. Discounted M.ay 20. f y / Date of note. May 30. Time, 30 dys. Discounted June 15. / ; i' Find the day of maturity, the bank discount and the proceeds in the following cases :-^ t> u^j/ ^ ^ - 1 5 '» ■ .^1 ^* 4. A note for ^SOO, dated Feb. 11, 1801, and due in 3 months; discounted two days after date at 7%.' 5. A note for .$576, dated Oct. 3, and due in one month; discounted Oct. 12 at (f/^j/auo^l'A^ /6' ' 7. A note for $^000, dated U March and due in 3 ^^ mos. ; discounted at da.^e at 0%. , , v. • !(. \'i •(.( ^^ C{Vj ■{ ' ' 8. A note for $300, dated Oct. 14, and due in 90 days; discounted Nov. 4 at 10%. Fill out this note from yourself to George Ross as payee. • . c- jl SQ. % '^P' n , o >■ 4 5„ I 68 DISCOUNT. O. A inorchar s custoinor sold ^'oods to the amount of $:U0, tt amount due in 3 months witliout interest. Ho immediately had the note discounted at the bank at G%. What did he receive f ^ ' 10. A merchant bought $G800 worth of goods for cash. He sold them at a profit of 15 per cent, agreeing to accept Ins customer's note due in 4 months. He immediately had this note discounted at the bank at 67 Find (1) the face of the note, (2) the proceeds of the note! (.3) the merchant's profit. '- ■ -^4 "7 f U .Sj Y 'ifC >■ 1 1. Walter Green bought some goods from Peter Smith on JMarch 15, 1895, giving in payment his note for $500 due in two months without interest. Write out this note. Smith needed tlie money and had the note dis- counted on the day it was dated. H the rate of discount was 7 /^, what sum was received by Smith ? Suppose Smith had kept the note till the end of April, and then discounted it, what would he have receivedl a-) •a. H ^4 H-' Trade Discount. M ^ ^ . ' ^. -. ^ 1. A tradesman allows a discount of 5 per cent, for cash ; what is the cash payment on ^n account for $210 ? 2. A tradesman allows a discount' of 15 per cent, for cash. Find the cash price of articles marked $5. S3 50 $1.12J. - J ■ •ff',^.ou, 3. What reduction shall I get from the price of a book published at $1.25, when the bookseller deducts 10% ? 4. The list price of a piano is $480. A trade discount of 33J per cent, is allowed and a further discount of 5 per cent, for cash. What is the cash price ? \ / c L PUESENT WOKTH. 6. What is the net viihie of a bill of books 09 amounting to ^568.50 with 10 per cent. oH' for cash F.:/ e. What is the net value of a bill of goods amounting to $4372 at 15% discount and 2^% off for cash ? ■ - - : 7. Goods are invoiced at $0500, less 8 per cent, and 6^ per cent. Find the cost. 8. Find the net amount of a bill of $930, discounts being 33J, 20 and 2,^. 0. List price, $150. Discounts, § and ITJ.^^Find the - cost price. -■ / ' *' . • . . 10. A dealer sold 2631 bushels of wheat at $1.13 a. i/ bushel Jes^a2i%. and 342 tons of hay at $17.50 a ton?!^ less 157^,' He allowed a further discount of 5% for cash.' Find the net amount of the bill. ^ ' ' ^ - " 11. Montreal, April 11, 1896. — Edward Green, Waterloo, bought of Thompson & Co., 36 pairs of boots at $5.17; 216 pairs thick shoes at $1.37i; 135 pairs gaiters at $1.38 ; 240 pairs buskins at $0.83 ; 134 pairs slippers at $0.68 ; 87 pairs rubbers at $1.13. Discounts, 20 per cent and 5 per cent. Write out the above invoice and show net amount of the bill. - " 12. What is the difference on a bill of $200 between a discount of 30% and discounts of 20% and 10°/ ? XIX. PRESENT WORTH. The present worth of a debt is the sum which put at interest is sufficient to discharge the debt when it becomes due. 1. I have to pay $106 in a year from date. What sum of money should I put at interest at 6 per cent, in order to discharge the debt when it falls due ? 60 COMPOUND INTEREST. 2. I have the option of paying $208 a year hence, or $200 now ; which is better, money being worth 4°/ ? a A creditor agreed to allow discount at themte of ^ U for the immediate payment of a debt of $210 due in lyear. How iimch Vvvuld the debtor need to pay ? 4. What is the present worth of $420 due 1 year hence at 5 per cent. ? What is the discount allowed for mimediate payment ? .' - Find the present worth and true discount of :-^Jm 5. $420 due 3 years hence at 4 per cent. ^ ' ' - . ,- 6. .^1260 rliiP A v«ova 1,^,,.^ „^ o , -- ^y -^ 7. 8. 9. 10. ^ xxiv^iiuiio au uj per cenc ^ $420 due 3 years hence at 4 per cent. $1260 due 4 years hence at 3 per cent. $170.50 due 3 yrs. 5 mos. hence at 4 per cent. $1018 due 219 days hence at 3 per cent. $187 due 292 days hence at 2\ per ceiiL $322.35 due in 8 months at 3^ per ceffi* XX. v.. COMPOUND INTEREST. ^'X 6 Lf,0(- y Find the compound interest ^ 1. For 2 years at 6% on $800 ; on $625. ^ 2. For 2 years at 4% on $375 ; on $775i ' '.' /' 6 J >1 u 3. For 2 years at 31% on $675 ; on $720. ,;). . , ^^ -! ' , Fiml the amount ' j ' ' 4. Of $240 in 2 years at 5°/^ compound interest ;j ^^t, L ;, I 6. Of $1000 in 3 years at 57^ compound interest. hXy^^ 6. Fmd the compound interest on $100 for U years '^ ~ at 3 per cent, quarterly, /i^r /J ^"5 '^ . ■ 7. What is the compound interest and amount of $52.62 J for 3 years at 5 per cent. ? by 3, by 4, by 5, by 6, by 7, by 8, by 9. 2. Multiply each of the above numbers separately by 20, by 30, by 50, by 25, by 100, by 600, by 4000. 3. Find separately 17 , 27 . 77 8°/ 9°/ 10°/ 90° / ^^ /o' ^^^ /o 0* each of the above numbers. 4. Multiply each of the above numbers separately by •5, by 425, by 1, by -001, by -2, by '8. 6. Find the cost of articles represented by the abov numbers at the following prices : $0.50 each. $0.05 each. $0.12J each. .15 « $0.37* ).20 « S0.33J " $0.62J ).10 " $0.66f « $0.87J 6. Multiply 81-6, -086, each by 10, by 100, by 1000 7. Divide 97-8, -005, each by 10, by 100, by 1000 8. Multiply 1-6, 6-4, 8-4, 12, each by 20, by 40 bv 60, by 80. ^ ' ^ ^^> ^^y O. Divide 1-6, 6-4, 8-4, -12, each by 20, by 40, by 50 by 80. ' tc €t U 8J each. $0.16J $0.75 $1.25 tt €t H BAPID ARITHMETIC. 63 C (Sight). DRILL EXERCISES TO SECURE RAriDITY AND ACCURACY IN BUSINESS ARITHMETIC. 1. Read the followiug decimal fractions (a) as parts of a dollar, in cents or dollars and cents, (/;) as rates per cent., (c) as common fractions in lowest terms :— 31. 3125. 32. 8-575. 33. 6-775. 34. 4-925. 35. 1075. 36. 5-55. 37. 8-2. 38. 7-65. 39. 3-225. 40. 9-875. 1. -4. 11. -825. 21. -275. 2. -a 19. -525. 22. -15. 3. -6. 13. -375. 23. -1. 4. -3. 14. -975. 24. -35. 6. -9. 15. -675. 25. -475. 0. -7. 16. -025. 26. -125. •7. '45. 17. -85. 27. -625. 8. -95. 18. -5. 28. -175. 9. -75. 19. -25. 29. -05. 10. -325. 20. -425. 30. -725. 2. Find the percentage in following (25 examples) :— l^ase. Rate. 1. Sioo. («)57. 2. $50. (h) 47° 3. $2000. (,) 107. 4. $1200. (d) 2^/. 5. $250. (e) QyJ 3. Find tlie base in the following • Perceutage. Rate. 1. $3. (a) 57^. 2. $15. (h) 47. 3. $0.50. (c) 10°7 . 4. $2.50. (d)2iy, 6. $10.50. (e) 1217. 64 RAPID ARITHMETIC. 4. Find the rate % in the following :— Percentage. Bi ase. 1. $50. 2. $200. 3. $100. 4. $1000. 6. $2000. (a) $10. (h) $5. (c) $15. (d) $25. - (e) $40. 5. Find selling price in following (30 examples) ; Cost price. 1. $100. 2. $500. 3. $20. 4. $350.^ 6. $10. Rate 7o profit or loss. (a) 57^ profit. (6) 57^ loss. (c) 107^ profit. (d) 207, loss. (c) 307, profit. 6. $120. 6. Find the profit or loss °/^ in the following :-- Cost price. 1. $100. 2. $200. 3. $400. 4. $000. 6. $800. 6. $1200. Gain or loss. (a) $20 gain. (h) $20 loss. (c) $40 gain. (c^) $60 loss. (e) $5 gain. 7. Find the cost price in the following : — Selling price. 1. $120. 2. $150. 8. $300. 4. $750. 6. $600. 6. $3000. Rate 7o profit or loss. (a) 20 p.e. gain. (h) 20 p.c. loss. (c) 25 p.c. gain. (d) 25 p.c. loss. (e) 50 p.c. loss. W' RAriD ARITHMETIC. fJ^ 8. Find the simple interest on ((50 examples) ; Principal 1. $100 2. $300 3. $500 4. $1100 5. $1200 6. $r)0 7. $150 8. $250 9. $1000 for Time. \a) 5 years at 4 per cent. {h) 8 years at 4 per cent. {c) 6 years at 3 per cent. {d) 4 years at 2^- per cent. {e) 2% years at 2 per cent. if) H years at 2 per cent. 9. 10. $450 ^ Find the lime in the following (25 examples) :- Principal. Rate. \a) $100 at 1 per cent. {h) $;]00 at 2 per cent. {c) $400 at 3 per cent. {d) $450 at 4 per cent. \{e) .$400 at 2^ per cent. Intci'est. 1. $45 "^ 2. $54 3. $60 4. $90 5. $120 10. Find the rate in the following: Principal. \a) $100 (&) $500 (c) $200 {d) $250 l(t') $200 Interest. 1. $25 ^ 2. $45 3. $30 4. $150 6. $135^ 11. Find the principal in the following: Time. 1 year. 2 years. 3 years. 8 years. 2i years. Interest. 1. $7001 2. $450 3. $;]oo 4. $850 6. $250J \ Rate. Time. \a) 1 per cent. 1 year. {h) 5 per cent. 2 years, (c) 3 per cent. 4 years. {d) 2h per cent. 6 years. {e) IJ per cent. 2 years. 66 RAPID AiaillMETIC. Add vertically and horizon tally, without copying down.w 8. 0. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 1 7003 5088 70G6 8G44 3716 0215 9284 7107 5006 7013 8015 7008 3728 6069 I 22 29. 90G7 30. 569 31. 3021 32. 705 33. 808 34. 906 35. 5002 36. 7006 37. 769 38. 606 39. 7021 40. 906 41. 6086 42. 509 2 8025 9067 5067 3815 9205 7063 8435 9219 80;2 9586 9080 7025 8004 7021 23 3706 109 2006 7006 9006 5060 7021 9117 9009 3967 1509 62 384 1055 3 9051 8007 2308 7016 5008 7046 3021 8069 8729 95G9 7219 6068 7216 6585 24 207 3709 9216 806 7219 3003 2016 707 9061 729 3069 501 15 7020 4 2107 3206 9063 8025 9206 3058 7021 9086 5721 3102 8607 2'»06 3106 8207 25 6064 7216 9608 3016 7213 9065 7213 906 7008 6068 7213 900 7906 612 5 1006 3003 7067 8206 3015 7068 5069 8725 9683 7025 8067 9213 3506 26 2001 786 2007 726 3015 900 7203 506 9603 729 1901 729 839 8879 6 7206 9025 8396 7215 9604 3726 9063 7158 3102 2002 7206 9608 3728 7 9020 7210 1856 1876 9215 3734 1000 2100 7200 6000 9989 7005 7683 7007 1559 9215 27 9002 2071 6068 7219 3068 7065 8219 2007 956 7029 606 7968 707 1906 28 6900 900 9000 9000 8888 777t 6660 6506 7766 9085 703 37 6921 fi9n H RAPID AUmiMETIC. 67 7 902G 7210 185G 187G 9215 37')-i 1009 2100 7200 6999 9989 7095 7683 9215 43 44 45 46 47 48 40 290G1 50216' 29113 39061 12345 96044 60. » 70635 79613 7029 72096 67891 3726 51. 92186 80156 69031 59185 23456 96921 52. 59147 7007 79103 72096 78912 72156 53. 99081 30916 80217 3095 34567 9213 54. 79G98 50911 ^ 9056 69002 89123 87215 55. 39091 72196 89215 7358 45678 9061 56. 87296 39167 90061 92015 91234 70123 57. 99896 90l>6 7213 8017 5G789 9686 58. 79684 907'.G 98175 29163 1237 500 59. 59607 9667 3007 7215 86041 72156 60. 79061 39286 90216 96003 88139 9 ^^ .i. x./ \J 36363 61. 59692 99081 72136 7215 71031 59081 62. 79683 -7296 9021 27568 6944 7216 63 64 65 66 67 68 69. 29137 90716 70140 40317 40211 20191 70. 59038 3824 92382 9856 70130 79386 71. 29537 96864 90368 47256 9035 59406 72. 90613 72196 59376 89666 79032 39601 73. 96928 39185 90213 37694 80965 89063 74. 57216 96072 7G384 59465 79632 79158 75. 90317 38067 96058 70315 1560 9091 76. 20313 47215 37213 96018 9G876 ^•f \y tj ju 19090 77. 69681 90516 96474 86219 94032 70215 78. 72136 38296 58169 47206 5968 90217 79. 9063 39285 39467 96081 11411 5038 80. 70031 37216 29G06 47216 5917 4715 81. 2931 P* /% O /• rt 90213 70915 17129 86928 9624 C3^. U"JO0C> 13729 80706 29615 37169 7968 r 68 RAPID ARITHMETIC. Make out the foUowiiiL' bills :— 1. 5^ lbs. cheese at 9/. 3 1 lbs. clieese at 8/. 16 lbs. 12 oz. bacon at 8/. 14| lbs. ham at 11/. 9f lbs. lard at 7/. 8L doz. eggs at 14/. 3. 71 lbs. soap at 3|/. 5^ doz. lbs. soap ai 8J/. 5 bars do. (each 3 lbs.) at 4/. 18 doz. lbs. candles at 6|/. 13 J qts. oil at 6/ per gaL 3 J gross matches at 5/ per dozen boxes. 5. 52 yds. alpaca at 19/. 3 pieces merino (each 29|- yds.) at 27/. 4 pieces poplin (each 156 yds.) at 54/. 14^ yds. lilac silk at $1.40. 11^- yds. black silk at 43i/. 3 1 yds. satin at $1.50. Package, 42/. 7. 13 J yds. carpet at 54/. 18 yds. drugget at 25|/ 5J yds. matting at 57/. 30 yds. binding at If/. 8| yds. oilcloth at 38/. 5 mats at 66/ each. Less discount of 7J per cent, for cash. 2. 3J lbs. tea at 40/. 7i lbs. tea at 46/. 21 lbs. sugar at SJ/. 3 J doz. lbs. sugar at 5 J/. 6 J lbs. coffee at 20/. 9 lbs. cocoa at 19/. 4. 3 1 yds. calico at 6/. 8f yds. calico at 8/. ' 19^ yds. grey calico at 9/. ISJ yds. flannel at 36/. 11 J yds. ticking at 24/. 5^ yds. linen at 28/. 3 1 yds. linen at 42/. 6. 13 lbs. 5 oz.,beef at 8/. lljlbs. beef at 11/. 3 legs mutton (each 8 lbs. 8 oz.) at 91/. . 2 shoulders mutton (each 7 lbs. 5 oz.) at 8/. 10 lbs. 8 oz. veal at 10}/. 5 J lbs. pork at 7/. 8. 3 vols. Cowper at 60/ vol. 3 void. Longfellow at 42/. 1 set Waverley Novels (24 vols.) at $1.02 per vol. 13 quires foolscap at 8 J/. 3 J reams note at 4/ quire. 3250 envelopes at 6/ 100. 64 five-cent stamps, 54 two-cent do., 152 cent do. RAPID ARITHMETIC. 69 9. 30 lbs. leaf tobacco at 84/. 1 0. 8 lbs. 3 J oz. Virginia at 96/. 15 J lbs. Virginia at 90/. 13 boxes cigars (each 3J lbs.) at $1.32 per lb. 9 boxes Havanas (each 4 lbs.) at $1.89 per lb. 57^ discount for cash. 28 lbs. cut nails at 9/. 13i lbs. cut nails at 10/ 6 lianimers at 70/ each. 6 chisels at 21/ each. 13^ gross screws 5/ doz. 8^ gross screws 10/ doz. 1 doz. rakes at 15/ each. 3 spades at $1.08. 15 J lbs. white lead at 8/. 1. 2. 3. 4. 6. 6963519 X 8090 6978954x3906 6931768x8009 672976x5006 705968x6069 6. 7215698x5098 7. 99278x8837 8. 928417x8300 0. 6976x6976 10. 3884x3884 11. 9608x9608 12. 5327x5327 13. 8796x8796 14. 694x694x694 16. 765x765x765 16. 308x308x308 17. 8907x8907x8907 18. 6009x6009x6009 19. 9876x9876x9876 20. 967188x34562 21. 6990880x409006 22 2340600x607098 23. 2159063 -f 729 24. 926104513^217 25. 37l321617-r546 26. 70213169 -f- 947 27. 6120l793-r795 28. 713061311^864 29. 49031702^979 30. 47603136-^-847 31. 6956982-f861 32. 12345608 -f 987 33. 391760344-5968 34. 72041358-^9215 36. 20304054-4725 36. 43728514-6104 37. 192736653 -r 3856 38. 615274528 -f 7648 39. 706050494-8570 40. 4678179384734-2100 41. 3678179384294-36500 42. 2678179381154-1360000 43. 1,000,000,000,000,0004-81 111,11111. 70 MISCELLANEOUS EXAMPLES. I MISCELLANEOUS EXAMPLES. A {Simple Mules). 1. Y'lM the sum of nil ih:-. numbers between 897 and 904. 2. The product of two numbers is 252 and the multi- plier is 18 ; find tlie niultiplicund. 3. The sum of two numbers is 250 and their difference is 50. Find the numljers. 4. The lei^s of two numbers is contained 14 times in 252 ; the^gre}>ter is^49 times the les8. Find the numbers. 6. What number multiplied by 789 gives 3771420 ? 6. Divide 900 into two Darts so that one may be 62 more than the other. -CCL^/ 7. Express in words the following numbers :— 70070 707, 5706, 9011610, 3210, 10176, 40400. 8. Take thirty-seven millions thirty-five thousand six hundred and eighteen from 110011007; and give the result in words. 0. How many dozen are there in 126 score ? 1 0. Multiply half of 1162 by twice the third part of 402. ^ 11. The sum of 250 and 173 is multiplied by their difference, and the product divided by 4j; what is the quotient ? 12. If every page of a book contains 36 lines and each line on an a\erage 11 words, how many pages will be filled with 62172 words ? 13. I multiply a number by 36 an*" divide the result by 12 and obtain 374181. What is the number ? 14. What number must be added to 32684 to make it exactly divisible by 126 ? 16. What number muPt be subtracted from 461633 to make it exactly divisible by 758 ? MISCELI^NEOUS EXAMPLES. 71 B (Gmnmvyi Fractions), 1. Find the sum of J, J, J, | and J. 2. From(Aof|o,'5):ake(Vof|). a. Multiply the sum of f and ^ by their difference. 4. By how much is H of 15 greater than 14^ x 1.^ ? 6. At $;]^ a dpy, what can a man earn in 25} days ? 6. The dividend i« 42^ quotient ^ ; find the divisor. P J- .1 .' ^""^'^'^ ^ "^^^ ^^^ ^20^ md some sheep tor ^.)2\ ; what change from a 8100 bill ? 8. How much longer is G feet than J of a foot ? 0. What must be added to (31-27 +4,V) to make 8| ? 1 0. How many times is (3i - 1 1) contahied in 6} x U ? 1 1. What must be subtracted from (7i-r6J) to leave A ? 12. By how nmch does 7i divided by 6^ exceed 6 A divided by 71-? ^^ 13. 16f is J of what mimber? 14. 18| is fV of 'vhat number ? 15. A of a ship cost $8;]60; what is the ship worth ? 16. I spend I of my money and have $18 left: what had I at first ? 17. After walking 12 1 miles I have still |i of my journey to travel. How long is my journey ? 18 When 24 lbs. have been taken f >m a r:hest of tea It IS \\ full. What was the weight of tue tea ? 19. If I buy Ji of a ship and sell | of what I buy what part o^ the ship shall I still own ? 20. Afte. spen.iing f of my money and losing i of the remainder, I have $21 left. What had I originally ? 21. I pay I of a debt in silver, | in gold and the remamder with 36 one-d.>lIar bills. What was my debt ? 22. A gets -jS. of an estate worth $4000, B ■§- of the remainder, and C whaL is Ipft. TTnwp.,,pi, ^^.„ „^_._ ,, - — u. — „ imtLii Qoeo uacii get f 72 MISCELLANEOUS EXAMPLES. U I II. I C (Decimals). 1. What is meant by the term "decimal fraction"? 2. Express in words •51:^2. 3. Kxproaa as common fractions -031, -0079, -001, 7103. " J)ivide -031 by 10, and 1037 by 1000. ' From 1 iiiko -0031, nniltiply the remainder by -07. I )i vide the sum of 825 and 4125 by their diilference.* How many times can 125 be taken from 10 ? What decimal represents the difference between J and ^ ? O. Add$-375 + $-0604 + S5-90G4-$30125. 4 6 6. 7. 8. 10. Add 11. From 12. From 13. 63 . 9-9 5-6 '' 5 J •88 •57 •76 •36 take •084 io-5* take '^1. 5-2 Find tlie product of the two smallest decimals that can be expressed by the finrures 0, 0, 9 and 3. 14. Divide 420 liundredtlis by 5 milliontlis and from the quotient subtract 425 thousandths ; express the result as a common fraction in lowest terms. 15. Cost of 6284 feet of lumber at .!;12.35 a thousand ? 16. Cost of 3684 lbs. of pork at $9.24 a hundred ? 17. One hundred and eight steps, each -581 feet hicrh lead to the summit of a tower. What is its height ? ° ' 18. The height of a dwarf is -1875 of that "of a giant who is 8-88 ft. high. What is the dwarf's height ? 10. A person owns -675 of a business worth $47,500 What should he receive for -375 of his share ? 20. Simplify 111^ and give answer as a decimal. MISCELLANEOUS EXAMPLES. 73 D (Compound Quantities). 1. Reduce 1 mi. 870 yds. 2 ft. to feet. 2. Reduce 4i:U 10020 seconds to years. 3. A boat race started at 2 hrs. 12 min. 11 sec. and finislied at 2 hrs. 31 niin. 5J sec. ; how long did it last ? 4. Three gardeners rent 5^ ac. of ground; one has U ac. and another 7216 sq. yds. How much has the third ? 6. If sound travels 1130 feet a second, how long does It take to travel 226 miles ? 6. What is the total length in yards, feet and inches ot 770 pieces of string each 29 inches long ? 7. From a plank measuring 19 ft. 6 in. there is cut away 2 J of ^\ of the whole. What length remains ? 8. How many sixteenths of an inch in U yards? O. Value of 7-125 of £5. 4s. 10. The cost of a cable message is 9d. a word; how many words can be sent for £1. 3s. 3d. ? 11. Add together ^ of a bushel, f of a peck, i of 24 bushels, and -f of 7 bu. 3 pks. 4 qts. 12. Find the exact number of days between April 10 1890, and Aug. 25, 1891. 13. How many times round a garden 90 feet long 42 feet wide will make a walk of 3 miles ? 14. A ship sailing westward reached a point where its chronometer at noon showed the time at Greenwich to be 6 hrs. 48 min. 28 sec. v.m. Find the longitude. 16. When it is noon at Montreal, long. 73° 25' West what is the time in Paris, long. 2° 20' East ? 16. A circular track is 600 yards round; A runs twice as fast as B; A and B start from the same place in opposite directions, and they meet in 45 seconds. How long would B take to run a mile at the same rate ? H MISCELLANEOUS EXAMPLES. E {Prcportion). 1. If I walk 21 miles in 5 hours, how faj Jo I walk in 2 hours? S" .-^ ••' * ^ 2. If 55 quires of paper are used in 18 days, how lono will 33 quires last ? :V^_ J > h 3. While a wheel 15 feet in circumference turns 400 times, how o^ten does a wheel 12 ft. in circumference turn ?' 4. If 75 lbs. of Lea last 8 persons for a year, for how many days will 45 lbs. last them ? ,; , ^/ . ■ . 6. If 75 lbs. of tea last 8 persons for a year, how many lbs. will be required for 146 days ? -^t ' ^ 6. If 75 lbs. of tea last 8 persons for a year, how many lbs. will be required for 12 persons ? 7. If 75 lbs. of tea last 8 persons for a year, for how long will they last 20 persons ? ; ; , 8. If 75, lbs. of tea last 8 persons for a year, for how many persons will 600 lbs. suffice ? ^ V . • - ^ - 9. If 75 lbs. of tea last 8 persons for a year, how many persons will they last for 292 days ? 1 0. If 25 men do a piece of work in 3^ hours, how many can do the same work in 6f hours ? ' ,- y 11. A bankrupt pays 66| cents on the dpllar. His assets are worth $452.50. What does he owe f^ > (^ >.i ' 12. What does a bankrupt pay on the dollar, if his creditors receive $850, and his debts are $3000 ? 7 . 13. A person travels 109 miles in 36 hrs. 20 min.; in how many hours will he travel 50 miles ? 14. If the price of a score articles exceeds the price of . a dozen by $2, what would be the price of 3 score and 10 ?'' ' 16. Nineteen men perform a certain piece of y/ork in 76 days of 7 hours each; how many men would be required to do it in 133 hours ? , I x A' MISCELLANEOUS EXAMPLES. F {Mensuration). 75 1. A garden fence is 63 yds. long and 9 ft. 4 in. high J what will it cost to paint it on both sides at 11 cents a sq. yard ? 2. How many boards 12 ft. 6 in. long by 9 in. wide would be required for a room ll^ ft. by 10 ft. ? 3. The walls of a room 15 ft. long by 14 ft. 6 in. broad and 8 ft. 6 in. high are to be painted, a window 5 ft. 6 in. by 4 ft., and a fireplace 3 ft. 6 in. by 4 ft. being deducted How many sq. yds. of surface are to be painted ? 4. What is the area of a piece of land in the form of a rhomboid 200 ft. long, if the distance between the parallel sides is 90 ft. ? ^; ^ ^ / 6. Find area of blackboard surface in your room. 6. How many times will a wheel 3^ feet in diameter turn m going 2| miles ? 7. In going a certain distance a wheel 4J feet in dia- meter makes 1430 revolutions. What is the distance ? 8. If the equator is 25211-34 miles in circumference, what IS the length of the diameter of the earth ? 0. The radius of a semicircular flower-bed is 20 feet * find its area. ' 10. Find the capacity of a round basket 20 in. in diameter and 2^ in. deep. 11. Find the solidity of a prism whose base is 6 feet square and height 15 feet. ^ 12. Of two pieces of land, the one a circle L8 rods in diameter, the other a triangle whose base is 24 rods and height 18 rods, which is the larger and how much ? ^ 13. What is the area of a triangular field whose base V IS 325, yards and perpendicular height 160 yards. Express m acres and square yards. I ^^ MISCELLANEOUS EXAMPLES. G {Metric System). 1. What is tbo price of a can of coffee containing 474- Kg. at 2-20 francs the Kg. ? * 2. If the average weight of 5 packages is 4-625 kilos and the weights of four of them are 3'675 kilos 8-675 Ivilos 2-25 kilos, and 7725 kilos; what is the weight of the nrth ? ^ 3 If I walk 6-056 Km. in an hour, how far shall I go in 6 hrs. 48 min. ? How many miles shall I go, allowing a kilometre to be | of a mile ? 4, From 10-06 Km. take 354-406 m. 6. At 7/ a litre, what will a decalitre of milk cost ? 6. A druggist put up half a kilo of opium in boxes containing 1| grams each. How many boxes did he need ? 7. How many grains of opium did each box contain ? 8 A litre of air weighs 1-3 grams; what will be the weight of air in a room 3 m. long, 2 J m. wide and 2 m. high ? 9. Into how many lots of 3-75 a. may 8-40 Ha. be divided ? 10. A vessel when empty weighs 1-02 Kg.; when full of pure water it weighs 3-8 Kg. Find the capacity of the vessel in litres. 11. A train which travels 56-25 kilometres an hour take 3i hours between two stations What is the dis- tance between them in metres ? 12. I can buy 526-2 kilos at $157.15 the kilo; what would be the price per kilo, if I bought 1841-7 kilos for the same monsy ? 1 3. A man cut 75-60 m. of wire into pieces each 25 mm long, and sold them at 6)^ a doz. ; how much did he receive? 14. A cask weighs 227-5 Kg. more full than empty: how many HI will 29 such casks hold ? MISCELLANEOUS EXAMPLES. 77 H (Percentage). 1. In a shipwreck 45 people are lost out of 180; what per cent, is saved ? 2. If a person spend 10% of his income in rent, what has he left out of $460 per annum ? 3. In 1880 the population of a town was 129,181, and in 1890 the population was 113,387. Find the decrease per cent. 4. The population of a city increased from 401,321 to 460,428 ; find the rate per cent, of increase. 5. Find the prime cost of an article which, when sold for $24, yielded a profit of 20%..>- 6. What per cent, of 2 ^ is 1^ ? 7. What is |% of $1728 ? 8. What is the difference between BhV of $800 and 6|% of $1050 ? . 0. A man received from a bankrupt $397.50, which was 37|% of the sum due. What was his loss ? ^10. For what price per pair must shoes bo sold to gain 25^, if 15% is lost when they are sold at $1.27| per pair ? 11. A man owning 40% of a ship sold 25% oi his share for $4500. What was the ship worth ? ^12. A sold two lots for $260 each, gaining 20% on one and losing 20% on the other. Did he gain or lose on the whole transaction, and how much ? > 13. A buys a horse for $60 and sells it to B for $120, who sells it for $200 ; how much per cent, did A gain' more than B ? 14. Bought 60 barrels of flour at $8.50 a barrel. Half '^ was sold at a loss of 10%, and the remainder at $9 a barrel. Find the actual loss and the loss per cent. 78 MISCELLANEOUS EXAMPLES. ■' ' i' fc_,-^- I amonnt to I (Interest and Discount). 1. Interest on $290 for 11| years at 2J 2. Interest on $500 from May 15 to N( 3. At what rate per cent, will $50( $5400 in 1. year 219 days It'^P'C, <.Qn^ ^^ ""^^'"^ ''''^' P"" ''''^- ^^^^ ^^« «i°^Ple interest on $300 amount to $36 in 4 years Ic^ <' ^ 6. In what time will the simple interest on $550 amount to $88 at 4%? ^ '^T^i - ^6. In what time will $6060 amount to $6696 30 at 3 per cent, per annum ? 3 "^ 7. Whac principal will produce $50 in 4 years at 2 J per cent, simple interest^* : v 8. What principal will amount to $377 in 4 years at 4/^ simple interest ? .^^IZ ^""^ ""'"''^ ^ "^^^^^ '^^^^^ I ^e^t a house that cost $o200, so as to receive 6% per amma fv/^ 10. Find the net amount of a bill (A goods, the list price of which is $435, discount 8% and 5% off for cash^, o,;, 11. On a bill of $025 what is the difference between a discount of 30% and a discount of 26% and 5/ ? , i . ; f f- Find the proceeds and discount on ° ° '• 12. A note for $700 drawn Nov. 13 at 90 days dis- counted Jan. 1 at 7%. 6- ^^ ^ X L y 3- /> . 13. A note for $500 drawn July 9 at 90 days dis- counted at date at 3|%. ^f^-. ^ ..i 14. A note for $400 drawn March 3 at 8 months, dis- counted June 13 at 4 per cent. > ^"'3 "^. ^- Q ' ^ 16. Find the amount at compound interest on $89 50 in 3 years at 5 per cent. / O I . h / 16. Find the difference between the simple and com- pound interest on $5000 for 2 years at 4 per cent.^ TEST EXERCISES. 79 XXII. TEST EXERCISES {Mental), 1. What is the largest number that can be formed by the figures G, 0, 7, 4 ? . ^ 2. How many apples must be cut up to give 300 boys f of an ajiple each ? 3. Multiply 30 by 4, subtract 50, add 10, divide by 5 multiply by 7. 4. The remainder is 5, quotient 6, divisor 7. Find dividend. 5. A woman bought 13 yards of goods at 30 cents a yard. What change did she receive out of a $5 bill ? 6. I divide 25 oranges between 2 boys, giving one 7 more than the other. How many did each receive ? 7. What part of 10 miles is | of 8 miles ? 8. A horse costing $60 is sold for $75. What part of the outlay is the gain ? What per cent. ? 0. If 8 pts. of berries cost 32^, what will a peck cost ? 10 A market woman having 6 doz. eggs broke 9 and sold the remainder at 20^ a doz. What did she receive ? 1. How many days from April 24 to June 19 ? 2 3 What will a boy earn in 98 hrs. at 15/ an hr. ? Prime factors of 210. 4. Express | of one-hundredth as a decimal. 6. Difference between 2^% and 3i% of $800. « Value of ^ of a dollar. Express f of a doIL:: a? a decimal of $2-J. Interest on $40 !• i- 2} years at 57. Divide 54-8 by 100. ° 1 a Bought goods for $2| and sold for $3. Gain 7 ? 6 7 8 9 I" 1 80 TEST EXEIJCISES. 1. At 15ff a yard, liovv imicli can be bought for $3 ? 2. From a piece of cloth J and J of it have been cut, Wliat part of it is left ? 3. J our its How much per gallon ? 4. What part of 100 is 121 ? wj^^^t p^^. ^^^^^ ^ 6. By selling o. liat for $5.40 I gain 207 How much do I gain ? ^° 6. I borrow $500 at 6% and pay it back at the end of y months. What sum must I return ? 7. I bought 40 yds. of carpet at 75/ a yd After iismg it 5 yrs. I sold it for $15. If the carpet was worth a year to me while I used it, wliat did I gain or lose ? a What is f of I of $10 ? ©. Bring li to a decimal. 10. Express 3 ounces as a fraction of 7 lbs. 1. Exchanged 11 tons of hay for 15 yds. of cloth at and 4 yds. at $5. What is the hay worth a ton ? 2. How long will it take 11 men to do what 10 men can do in 11 d.^ys? 3. In a certain school there are 20 boys and 4- as many girls. Required the total number of pupils. 4. How many steps, each 2 feet long, will a child take in walking 110 yards ? 6. A boy can pick 3500 stones off a summer fallow in a day. At 20/ per m. how much will he earn in a week ? 6. A man bought some apples for 8S^' at the rate of 5 for 11/, and divided them among his 4 children. How many did each child receive ? 7. 3 + J + 2 + J, 8. From 3-5 take 1-75. 0. What is -125 of a dollar ? 10. Interest on $44 for 3 years at 21%, ^'^ TEST EXERCISEa 81 for $3 ? been cut. 1? It.? %. How- he end of i. After ^as worth or lose ? cloth at >n? 10 men nd I as a child allow in I week ? ate of 5 . How I by 128 Multiply IG by 12, add 8, divide by 400, multiply 2. At $16 acre, what will 2 ac. 40 rods of land cost ? 3. I buy 108 articles at i)^ for every 12, und pay for them with a $2 bill. What change sliould I receive ? 4. The diil'ercnce in lbs. between i cwt. and J cwt. 6 Bought 4 bushels of nuts at 12J cents a peck. Gave $2 bill. What change ? 6. Apples costing 2f' each are sold for 3/. Gain V ? 7. What is 4 of a dollar ? 8. Interest on $50 at 5% for 5 years. 9. I of a cent is what decimal of a dollar? 10. 5 oranges cost 7|/, what will 3 cost ? 1. If a plant doubles its number of IJossoms every year, and lias two blossoms the lirst year, how many blossoms will it have the liftli year ? 2. How many square tiles G inches on a side will be required to make a hearth 4 ft. by 2 ft. ? 3. From | of a cask f of the cask is drawn off. If the cask holds 48 gallons, how many gullons remain ? 4. Bought 3 quires 12 sheets of paper at 25/ a quire VVhat change from a dollar ? 6. A quantity of sugar which weighed 900 lbs! lost ^/o m drying. What did it then weigh ? 6. If you buy a knife for 50/^ and sell it for GO/, what per cent, of the cost do you gain ? ^ 7. A flight of stairs consists of 20* steps. Each step IS 6 inches high and 12 inches broad. How many yards of carpeting will be required to cover the stairs ? 8. What per cent, is 5 of 75 ? 0. Amount of $1000 for 10 years at 5y. _ 10. From 8 times the half of 17 take 4x4x4. i 82 TEST EXERCISES. 1. A.M 5, 18, 23, 7, 0, 14, 19, 3, S^k .cot ^''f''^''^'^-'^^'^^-^-^^ and sold them at ci cent each. Wliat was the gain on 10 gi'oss ? 3. If 20 men do a piece of work in 15 days, how lone, will It take 12 men to do it ? ^ 4. A man owns f of an estate and gives his son i of his share ; what part of the estate has he then left ? 6. Whieh is greater and by how much, l yd. or ^ yd ? 6. How many lbs. sugar at 91/ ean be bought for $3.80 ? 8. Apples are 5 for 4f. How much per doz. ? 0. Cost of G| yds. ribbon at 6.1/ a yd. ? 1 0. How many scj. metres in tl^e walls of a room 12 m long, 8 m. wide and 6 m. high ? wm 7 ii rjr * ''^''' ^^ "''^^ '^■-■^ ''"^' "- ^"'=" 2. J of a pole is in water. Tlie part al,ove water measures 24 ft. What is the length of the pole ? 3 Three men did a piece of work. The first did -37 and the second -33 of it. What part did the tliird do ? 4. The product of the sum and diflerence of 18 and l"? wil^; l" f ' ,T.' "^ " '""■' ^"' ^'^ '^'^y^ '"^ «»0> '^°>v muesli Will it be for 17 days ? 6. A careless pupil wrote "7 instead of -07. What was the amount of his error ? 7 A man sold something that cost him $240 at a loss '^/o' ^V hat was the selling price ? 8. 4 cwt. of coal at $7.50 a ton. Change from $2 0. If 60 lbs. cost 84c, what will 65 lbs. cost ? 10. How many cubic decimetres in a rectangular stick 4 dm. square and 50 dm. long ? of 25° TEST EXERCISEa 83 1. A piece of work is done in 4 days of 12 hours each ; how long will it take when the days are 8 hours ? 2. I pay away J my money and then J of what remams, and have $3 left. How much had I at first ? 3. The four sides of a square room together measure 48 teet. Fnid its area in sq. yards. 4. Bouglit an article for $8 and sold it for $7. What is the loss per cent. ? 6. A man sells GO sheep. This number is 66 f/ of his flock. How many sheep in the liock ? 6. Cost of 2 gi-oss slate pencils at 3 for a cent ? 7. In -75 of a mile how many yards ? 8. What is $250 less 1% of $250 ? 9. On $oO I gain '5 of $10 in -5 of a year. Find ra^.o. 1 0. How many cubic metres in a cellar 20 m. lone/ 8 111. wide and 2J m. deep ? °' 1. Cost of 19 tons 1000 lbs. of coal at $6 a ton ? 2. How many minutes in a day ? 3. A farmer put 1200 bushels of wheat into 480 bags of uniform size. How much did he put into each ba^ ? 4. An iron bar weighing 12 lbs. 8 oz. is made into 5 equal bolts worth 4/ a lb. What is each bolt worth ? 6. How much per dozen is 87i^ per pair ? 6. What must be added to J o"f 2f to make 1 ? 7. An assembly hall contains 20 rows of 15 seats each and 30 rows of 5 seats each. How many will the hall seat ? 8. A woman is 42 years old, which is f of her hus- band's age. How old is he ? 0. At 25/ a sq. foot what is the cost of a piece of ground 20 feet front and 40 feet deep ? 10. A regiment of 800 men lost 8% of its number. How many remained ? u 84 TE«T EXEIiriSES. 1. How many tiine« will a wheel, 10 feet in circiun- fereiiee, turn in going hulf-u-mile ? 2. }]y Helling goods at $7.20 I make a in-ofit of L'O per cent. What did T give for tlxnu ? 3. What is that nuniher of which, if 8 be added, and the sum divided hy 3, the quotient will be 12 ? 4. At 37?./ a yard, how many yards of lace can be bought for So I ? 6. How many lioiins from noon of the 4th to midnind. r. Express -725 as a common fraction. 8. I acre is worth $120. What for ^ acre ? 9. From -07 take -007. la Interest $50, rate 5%, 4 years. Find principal 1. Divide I of 1347 by A of 449. 2. What is 500 less 3% ? . 3. 2 gross pens at 9^^ a dozen. 4. At 22 cents a lb., how much for 2 oz. ? 5. How long will it take $300 to double itself at 5% ? 6. How Liany five-cent pieces in -25 of $8 ? ' ° 7. How many inches in 3-75 yards ? 8. Amount of $400 for 4 years at 3|-%. 0. If I of a house cost $6000, what for the whole ? 10. Divide I of f by f. "f mm ,b. <> ^> \%ii > V] >» '^- .>^ .^ /y ^a (p w IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I •IT i^ It |4o 11:25 i 1.4 M M 1.6 6' Photoeranhic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 /. ^ X^^#/.% .v*;^ / C/j ■& 4. ■^ JV ■4^^ <^ r^^ 6^ 86 TEST PAPER& xxni. TEST PAPERS. 1. What number contains 3756 exactly 13|- times ? 2. Cost of 75^ doz. eggs at two for li cents. J'^ 8. How many sleepers, each 3 ft. apart, would be (required for a double line of rails 3| miles long ? 4. Cost of 11 yds. 2 ft. 6 in. of iron palisades at $3.75 a yard ? 6. If 35 workmen can do a piece of work in 18 days how long would it take 210, working only half as quickly? e. How many bricks, each 9 in. by 4| in., will pave 3 courtyards, each 81 feet square ? B 1. If a man walks ^ miles in 2i hours, how far can A he walk in 3^ hours ? 2. How much greater is the area of a lot 50 rods square than of a lot containing 50 sq. rods ? 8. A farmer sold in a week 5*825 tons of hay. On Monday he sold 1350 lbs. ; on Tuesday, i ton ; on Wed- nesday, IJ tons; on Thursday, 1-415 tons; and on Friday, 1} tons. How much did he sell on Saturday ? 4. Express 2 ft. 7^ in. as the fraction of 100 yds 6. 1 A - (i of 4). 6. In a school numbering 200 the daily attendance is 160. What is the per cent, of attendance ? The number absent is what per cent, of the number present ? C ^ ^ 1. A train travels QJ miles in ten minutes; how far "will it go in 1 hr. 45 niin. ? TEST PAPEK3. SI 2. Multiply tlie liulf of 7} dollars by 7. 3. Divide 3 times the half of 1108 by 5 times the fourth part of 7 times 16. _ 4. From $3-1475 take $310475 and reduce the remainder to the decimal of 50 cents. 5. If a i)erson receiving $42 a week gets an advance of 15%, what will he then receive ? 1^ 6. Find the area of a triangle whose base is 9 fc 8 in. and perpendicular height 5 ft. 3 in. D 1. f of a week + f of a day + f of an hour. 2. What fraction of 25 lbs. is 3 lbs, 2 oz. ? What per cent. ? What decimal ? — , 3. If f of a yard of ribbon cost $J, what will be the price of 5f yards ? 4. A man earns $2.75 a day. How much will he earn in July, the first day of which is Thursday ? 6. Find | of 8 tons 16 cwt. 24| lbs. 6. -475 cwt. + -75 lb. + -125 oz. 1. What is the profit on the sale of 7 gross, 3 score and 3i dozen newspapers a^t one cent each, if they are bought at. 81- cents a dozen I'J 'J - .:. 2. In a town containing 11,500 inhabitants there are 22 deaths and 73 births per year in each thousand. Wliat will be the increase in 20 years ? - 3. A field of 7 ac. 80 rods is rented for $37.50. How much is that for 19 ac. 120 rods ? i,' 4. Simple interest of $720 from March 11 to July 9 at 7| per cent. 6. Take 2\ from the sum of 5f + 7 ^^ -|- 3«. 6. How many yds. of carpet a yard wide for a room 27 ft. long, 21 ft. 3 in. broad, if strips run across room? m I. , 88 TEST rAJ'^KS. 1. Value cf i_^Ji of 21. i X I- 9. Gained 12f /^ by selling eggs for f cent apiece. What was the cost price per dozen ? 3. How many pieces, each measuring 2^ inches, can be cut from 90 yards ? u^. Kent of a house for 5 wks. at $260 a year? 6. Express fd. as the decimal of £1. 6. A square court whose side is 42 yds. is paved with 28,224 square tiles. Find the dimensions of each tile. 1. Cost of 700^ feet of boards at $22.50 a thousand. 2. Cost of -725 of a ton at $8 a cwt. ,/ 3. What is the profit per cent, on goods bought for $11§ and sold for $14 ? 4. What is the weight in lbs. of the contents of a box 5 feet long, 4 feet broad and 3 feet deep, if 60 cubic inches weigh 9 ounces ? 6. What is the total surface of a cube, the edge of which measures 4i inches ? 6. What sum put at interest at 7^% will amount to $2500 in 3i years ? H 1. Bought 15 cwt. 22 lbs. of rice at $4.25 a cwt., and 6 cwt. 36 lbs. of barley at $5.60 a cwt. What will be gained by selling the whole at G^f^ a lb. ? 2. A merchant sells cloth at $3.60 a yard, gaining \207o. At what price must he sell to lose 15% ? 3. Kow much will it cost, including waste, to carpet a room 18 ft. square with carpet | yd. wide, at $1.50 a yd. ? 4. Five cents a day is the interest on what sum at 7 per cent, per annum ? TEST PAPERS. 89 6. The sum of two numbers is 187G. The greater ia three times the less. Find the numbers. 6. From sixteen ten-tliousandths take 27 milHonths, and multiply the difference by 20-5, 1. By how much does the difference between 5ff and 2f exceed the sum of |, ^^.^ and J ? 2. Add by decimals |, ^V, h '65, -375. 3. If -1-^ cwt. cost £7. 3s. what will -,«j. ton cost ? jl 4. Simple interest on $9000 from March 8 to July 6 At 7^ per cent. 6. Cost of 18 ac. 136 sq. rods of land at $50 an acre ? 6. What is gained per cent, by buying coal by the long ton (2240 lbs.) and selling it by the short ton at the same price ? J 1. J - -05 + J + -5 - -025 + } - J. 2. Eeduce 83 sq. rods to the fraction of 3 acres. 3. Cost of 3 tons 15 cwt. 10 lbs. at $12 a ton ? * 4. A garden 180 feet long by 150 feet wide is sur- rounded by a tight board fence 6 ft. high. What will it ^ cost to paint the fence both sides at 12 cents per sq. yd ? ,j/ ^ 6. Interest on $125 from May 15, 1896, to December / > 20 of same year at 4 per cent. 6. If I buy at 60 cents a score, at how much a dozen " must I sell to gain 40 per cent ? K 1. How many loads of earth, each | of a cu. yd., must be removed in making an excavation 21 feet long, 3 feet wide and 3 feet deep ? 2. A man's interest on his money, invested at 67 gives him $90 a month. What is he worth ? 90 o/ TEST PAPERS. 3. Interest on $500 for 156 days at 7 per cent. 4. Add J, J, I, 1; subtract the sum from 2 and multiply the result by f of j^. 5. A man earning $1.75 a day (10 hours) works on a certam day from 1 p.m. to 4.30 P.M. What will he earn ? 6. How many yards of paper 30 in. wide will cover the walls of a room 15 ft. long, 12 ft. wide. 8 ft. high? L 1. Half the product of two numbers is -05 ; one of the numbers is -0005. What is the other ? ^ 2. A farmer sold 24 doz. eggs at 22 J cents a doz., and 12 lbs. butter at 27i cents a lb. He was paid in tea at • S/i cents a lb. How many lbs. of tea should he receive ? 3. Value of '965625 of a mile. 4. If gunpowder contains 75% of saltpetre, IO7 of sulphur and 15% of charcoal, how many lbs. of each are there in a ton of powder ? 6. The rent of a house is $330, which is 11 per cent of its value. What is its value ? 6. What sum in 10 months at 417^ produces $3.96 ? M ^ 1. A note for $730, dated August 3, payable in 3 mos., IS discounted Sep. 15 at 77,. Find the proceeds. ^2. In what time will $858 give $128.60 in interest at 6 per cent, per annum ? ^ 3. A man invests i- of his fortune in land, ^ in houses, i m bank stocks, and loses the remainder, which was $8000, in speculation. What was his fortune ? 4. Find the sum of the third, fourth, fifth, sixth and seventh parts of 32760. ^ 6. Cost of 7i dozen books at 121- cents a copy? [ 6. Find the volume of a square prism if each side of its base is 4 ft. 6 in. and its height 20 ft. TfiST PAPEKa > N 91 1. Cost of 912 lbs. of hay at $14.50 a toa 2. At what rate per cent, must I invest $600 that in 2J years it may amount to $705 ? , 3. A man buys 1000 bushels of wheat for $1250. XHe finds 15'/^ of it worthless. At how much a bushel must he sell the remainder to gain 207^ on the cost ? 4. I have a sum of money. I deposit 80% of it in the bank and afterwards withdraw 20% of the^deposit. $5760 remain in the bank. How much had I ? 6. If a bird can fly 12 j miles in J hour, how far can it fly in 5 J hours ? 6. What will be the cost of painting 8 circular pillars, each 42 in. in circumference and 15 ft. high, at 20/ sq. yd.? ^ 1. What per cent, of f is J ? 2. If 200% of a number is f of 108, what is the number ? 8. A note of $300, payable in 2 months, is dated Aug. 12 and discounted Sept. 1 at 6%. Find the proceeds. 4. Find the difference in time between two places whose difference of longitude is 5'' 40'. 6. If I sell wood at $7.20 a cord and gain 20 per cent, what did it cost me per cord ? 6. What is the area in acres of a triangular piece of land whose base is 156 rods and height 63 rods ? P 1. A careless pupil subtracted f instead of f Was the answer too large or too small, and by how much ? 2. Cost of 76 bushels 2 pecks 1 gallon of clover seed at $2.40 a bushel 3. How much must a man's salary be in order that 17 per cent, of it may be $204 ? ! r 92 TEST PAPERS. 4. Interest on $7300 from March 6 to August 3 at 7 per cent. _ 6. In what time will 8525 give $257.25 simple mterest at 7 per cent. ? ' 6. Find tlie cubic content of a round column of marble , wliose diameter is 16 inches and height 12 feet Q ' 1. Divide ^ of 2 1 by f of 1-4. 2. Heduce 1-047 of 2 weeks 5 hours to minutes and the decimal of a minute. ^ 3. If sound travels at the rate of 1125 feet a second m how many seconds after the flash would you hear the report of a gun fired at a distance of 1-375 mile ? 4. Find (by practice) the cost of warming a building for 11 dys. 17 hrs. 28 min., if the cost is $4.50 per day. ^ 6. Find the compound interest on $4500 for 2 years p 4 per cent. 6. Find the circumference and area of a circle whose radius is 2 ft. 4 in. R ^1. From a vessel f full 22 gallons are drawn, and it IS then J full. How much does the vessel hold I 2. Goods are sold for $7| at a loss of 8 per cent. Find Uheir original cost. ^ 3. Find the number of bricks, 9 in. long, 6 in. wide 4 m,4eep, required for wall 18 ft. long, 1 ft. wide, 6 ft. high. ^ 4. What is the present worth of $1056, due 8 years Iience, at 47^ per annum simple interest ? 6. Take J of -037 from the product of 2-307 and 60-3. 6. :Bought oysters at $10 a thousand and sold them* cents a dozen. What is the gain per cent. ? EEVIEW EXERCISBa. 93 REVIEW EXERCISES. 1. How may two fractions be added or subtracted when the numerator of both is 1 ? 2. How multiply a fraction by an integer? (two ways). 8. How divide a fraction by an integer ? (two ways).' 4. What are complex fractions ? 6. How do weights and measures in the Metric system differ from those in the English system ? e. What is the base of the Metric system ? 7. How are names of higher denominations formed ? 8. How are names of lower denominations formed ? O. What is the standard unit of length ? Of capacity? Of weight ? t^ J 10. Which units are most used in measuring length? Surface? Volume? ^ ^ 11. Which units are most used in measures of capacity ? In weight ? ^ 12. For what is the are used ? The stere ? 18. How are compound quantities, expressed in the Metric system, added, nmltiplied, subtracted and divided ? 14. What is mensuration ? 15. What is a straight line? A perpendicular line?' Parallel lines ? iO. What is an angle? A right angle? An obtuse angle ? An acute angle ? 17. What is a parallelogram ? Draw, name and describe four kinds of parallelograms. 18. What difference between a square and a rhombus ? 19. What is the difference between a rectangle and a rhomboid ? 20. What is a triangle ? A right-angled triangle ? An equilateral triangle ? An isosceles triangle ? ir 94 REVIEW EXERCISES. 21 Show by diagram how to find the area of a pcarallelogram. 22. Show by diagram how to find the area of a triangle. 23. What isa circle ? The circumference ? Diameter ? Ivadius ? 24. How find circumference when diameter is given? 26. How find radius when circumference is given ? 26. What is a cube ? A prism ? A cylinder ? 27. Wliat is a triangular prism ? A square prism ? 28. How find the solid content of a prism or cylinder ? 29. How find the upright surface of a cylinder ? The total surface of a prism ? SO. What does per cent, mean ? How is it expressed ? 31. How change a common fraction to per cent ? A decimal fraction ? 82. In questions on percentage what is the base ? The rate per cent. ? The percentage ? The amount ? The difference ? 33. How find percentage when base and rate are given? 34. How find the rate from base and percentage ? 35. What are profit and loss ? 36. What is interest ? Principal ? Rate ? Amount ? 37. What is the difference between simple interest and compound interest ? 38. What is discount ? True discount ? Bank dis- count ? Commercial discount ? 39. What is a promissory note ? The face of a note ? The proceeds ? 40. When is a note negotiable ? When does it mature? How find the discount of a note ? 41. For what is circular measure used ? 42. What is latitude ? Longitude ? TABLES. 96 WEIGHTS AND MBASURBS TABLES. Time. 60 seconds (8ec.) = l minute (min.) 00 minutes =lhour(iir.) iMliour* =ldjiy(ay.) 7 (lays =lweek(wk.) 3(55 (lays « 1 common year (yr.) 100 years =1 century (C.) Capacity. 2 pints (pt.) = 1 quart (qt.) 4 quarts = 1 gallon (gal.) 2 pints (pt.) S ((uarts i pecks 1 quart (qt.) 1 peck (pk. ) 1 bushel (bu. ) 1 pint (water) weighs IJ lbs. 1 gallon contains 277 cubic inches. Wkight. 16 ounces (oz.) = 1 pound (lb.) 100pounds= 1 hundredweight(cwt.) 20 cwt. or 2000 lbs. = 1 ton. 2240 lbs. s 1 long ton. English Money. 4 farthings a 1 penny (d.) 12 pence s 1 shilling (s.) 20 shillings = 1 pound (£.) Surface. 144 square inches ss 1 square foot (sq. ft.) 9 square feet = 1 square yard. 30| 8(iuaro yards = 1 square rod. 100 sijuare rods or , 4840 square yards =" * ^^^ i^-) 640 acres = 1 square mile. Volume. 1728 cubic inches = 1 cubic foot. 27 cubic feet = l cubic yard. 16 cubic feet := 1 cord foot. 8 cord ft. or 128 cubic ft. = 1 cord. Miscellaneous. 12 units = 1 dozen. 12 dozen = l gross. 20 units = 1 score. 24 sheets = l quire. 20 quires = 1 ream. 4 inches = l hand. 6 feet = 1 fathom. Length. 12 inches (i::.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 5i yards = lrod(rd.) 320rods, 1760 yards , ., / • v or 6280 feet =1 mile (mi.) Troy Weight. 24 grains = 1 pennyweight (dwt.) 20 dwt. = 1 ounce. 12 ounces = 1 pound. Circular Measure. 60 seconds (") = 1 minute ('). 60 minutes = 1 degree (•). 360 degrees = 1 circumference. 69J miles = l degree. 96 TABLES. Money. lOOcentiinea m lfrano(fr.) METRIC SYSTEM. Capacity. 10 mllliHtre8(inl.) = i centilitre (ol.| 10 centilitres = 1 decilitre (Ul.) 10 decilitres = 1 litre (1.) 10 litres a 1 decalitre (Dl.) 10 decalitres = 1 hectolitre (HI.) Length. 10 millimetres (mm. )= 1 centimetre (cm.) Weight 10 centimetres = 1 decimetre (dm. ) 10 milligrams (mu ) L 10 decmietres =1 metre (m.) i i ♦. 10 metres « 1 decametre /nm i in xs I centigram (eg.) in A . uecametre (Um.) 10 centigrams = 1 decicram (da \ 10 hectograms =1 kilogram (Kg.) 1000 kilograms make a metric ton. Surface Measure. 100 square millimetres = i square centimetre (sq. cm.) OOaquarecenWtres = 1 square decimetre (sc. dm.) 100 square decimetres = 1 square metre (sq. m.) Land Measure. 100centiares(ca.)=l are(a.) 100ares = l hectare(Ha.) A centiave is the same in size as a sq. metre. Solid Measure. im cubic millimetres = i cubic centimetre (cu. cm.) 000 cubic cenimetres = 1 cubic decimetre (cu. dm.) 1000 cubic decimetres = 1 cubic metre (cu. m.) In measuring wood the cubic metre is called a Stere. Equivalents. 1 metre = 39-37 inches. 1 kilometre = -6214 mile. 8 kilometres = 5 miles (nearly.) 1 sq. metre = M96 sq, yards. 1 hectare = 2 471 acres. 1 litre = 1-76 pints. 1 hectolitre = 22 01 gal Igram = 15 -432 grains, 1 kilo « 2-2046 lbs. 1 metric ton = 1-1023 tons. Prefixes. Deca means 10. Hecto Kilo Myria Deci Centi MilU 100. 1,000. 10,000. ^• )ntnitre(oI.| litre (dl.) (1.) litre (Dl.) alitre (HI.) igram (eg.) •am (dg.) (g.) [•am (Dg.) fram (Hg.) ram (Kg.) netrio ton. [. cm.) dm.) H».) !m.) 1.) 0. 00.