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 iX-t- 
 

 Mental ARixHMfifi 
 
 
 • « 
 
 -PART 11. 
 
 BY v 
 
 
 CHAS. G. FRASER, % V 
 
 ^s»i«/rtn< Master, Gladstone Ave. School, Toronto. ! 
 
 ..I? 
 
 
 PRICB - " 15 CENTS. 
 
 
 *^\ 
 
 THE EDUCATIONAL PUBLISHING CO. 
 Toronto, 1899. 
 

 Entered according to Act of Parliament of Canada, in the year one 
 thousand eight hundred and ninety-nine, by the Educational Publishing 
 Company, at the Department of Agriculture. 
 
 -o 
 
 !» * 
 
 A\Ci'ib\ 
 

 PREFACE. ' 
 
 fe 
 
 XT 
 
 The complaints that business men are, making of the 
 lack of accuracy and thoroughness in the rising genera- 
 tion, would indicate a lack of system in presenting the 
 subject of arithmetic, or insufficient drill to firmly ground 
 the principles presented. We have perhaps been taking 
 up too many subjects, taking them up at the same time, 
 and in the same lesson, and the result is unsatisfactory. 
 We have been taking up subjects that require faculties 
 which' are not developed and do not naturally mature at 
 an early period of the child's life. The old rule. One 
 thing at a time^ and that done well^ is being discarded, 
 and we are of the opinion that this is being d. \t at the 
 sacrifice of the true development of the child. 
 
 In the two little " School Helps " which we now place 
 before the public, we have endeavored to supply a set 
 of questions so graded that, under the supervision of the 
 teacher, the pupil himself will take step after step with 
 little "telling," — so logical as to be natural — so 
 difficult as to call for effort— so full as to be thorough. 
 The pupil will thus be led to have a confidence in him- 
 self, and be so thorough that he will not need to stop 
 and think to tell how much 6 times 9 is. The province 
 of the teacher has not been invaded by inserting pages 
 to explain how to add or subtract ; but the questions 
 suggest the successive steps in the presenting of the 
 subject, and the books can be used in the teaching of it. 
 
 In the few pages at our disposal we have included over 
 20,000 questions, covering the whole field of public 
 
 r 
 
 I 
 
 v 
 
 % 
 
 ' ' ^ii. 
 
school arithmetic. To secure this great number of 
 questions we have resorted to an expedient which we 
 believe to be original, and which enables us to include 
 three questions in the space usually occupied by one, by 
 inserting, in brackets, the numbers for the additional 
 questions. The^se may, or may not, be used at the dis- 
 cretion of the teacher ; but even in these we have 
 endeavored to have the questions progressive. The 
 example : ^^ I bought a sheep for 8 (4, 7) dollars^ and sold 
 it to gain 2 (5^ 3) dollars. How much did I get for it f " 
 is really three questions involving the addition of 8 and 2, 
 4 and 5, and 7 and 3. 
 
 The work has been divided into two parts. The first 
 includes Numeration and Notation, Addition, Subtrac- 
 tion, Multiplication, Division, and Weights and Measures, 
 which i'lcludes Reduction and the Compound Rules. 
 The second part includes Measures and Multiples, 
 Vulgar Fractions, Decimal Fractions, Percentage, Me- 
 chanical Measurements and Type Questions. Each 
 chapter takes up its work sufficiently thoroughly for our 
 most advanced classes, and concludes with an exercise 
 on theory which, we trust, will lead to the mastering of 
 the why3 and wherefores of the rules of Arithmetic. 
 
 C. G. F. 
 
 Toronto, August iqth, 1899. 
 
 i 
 
 
 ■^<^-'y^%--:*'^v^e''''fm^mmm^mmmmtm»-- 
 
»■■ 
 
 tt number of 
 ent which we 
 us to include 
 id by one, by 
 he additional 
 ed at the dis- 
 'se we have 
 issive. The 
 iars, and sold 
 ^ get for it r^ 
 »n of 8 and 2, 
 
 s. The first 
 on, Subtrac- 
 id Measures, 
 >und Rules. 
 Multiples, 
 jntage. Me- 
 ns. Each 
 g:bly for our 
 an exercise 
 lastering of 
 melic. 
 
 C. G. F. 
 
 MEASURES AND MULTIPLES. 
 
 A Number is a unit, or a collection of units. 
 
 An Even Number is one that is exactly divisible by 2. 
 
 An Odd Number is one that is not exactly divisible by 2. 
 
 A Composite Number is one that is exactly divisible by 
 some other number. It is a number that can be factored. 
 
 A Prime Number is one that is not exactly divisible by 
 some other number. It is a number that cannot be factored. . 
 
 A Factor, or Measure of a number, is a number that will 
 exactly divide it. 
 
 A Prime Factor, or Prime Measure, of a number, is a 
 prime number that will exactly divide it. 
 
 A Common Factor, or Common Measure, of two or 
 more numbers, is a number which will divide each of ihem 
 exactly. 
 
 The Greatest Common Factor, or Measure (H.C.F., 
 or G.C.M.) of two or more numbers, is the greatest number 
 which will divide each of them exactly. 
 
 A Multiple of a number is a number which will contain it 
 exactly. 
 
 A Common Multiple of two or more numbers, is a 
 number which will contain each of them exactly. 
 
 The Least Common Multiple (L. C. M) of two or 
 more numbers, is the least number which will contain each 
 of them exactly. 
 
 Exercise i 
 
 2, 3. 
 
 Which of the following numbers are even : — 
 5, 8, 1 1, 24, 27, 35, 39, 42, 48, 56, 80. 
 
 2. Which of the following numbers are odd : — 
 4, 6, 7, 9, 12, 20, 25, 27, 32, 38, 45, 75. 
 
 3. Which of the following numbers are composite :— 
 3» 5. 6, 7, 9. 10. 12, 15, 18, 30, 45, 60. 
 
 5 
 
 
tS. *■«» **.Mix\i.t„:%^., ,< 
 
 iWi^ •' '■ 
 
 r 
 
 [ 
 
 6 MENTAL ARITHMETIC. 
 
 4. Which of the following numbers are prime :— 
 2, 4, 7, 8, II, 15, 17, 2o, 25, 27, 29, 39, 49. 
 
 6. Name all the measures of 24, 36, 72. 
 
 « 
 
 Exercise a. 
 
 What two numbers multiplied together produce :— 
 
 1. 8. 
 
 22. 
 
 42. 
 
 56. 
 
 80. 
 
 94. 
 
 52. 
 
 2. 10. 
 
 27. 
 
 44. 
 
 60. 
 
 87- 
 
 95. 
 
 57. 
 
 8. 14. 
 
 28. 
 
 45. 
 
 63. 
 
 88. 
 
 96. 
 
 62. 
 
 4. .5. 
 
 33- 
 
 49. 
 
 66. 
 
 90. 
 
 98. 
 
 68. 
 
 0. 21. 
 
 35- 
 
 55- 
 
 n- 
 
 93- 
 
 99. 
 
 91. 
 
 Exercise 
 
 What are the factors of: — 
 
 1. 21. 
 
 16. 
 
 
 33- 
 
 
 66. 
 
 24. 81. 
 
 2. 35. 
 
 18. 
 
 
 55. 
 
 
 44. 
 
 32. 76. 
 
 3. 49. 
 
 25. 
 
 
 54- 
 
 
 42. 
 
 29. 95. 
 
 4. 63. 
 
 45. 
 
 
 56. 
 
 
 22. 
 
 39. 91- 
 
 6. 28. 
 
 64. 
 
 
 48. 
 
 
 30. 
 
 46. 60. 
 
 
 
 Exercise 4 
 
 • 
 
 
 Resolve 
 
 into factors : 
 
 
 G 
 
 ive the 
 
 co-factors of: — 
 
 1. 4. 
 
 18. 
 
 32. 
 
 
 SO- 
 
 81. 
 
 26. 58. 
 
 2. 6. 
 
 20. 
 
 34- 
 
 
 64. 
 
 82. 
 
 38. 69. 
 
 3. 9. 
 
 24. 
 
 36. 
 
 
 65. 
 
 84. 
 
 39. 75. 
 
 4. 12. 
 
 25. 
 
 40. 
 
 
 70. 
 
 85. 
 
 46. 76. 
 
 6. 16. 
 
 30. 
 
 48. 
 
 
 72. 
 
 86. 
 
 51. 78. 
 
 Exercise 5. 
 
 Give all the numbers that are measures of : — 
 
 1. 8. 
 
 24. 
 
 42. 
 
 64. 
 
 81. 
 
 100. 
 
 128. 
 
 2. 12. 
 
 30. 
 
 48. 
 
 70. 
 
 84. 
 
 108. 
 
 132. 
 
 3. 16. 
 
 32. 
 
 56. 
 
 72. 
 
 88. 
 
 112. 
 
 144. 
 
 4. 18. 
 
 36. 
 
 60. 
 
 75- 
 
 90. 
 
 120. 
 
 160, 
 
 6. 20. 
 
 40. 
 
 63. 
 
 80. 
 
 96. 
 
 125. 
 
 196; 
 
 I 
 
MEASURES AND MULTIPLES. 
 
 ExercUe 6 
 
 rs 
 
 52- 
 
 57. 
 
 62. 
 68. 
 91. 
 
 81. 
 76. 
 
 95- 
 91. 
 60. 
 
 of:- 
 
 58. 
 69. 
 
 75. 
 76. 
 
 78. 
 
 128. 
 132- 
 144. 
 160, 
 196. 
 
 Give the prime factors of :- 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 
 4. 
 6. 
 
 8. 
 
 9- 
 10. 
 12. 
 18. 
 
 21. 
 
 32. 
 
 15. 
 
 36. 
 
 27. 
 
 40. 
 
 28. 
 
 42. 
 
 30. 
 
 ^§- 
 
 33. . 
 
 48. 
 
 35. 
 
 50. 
 
 44. 
 
 55- 
 SI- 
 56. 
 
 54. 
 60. 
 63. 
 
 64 
 66 
 70 
 72 
 
 75 
 76 
 
 77 
 
 78. 
 
 79. 
 80. 
 81. 
 84. 
 90. 
 96. 
 
 Exercise 7. 
 
 What prime factors are common to 
 
 1. 
 2. 
 3. 
 4. 
 6. 
 6. 
 7. 
 
 24 and 30. 
 18 and 30. 
 
 35 and 42. 
 20 and 28. 
 28 and 36. 
 
 36 and 48. 
 45 and 63. 
 
 35 and 45 
 , 36 and 42 
 28 and 42 
 35 and 49 
 42 and 63 
 55 and 77 
 63 and 72 
 
 Exercise 8. 
 
 $28 and $32. 
 
 $33 and $66. 
 
 $48 and $64. 
 
 J63 and /84. 
 ^99 and ^36. 
 ;^55 and ^75. 
 ^75 and ^125. 
 
 Is 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 
 1. 
 2. 
 
 Find the largest number which will exactly divide : — 
 
 36 and 42. 
 15 and 25. 
 28 and 49. 
 32 and 44. 
 
 35 and 65. 
 44 and 77. 
 
 36 and 96. 
 
 Exercise 9. 
 Find the G. C. M. of :— 
 
 30, 42, and 48. 
 25, 30, and 40. 
 28, 35, and 49. 
 32, 36, and 48. 
 36, 54, and 63. 
 45, 63, and 81. 
 56, 42, and 7©. 
 
 15 and 18. 
 
 18 and 27. 
 
 3. 24 and 36. 
 
 4. 25 and 45. 
 
 5. 27 and 45. 
 
 6. 30 and 48. 
 
 7. 45 and 72. 
 
 $21 and $28. 
 $14 and $35. 
 $35 and $49. 
 $63 and $81. 
 $54 and $45. 
 $45 and J8f. 
 $54 and $81. 
 
 36 tons, and 40 tons. 
 25 cwt., and 35 cwt. 
 44 gal., and 66 gal. 
 36 cents, and 54 cents. 
 28 boys, and 49 boys. 
 39 pens, and 65 pens. 
 46 pks., and 69 pks. 
 
8 
 
 MENTAL ARITHMETIC. 
 
 Exercise lo. 
 
 2. 
 
 6. 
 7. 
 
 Find the H. C. F. of :— 
 ,15, 25, and 30. 
 
 21. 28, and 42. 
 18, 30, and 42. 
 28, 42, and 49. 
 42, 48, and 60. 
 24, 36, and 42. 
 
 $18, S24, and $36. 
 
 $25, $35, and $45. 
 $50, $75, and $125. 
 $63, $84, and $(05. 
 $55» S77i and $220* 
 $36, $72, and $144. 
 $45, $75, and $150. 
 
 72, 90, and 108. 
 
 Exercise if. 
 
 Find the G. C. M. of : — 
 
 1. 16 feet, and 28 feet. i ', 6", and i ' 9". 
 
 2. 18 yds., and 12 yds. 3 yds., i ft., and 8 yds., 1 ft. 
 
 3. 36 inches, and 48 inches. 6 ft., 3 in., and 8 ft., 9 in. 
 
 4. 40 mi., and 25 mi. 6 bu., i pk., and 8 bu., 3 pk. 
 
 5. 36 tons, and 28 tons. 3s. 9d., and 4s. 2d. 
 
 6. ^30, and £42- £2 ids., and £'i 15s. 
 
 7. $42, and $62. 7 mi., 4 fur., and 10 mi. 
 
 Exercise 12. 
 
 Find the largest bills with which I can pay : — 
 
 1. $45, $60, and $8q. 
 
 2. ^35. £45* and £7S- 
 
 3. $30, $45, and $80. 
 
 4. ^42, £63, and £70. 
 
 6. $50, $75, and $90. 
 
 0. £7 St jC^oOy and ;^ 120. 
 
 7. $90, $135, and $180. 
 
 $50, $60, and $72. 
 £60, ;^8o, and ;^9o. 
 $45, $90, and $100. 
 ;^6o, ^75, and ;^i2o. 
 $75, $225, and $150. 
 ;^8o, ;^i20, and ;^2oo. 
 $1.25, $2.00, and $2.75. 
 
 Exercise 13. 
 
 Find the largest number which will exactly divide 
 
 1. 
 
 12, 18, 24, and 27. 
 
 18, 24, 27, 36, and 48. 
 
 2. 
 
 18, 27, 45, and 48. 
 
 35. 45. 70, 90, and 105. 
 
 3. 
 
 32, 64, 80, and 88. 
 
 36, 54, 60, 72, and 90. 
 
 4. 
 
 54, 81, 108, and 99. 
 
 28, 42, 70, 84, and 98. 
 
 6. 21, 35, 84, and 91. 
 
 6. 42, 63, 84, and 77. 
 
 7. 28, 56, 84, and 63. 
 
 33. 66, 99, 88, and 77. 
 75, 90, 45, 60, and 120. 
 45. 60, 75, 120, and 150. 
 
MEASURES AND MULTIPLES. 
 
 3. 
 
 Exercise 14. 
 
 What is the largest unit which will measure : — 
 
 1. I15, $30, $20, $45, and $55 ? 
 
 2. 15 bush., 30 bush., 60 bush., 90 bush., and 100 bush. ? 
 
 3. 2omin., 4omin., 6omin., 75 min., and 80 min. ? 
 
 4. 45 sheep, 60 sheep, 75 sheep, 120 sheep, and 150 
 
 sheep ? 
 
 5. 42 tons, 56 tons, 70 tons, 84 tons, and 91 tons? 
 
 6. 63 cords, 84 cords, 126 cords, 105 cords, and 147 
 
 cords ? 
 
 7. 45 yds., 75 yds., 90 yds., 180 yds., and 270 yds. ? 
 
 rds., I ft. 
 , 9 in. 
 )U., 3 pk. 
 
 s. 
 3 mi. 
 
 Exercise 15. 
 
 Find the number of which the factors are 
 
 1. 
 
 2 and 3. 
 
 2, 2, and 3. 
 
 22, 32, and 5. 
 
 2. 
 
 5 and 3. 
 
 3, 3, and 5. 
 
 22, 58, and 72. 
 
 3. 
 
 6 and 7. 
 
 3, 5, and 7. 
 
 23, 3, 5", and 7. 
 
 4. 
 
 8 and 5. 
 
 2, 3, 5, and 7. 
 
 2*, 3^ and 5*. 
 
 5. 
 
 3 and 7. 
 
 5, 7, and II. 
 
 3S 5^ and 7«. 
 
 ). 
 ►o. 
 
 0. 
 [CO. 
 
 2.75- 
 
 divide :- 
 
 48. 
 105. 
 90. 
 98. 
 
 120. 
 1 150. 
 
 Exercise 
 
 Find the square of : — 
 
 16. 
 
 1. I. 
 
 8. 
 
 12. 
 
 40. 
 
 25. 
 
 75. 
 
 2. 2. 
 
 7. 
 
 II. 
 
 80. 
 
 35- 
 
 95. 
 
 3. 3. 
 
 9. 
 
 IS- 
 
 60. 
 
 45. 
 
 55. 
 
 4. 4. 
 
 6. 
 
 20. 
 
 50. 
 
 65. 
 
 105. 
 
 6. 5. 
 
 10. 
 
 30. 
 Exercise 
 
 90. 
 ■7. 
 
 85. 
 
 115. 
 
 Find the cube of : 
 
 — 
 
 
 
 
 1. I. 
 
 6. 
 
 II. 
 
 30. 
 
 80. 
 
 200. 
 
 2. 2. 
 
 7. 
 
 12. 
 
 60. 
 
 100. 
 
 300. 
 
 3. 3. 
 
 8. 
 
 15. 
 
 90. 
 
 no. 
 
 500. 
 
 4. 4. 
 
 9- 
 
 20. 
 
 50. 
 
 120. 
 
 700. 
 
 6. 5. 
 
 10. 
 
 40. 
 
 70- 
 
 150. 
 
 900. 
 
lO MENTAL ARITHMETIC. 
 
 Exercise i8. 
 
 Find the equal co-factors of : — 
 
 1.4. 
 
 49. 
 
 169. 
 
 400. 
 
 1600. 
 
 1225. 
 
 2. 9. 
 
 81. 
 
 144. 
 
 900. 
 
 3600. 
 
 2025. 
 
 3. 16. 
 
 64. 
 
 196. 
 
 625. 
 
 2500. 
 
 3025. 
 
 4. 36. 
 
 100. 
 
 225. 
 
 484. 
 
 8100. 
 
 4225. 
 
 6. 25. 
 
 121. 
 
 256. 
 
 576. 
 
 4900. 
 
 5625. 
 
 
 
 Exercise 19- 
 
 
 
 1. Divide 10 X 12 X 14 by 21 X 20. 
 
 2. Divide 12 x 14 x 18 by 21 x 24. 
 
 3. Divide 1 5 x 18 x 2 1 by 27 x 35. 
 
 4. Divide 21 X 24x25 by 30x35 x 12. 
 6. Divide 22 x 24 x 28 by 33 x 14 x 32. 
 
 6. Divide 28 x 30 x 32 by 24 x 40 x 14. 
 
 7. Divide 32 x 33 x 35 by 24 x 28 x 35. 
 
 . 
 
 1. 
 
 2. 
 
 6. 
 
 lOX icx 16 
 
 ^ ^ 
 
 25 X 24 
 
 18x20x21 
 
 28 X 30 
 
 22 X 24 X 25 
 
 33 X 40 
 
 27 X 35 X 40 
 
 45 X 56 
 24 X 28 X 30 
 "36x42 
 
 30 X 32 X 33 
 44 X 48 
 
 28 X 30 X 36 
 42x45 
 
 Exercise ao. 
 
 27 X 28 X 30 
 
 35 
 
 X36 
 
 X18 
 
 27 
 
 X32 
 
 X35 
 
 21 X36 
 
 X40 
 
 33 
 
 X35 
 
 X36 
 
 27 
 
 X28 
 
 X55 
 
 35 
 
 X40 
 
 X42 
 
 25 
 
 X48 
 
 X49 
 
 44 
 
 X45 
 
 X49 
 
 28 
 
 X33 
 
 X35 
 
 45 
 
 X48 
 
 X50 
 
 25 
 
 X36 
 
 x6o~ 
 
 54 
 
 X56 
 
 x6o 
 
 42 X 45 X 48 
 
 54 X 
 
 55 X 
 
 56 _ 
 
 35 X 
 
 66 X 
 
 72 
 
 55 X 
 
 56 X 
 
 60 
 
 25 X 
 
 32 X 
 
 n 
 
 56 X 
 
 64 X 
 
 65 _ 
 
 40 X 
 
 32 X 
 
 26 
 
 64 X 
 
 65 X 
 
 70 
 
 50 X 
 
 52 X 
 
 56 
 
 70 X 
 
 72 X 
 
 80 
 
 56 X 
 
 60X 
 
 60 
 
 75 X 
 
 Sox 
 
 81 
 
 45 X 
 
 45 X 
 
 6o~ 
 
 Sox 
 
 91 X 
 
 90 
 
 45X56X 130 
 
MEASURES AND MULTIPLES. 
 
 II 
 
 Exercise 21. 
 
 1. What is the longest measure whicli can be used to 
 find the size ofafield [96'x 132]? [84' x 120']? [72' x 120']? 
 
 2. Find the length of the longest boards which can be 
 used to fence a garden [48' X 84'J, [72' x 132'], [68 yds. 
 X 84 yds.]. 
 
 3. Find the greatest distance at which the posts may 
 be placed to fence a garden [84' x 108'], [80' x 112'J, 
 [168' x 200']. 
 
 4. How many posts, placed at the greatest distance 
 possible, will be required to fence a lot [24' x 64'] ? [36 ' 
 X84']? [45'x8i']? 
 
 5. How many boards, the longest possible, will reach 
 around a lot [24' x 56'] ? [36' x 8i'J ? [72' x 132'] ? 
 
 6. How many boards, of the greatest length possible, 
 will be required for a 5-board fence, for a lot [36' x 60'] ? 
 [48'x88'J? [56'x88'J? 
 
 7. What is the least cost, at 25 cents each, of the 
 boards required to make a 5-board fence, for a lot [45 ' x 
 63].? [4o'x88']? [6o'x96']? 
 
 Exercise aa. 
 
 1. A grocer has 49 (56, 45) pounds black tea and 63 
 (72, 85) pounds green tea. He puts it up in caddies, the 
 largest possible, without mixing it. Find the weight of 
 the caddies. 
 
 2. A grocer has 45 (39, 60) pounds of ^reen tea and 
 65 (45, 84) pounds black, and puts it up m the largest 
 caddies possible, without mixing the teas. Find the 
 number of caddies of each. 
 
 3. A grocer has 48 (65, 63) pounds green tea and 88 
 (85, 77) pounds black. He puts it up in the largest cad- 
 dies possible, without mixing the teas. Find the value, 
 of each caddie of tea at 75c. a pound. 
 
 4. A grocer has 51 (63, 88) pounds green tea, and 57 
 (75, 100) pounds black tea. He puts it into caddies the 
 largest possible, without mixing the teas. How many 
 caddies will he require ? 
 
'i^^i^i ^m^aimmi^ii^is^mmiitiMiiu,^^ 
 
 j jiy w n J ■ 
 
 n i ) i W i i . i i ili HH W I WW 
 
 12 
 
 MENTAL ARITHMETIC. 
 
 Exercise 23. 
 
 1. Give a multiple of 2, 3, 5, 6, 9, 11. 
 
 2. Give two multif}les of 4, 6, 7, 8, 12, 15. 
 
 3. What number is a multiple of 3 and 4 ? 5 and 6 ? 
 
 7 and 9? 8 and 12? 9 and 15? 
 
 4. What multiple is common to 2 and 5 ? 3 and 7 ? 
 
 8 and 9? 6 and 8? 10 and 15? 16 and 24? 
 
 6. What multiples, less than 50, are common to 2 and 3 ? 
 3 and 4 ? 3 and 5 ? 4 and 6 ? 
 
 Exercise 34. 
 
 Find a Common Multiple of : — 
 
 1. 2 and 3. 3 and 6. 
 
 2. 3 and 4. 4 and 8. 
 
 3. 2 and 5. 3 and 9. 
 
 4. 3 and 5. 5 and 15. 
 
 5. 5 and 6. 7 and 11. 
 
 4 and 6. 
 8 and 10. 
 
 8 and 12. 
 
 9 and 12. 
 9 and 1 5. 
 
 »r. 
 
 Exercise as. 
 
 Find the Least Common Multiple of 
 
 1. 4 and 6. 15 and 25. 
 
 2. 6 and 8. 28 and 35. 
 
 3. 9 and 12. 32 and 42. 
 
 4. 8 and 12. 32 and 48. 
 
 5. 12 and 16. 56 and 70. 
 
 28 and 49. 
 63 and 81. 
 45 and 63. 
 72 and 84. 
 96 and 108. 
 
 Find the L. C. 
 
 1. 2, 3, and 4. 
 
 2. 3, 4, and 6. 
 
 3. 6, 8, and 9. 
 
 4. 8, 9, and 12. 
 6. 8, 10, and 15. 
 
 Exercise a6. 
 
 M. of: — 
 
 2, 4, 6, and 8. 
 6, 9, 12, and 15. 
 
 9, ID, 12, and 15, 
 
 10, 12, 15, and 20. 
 9, 15, 20, and 45. 
 
 18, 24, and ^6. 
 15, 25, and 35. 
 18, 27, arid 45. 
 36, 48, and 60. 
 54, 72, and 81. 
 
MEASURES AND MUr/riPI,KS. 
 
 t3 
 
 Exercise 27. 
 
 Find the least sum of money which can be paid with : — 
 
 1. 5-cent pieces, or lo-cent pieces. 
 
 2. 10-cent pieces, or 25-cent pieces. 
 
 3. 20-cent pieces, or 25-cent pieces. 
 
 4. 20-cent pieces, or 50-cent pieces. M 
 6. $2 bills, or $5 bills. ^ 
 
 6. $4 bills, or $5 bills. 
 
 7. $2 bills, $4 bills, or $10 bills. 
 
 Exercise a8. 
 
 Find the least sum of money which can be paid with : — 
 
 1 . 4-penny pieces, or 6-penny pieces. 
 
 2. 3-penny pieces, or 4-penny pieces. 
 
 3. 6-penny pieces, or shillings. 
 
 4. 9-penny pieces, or shillings. 
 6. Shillings, or half-crowns. 
 
 6. Shillings, or crowns. 
 
 7. Crowns, guineas, or sovereigns. 
 
 Exercise ap. 
 
 1. Find the least number which is exactly divisible by 
 6 or 9, 8 or 12, 12 or 15, 
 
 2. Find the least number which is exactly divisible by 
 6, 8, or 10 ; 9, 12, or 15 ; 16, 20, or 24. 
 
 3. Find the least number which when divided by 5, 7, 
 or 10 leaves a remainder of 2 (3, 4). 
 
 4. What are the least two numbe s exactly divisible 
 by 6 or 10? 12 or 15 ? 15 or 20? 
 
 6. Find two numbers each of which leaves a remainder 
 of 3 (5> 4) when divided by 6, 9, or 12. 
 
 6. What is the least sum of money with which I can 
 buy sheep at $9, cows at $15, or horses at $25 ? 
 
 7. I have enough money to buy lambs at $3 ($4, $5), or 
 sheep at $5 ($6, $8), or pigs at $8 ($10, $12), and have 
 $2 left. How much money have I at least ? 
 
 \ 
 
-.iiiV■#&^^Mi^tf^i^ij,4l»i/;«w,l«■%^«^«^ 
 
 M 
 
 MENTAL ARITHMETIC. 
 
 Exercise 30. 
 
 1. What is the least number of bushels of wheat that 
 would make an exact number of full loads of 30, 32, or 
 36 bushel^ ? 
 
 2. What is the least sum of money with which I can 
 Wiy an exact number of 3-cent, 5 -cent, 6-cent, 8-cent, 
 W la-cent, stamps ? 
 
 3. A farm can be divided into fields containing 8, 9, 
 10, 6r 12 acres. Find the size of the farm. 
 
 4. A farm can be divided into fields of 9, 12, or 15 
 acres. Find value of farm at $25 ($75, $125) an acre. 
 
 6. When the boys of a school are divided into sixes, 
 sevens, eights, or elevens, there ai-e five over. How 
 many boys are there ? 
 
 6. When a farm is divided into fields of 8, 10, or 1 5 
 acres each, there are 5 acres over. How many 5-acre 
 lots could be made of it ? 
 
 7. How many logs, of the longest uniform length, can 
 be made of two tree trunks 63 feet and 105 feet long ? 
 
 Exercise 31. 
 
 1. What measures could be used to em, ty, or fill, a 
 24-quart basket ? a 36-quart basket ? a 48-quart basket ? 
 
 2. What weights could be used to weigh out 20, 
 (3o> 45) pounds of sugar ? 
 
 3. Find all the measures which could be used to 
 exactly fill a bushel basket. 
 
 4. Find all the measures, longer than a foot, which 
 could be used to find the length of a pole 25 (30, 60) 
 yards long. 
 
 5. A man has a tree 36 (40, 48) feet long. What 
 lengths of boards may he make of it and lose none of 
 the log ? 
 
 6. Into what various sizes of fields c^n I ^ivide a farm 
 of 50(60, 96) acres, and have an exact number of acres 
 in each ? 
 
 7. A chest contains 72 (80, 100) pounds of tea. What 
 choice of sizes has the grocer in putting this into parcels, 
 each having an even number of pounds of tea ? 
 
MEASURES AND MULTIPLES. 
 
 n 
 
 at that 
 32, or 
 
 h I can 
 8-cent, 
 
 ing 8, 9» 
 
 , or 15 
 
 acre, 
 ito sixes, 
 r. How 
 
 10, or 15 
 ny 5 -acre 
 
 ngth, can 
 It long ? 
 
 ', or fill, a 
 ,rt basket ? 
 h out 20, 
 
 e used to 
 
 bot, which 
 25 (30, 60) 
 
 ng. What 
 ose none of 
 
 vide a farm 
 jer of acres 
 
 tea. What 
 into parcels, 
 1? 
 
 Exercise 33. 
 
 1. Find the largest number which cun be subtracted 
 an exact number of times from 56 (63, 85). 
 
 2. What is the greatest number of which 84 (96, 85) 
 and 108(120, 119) are multiples? 
 
 3. Find the least number of which 17, 15 and 18 
 are divisors. 
 
 4. Find the number which divides 78 (68, 1 56) and 
 90 (99, 181), leaving a remainder of 6 in each case. 
 
 6. Find the number which divides 82 (85, 151) and 
 133 (138, 136) leaving remainders of 7 and 8 respectively. 
 
 6. What is the le^ast number of marbles which can be 
 divided equally among 6, 8, 12, or 15 boys ? 
 
 7. Two men dig 16 and 20 post-holes in a day. Find 
 the least number of post-holes which would supply 
 exact days' labor, either for each working, alone, or for 
 both working together. 
 
 Exercise 33. 
 
 1. The wheels of a carriage ar^ 7 feet, and 9 feet in 
 circumference. How often will the wheels be in the 
 same relative position ? 
 
 2. A earns $3 a day, and B earns $4 a day. Find the 
 least sum of money which would pay an exact number of 
 days' wages for A and. B, working alone, or together. 
 
 3. A battalion of sokliers can be divided into com- 
 panies of 64, 72, or 80 men. Find the number of men 
 in the battalion. 
 
 4. A fence is to be built across the front of a lot. The 
 posts may be put 8, 9, or 12 feet apart. How long is 
 the fence at least ? 
 
 6. A boy bought a number of dozens of oranges, and 
 finds he can divide them into fives, sevens, or nines. 
 How many did he buy? 
 
 6. Three pieces of carpet 32, 64, and 80 yds. long are 
 used to carpet a hall, cutting the pieces into equal lengths. 
 Find the length and width of the hall. 
 
'0'^'. ■■'^s'MfiMm^Mm^isimiiti 
 
 16 
 
 MENTAL ARITHMETIC. 
 
 I" 
 
 ^1 
 
 i 
 
 Exercise 34. 
 
 1. Find the longest boards possible with which I can 
 enclose a triangular lot whose sides are 36, 54 and 81 
 feet. 
 
 2. A, B, and C, have 45 acres, 60 acres, and 7$ 
 acres respectively. They divide their farms into fields 
 
 |pf the same size. Find the least number possible for 
 each. 
 
 3. Three pieces of dress goods, 48,64, and 72 yds., are 
 cut into equal dress lengths. Find the least number 
 possible. 
 
 4. I have a ditch which can be dug in an exact number 
 of days by any one of three men who dig 4 rods, 5 lods, 
 and 6 rods a day, respectively. Find length of the ditch. 
 
 5. Cattle are selling so that I can buy an exact number 
 with $45, $75 or $90. Find the price of cattle. 
 
 6. Find the smallest sum of money with which I can 
 buy sheep at $8 ($9, $9) each, pigs at $12 ($15, $12) each 
 or cattle at $15 ($20, $20) each. 
 
 7. Find the least sum of money with which I can buy 
 sheep at $6 ($6, $8), or pigs at $8 ($9, $12), or an equal 
 number of each. 
 
 Exercise 35. 
 
 1. The product of three numbers, less than 10, is 240 
 (432,252). Find the numbers. 
 
 2. The product of two consecutive numbers is 42 (56, 
 132). Find the numbers. 
 
 3. The product of two consecutive numbers is 210 (600, 
 870). Find the numbers. 
 
 4. The product of three consecutive numbers is 24 (60, 
 120). Find the numbers. 
 
 6. The product of three consecutive numbers is 210 
 (720, 3360). Find the numbers. 
 
 6. The product of three consedHtive even numbers is 
 48 (192, 960). Find the numbers. 
 
 7. The product of three consecutive odd numbers is 
 ioS> 3^5 (^^93)- Find the numbers. 
 
MKASURES AND iMUl/ni'LKS. 
 
 17 
 
 1 I can 
 and 81 
 
 and 75 
 to fields 
 ible for 
 
 rds., are 
 number 
 
 t number 
 ;, 5 lods, 
 he ditch, 
 t number 
 
 ich I can 
 $12) each 
 
 I can buy 
 r an equal 
 
 10, is 240 
 is 42 (56, 
 s 210(600, 
 rs is 24 (60, 
 bers is 210 
 numbers is 
 numbers is 
 
 Exercise 36. 
 
 1. The wheels of ^ carriage are 12 and 15 feet in 
 circumference. How far will they travel before each 
 wheel has made an exact number of revolutions ? 
 
 2. The wheels of a carriage are 12 and 15 feet in 
 circumference. In going a mile, how often will the 
 wheels be in the same position as at starting ? 
 
 How many revolutions will each have made? 
 
 How many will one have made more than the other? 
 
 3. Two wheels having 15 and 25 cogs work together. 
 How many revolutions will the smaller wheel make 
 before the same cogs touch each other again ? 
 
 4. Two wheels having 24 (36, 30) and 30 (40, 42) 
 cogs work together. How many revolutions will each 
 make before the same cogs touch each other again ? 
 
 5. Two wheels having 24 (28, 36) and 32 (35, 45) cogs 
 work together. The larger makes 48 (36, 24) revolutions 
 a second. How often will the same cogs touch each 
 other ? 
 
 6. Two wheels having 28 (32, 35), and 42 (40, 42) cogs 
 work together. The larger wheel makes 40 (48, 30) 
 revolutions a second. How often will the same cogs 
 touch in running for five minutes ? 
 
 7. A and B travel at the rate of 20, and 25, yards a 
 second around a Mcycle track, 300 yards in circumfer- 
 ence. How far will each have travelled before they are 
 again together at the starting point ? 
 
 8. A, B, and C travel around a bicycle course, 240 yards 
 in circumference, at the rate of 20, 24, and 30 yards a 
 second. When will they be at the starting point 
 together again ? 
 
 9. A and B travel . a|. the rate of 18 yards, and 24 
 yards, a second, aroun^a bicycle course, 360 yards in 
 circumference. How often will they be at the starting- 
 point together ? 
 
■xikiii<'»:Ammmm>-A*4',>^M*»iii^^ 
 
 18 
 
 MENTAL ARITHMETIC. 
 
 BxerclM 37- 
 
 B«^"" ^ , C M of thre. 
 
 numbers. .^^ methods of findmg 
 
 2. Show that the tw -^jentical. p r M of two 
 
 oftwo or rnr« ".nuSber^aid to be the G.C.M 
 
 a When IS one numo , r M of two 
 
 8. Show that a la ;jf„e„ce. „{ all its 
 
 of their sum, and the t ^ ^^^^^er .s a factor 
 
 g Show that a ...ct „„„bers by 
 
 multiples. g^ jjie G.C.M. 01 tw 
 
 10. Show how to fina ,(. 7), and their 
 
 factoring. of two numbers >« 3 " <" find the 
 
 11. The H.C.F. ot tw ^^^ .^ ^ ^,5, 35). 
 
 L.C.M, IS 36 (6°- ^'°' . o), and their 
 
 "icT'-The G.C.M of two n-r^'^^'^e nu4^«s^' 
 
 ,^ C M is 80 (44<, 567)- ^'"1** "is 3 (,, 6) and the.r 
 
 "^13. The G.C.M^f tlge ^TTofU Ubers are .3 
 
 Vc J'-U^^O 57S! 753^ Vrr^ro^e Wmd and 
 15 A grocer has 13^ f J-^^.'^r ^Cide them into the 
 ''t(^8^43) ^fXSt&thekinds 
 ,„ge,t lots possibte, w ^"-^ JS'ocks possi- 
 
 V^- 'sS *i^^vidJUintothelarg^.»tfloc^^^^^ 
 ■white sheep. *. , colors, rmu t» 
 
 t'u'T'rw^flocls^of'-'''''"''"^' 
 
VULGAR FRACTIONS. 
 
 A 
 
 )f three 
 
 L.C.M. 
 
 VI of two 
 
 . of two 
 
 leG.C.M. 
 
 le to each 
 
 the digits, 
 so a factor 
 
 or of all its 
 
 lumbers by 
 
 \ and their 
 Find the 
 
 )), and their 
 
 ■ 
 
 6) and their 
 tibers are 12 
 
 25) and their 
 
 ers. 
 
 one kind and 
 
 them into the 
 
 ds. 
 
 135 (92, U5) 
 St flocks possi- 
 
 3 size of each 
 el? 
 
 An Integer is a whole number — a unit or collection of units. 
 
 A Fraction is a pari of a unit. 
 
 The Terms, or parts, of a fraction are its numerator, and 
 its denominator. 
 
 The Denominator tells into how many equal parts the 
 unit is divided. 
 
 The Numerator tells how many of the.«e equal parts are 
 taken to form the fraction. 
 
 A Mixed Number is one that is composed uf a whole 
 number and a fraction. 
 
 There are two kinds of fractions— Vulgar and Decimal. 
 
 A Vulgar Fraction is one in which both numerator and 
 denominator are expressed by figures. 
 
 A Decimal Fraction is one in which the denom'nator is 
 merely indicated, and is 10, or a power of 10. 
 
 There ar9 three kinds of Vulgar Fractions : — 
 
 a. Simple Fractions — Proper, and Improper. 
 
 b. Compound Fractions. 
 
 c. Complex Fractions. 
 
 A Simple Fraction is one whose numerator and denomin- 
 ator are simple numbers. It is a Proper Fraction if the num- 
 erator is less than the denominator. It is an Improper 
 Fraction if the numerator is equal to, or greater than the de- 
 nominator. 
 
 A Compound Fraction is a fraction of a fraction. 
 
 A Complex Fraction is one ihat has a fraction, or a mixed 
 number, for one, or both, of its terms. 
 
 Equivalent Fractions are those which are equal in va*ue. 
 
 Exercise 38. 
 
 1. What name is given to each part, when an apple 
 is divided into 2 equal parts ? 3 equal parts ? 4 equal 
 parts ? 5 equal parts ? 
 
 2. An apple is divided into 4 equal parts. What is 
 one part called ? What are two of the parts called ? 
 three parts ? four parts ? 
 
 19 
 
.l^t^yMt «^i«**:»-ii«**-*^-*' 
 
 ,'mas^.mmmmx 
 
 MBNT,V.. ARtTHMMlC. 
 
 5. 
 
 fourlVis oi a.. -rr-. ^^^^^, 
 
 \ZTor one-t.rth ? ^„^.,,i,a, two-thirds, 
 
 7. Write .n fig"f«^ ^ jhree-tourths, five-s-xt 
 one-fourth, two-fourths, 
 
 , 1. interpret these f,.ct,o„V-j|^^^ 
 2. interpret these fr<:„^j_^, in wor<\s. 
 
 t. Whatfract;onof8.s 'J 3 / ^,^^,, days 
 
 do in 1 day ? ^^^ ^ """^ 
 
 ExercUe 4® 
 
 in 
 
 can he do 
 
 oranges? in 5 V"°' [ -^ ;„ one orange? » 3 P» 
 
 iinches? inS' „„„rter3 in 2, 3. 5. **• "' . ', ^ 
 
 3. How many Vf"\^ ,^, ^nd 32 to stxths. 
 
 4. Reduce 5. 7, 9. « - ' • % „, ,3, ,5, and 25- 
 5 Express in sevenths ., 5. . ^jghths. 
 
 I; Convert ., 2, 3. 7. 9- •^. ^"^ „ ,, factions wuh a 
 
 (3'4)?o?reno— ;.ou,d each get >^W.^) "'- 
 lp%"ouTor(lt's%,7,-)^PP'-' • 
 
VULGAR FRACTIONS. 
 
 21 
 
 parts, 
 s? 
 ? one- 
 
 > three- 
 
 le-tbird? 
 
 -o-tbirds, 
 
 s. 
 » 
 
 .? 2? 
 
 ys? 4<iayS? 
 
 r much of it 
 1 5 days ? 
 
 pears? i^ 3 
 lyS ? 
 3 plums? m 
 
 |ngs? 
 16, and 20 .' 
 
 sixths. 
 5, and 25. 
 eighths, 
 factions with 2 
 
 2:1? 
 
 Exercise 41. 
 
 1. How many halves in I .} apples? in 2.J apples? in 
 3J pears? in 5^ things? in 7 J dozen ? 
 
 2. How many bovs could each get J of an apple from 
 ij ('ii* 2?, 3's,5j,6S,8i) apples? 
 
 3. How many books at $\ each could I buy with III? 
 $i£? $2i? $3i? $5i? $72? $9^'^ 
 
 4. What improper fraction is equivalent to 1 }, ? 
 
 3V 4F 5 J? 7^? 9i\)? 
 
 6. Reduce these mixed numbers to improper frac- 
 tions :-2j,3§, 5§, 62, 8^, 9I, and i2iV 
 
 6. Express as simple fractions : — 
 
 ih 2h 3$, 4» 5A. 6i, and 7iV 
 
 7. Convert i|^, 2^, 4g, 5^, 6^, 9J, and 6, to equivalent 
 fractions. 
 
 Exercise 4a. 
 
 1. How many pears would give 2 a pear to each of 
 4(6, 10, 12, 18, 24, 36) boys? ' 
 
 2. How many apples would give half an apple to each 
 of5(7» ii» i5» 21, 33. 45) girls? 
 
 3. At $J each, how much must I pay for 4 (8, 16, 24, 
 36, 48, 60) books ? 
 
 4. Find the cost of 5 (7, 11, 17, 25, 38, 42) pails at 
 $} each ? 
 
 6. What whole, or mixed, number is equivalent to 
 
 I? \^? s? V? ¥? ¥? ¥? ¥? ¥? 
 
 6. How many boys could each receive ^ of an apple 
 from i^ apples ? 2§ apples ? 3 apples ? 5^ apples ? 
 
 7. How many lots, each f of an acre, can be made of 
 3 acres ? 5 J acres ? 9^ acres ? 7^ acres ? 8 acres ? 
 
 Exercise 43. 
 
 1, What part of a dollar is 50c. ? 25c. ? 20c. ? lOc. ? 
 40c. ? 60c. ? 80c. ? 75c. ? 90c. ? 
 
 2. What fraction of a pound of tea, is 8 oz. ? 4 oz, ? 
 2 oz. ? 6oz. ? 12 oz. ? 7 oz. ? 9 oz. ? 
 
igsii»<l»*' iMiiii(iiiiiiiiiiiiiiii)<>iii»W(ii^^ 
 
 MBNTM. ARITHMETIC. 
 
 I I: 
 
 ,--.^:r«Sl 're^r/40s,.,as.. .OS. MS.. 
 5. What part of an ac ^^^ 
 
 l'fwVat'par2'of&«>>-'"'-'^'"'^- 
 1 ? 1 at -* I P^ ^ 
 
 1 How much of an apple >s left after i, 
 
 I Find the """^ej^Jfthlch 8 is the i 9 >« *e „ 
 
 «3Se"'''8""t1.7 . ,,<,r,tisS4'. S8? S.6? 
 7 How much money i .^ ^^^^ spenamg . 
 
 I''-^^-*- Exerc.se 45 „^„,„eh 
 
 1 ,f »(^ 4)ofmymoney.s$45W''«' 
 money have' I? ^ . „,,, ,6). Find the number. 
 
 "2. t «, I) f ^ Tf^l :Soli, and then had $..- 
 H^^muchhadheatfirstJ^^,^^^^^ , ,,,„ ,,d -5 
 
 ,tp^ X;-^ J:: P^t^^rs^ *>. and he then 
 
 % A mans flock in^^^^^Hiid [lie increase. ■ 
 
 then he had as (^^^^^^ , class, it » (^ i) a- ^^OV^ 
 
 7 How many pupils -^^ 
 and'24 are girls? 
 
VULGAR FRACTIONS. 
 
 23 
 
 Exercise 46. 
 
 •s? 18 
 o lbs. ? 
 :[. rds. ? 
 
 rds.]? 
 2 gal. ? 
 
 away I ? 
 
 17, 25- 
 
 >2, 13- ^ 
 .6, 24, 3»- 
 18, 24, 30- 
 
 1 is the Y> 
 
 $8? $16? 
 ling T of ^^' 
 
 I, how much 
 
 the number. 
 tienhad$i2. 
 
 then had 15 
 
 , and he then 
 
 : wages. 
 
 , a year, and 
 
 icrease. 
 
 ^^ I) are boys 
 
 1. Show that 
 
 1 =—^=1. 2. Show that 1^ =^^ = ^. 
 
 2x2 6-r2 
 
 3. 
 4. 
 5. 
 
 When is a fraction reduced to its lowest terms ? 
 Reduce f, ^, |, f, i^g, ^, ^§, to their lowest terms. 
 
 48' 
 
 Find other fractions equivalent to :— H, |^, f|, f^, 
 
 f i, V'^ =^'' 
 
 ii4» 1«-J' 
 
 6. Find the' lowest terms for if, |g, §f, fi §g, ff, ff . 
 
 7. From If (if, M) take ^% (|?, j^). 
 
 Exercise 47. 
 
 1. Reduce J to fourths, sixths, eighths, twelfths, six- 
 teenths, twenty-fourths. 
 
 2. Convert J to sixths, ninths, twelfths, twenty- 
 fourths, thirty-thirds. 
 
 3. Reduce ^ to equivalent fractions having 4, 6, 8, 12, 
 18, 24, and 36 for denominators. 
 
 4. Reduce ^ to equivalent fractions having 6, 9, 12, 
 15, 18, 24, and 36 for denominators. 
 
 5. f = ^ = T^ = TF = 2T = 3ff = n- 
 
 7. Give four pairs of fractions, each pair having the 
 same denominator, and equivalent to ^ and § (^ and f, 
 3 and I). 
 
 8. Reduce I and § to sixths, twelfths, and eighteenths ; 
 and I and f to twelfths, twenty-fourths, and thirty-sixths. 
 
 Exercise 48. 
 
 Reduce the following to equivalent fractions having a 
 common denominator : — 
 
 1 . ^ and ^. 
 
 2. ^and§. 
 
 3. § and \. 
 
 4. ^andf. 
 
 f and f . 
 I and f . 
 § and f . 
 f and /^. 
 
 i, i and I 
 
 
 and f . 
 
 -g, 4 ana f. 
 
 3 _ 
 
 4» 5 
 
 ^ and |. 
 
 5. I and f . 
 
 f and f . 
 
 4) 
 
 f and f . 
 
24 
 
 MKNTAI. ARITHMETIC. 
 
 Exercise 49. 
 
 Reduce the following to equivalent fractions having 
 the least common denominator : — 
 
 1. I and |. § and f. ^, § and f. 
 
 2. I and f f and |. hi and i 
 
 3. f and f . f and fg. |, f and f . 
 
 4. f and f f and H- i ^ and f . 
 
 5. f and f. f and 1|. f , | and ,%. 
 
 f and 11. 
 
 Exercise 50. 
 
 Compare these fractions as to value 
 
 1. I and f 
 
 2. § and f . 
 
 3. f and f . 
 4. 
 5. 
 
 I and f . 
 i and f 
 
 § and 
 f and 
 § and 
 f and 
 f and 
 
 .3 
 
 5* 
 
 3 
 J- 
 
 5 
 r- 
 
 B 
 7- 
 4 
 T 
 
 ^ and ^ 
 
 n 
 
 »• 
 
 f and f . 
 ? and i. 
 
 -3. 
 11 
 
 and w. 
 
 I and 4. 
 f and 
 I and 
 
 f and f . 
 
 f and 
 land 
 
 Exercise 51. 
 
 Arrange the following groups of fractions, in ascend- 
 ing order of magnitude : — 
 
 h h h and ^ 
 
 1. 
 
 2. I, I, 1 and }. 
 
 3- ^> 3^5 T» and f . 
 
 4. "(jj «> '8' and f . 
 
 O. 8' Ti» t's' and og* 
 
 i i h and f. 
 §, f , f , and f . 
 
 i ^ 3 nnrl 2 
 7» 5» 7» """ 9* 
 
 I I, §, and f . 
 
 7 J I)* 2' and f . 
 
 Exercise 52. 
 
 Arrange the following fractions, in descending order 
 of magnitude : — 
 
 1. }, J, }, and 1 
 
 2. I, I, f , and f . 
 
 3. |, I, g, and |. 
 
 4' fi> ^j 4» and f . 
 
 5 5 § -B_ nnrl 5 
 
 5» 
 
 8 
 1»> 
 
 3 
 
 3» 
 
 2_ 
 
 5» 
 
 4 
 
 tt» 
 
 3 
 
 2' 
 
 J) 3 
 lff» 4» 
 
 and \. 
 
 and §. 
 
 and ^. 
 
 and 
 
 11 
 
 12' 
 
 li, 1^, and 11 
 
having 
 
 § and ^. 
 i and I 
 f and |. 
 I and f . 
 I and ,\. 
 
 I and i 
 f and f . 
 f and f . 
 f and ^. 
 
 f and 
 
 in ascend- 
 
 mding order 
 
 n 
 
 T2' 
 
 
 VULGAR FRACTIONS. 
 
 25 
 
 
 • 
 
 Addition. 
 
 
 
 
 Exercise 53. 
 
 
 ( 
 
 Simplify :- 
 
 — 
 
 
 
 1. Hi- 
 
 Hf. Hl- 
 
 i+f- 
 
 ? +1£- 
 
 2. i + |. 
 
 §+f. Hit- 
 
 §+f. 
 
 f + |. 
 
 3. i+f 
 
 S+f. i+l- 
 
 f+l- 
 
 f + f- 
 
 4. Hi- 
 
 f+f- Hf 
 
 HH- 
 
 f + f 
 
 6. i+i- 
 
 f+f Hi- 
 
 f+iV 
 
 ^ +iJ- 
 
 6. Hf 
 
 Hf. HiV 
 
 Hi 
 
 f +11 
 
 7. Hh 
 
 f+f. i+i 
 
 i+A- 
 
 H+ i 
 
 Exercise 54. 
 
 1. A man hadf (f, §) of a dollar after spending f 
 ih I) o^ * dollar. How much had he at first ? 
 
 2. A man had § (^^, f ) of a ton of coal, and bought f 
 (|» i) of * to'^' fiow much had he then ? 
 
 3. A book cost $f ($J, $f), and was sold to* gain $} 
 {^h $f )• ^^"^ t^® selling price. 
 
 4. John spent $§ ($4, $f), and saved $| (S^^, $}f). 
 How much did he earn r 
 
 5. I sold a book for $^ ($f , $f), and lost $1 ($^, $f ). 
 Find the cost of the book. 
 
 6. I mixed f (^, ^) lbs. black tea, with f (f , f ) lbs. 
 green tea. How much was in the mixture ? 
 
 7. I paid $1 ($1, $W) for a hat, and $^ ($f , $|) for a 
 cane. Find the cost of both. 
 
 Exercise 55. 
 
 Find the value of: — 
 
 151 
 
 20' 
 
 1. IH+h 
 
 2. Hi+f- 
 
 3. Hl+I- 
 
 4. S+f+i 
 
 6. f+Hi- 
 
 6. f+Hi- 
 
 7. Hf +f 
 
 Hi+i 
 HHf. 
 f+Hf. 
 
 Hi+i 
 f+l+f 
 HHf- 
 
 HI +h 
 
 HI +1 
 
 HI +h 
 
 HI +f- 
 
 Hf +H- 
 
 f+l +A- 
 
 H^+i 
 
i; 
 
 f' 
 
 i . 
 
 26 
 
 MENTAL ARITHMETIC. 
 
 Exercise 56. 
 
 Wha^ is the value of : — 
 
 1. 
 
 li + ij. 
 
 3f + 2j. 
 
 8f + 6t. 
 
 3J+4^ 
 
 2. 
 
 a+ii. 
 
 3i + 3f. 
 
 sHsi- 
 
 5§ + 3i. 
 
 3. 
 
 I§ + 2}. 
 
 3f + 4f. 
 
 8H2i.. 
 
 6H2f 
 
 4. 
 
 2S + 2f. 
 
 2^31- 
 
 3t + 4f 
 
 3j+7i 
 
 6. 
 
 2§ + 2f. . 
 
 4t + 2i 
 
 5f + 4f- 
 
 it + 3f 
 
 6. 
 
 2f + 2|. 
 
 3.H21V 
 
 4f + 2l. 
 
 3f + 5^ 
 
 7. 
 
 3H2^ 
 
 .4f + 2i. 
 
 3f + 2|. 
 
 4l + il 
 
 Exercise 57> 
 
 1. A man mixed 2| (3J, if) gal. water \vith 5^ (8f, 6^) 
 gal. vinegar. How much was in the mixture ? 
 
 2. A grocer mixed 3f (3.I, 2|) lbs. chicory with 8^ 
 (9J, 9f) lbs. coflfee. How many lbs. were in the mixture ? 
 
 3. One field contains 8f (gf , 1 1|^) acres, and another 
 7f (i2§, 9I) acres. How much land do the two contain ? 
 
 4. I walked 3| (5 J, 6f) miles one day and 5I (6f , 3§) 
 miles the next. How far did I walk in the two days ? 
 
 5. A has $4f ($8|, $9|), and B has $6| ($4j9<j, $5^). 
 How much have the two ? 
 
 6. A cow cost $i6|($25§, $3o|), and a horse cost $28^ 
 ($35f. $456)' Find the cost of both. 
 
 Exercise 58. 
 
 1. I gained $ii ($2}, $3§), by selling an article that cost 
 $3| ($51, $6J). Find the selling price. 
 
 2. The cost of an article was $3f ($5}, $6|). The 
 gain was $1^ ($2^^, $if). Find the selling price. 
 
 3. James spends $if ($i|, $if) every day, and saves 
 $i| ($f» $3^)« Find his daily wages. 
 
 4. How much tea in a mixture of 3| (4I, 5f) lbs. 
 black tea, and 4^ (5^, 6f ) lbs. green tea ? 
 
 6. I owe John $35^ ($5f, $6§) after paying him 
 $5t ($9i, $8^). Find the original debt. 
 
 6. I paid $2^ ($if, $if) for a book, and $3f ($2|, $1^) 
 for paper. Find the cost of both. 
 
 
 If. 
 
VULGAR FRACTIONS. 
 
 27 
 
 3i + 7i 
 it + 3f 
 
 4 + ii 
 
 (8£, 6i) 
 
 with 8^ 
 lixture ? 
 another 
 :ontain ? 
 
 (6f , 3§) 
 lays ? 
 
 :ost $281 
 
 that cost 
 I). The 
 ind saves 
 • 5f) lbs. 
 ^ing him 
 
 ($2|, $lf) 
 
 , ' 
 
 
 Subtraction. 
 Exercise 59, 
 
 
 
 
 Find the value of : 
 
 — 
 
 
 
 
 1. i-h 
 
 s-^ 
 
 *-f 
 
 i- 
 
 ~f. 
 
 f-f 
 
 2. i-h 
 
 l-f. 
 
 1-?. 
 
 ^ 
 
 •|. 
 
 X-i 
 
 3. 4-i 
 
 f-^- 
 
 l-h 
 
 5- 
 
 -1- 
 
 i-l 
 
 4. i-f 
 
 i-l 
 
 f-f. 
 
 8 
 
 -f. • 
 
 f-t 
 
 5. i-1. 
 
 f-f 
 
 !-i 
 
 I- 
 8 
 
 "1. 
 
 f-^ 
 
 6. i-f 
 
 f-f. 
 
 i-^. 
 
 f- 
 
 -A- 
 
 2-1 
 
 7. l-h 
 
 f-^. 
 
 l-f. - 
 
 5 
 
 __4 
 11* 
 
 l-f 
 
 • 
 
 
 Exercise 60. 
 
 
 
 
 1. If § (f, f) of a number is 18, find the number. 
 
 2. If 4 (f, I) of a number is 6 (8, 5) more than § (^, g) 
 of it, what IS the number ? 
 
 3. If § (^, 1%) of my money is $10 ($5, $9) more than 
 ? (f » f ) of itj how much money have I ? 
 
 4. I spent ^ of my money for a hat, and f of it for a 
 coat. Find the cost of each, if one cost $1 more than 
 the other. 
 
 6. Find f (|, f) of my money, if § Q, |) of it is $8 
 ($11, $11) more than ^ (|, f ) of it. 
 
 0. Iff (f, §) doz. eggs cost 6 (9, 10) cents more than 
 1 (4, I) doz., find the cost of 2 doz. 
 "7. If ^ (§, f) of my money is $4 ($5, $7) more than 
 i (f » §) of it, how much have I ? 
 
 Exercise 61. 
 
 Simplify : — 
 
 1. 3|-2 
 
 2. 2f-I 
 
 3. 5^-3 
 
 4. 2f-2 
 
 5. 3I-2 
 
 6. 4|-2 
 
 7. 4-3 
 
 2-|. 
 
 8-i. 
 3-i. 
 
 2-§. 
 
 5-f. 
 6-i 
 
 2§-i 3I-2I-. 2i-l|. 
 
 ^3 _ 1 
 
 24 _« 
 '^S 5* 
 
 3^-f. 
 6J-5- 
 
 o3 — " 
 
 9b- ^- 
 
 2i. 
 
 4f 
 
 5^-3§. 
 
 3j-2i 
 
 5t-3f. 
 
 3|-2f. 
 
 6A-i\. 4t-3i. 
 
 3l - 2i. 
 5S-3f. 
 3|-2i 
 
 3i-2|. 
 
 3|-2f. 
 
 2i-ll 
 

 28 
 
 MENTAL ARITHMETIC. 
 
 Exercise 6a. 
 
 ($1, m 
 
 1. A man had $f ($§, $§) and spent $§ ($f, $^). How 
 much was left ? 
 
 2. I owned f (f, f) of a mill and sold § (f, f ) of it. 
 How much have I left ? 
 
 3. A boy earns $|, ($f, $,'^5) a day, and spends $| 
 How much does he save ? 
 
 4. John earns $^ ($^, $^?^) a day, and saves $| ($§, $f ). 
 How much does he spend ? 
 
 5. A man sold f (f , f) of his farm. How much less 
 than that had he left ? 
 
 6. What number added to ^% (|, f ) will make f (f , ?) .? 
 
 7. What number taken front § (f, |) will leave a 
 remainder of f (f , § )? 
 
 Exercise 63. 
 
 1. The sum of two numbers is 3^ (5!^, 6|). One of 
 them is if (2f, 3§). Find the other. 
 
 2. I had $3f ($6§, $7^) and spent $i£ ($2|, $3f). How 
 much have I left ? 
 
 3. How much wood can I sell out of 8| (9^, 11^) 
 cords, and have 2^ (3I, 8|) cords left ? 
 
 4. I bought 61 (7f, 8g) tons of coal, and now I have 
 only 3^ (4f, 3f) tons. How much have I used ? 
 
 6. I sold a watch for $5§ ($9|, $8|) and gained $2j 
 ($i|, $2^). Find the cost of the watch. 
 
 6. I sold a clock which cost $6§ ($5f, $7f) for $84 
 ($8f , $8f). Find the gain, or loss. 
 
 7. I earn $2^ ($3|, $5^) and spend $i| ($2g, $3^). 
 How much do I save ? 
 
 3. I earn $i4 ($3^, $3^) and save $ii ($2§, $2|). How 
 much do I spend ? 
 
 9. I spend $2f ($3^, $2f) a day, and save $2j 
 ($1^, $1^). How much do I earn in a working week ? 
 10. I bought a hat for $if ($if, $1^) and sold it to gain 
 H (Hy $f )• How much did 1 get for it ? 
 
VULGAR FRACTIONS. 
 
 29 
 
 Exercise 64. 
 
 1. Three men own a farm. One owns ]^ of it and 
 another owns f of it. Find the third man's share. 
 
 2. How much must be added to § and J to make 
 unity ? 
 
 3. A, B, and C can do a work in a day. A does f of 
 the work. B does ^ (J, ^) of it. How much does C do ? 
 
 4. A keg which would hold 9| gallons contains 4| 
 (sh 42) gilllons. How much water would fill it ? 
 
 5. A can do a work in 2 (3 4) days, and B in 3 (4, 5) 
 days. How much will the two do in a day ? 
 
 6. A can do a work in 3 (4, 6) days, and B in 4 (5, 9) 
 days. How much does A do in a day more than B ? 
 
 7. A can do a work in 3 (2, 3) days, and B in 5 (4, 4) 
 days. Find the share of each for doing the work 
 together for $15 ($6.40, $3.00). 
 
 Exercise 65. 
 
 1. After spending § (f, f) of my money, I have $12. 
 How much had I at first ? 
 
 2. Spending f (f , |) of my daily wages, I save 25 
 cents. How much do I earn in a week ? 
 
 3. After selling f (|, f) of my farm, I have 18 acres. 
 Find the value of the farm at $25 an acre. 
 
 4. A does I (t%, f ) of a work. B does J (f, §) of the 
 remainder. How much is left for C to do ? 
 
 6. I spent § (f , ^) of my money, and then f (f, f ) of 
 the remainder, and have 25 (75, 48) cents left. How 
 much had I at first ? 
 
 6. A can do a work in 2 (4, 5) days, and B in 3 (5, 6) 
 days. They do the work together. What part does 
 each do ? 
 
 7. A can do a work in 3 (2, 4) days, and B in 4 (3, 6) 
 days. How long will it take the two together? How 
 much does A do more than B ? 
 
il 
 
 30 
 
 MENTAL ARITHMETIC. 
 
 Simplify : — 
 
 1. 1^4- 
 
 2. ^XQ. 
 
 3. JX 12. 
 
 4. ^x 10. 
 6. jx 18. 
 6. JX27. 
 
 riultiplication. 
 
 Exercise 66. 
 
 Find the product of :- 
 |x6. 2^x4. 
 
 fx8. 1^x6. 
 
 fXI2. 2^X12. 
 
 fxi5. 3^x20. 
 
 |XI6. 2fX2I. 
 
 ^X36. 4fxi8. 
 
 Exercise 67. 
 
 Find the cost of - — 
 
 1. § lbs. nails @ 6c., 9c., or 15c. 
 
 2. f lbs. sugar @ 8c. loc, or 12c. 
 f lbs. starch @ loc. iic, or 12c. 
 ^ lbs. cheese @ 12c., 13c., or 15c. 
 ^ lbs. biscuits @ 12c., 14c., or 15c. 
 f lbs. tea @ 28c., 35c., or 50c. 
 
 Exercise 68. 
 
 Find the value of : — 
 
 1. 1} yards ribbons @ 4c., 6c., or 8c. 
 
 2. if yards elastic @ 6c., 7c., or loc. 
 
 3. 2I yards cotton @ loc, 12c., or 15c. 
 
 4. 3I yards flannel @ 20c., 24c., or 30c. 
 
 5. 3g yards silk @ 30c., 36c., or 40c. 
 
 6. 3I yards dress goods @ 45c., 50c., or 60c. 
 
 Exercise 69. 
 
 Find the value of : — 
 
 1. |xij. 
 
 2. fx2i. 
 
 3. 
 4. 
 5. 
 6. 
 
 3. 
 4. 
 6. 
 6. 
 
 7. 
 
 txi§. 
 fx3f. 
 
 iX2j. 
 
 fx4i. 
 
 |X2§. 
 
 51 
 
 xA 
 
 ^ 
 
 X 5- 
 
 3| 
 
 x^^ 
 
 2i 
 
 xf. 
 
 4^ 
 
 x|§ 
 
 2t 
 
 xf. 
 
 3f 
 
 xf. 
 
 2§ 
 
 XI^. 
 
 3^ 
 
 xii 
 
 2| 
 
 X2f. 
 
 2^ 
 
 xi|. 
 
 2f 
 
 X2f. 
 
 I| 
 
 Xlf 
 
 2| 
 
 XlJ. 
 
 fx^. 
 
 §xf. 
 
 fxf. 
 
 ix|. 
 
 ^ X a?. 
 
 fxVlj. 
 
 2^ 
 
 Xlf. 
 
 I^ 
 
 xsi- 
 
 I* 
 
 X3f. 
 
 2i 
 
 XI J. 
 
 2* 
 
 XIi*i 
 
 I* 
 
 X5i 
 
 If 
 
 xi/t 
 
VULGAR FRACTIONS. 
 
 31 
 
 10' 
 
 Exercise 70. 
 
 How much must I pay for : — 
 
 1. f yd. cotton @ 7^c. ? 5^c. ? 8^c. ? 
 
 2. i yd. print @ 5^c. ? 63c. ? 5Jc. ? 
 
 3. ^ yd. calico @ i2jc. ? 7^c. ? iijc. ? 
 
 4. I yd. ribbon @ 5^c. ? io§c. ? 4fe. ? 
 
 5. ^ yd. braid @ 3|c. ? 4k. .? 5fc. ? 
 
 6. I yd. lace @ S^c. ? lo^c. ? 5fc. ? 
 
 7. f yd. lining @ 4jc. ? 3gc. ? 4fc. ? 
 
 Exercise 71. 
 
 Find the value of the following fractions : — 
 
 1. ^of6. 
 
 iof§. 
 
 Jofii. 
 
 I* of 2§. 
 
 2. 1 of 12. 
 
 *ofi. 
 
 § of I^. 
 
 li of li 
 
 3. §of9. 
 
 ioff. 
 
 § of If. 
 
 2}ofl}. 
 
 4. f of8. 
 
 foff. 
 
 1 of 2i 
 
 4 of 3.1 
 
 6. ^ of 20. 
 
 fofU- 
 
 f Of If. 
 
 2§ of 3f . 
 
 6. iofi8. 
 
 lofM. 
 
 fof3i. 
 
 4| of 5^. 
 
 7. ? of 14. 
 
 fof^. 
 
 iVof3S. 
 
 5|of6f. 
 
 Exercise 72. 
 
 1. Rob had $f ($f, $|), and spent | (4, f) of his 
 money. How much did he soend ? How much had 
 he left? 
 
 2. A man had J (f , ^^g) of an acre of land, and sold 
 I (h t) of his lot. How much land had he left.? 
 
 3. A man earns $i| ^$2'^, $3f) a day, and spesnds 
 i (f » t) of it. How much does he save in a week ? 
 
 4. I owned f (f , f) of a mill, and sold § (f , f) of my 
 share for $900. Find the value of the mill. 
 
 5. I owned f (^, f ) of a farm. I sold ^ (J, f ) of my 
 share for $600. Find value of my former share. 
 
 6. I owned f (^, ^\) of a boat, and sold £ (i, §) of my 
 share for $120. Find value of my present share. 
 
 7. I owned f (|, f ) of a farm, and sold | (j|, ^) of my 
 share for $8,400. Find value of the farm. 
 
32 
 
 MENTAL ARITHMETIC. 
 
 
 Division. 
 
 
 
 Exercise 
 
 73. 
 
 
 Simplify :— 
 
 
 
 
 1. 2-r3. 
 
 3T-2. 
 
 J^2. 
 
 lS-f2. 
 
 2. 4-^5- 
 
 f-3. 
 
 J-2. 
 
 3)1^2. 
 
 3. 5-7-7. 
 
 «^3. 
 
 ii-3. 
 
 2i-^5- 
 
 4. 8-r9. 
 
 Hs- 
 
 1-3. 
 
 3i-^5. 
 
 6. 6-:-ii. 
 
 f-^4. 
 
 K4. 
 
 2S-4. 
 
 6. 5-5-9. 
 
 H-6. 
 
 Ji-8. 
 
 3f-5. 
 
 7. 8-rl7. 
 
 il-9. 
 
 H9. 
 
 6^4. 
 
 Exercise 74. 
 
 1 . Two hens cost $^. Find the cost of i (3, 8) hens. 
 
 2. Three geese cost $i%' ($A, $t|). Find the cost of 
 I (4, 7) geese. 
 
 3. Divide ^ (f, }^) of an orange among three boys. 
 
 4. Four men do ^ (f, If) of r work in a day. How 
 much will I (2, 3) men do in a day ? 
 
 6. Eight men can do J (f » f ) of a work in a day. 
 How much will a man do in i (3, 4, 5, 7) days ? 
 
 6. I can walk | (^f, I) of a mile in 10 minutes. Find 
 the rate per hour. 
 
 7. Four men owned | (^^, ^^) of a farm worth $6,000. 
 Find the value of each man s share. 
 
 Exercise 75. 
 
 Find the value of : — 
 
 1. Hi 
 
 2. ^^ 
 
 7. If-t 
 
 K4 
 
 f-3l 
 
 f-2t 
 A-2} 
 
 A-2§ 
 
 3f-f 
 2Kf 
 
 4?z 
 6§ 
 
 I 
 
 
 3j-ii 
 7i-:-2j 
 9-^21 
 
 6H1I 
 2i-5^ 
 
VULGAR FRACTIONS. 
 
 33 
 
 Ij-r2, 
 3K2 
 
 3i-J-5 
 3f-5 
 
 6S-r4. 
 
 5) hens. 
 I cost of 
 
 je boys. 
 How 
 
 n a day. 
 
 ). Find 
 
 I $6,OOQ. 
 
 3l-'l 
 7i-:-2j 
 
 72-^12^ 
 
 Exercise 76. 
 
 Simplify these complex fractions : — 
 
 In what other way could they be expressed ? 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 M 
 
 i? 
 
 if 
 
 B 
 
 M 
 
 10^ 
 
 7i 
 
 bi 
 
 5i 
 
 3^ 
 
 M 
 
 M 
 
 M 
 
 fl 
 
 IS 
 
 i. 
 
 IS 
 
 f^ 
 
 6 
 
 8 
 
 9 
 
 7 
 
 5 
 
 12 
 
 15 
 
 i 
 
 1 
 
 ^ 
 
 i 
 
 f 
 
 f 
 
 U 
 
 f 
 
 ft 
 
 f 
 
 n 
 
 1 
 
 A 
 
 A 
 
 4 
 
 10 
 
 4 
 
 15 
 
 14 
 
 27 
 
 24 
 
 8 
 
 6 
 
 8 
 
 9 
 
 7 
 
 12 
 
 16 
 
 i^ 
 
 2i 
 
 3^ 
 
 2i 
 
 i^ 
 
 2^ 
 
 sh 
 
 3t 
 
 4:4 
 
 6.^ 
 
 2} 
 
 4! 
 
 4i 
 
 6} 
 
 18 
 
 14 
 
 38 
 
 6 
 
 38 
 
 28 
 
 36 
 
 .5^ 
 
 6f 
 
 6^ 
 
 n 
 
 6-^ 
 
 JJ 
 
 2tV 
 
 4? 
 
 4^ 
 
 3j 
 
 6? 
 
 5i 
 
 4^ 
 
 3f 
 
 2i 
 
 Si 
 
 7^i 
 
 8 
 
 Exercise 77. 
 
 1. A man owed $J ($f, $}J) and paid $| ($J, $i). 
 What fraction of the debt did he pay ? 
 
 2. A man had $24 ($29, $43), and spent $2^ ($5^, $5|). 
 What fraction of his money did he spend ? 
 
 3. A man has to walk 28 (39, 51) miles. What part 
 of the distance is over, when he has walked 5 j (8|, 6^) 
 miles ? 
 
 4. How many bags, each containing 7 J (8f, 5|) lbs., 
 will weigh 29 (3?, 35) lbs. ? 
 
 . 6. I had $45 ($65, $20) and spent %2\ ($6J, 6|). What 
 fraction of my money have I saved ? 
 
 6. ^ A has $7i ($7i, $5|). B has $8| ($8f , $9^). What 
 fraction of B's money is A's ? 
 
 7. I owed $26 ($44, $60), and paid $5^ ($9f, $6?). 
 What part of the debt remains unpaid ? 
 
34 
 
 MKNTAL ARITHMKTIC. 
 
 Exercise 78. 
 
 1. If a pound of tea costs $ij ($g, $4), how much 
 could you get for $35 ($2i'<j, $2§) ? 
 
 2. How much wheat can you buy for $5.} if the price 
 be$|($iV $§) a bushel? 
 
 3. How many lots each containing f of an acre can 
 be made from 3I (5^, 6§) acres ? 
 
 4. The product of two numbers is ]|f (|, g). One is 
 I J (i§> 2§). Find the other. 
 
 6. What fraction divided by | (^, 2) will give a quo- 
 tient of H^, *) ? 
 
 0- If f ih I) of a cord of wood cost $4^ ($65, $6§) 
 find the cost of a cord. 
 
 7. How many books at $2.25 ($.66§, $.87^) can be 
 bought for $36 ($24, $49) ? 
 
 Exercise 79. 
 
 1. Divide ^ (f, f ) into two equal parts. 
 
 2. Divide $4} ($2|, $32) into two equal shares. 
 
 3. Divide f (f, ^) into two parts, one being ^ (], ^) 
 more than the other. 
 
 4. Divide $3^ ($4}» $6§) between two men, giving one 
 $2 ($1, $1) more than the other. 
 
 6. A man earns $3| ($2f, $3}) a day, and he spends 
 $f a day more than he saves. How much does he save 
 in a day ? How much does he spend in a week ? 
 
 6. A man owns 7^ (8.^, 9 J) acres, and he sells 2 J 
 (23:, 3j) acres more than he keeps. How many acres 
 does he keep ? How many does he sell ? , 
 
 Exercise 8o. 
 
 1. From the sum of | and § (§ and f) take their 
 difiFerence. 
 
 2. To the sum of § and f (2 and f) add their difference. 
 
VULGAR FRACTIONS. 
 
 35 
 
 V 
 
 much 
 he price 
 acre can 
 
 One is 
 e a quo- 
 :$63. $6'd) 
 I) can be 
 
 'es« 
 
 ng h ih i) 
 
 giving one 
 
 he spends 
 )es he save 
 ek? 
 
 he sells 2| 
 nany acres 
 
 I take their 
 r difference. 
 
 3. From the sum of irj and 3[ (2.} and 3-^), take their 
 difference. 
 
 4. To the sum of 3 J and 2?j (5 J and 2j|), add their 
 difference. 
 
 5. A has $32 ($33, $5l), and li has $^ ($2, $1.5) less. 
 How much have both ? 
 
 6. A has $2)1 ($32, $5j), and li has $2 ($2, $^) more. 
 How much have both ? 
 
 Exercise 81. 
 
 What is the value of: — 
 
 1 ^^? ^? ^? III^?:? 4 days p 
 $4 ^5 ;^'o 6 gals. 3 days 
 $i£p 2^4? 35 wks. p 36 ft. p 39 lbs, p 45_g«i}^? 
 
 8 
 
 13 
 
 $5 p 2 dys. p 3 bush, p 8 yds. p 5^ p 
 
 50c. I2hrs. 2 pks. 2 ft. 6d 
 
 3 yds., 2 ft. p7J-. 6(i. p 8a., i2osq. rds.p 12 lbs. 8 oz. p 
 
 4 ft. 
 
 2y., ^. 2a., 30 sq. rds.' 2 lbs., 8 
 
 oz. 
 
 17 gals, p 16 doz. p /4f p 6g//. p $28 p 
 4]: gals. 3.5 floz- .^^^ 2o^« $5t 
 
 Exercise 83. 
 
 Find, in lower denominations, the value of : — 
 
 1. f of a yd. 
 
 2. I of a bush. 
 
 3. f of a fath. 
 
 4. f of a mile. 
 
 5. f of a gal. 
 
 6. ^ of an acre. 
 7- f of a wk. 
 
 § of a ton. 
 f of a cwt. 
 I of a gal. 
 § of a bush. 
 
 ^ of a yd. 
 
 J of 2^. , 6d. 
 
 § of 2 gal., I qt. 
 
 f of ;^I. 125. 
 
 f of I ton, 1 5 cwt. 
 f of 2 lbs., 4 oz. 
 f of 2 wks., 4 da. 
 
 I of a league. i ^^ 2 yrs., 4 ms. 
 
36 
 
 MENTAL ARITHMETIC. 
 
 Exercise 83. 
 
 / ii 
 
 Find the G.C.M. of:— 
 
 1. ^ and I. § and 
 
 2. J and ^. f and 
 
 3. i and }. f and 
 
 4. ^ and I. f and 
 6. ^ and ^V* tIj 
 6. i and tV- i^ 
 
 Find the L.C.M. of 
 
 1. i and ^. f and 
 
 2. ^ and J. f and 
 
 3. } and J. 
 
 4. % and 
 
 i 
 
 am 
 
 5. f and f , ^^ 
 
 6. f and ^. ^^ an 
 
 Simplify : — 
 
 1. a+^)+a^i)+(i 
 
 2. a-j)+a-i)+(i 
 
 3. a-i)+(i-i)-a 
 
 4. (§-})-(f-i)+(f 
 
 6. (l^-lJ)-(2§-2j) 
 
 0. (3f + 2§)-(i§+-2) 
 
 Simplify : — 
 
 1. §~foff + fofiV 
 
 2. fxf + fx-^l-fxH. 
 
 3. fof^xf of^fxfof,^,. 
 
 4. fofT^^fof^xfoff. 
 
 6. f+f-f-|xHi. 
 
 If. 
 
 2| and 3|. 
 
 4^ and 6. 
 
 if 
 
 3! and 6f . 
 
 7^ and 10. 
 
 i^- 
 
 6J and 7^. 
 
 6| and 9. 
 
 IH- 
 
 6f and 4J. 
 
 8f and 7. 
 
 id 2V 
 
 8f and 3f . 
 
 5f and 10. 
 
 Id If. 
 
 3f and St 
 
 3I and 9. 
 
 Exercise 84. 
 
 f- 
 
 
 L • 
 
 2} and 3|. 
 
 4f and 6. 
 
 lA- 
 
 3| and 4^. 
 
 3^ and 5. 
 
 iio. 
 
 33 and 8J. 
 
 3l and 5. 
 
 IdM. 
 
 41^ and si 
 
 5| and 7. 
 
 idM. 
 
 5i and 6|. 
 
 3i a d 8. 
 
 Exerc 
 
 i| and 2^V. 
 ise 85. 
 
 4| and 10. 
 
 +i)- 
 
 (§+f)+(i+.l)+(§+f). 
 
 -i). 
 
 (!-§)+(§- 
 
 ■i)+(!-^). 
 
 -i). 
 
 (i-f)+(f- 
 
 -§)-(!-§). 
 
 -1). 
 
 a+f)+(^ 
 
 -§)-(f+t). 
 
 )+(!- 
 
 l).(f-f)-(f- 
 
 -f)+(J+f). 
 
 -(2i4 
 
 ■i).a+T'^)-(f 
 
 -i%)-(Kf). 
 
 Exercise 86. 
 
 
 foff + fof^-^ofjl 
 f-|ofixK§ofiJ. 
 
 ?-^lJXlJ-fXi4^~-lJ. 
 
 a +f) (I -!)-(§ Of i). 
 
 (f-f)(fxi)^(Hi). 
 
VULGAR FRACTIONS. 
 
 37 
 
 Exercise 87. 
 
 1. Find the sum of the proper fractions with one 
 figure in each term which can be written with the first 
 three digits. 
 
 2. How can you show, by inspection, whether a num- 
 ber is exactly divisible by 2 ? 4? 8? 3.? 6.?9?5? 10? 
 25? 50? 100? 
 
 3. Find the number whose half - 2= its third +7. 
 
 4. Find the product and the two quotients of f and f . 
 6. What length of wire will be required to make a 
 
 5-strand wire fence around a field f mile x f miles ? 
 
 6. Of what two numbers is 18 (24, 30) the LC.M. ? 
 
 7. The bells of a chime strike each second, two 
 seconds, three seconds, and four seconds, respectively. 
 How often will they strike together each minute ? 
 
 8. Find the square root of : — 
 
 (0 T> »> 5 5> lV» 35» 49> T5T» 6 4> jhxS' 
 
 (3) 2}, 15, iiV 2i, 3rV»6J, i2i, 32%, iij. 
 Exercise 88. 
 
 1. How many books at 6 J (8 J, 1 1|) cents will cost $5 ? 
 
 2. Simplify 3ix5| + 2§x 5^ + 51x3,12. 
 
 3. How many boxes 4|" x 3^" x 5|" will hold as much 
 as 60 boxes 2 J" x 2^" x i|"? 
 
 4. Divide $35 ($85, $108) between A and B so that 
 I (f , ^) of A's share =1 (§, f) of B's share. 
 
 6. The sum of two numbers is f (2J, 3j) and their 
 difference is ^ (f , §). Find the numbers. 
 
 6. Minuend f(f). Subtrahend |(^). Find difference. 
 
 7. Subtrahend ^ (|). Difference §(|). Find minuend. 
 
 8. Dividend f (I, f). Quotient f (f, if). Find divisor. 
 
 9. Quotient I (§, 2^). Divisor f (J, f). Find dividend. 
 10. Product 1(1). Multiplier § (I). Find multiplicand. 
 
.-„.T-*«- 
 
 38 
 
 MENTAL ARITHMETIC. 
 
 t-J. 
 
 a 
 
 Exercise 89. 
 
 1. How is a vulgar fraction written, or expressed ? 
 
 2. Name the terms of a fraction. Give the function 
 of each. 
 
 3. When is a vulgar fraction greater than unity? 
 Why is an improper fraction so named ? 
 
 4. How could you compare two or more fractions ? 
 
 6. How do you reduce a fraction to its lowest terms ? 
 State the theorem on which this depends. 
 
 6. Give the steps necessary to find the sum (i) of two 
 fractions, (2) of two mixed numbers . 
 
 7. How may a fraction be (i) multiplied ? (2) divided ? 
 
 8. Prove that ^ of 2 = | of i ; | = | ; and A o{^ = }. 
 
 9. Prove that the value of a fraction is not altered by 
 multiplying or dividing its terms by the same number. 
 
 10. What efifect does adding, or subtracting, the same 
 number from both terms of a fraction have upon the 
 value of the fraction ? 
 
 11. Show that multiplying the numerator of a fraction 
 multiplies the value of the fraction, and multiplying the 
 denominator divides its value. 
 
 12. Show that the value of a fraction is decreased or 
 increased as you divide the numerator or multiply the 
 denominator. 
 
 13. Supply denominators : — |=:fi = fl=:il=:2i=M=:Afl. 
 
 14. Supply numerators :— 1 = 5 = ^^ = ^=^=3= y^=^^. 
 
 15. By inspection, arrange in order of magnitude : — 
 
 2> ¥> T» 1 5» 3» l8» ^0» 58» 2¥> 17> 19» uV* 
 f» f» f> 10> l%f 1%» 'J^» ^V tiy T»> bV» 1^* 
 
 h h h Ih h U- iV ii U. if, Ih Fa- 
 
 !»» Tr» 13> a^) TT» 2 1» f.Jf 33* 
 
 T» 9» 6r 19> 
 
 16. Show that additions and cdbtractions, or multipli- 
 cations and divisions, may be made in any order. 
 
 17. How do you find the G.C.M. and the L.C.M. of 
 two or more fractions ? 
 
DECIMAL FRACTIONS. 
 
 id? 
 unction 
 
 unity ? 
 
 3ns? 
 terms ? 
 
 ) of two 
 
 iivided ? 
 
 tercd by 
 mber. 
 
 he same 
 ipon the 
 
 I fraction 
 lying the 
 
 reased or 
 Itiply the 
 
 tude : — 
 
 r multipli- 
 er. 
 L.C.M. of 
 
 A Decimal Fraction is one whose denominator is merely 
 indicated, and is lo, or a power of lo. It is generally called a 
 decimal. 
 
 The decimal point, by its position, indicates the denom- 
 inator of the fraction. 
 
 A Pure decimal is one that is made up of decimal figures 
 opW ; as .4, .48. 
 
 A Mixed decimal is one that is made up of a whole num- 
 ber and a decimal ; as 4.3, 2.47. 
 
 A Complex decimal is one that has a vulgar fraction to 
 the right of the decimal ; as .3^, .5J. 
 
 There are two kinds of decimal fractions: — 
 
 Terminating decimals, and Circulating decimals. 
 
 Terminating decimals are those whose division is 
 complete. 
 
 Circulating, Repeating, Recurring, or Interminate 
 decimals are those whose division cannot be completed. 
 
 A Pure Circulating decimal is one in which all the 
 figures of the decimal part repeat. 
 
 A Mixed Circulating decimal is one in which some of the 
 figures of the decimal part do not repeat. 
 
 The Repetend is that part of the decimal fraction which 
 repeats. 
 
 Numeration and Notation. 
 Exercise 9o. 
 
 1. Show the relation of 100 to ro, of 200 to 20, of 
 400 to 40, of 700 to 70, of 900 to 90. 
 
 2. Show the relation of 10 to i, of 20 to 2, of 40 to 4, 
 of 70 to 7, of 90 to 9. 
 
 3. Show the relation of i to .1, of 2 to .2, of 4 to .4, 
 of 7 to .7, of 9 to .9. 
 
 4. Show the relation of .1 to .ot, of .2 to .02, of 
 .4 to .04, of .7 to decimal .07. 
 
 39 
 
•w • i| ' 
 
 I i' 
 
 40 
 
 MENTAL ARITHMETIC. 
 
 6. Compare the value of each of the figures of 1 1. 11 to 
 th6 others. 
 
 6. Show the relation of the figures of 555.55 to each 
 other. 
 
 7. Show the relation of the figures of 777.77 to each 
 other. 
 
 Exercise 91. 
 
 1. An apple is divided into ten equal parts. What is 
 one part called } two parts .? four parts } seven parts ? 
 
 Write these fractions in two ways. 
 
 2. Interpret:—.! apple, .2 pear, .3 pie, .5 dollar, 
 .7 loaf, .8 quart, .9 gallon. 
 
 3. Read, and interpret : — . r, .2, .4, .6, .3, .9, .5, .8, .7. 
 
 4. Read, and interpret: — .40, .50, .70, .83, .25, .67. 
 
 5. How could you change tenths to hundredths } 
 How many hundredths are in .1 ? .2? .3.? .5? 
 
 .2= = ; .4= = ; .7= = . 
 Show that .3 = . 30; .5 = . 50; .7 = . 70; .9=. 90. 
 
 7. How could you change hundredths to thousandths ? 
 How many thousandths are in '24 ? '37 ? '45 ? 
 
 Exercise 9a. 
 
 Read the following decimal fractions : — 
 
 Write them in words. 
 
 Pupils will write decimally as the teacher dictates. 
 
 1. 
 
 .1 
 
 .23 
 
 .124 
 
 .3546 
 
 .47683 
 
 •30765 
 
 2. 
 
 .4 
 
 •44 
 
 .303 
 
 .0367 
 
 .50047 
 
 .81207 
 
 3. 
 
 .6 
 
 •35 
 
 .548 
 
 .2059 
 
 .98035 
 
 ,60509 
 
 4. 
 
 .7 
 
 •97 
 
 .082 
 
 .6004 
 
 .67309 
 
 .49032 
 
 6. 
 
 •3 
 
 .62 
 
 .865 
 
 .0083 
 
 .03452 
 
 .02345 
 
 6. 
 
 .8 
 
 .86 
 
 .297 
 
 .0796 
 
 .00908 
 
 70086 
 
 7. 
 
 •9 
 
 •59 
 
 .006 
 
 .0005 
 
 .36004 
 
 53094 
 
DECIMAL FRACTIONS. 
 
 41 
 
 ri.ii to 
 to each 
 to each 
 
 ^hat is 
 1 parts ? 
 
 dollar, 
 
 5> -^j •7' 
 .25, .67. 
 
 hs? 
 
 ? .5? 
 
 )=.9o. 
 sandths ? 
 ? -45? 
 
 tates. 
 .30765 
 .81207 
 .60509 
 .49032 
 
 .02345 
 .70086 
 
 .53094 
 
 Exercise 93. 
 
 Express decimally : — 
 
 1. One tenth, three tenths, five tenths, eight tenths, 
 twelve tenths, twent]^-five tenths. 
 
 2. Seven hundredths, two hundredths, nine hun- 
 dredths, twenty-four hundredths, thirty-eight hundredths, 
 forty-seven hundredths, ninety-six hundredths. 
 
 . 3. Five thousandths, eight thousandths, four thous- 
 andths, sixteen thousandths, fifty-eight thousandths, 
 eighty-five thousandths, seventy-two thousandths, three 
 hundred and sixty- one thousandths, four hundred and 
 three thousandths, five hundred and seventy-nine 
 thousandths. 
 
 4. Eight ten-thousandths, twelve ten-thousandths, one 
 hundred and nine ten-thousandths, seven thousand and 
 ninety-four ten-thousandths, nine hundred and three 
 ten-thousands. 
 
 5. Eleven hundred-thousandths, six millionths, twenty- 
 one ten-millionths, three hundred and four millionths, 
 seven thousand and six millionths. 
 
 0. Va, r% 1% A. \h 1B» M, fa, f8, fl ?^. 
 
 7' A^» nf(y» iVuy iM» iM> foff» tSuj t8tj, i5u» 1^0, v^w 
 
 8JL56 _2 8B 2 8 34 K S Sfiifi UiSJljS 
 
 • I00ff» 100U> TSITU, TUOUj TUIRT, T50U» tUtitJ* lOUb- 
 
 Exercise 94. 
 
 Read the following mixed decimals : — 
 Write the following decimals in words : — 
 Pupils, write decimally as the teacher dictates. 
 
 1. 
 
 2.3 
 
 35-46 
 
 345-687 
 
 3.004 
 
 63.4708 
 
 2. 
 
 4.7 
 
 9-35 
 
 58.076 
 
 53-07 
 
 9.0305 
 
 3. 
 
 9.6 
 
 20.08 
 
 526.35 
 
 6.3 
 
 70.9006 
 
 4. 
 
 7.8 
 
 48.62 
 
 603.009 
 
 80.045 
 
 837.326 
 
 5. 
 
 3.5 
 
 63-7 
 
 700.562 
 
 204.09 
 
 300.04 
 
 6. 
 
 5-9 
 
 87.54 
 
 860.045 
 
 .008 
 
 42.8507 
 
 7. 
 
 8.2 
 
 12.91 
 
 497.803 
 
 126. 
 
 301.0001 
 
42 
 
 MENTAL ARITHMETIC. 
 
 Exercise 95. 
 
 Express as decimals : — 
 
 1. Three and five tenths, seven and one tenth, twelve 
 and nine tenths, sixteen and twenty-nine hundredths. 
 
 2. Seven and four hundredths, nine and forty seven 
 thousandths, forty and five hundred and ninety-eight 
 thousandths. 
 
 3. Twenty four and thirty-seven hundredths, forty- 
 seven and twenty-nine thousandths ; one hundred and 
 eight and three hundred and twenty-five thousandths. 
 
 4. Two thousand «nd three, and seven ten thous- 
 andths ; four, and eight hundred-thousandths ; five hun- 
 dred, and nineteen millionths ; forty-five, and sixty- 
 seven millionths ; seven hundred, and four ten-thous- 
 andths ; nine thousand and fourteen hundred-thous- 
 andths. 
 
 5- 6t^» 9tV' i2i%, 20^0:, ss^oy 4081^, 6oaj^. 
 Q' 5 tIjV 8tV(j> i^Tao» 37tuu> 55toou» ^^rtfuo- 
 7. 7T8oiy> 4t(:Po%u> ^7T«j^tnj» 3o7r§BSD» ^TUifeoiF- 
 
 Exercise 96. 
 
 The value of a figure in decimal notation depends on 
 its position in the number. Show this. 
 
 Read each figure in the following numbers : — 
 
 Read each two consecutive figures : — 
 
 Read any three consecutive figures : — 
 
 Read the three numbers : — 
 
 Express them in words, paying attention to the spell- 
 ing, punctuation, hyphens and periods. 
 
 463.897.125.579,286,714 325.546.897.638,454.789 
 309.620,087.045.403.078 403.024.710.505,860,076 
 500,064,000.379,000,308 500,030,004.730,064,080 
 
DECIMAL FRACTIONS. 
 
 43 
 
 Exercise 97. 
 
 Read the following decimal fractions : — 
 Show how each differs from the preceding fraction. 
 How is each obtained from its predecessor ? 
 Express decimally as the teacher dictates. 
 
 1- 350. 35. 3-5. .35, •035» -0035. •o35» •35» 3-5- 
 
 2. 47, 4-7» •47» .047, .0047, .47, 4-7, 47o. 
 
 3. 45, 450. 4-5» -045. 00045, -45. 450- 
 
 4. 475. 4.75. 47.5, 4750. 4.75. -0475. 47-5. 475o- 
 
 5. 3.08, 30.8, .308, 308, 3.08, .0308, .00308, 3.08. 
 
 Exercise 98. 
 
 Write the successive answers in a column. 
 
 Read each answer. 
 
 How does each compare with the other ? 
 
 1. 3708 X 10 X 10 X i6-j- 10-7- lo-rio-i- 10-7- lo-i- 100. 
 
 2. 5036~-I0-M0^I0X lOO-rlO-i-IOO-rlO. 
 
 3. 50.69X lO-r lOOX lOX lOX lOX lO-r lOOO-v-IOO. 
 
 4. 400.2 X loo-riooo-Mooox io,ooox 1 00 -j-i, 000, 000. 
 
 S- 7'345X 10 X IOO-7-IO-rIOOX lOOO-rlOOX lOOO-rlOOOO. 
 
 Exercise 99. 
 
 Express as vulgar fractions in their lowest terms : — 
 
 1. .1 
 
 .25 
 
 .125 
 
 .0625 
 
 .03125 
 
 .064 
 
 2. .3 
 
 •75 
 
 •375 
 
 .1875 
 
 •09375 
 
 .032 
 
 3. .4 
 
 •45 
 
 .625 
 
 •3125 
 
 .15625 
 
 .096 
 
 4. .6 
 
 .35 
 
 •875 
 
 .4375 
 
 •34375 
 
 .048 
 
 6. .5 
 
 .65 
 
 .128 
 
 .5625 
 
 .46875 
 
 .024 
 
 6. .8 
 
 .85 
 
 .256 
 
 .6875 
 
 .21875 
 
 .072 
 
 7. .7 
 
 •95 
 
 .512 
 
 .8125 
 
 .28125 
 
 .144 
 
 What vulgar fractions are equivalent to : — 
 
 .256, .128, .064, .192, .384, .096, .048, .024, .012, 
 
 .036, .084, .108, .216, .072, .288, .576, 
 .048, .24, .08, .04, .004.? 
 
 192, .096, .96, 
 
44 
 
 MENTAL ARITHMETIC. 
 
 1. 
 
 4 + . 3 
 
 2. 
 
 • 5 + . 6 
 
 3. 
 
 .8 + .7 
 
 4. 
 
 .3 + .9 
 
 6. 
 
 •9 + -4 
 
 6. 
 
 • 7 + . 8 
 
 7. 
 
 .6 + . 4 
 
 1. 
 
 Find t 
 
 Addition. 
 
 Exercise lOO. 
 
 Read the following questions : — 
 Give the answers at sight. 
 
 $.3 + $-4 
 $.5 + $.2 
 
 $.7 + $.6 
 
 $.9 + $-3 
 $.8 + $.5 
 
 $.6 + $.9 
 
 $.4"l"$«8 
 
 Exercise 
 
 amount of : — 
 .4 + .3 + .8+.6 + .94-.2 + .5 
 
 .6 + .4 + .9 + .3 + -8 + .5 + .7 
 .7 + .2+.8 + .5 + .4 + .9 + .3 
 
 2. Find the sum of : — 
 
 .23, .24, .25, .53, .62, .27 and .32 
 
 .35, .47, .84, .63, .72, .56 and .98 
 
 68, .34, .73, .26, .95, .42 and .57 
 
 3. Find the aggregate of : — 
 
 .824, .213, .342, .657, .448, .576 and 
 .487, .568, .359, .625, .834, .293 and 
 .329, .248, .765, .856, .935, .674 and 
 
 4. Find the amount or total of: — 
 6.37 + 2.45+3.39-1-5.64 
 
 3.09 + 3.54 + 2.3 + 3.67 
 5.48 + 3 + 3.04 + 6.7 + .345 
 
 5. Find the sum of : — 
 
 3. 245 + 1 .cxx)8 + 3.04 + .0025 + 3.403 
 2.326 + 32.24 + 25.009 + 304.405 
 3.0256 + 2.3004 + 5.0045 + .3045 
 
 .32 + .45 
 
 $2. 3 + $4. 5 
 
 .64 + . 34 
 
 $4.6 + $3. 2 
 
 .75 + -23 
 
 $5.2 + $6.8 
 
 .83 + . 15 
 
 $3.8 + 15.6 
 
 .48 + . 21 
 
 $6. 5 + $2.3 
 
 .27 + . 42 
 
 $7- 9 + $9- 8 
 
 .19 + . 6 
 
 $8.4 + $7.9 
 
 lOI. 
 
 
 ■384 
 
 .946 
 
 583 
 
DECIMAI, 1'RACTIONS. 
 
 45 
 
 
 
 
 
 Subtractionv. 
 
 
 
 
 
 
 
 Exercise loa. 
 
 
 
 1. 
 
 •3- 
 
 .2 
 
 $1.3- 
 
 -$.4 
 
 $3.4 -$2.9 
 
 $4.37- 
 
 -$2.57 
 
 2. 
 
 •4- 
 
 .2 
 
 $2.4- 
 
 -$.5 
 
 $5.6 -$3.8 
 
 $6.25- 
 
 -$3.75 
 
 8. 
 
 .6- 
 
 4 
 
 $3-5- 
 
 -$.8 
 
 $2.3-$!. 4 
 
 $7-43- 
 
 -$5-63 
 
 4. 
 
 •9- 
 
 •5 
 
 $1.6- 
 
 -$.7 
 
 $6.1 +$5.6 
 
 $3.92- 
 
 -$1.82 
 
 6. 
 
 •5- 
 
 ■3 
 
 $2.3- 
 
 -$.6 
 
 $4- 5 -$3. 7 
 
 $9.68 - 
 
 -$6.54 
 
 6. 
 
 .8- 
 
 .6 
 
 $4.7- 
 
 -$.9 
 
 $9. 2 -$4. 5 
 
 $5-74- 
 
 -$2.37 
 
 7. 
 
 •7- 
 
 •4 
 
 $3.2- 
 
 -$.3 
 
 $7.8 -$3.9 
 
 $8.56- 
 
 -$4.28 
 
 
 
 
 
 Exercise 103. 
 
 
 
 1. A boy had $3,4, and paid $1.6 ($2.3, $2.8) for a hat. 
 How much had he left ? 
 
 2. A man who had 9.63 acres of land sold 4.05 
 (2.78, 3.005) acres. How much had he left ? 
 
 3. Find the difference between .8 and .65, .45 and 
 .325, .48 and .279, 3.4 and 1.347, 2.004 and 1.568. 
 
 4. From 6.3876 take 2.3063 (1.4238, 1.5284). 
 
 6. Find the remainder after taking : — 
 
 .8 from 1.4, 2.6, 3.5, 2.9, 3.7, 4.3 and 6. 
 
 .46 from 3.58, 2.79, 3.82, 4.29, 3.24, 3.05 and 6.4. 
 
 .537 from 2.638, 3.205, 1.742, .836, .82, .9 and 6. 
 
 6. How much does 4.83 exceed 2.54 2.487? and 
 1.00834? 
 
 7. Fill the blanks in the following : — 
 
 Minuend 3.56 6.09 $3,067 $5,203 
 
 Subtrahend 1.49 .... 3.86 5.037 $1,549 
 
 Difference .... 2.35 2.54 3.325 ...... $2,565 
 
 Exercise 104. 
 
 1. What decimal added to .4, .35 or .428 will make 
 unity ? 
 
 2. Find the difference between unity and the sum of : — 
 .3 and .45, .4 and .38, 24 and .38. 
 
46 
 
 MENTAL ARITHMETIC. 
 
 3. How much does unity exceed the sum of: — 
 
 .3, .249 and. 133 ;.34, .522 and .026 ; .76, .025, .075? 
 
 4. Find the diflference between unity and the sum of : — 
 .3, .249 and .234 ; .34, .522 and .348. 
 
 6. How much must be added to the sum of .45, .36 
 and .96 to make 2 ? 
 
 6. How much does the sum of .56, .386 and .434 
 exceed unity? 
 
 7. What decimal fraction added to the sum of .45, .67 
 and .38 will make a whole number? 
 
 Exercise 105. 
 
 1. Find the sum of, and the difference between : — 
 .5 and .6 ; .46 and .34 ; 3.2 and 1.6 ; 4.56 and 2.34. 
 
 2. Find the difference between the sum and the differ- 
 ence between :— .4 and .9 ; .45 and .63 ; 3.4 and 5.9. 
 
 3. The sum of two numbers 134.5. ^"c of them is 
 2.3 (3.8, 2.9). Find the other. 
 
 4. The sum of two numbers is 3.8. One is .6 (1.2, .9) 
 greater than the other. Find the two numbers. 
 
 6. .5 (.25, .05) of my money is $4. How much have I ? 
 
 6. .247 of my money is $8.00 more than 1.22 of it. 
 How much money have I ? 
 
 7. Find the result of : — 
 
 .64 + 3.2 -1.44 $3.56+$2.33-$i.36 
 
 3;24 + 2.76-3.25 $5.49 + $2.5i-$3.67 
 
 4.56-3.25 + 3.44 $3.35 + $2.36- $4.71 
 
 Exercise 106. 
 
 Simplify, or give the result of: — 
 
 1. (2.3-i.4) + ([.3+i.4). 
 
 2. (3.4-2.6) + (2.8+i.9). 
 
 3. (5.3- 1.8)- (1.2 + 1.3). 
 
 4. (3.4 + 2.6)-(3.5-2.8). 
 
 6. (3.8 + 2.7)-(3.6-i.25). 
 g- (3-5 -2.7)-(3-4- 2.85). 
 
 7. (3.46 -2.25) -(4.48 -3-98). 
 
DECIMAL FRACTIONS. 
 
 47 
 
 3X.2 
 
 .3X.2 
 
 I.2X 1.8 
 
 5X-3 
 
 .4X.6 
 
 2.3x2.7 
 
 4x4 
 
 .8X.5 
 
 2.4 X 2.6 
 
 8x.6 
 
 •5X.3 
 
 3-5x3.5 
 
 6x .9 
 
 .7X.7 
 
 4.4x4.6 
 
 7X.5 
 
 .6X.4 
 
 2.9X 2.1 
 
 riultiplication. 
 
 Exerdie 107. 
 
 Simplify and verify by using vulgar fractions. 
 Show the reason for fixing the decimal point. 
 
 1. .4x2 1.2x2 
 
 2. .7x2 2.4x3 
 
 3. .6x3 3-5x4 
 4.-5x3 2.6x5 
 6. .8x4 3.7x6 
 6. .9x4 2.8x7 
 
 Exercise 108. 
 
 Find the cost of : — 
 
 1. .3 lb. sugar® 6c. 
 
 2. .8 lb. rice @ 5c. 
 
 3. .4 lb. sago @ 9c. 
 
 4. .9 lb. starch @ 8c. 
 
 5. .5 lb. cheese @ 12c. 
 
 6. .7 lb. butter ® 15c. 
 
 Exercise 109. 
 
 What is the cost of : — 
 
 1. 2.5 lbs. cocoa ® $.35 ? 
 
 2. 2.8 lbs. cheese ® S. 12 ? 
 
 3. 2.4 lbs. butter @ $.25 ? 
 
 4. 3.9 lbs. coffee ® $.41 ? 
 
 5. 4.8 lbs. lard ® $. 15 ? 
 
 6. 9.6 lbs. tea @ $.94 ? 
 
 Exercise no. 
 
 Find the area of fields : — 
 
 .4 lb. rice ® 7.5c. 
 .6 lb. barley @ 8.4c. 
 .3 lb. sago ® 9.3c. 
 .9 lb. butter® 12.5c. 
 .5 lb. cheese ® 10.7c. 
 .8 lb. currants ® 6.8c. 
 
 .34 lbs. butter ® $.26. 
 .48 lbs. cake ® $.25 ? 
 .75 doz. oranges @ $.32 ? 
 .25 doz. eggs® $.16? 
 .63 lbs. tea® $.77} 
 .55 lbs. coffee® $.45 ? 
 
 1. 
 2. 
 3. 
 4. 
 6. 
 6. 
 7. 
 
 1.2 X 1.8] ch. 
 
 1.4 X 1,6' rds. 
 
 1.5 X 1.5] mi. 
 '2.4 X 26] ch. 
 3.5x35] rds. 
 •33 X .37] mi. 
 [4.8 X 4.2] rds. 
 
 2.5 rds. square. 
 3.5 rds. square. 
 4.5 rds. square. 
 
 i3.8 X 4.2] yds. 
 9.3x8.7] yds. 
 3.6 X 44] yds. 
 
 9.5 yds. square. ^5-5 x 4.5] ft. 
 12.5 yds. square. [4.7 x 53] ft. 
 19.5 yds. square. 10.3 x 97] yds. 
 39.5 ft. square. [29.2 x 3.08] rds. 
 
! 
 
 48 
 
 MENTAL ARITFIMKTIC. 
 
 Exercise iii. 
 
 1. How many feet of inch lumber will cover a floor : — 
 12. 3' X 12.7'? 19.5' X 20.5'? 13.7 yds. X I.I yds. ? 
 9.4' X 9.6' ? 14. 5' X 15.5? 2.48 yds. X 2. 1 yds. ? 
 28' X 2.2'? 29.3' X 30.7'? 34.5 yds. X 3. 1 yds. ? 
 
 2. How many cords of wood are in a pile : — 
 
 3.2' X 6.4' X 16'? 2.4' X 3.2' X 12.3'? 48' X 3.6' X 7.2'? 
 
 3. Find the volume of a pile of stones : — 
 
 2.5' X3.6'x6.4' ; 1.25' x2.4'x4.3' ; 3.75' x 1.6' X3.6'. 
 
 Exercise iia. 
 
 Find the product of: — 
 
 1. 
 
 2 
 
 3 
 
 4 
 
 6 
 
 2.4x3.5 32 X. 38 95X-95 
 
 4.2x3.5 46X.44 4.9 X. 51 
 
 35 X6.4 53X-57 3.6 X. 25 
 
 45 X6.4 62X.68 7.4x8.6 
 
 5.6x4.5 ^ 39X.31 8.6x9.4 
 
 4.2x1.5' 39X.41 6.8X.72 
 
 ExercUe 11 3. 
 
 What is the continued product of : — 
 
 2.5x2.4 
 3.6x2.5 
 4.7x2.5 
 6.3x2.5 
 
 25 X7.5 
 
 6. 49 X2.5 
 
 .3, .6, and 2.2 ? 
 .9, .3, and 3.3? 
 .2, 1.3, and 3.4.? 
 1.2, .3, and 4.4? 
 
 1. .4, .6, and 2.6? 
 
 2. .7, .7, and 4.1.? 
 
 3. .9, .5, and 4.5.? 
 
 4. .7, .9, and 6.7? 
 
 5. .5, I.I, and 5.5? .7, .6, and 5.8? 
 
 6. .9, 1. 1., and 9.1 ? 6.4, .4, and 1.9? 
 
 Exercise 114. 
 
 1. Find the difference between .45 and .675. 
 
 2. Find the difference between three times .56 and 
 three times .257. 
 
 3. From 5.6x2.4 take 2.4x2.6. 
 
 4. Simplify 3.8x7.2 + 7.2x3.4 + 2-8x7.2. 
 6. Simplify 4.5x7.6-6.3x4.5 + 4.5x8.7. 
 
 6. Simplify 3.9x6.7 + 8.5x3.9+4.8x3.9. 
 
 7. I bought 4.6 lbs. tea at $.44 and gave 4.4 lbs. 
 sugar at $ 16. How much is yet to be paid? 
 
 6. 
 
 3. 
 4. 
 6. 
 6. 
 
 7. 
 
DKCIMAL FRACTIONS. 
 
 49 
 
 loor : — 
 I.I yds. ? 
 M yds. ? 
 3.1 yds. ? 
 
 6'x7.2'? 
 
 6' X 3.6'. 
 
 95X.95 
 
 4.9X.51 
 
 3.6X.25 
 
 7.4x8.6 
 
 8.6x9.4 
 
 6.8 X. 72 
 
 2.2? 
 
 3-3? 
 id 3.4? 
 d 4-4? 
 
 5.8? 
 
 id 1.9? 
 
 s .56 and 
 
 Division. 
 
 Exercise 115, 
 
 Divide, and verify by vulgar fractions :- 
 
 1. 
 2. 
 3. 
 4. 
 6. 
 6. 
 7. 
 
 .4-r2 
 .6^2 
 .64-3 
 .8-r2 
 .8-r-4 
 
 .9-5-3 
 .4^4 
 
 I.2-T-2 
 I.2-r3 
 
 3-2-^4 
 
 1.5^3 
 2.5-r5 
 3.6-r4 
 4.8-r6 
 
 .32 -f4 
 .24-^6 
 
 .36 -r9 
 
 .42-i-7 
 
 .8l-r9 
 
 .72-i-8 
 •45-^9 
 
 6.44-2 
 6.943 
 
 7-2-^4 
 8.5-5 
 9.6-46 
 
 8.4-^7 
 9.64-8 
 
 Exercise 116. 
 
 Find the price : — 
 
 1. If 2 ^4, 8) lbs. lamb cost $.64. 
 
 2. If 3 (6, 9) yds. ribbon cost $.72. 
 
 3. If 4 (7, 12) qts. vinegar cost $.84. 
 
 4. If 2 (4, 5) yds. cloth cost $5.9. 
 
 5. If 4 (5, 8) tons coal cost $24.6. 
 
 6. If 8 (9, 11) bush, wheat cost $19.8. 
 *7. If 6 (8, 12) cords wood cost $48.96. 
 
 1. .4^.2 
 
 2. .64-. 2 
 
 3. .84- 
 
 4. .64- 
 
 6. .9-^ 
 
 6. .84- 
 
 7. .3-J- 
 
 re 4.4 lbs. 
 
 1. Divide 
 
 2. Divide 
 
 3. Divide 
 
 4. Divide 
 6. Divide 
 
 6. Divide 
 
 7. Divide 
 
 Exercise 117. 
 
 1. 64". 2 564-.2 
 
 2.74-. 3 644-.4 
 
 . 3-64.4 72 4-. 3 
 
 4.84-. 5 844-. 5 
 
 7.64-. 5 75-^-4 
 
 9.84-. 8 694-. 8 
 
 . 9.94-. 8 584-. 5 
 
 Exercise 118. 
 
 1.35 hours by .45 minutes. 
 17.5 weeks by .25 days. 
 .625 bushels by 2.5 gallons. 
 30.25 minutes by 5.5 seconds. 
 422.5 feet by 6.5 inches. 
 .48 acres by .75 sq. rods. 
 9.021 yards by 9.3 feet. 
 
 4.3-^2 
 6.54-2 
 
 5-5-^4 
 6.54-4 
 7.64-5 
 8.74-8 
 9.94-5 
 
 4.56- 
 5.84- 
 6.75- 
 
 3-07- 
 3-56- 
 
 4.57- 
 9-87 
 
 .02 
 
 .03 
 ■.04 
 
 •05 
 •.08 
 -.04 
 -.08 
 
50 
 
 MKNTAI, AUITHMETIC. 
 
 Exercise 119. 
 
 Find, in lower denominations, the value of 
 
 1. .5 of 2i £. 
 
 2. .25 of a ton. 
 
 3. .75 of a bush. 
 
 4. .45 of a gal. 
 6. .75 of a yard. 
 
 6. .35 of a sq. yd. 
 
 7. .375 of a mi. 
 
 .45 of a ^. 
 .75 of a week. 
 .65 of an hour. 
 •33?} of a gross. 
 .2^ of a cwt. 
 .7^ of a ream. 
 .3! of a score. 
 
 Exercise lao. 
 
 ;^2.45. 
 4.75 acres. 
 3.65 bushels. 
 7.54 tons. 
 8.75 weeks. 
 7.25 yds. 
 5.35 sq. yds. 
 
 1. 
 2. 
 3. 
 4. 
 6. 
 6. 
 7. 
 
 Reduce these vulgar fractions to decimals : — 
 
 1^0- 
 
 1 
 ?• 
 
 -h' 
 
 i 
 
 -h- 
 
 f. 
 
 h- 
 
 3 
 
 8- 
 
 T%- 
 
 .V- 
 
 3 
 2 5* 
 
 8' 
 
 fa- 
 
 h- 
 
 16 
 25- 
 
 8* 
 
 1 
 
 5* 
 
 20* 
 
 \\- 
 
 A 
 
 f. 
 
 \h- 
 
 e- 
 
 1^. 
 
 4 
 5* 
 
 \t 
 
 21 
 
 2 5* 
 
 tk. 
 
 ^^• 
 
 
 1 
 
 3- 
 
 1 
 
 9- 
 
 ■i 
 
 ta- ^• 
 
 41 
 5J' 
 
 Exercise lai. 
 
 8 
 IT" 
 
 If 
 
 JL 
 11' 
 
 Ji- 
 ll- 
 
 3 
 T- 
 
 f 
 
 Reduce to equivalent vulgar fractions : — 
 
 1. 
 2. 
 
 3. 
 4. 
 6. 
 6. 
 7. 
 
 •3 
 
 •5 
 .6 
 
 .8 
 
 •4 
 
 •7 
 
 •45 
 •63 
 .81 
 
 • 36 
 •99 
 .27 
 
 •54 
 
 •345 
 .567 
 
 •.396 
 
 •495 
 
 •594 
 
 •954 
 
 •873 
 
 .16 
 
 •83 
 
 .083 
 
 .416 
 
 -583 
 .916 
 
 .0916 
 
 .06 
 
 •13 
 .26 
 
 .46 
 
 •53 
 
 •73 
 .86 
 
 99 
 
 333 
 666 
 
 4545 
 1666 
 
 0833 
 1818 
 
 Express as pure decimals : — 
 
 8. .2.1, .3I, .4;), .2^, .6/g-. 
 
 ^ •!&» •33- •4§, •3ff, .2t\. . -i 
 
 •2» •4» •«» -S' 'IIT* 
 
 1 
 
 ■4» 
 
 5 
 ■»» 
 
 5 
 
 •8» 
 4 
 
 r> 
 
 !• 
 
 l2^. 
 
 JL 
 15' 
 
 6 
 
 9 
 4 
 6 
 
 83 
 16 
 
 4_ 
 
 ii> 
 
 5- 
 IJ* 
 
DEGIMAI. FRACTIONS. 
 
 51 
 
 .45. 
 
 5 acres. 
 5 bushels. 
 
 4 tons. 
 
 5 weeks. 
 15 yds. 
 
 15 sq. yds. 
 
 11* 
 
 A- 
 II* 
 
 If 
 I. 
 
 t 
 
 
 4_ 
 13* 
 
 ? 
 
 3-4 
 
 33 
 
 5.6 
 
 66 
 
 3.9 
 
 545 
 
 7-4 
 
 666 
 
 1.6 
 
 833 
 
 5-83 
 
 818 
 
 9.16 
 
 4 
 
 7» • 
 
 1*1 > -iV- 
 
 Exercise 122 
 
 1. 7-5x-o75-^(-i5--o75) = 
 
 2. 8.4 + 6.4x2.5-3.5x2.4= ,. 
 
 3. 8.3X.87-6.4X .66 + .36x3.4=; 
 
 4. 5.2X2.8 + .56X2.6-4.5X 5.5 = 
 
 5. 6.3-r. 09x5.4-^.27 + 3.5x4.5 = 
 
 6. 5.4-3.2X.25 + 4 4X.75-.8r+.i62 = 
 
 7. .'7 + 3-54-2.36 + .5 + 2.6-2.8 = 
 
 8. 1.6x1.3 + 2.6+1.7 + 8(3.7-2.6)= + . 
 
 Exercise 123. 
 
 1. 2 ft., 6 in. is what decimal of a yard? 
 
 2. 2 qts., I pt. is what decimal of a gallon? 
 
 3. 4 hrs., 48 min. is what decimal of a day ? 
 
 4. 17s. dd. is what decimal of ;^i ? 
 
 6. 3 dys., 12 hours is what decimal of a week? 
 
 6. 6 sq. ft., 108 sq. in. is what decimal of a sq. yard? 
 
 7. 3 pks., I gal., 2 qts. is what decimal of 5 bushels ? 
 
 Exercise 124. 
 
 1. 6^. is what decimal of a shilling? a crown ? a sover- 
 eign? a guinea? ;^i, los. 6d? 
 
 2. Reduce 55. (15.5; 125. 6^^; 6^. Sd ; 135. 4^.) to ^ 
 decimal of ^i. 
 
 3. Express 3 pks. (3 gal.; 2 gal., i qt. ; i pk., i gal., 
 2 qts.) as a decimal of a bushel. 
 
 4. A piece of oilcloth 9' X 6' [9"xi2"] is what decimal 
 of a square yard ? 
 
 6. What decimal of a cubic yard is a stone [i' x 6' x 3'] ? 
 [18" X 72" X 12"] ? [6o"x 24" X 27"]? 
 
 0. What decimal of an acre is a plot [5 rds x 8 rds.] ? 
 [16 rds. X 15 rds.] ? [3 ch. x 8 ch.] ! 
 
 7. What decimal of 5 acres is a field [15 rds. x 24 rds.] ? 
 [8 ch. X 6 ch.]? [9 ch. X 12 ch.] ? 
 
 ONTARIO C0Ll£6E OF EDUCATION 
 
52 
 
 MENTAL ARITHMETIC. 
 
 Bxerwise 135. 
 
 1. A bought .3 (.4, .6) of a farm, and B bought 
 •4 {-St •75) of the remainder. Which bought the more ? 
 How much more ? 
 
 2. I owned .55 (.45, .75) of a ship, and sold .4 (.6, .25) 
 of my share. How much did I sell ? 
 
 3. I owned .45 (.64, .75)of amill, and sold .8 (.25, .25) 
 of my share. How much had I left ? 
 
 4. I owned .8 ^6, .25) of a farm, and sold .5 (.75, .25) 
 of my share. Find my former share if I sold 60 acres. 
 
 6. I owned .8 (.5, .25) of a farm and sold .25 (.5, .4) 
 of my share. How much was in the farm if I sold 16 ac? 
 
 6. I owned .8 (.45, .75) of a farm, and sold .6 of my 
 share. How much land was in the farm if I sold 12 
 acres more than I kept ? 
 
 7. The sum of two numbers is .37 (.493, 8.64), and 
 their difference is .05 (.125, ^.32). Find the numbers. 
 
 Exercise ia6. 
 
 1. Findmy weekly wages if I get $2.25 ($3,425, $1,875) 
 a day. 
 
 2. How much does a boy earn in a year, if he gets 
 $7-5 ($9-25, $8,625) a month? 
 
 3. A boy takes two steps in a second. How far will 
 be walk in a minute, if each step is 1.5'? 1.25'? .625 yds.? 
 
 4. A pint of water weighs 1.25 lbs. What is the 
 weight of 3 pints ? 5 pints ? 7 pints ? I quart ? 3 quarts ? 
 I gallon ? I gal., 3 qts., i pt. ? 
 
 6. If a cubic foot of water weighs 62.5 lbs., what 
 is the weight o*^ the water in a rectangular trough 
 [i'x2'x8^? [2'x2'x6']? r2'x4'x5']? 
 
 6. A does .55 (.35, .75) of a work. B does .6 of the 
 remainder. C finishes it. How much does C do ? 
 
 7. A does .375 of a work, B does .4 of the remainder, 
 and C finishes it. How much does each do ? 
 
 8. A does .35 of a $20.00 job. B does .6 of the 
 remainder and C does the rest. Find pay of each. 
 
DECIMAL FRACTIONS. 
 
 S3 
 
 Exercise 137. 
 
 1. I had .8 of a farm, and sold .63 (.456, .325) of it. 
 What part of the farm have I left ? 
 
 2. A owns .4 (.23, .425) of a farm. B owns .3 (.35, 
 .375) of it. C owns the rest. Find C's share. 
 
 3. A does .24 of a work. B does .356 of it, and C 
 does .234 of it. How much of it remains undone ? 
 
 4. I have 2.83 acres more than B, and together we 
 have 33.43 acres. How much land has each of us ? 
 
 5. I gave .55 of an apple to Tom, and .3 J of the re- 
 mainder to Will. How much had I left ? 
 
 6. I owned .5 of a vessel and sold .75 of my share for 
 $12,000. Find the value of my present share. 
 
 7. A can mow .13 of an acre in an hour, and B .25 of 
 an acre in an hour. How long would it take the two to 
 mow a 19-acre field? 
 
 Exercise 128. 
 
 1. Find the least number which contains -|, §, .75 or 
 1.2 an exact number of times. 
 
 2. Find the least number to be taken from 5 (8, 12) so 
 that the remainder be a multiple off (3 J, .45).'* 
 
 3. If .45 of a work is done in 2.25 days, how long will 
 it take to finish the work? 
 
 4. A can make an article in .25 of an hour, and B in 
 .35 of an hour. How many would the two make in 3.5 
 hours ? 
 
 5. I gave .34 of my money for a clock, .22 of it for a 
 table, and . 14 of it for a chair, and had $6 left. Find the 
 cost of each of them. 
 
 6. It took 24 yards of carpet 1.25 yards wide to cover 
 a floor. How many yards of carpet .75 of a yard wide 
 would be needed ? 
 
 7. I sold .3 J of my farm to A and .75 of the remainder 
 to B, and the rest, 36 acres, to C. How much did A and 
 Bget? 
 
54 
 
 MENTAL ARITHMETIC. 
 
 Exercise 139. 
 
 1. Show that decimal notation is but a continuation 
 of the Arabic system of notation. 
 
 2. How is a decimal fraction expressed ? 
 Distinguish a vulgar fraction from a decimal. 
 
 3. How is the value of a decimal fraction affected by 
 moving the decimal point to the right ? To the left ? 
 
 4. Show that a *' " may, or may not, alter the value 
 of a decimal fraction. 
 
 6. What caution should be observed in writing down 
 a question in addition, or subtraction, of decimals .? 
 
 6. How may a decimal be multiplied or divided by 
 10.? 100? 1000? 
 
 7. How many figures should there be in the decimal 
 part of the product of two decimals ? 
 
 8. Give, in order, the steps to be taken to divide a 
 decimal by a decimal. 
 
 9. Show that the quotient is not altered by multiply- 
 ing or dividing both divisor and dividend by the same 
 number. 
 
 10. Distinguish a problem from a theorem. 
 
 11. Upon what theorem does division by factors 
 depend ? 
 
 12. What vulgar fractions can be reduced to (i) ter- 
 minating, (2) pure repeating, (3) mixed repeating decimals? 
 
 13. Give the rule for reducing (i) terminating deci- 
 mals, (2) circulating decimals, to vulgar fractions. 
 
 Show that two of these rules are not absolutely correct. 
 
 14. Prove the rule for fixing the decimal point in the 
 answer to a question in multiplication of decimals. 
 
 15. How would you proceed to add, subtract, multiply 
 or divide, circulating decimals ? 
 
 16. What are the co-factors of : — 
 
 .24? .36? .28? .32? .35? .49? .64? .45? 
 
 6.3? 8.8.? 6.4? 3.3? 5.6? .055? .729? .625? 
 
 17. The product of two numbers is. 24. One of them 
 is .4 (.5, 4.8). Find the other. 
 
ntinuation 
 
 PERCENTAGE. 
 
 Percentage is a term applied to certain exercises in arith- 
 metic in which loo is used as the basis of computation. 
 
 Per cent, is an abbreviation of the Latin words per 
 centum^ which mean, by the hundred. 
 
 The sign % is u-ied for the wcjrds per cent. 
 
 The Base is the quantity on which the percentage is com- 
 puted. 
 
 The Rate per cent, is the number which denotes how 
 many hundredths of the base is to be taken. It denotes a part, 
 and can be expressed as a vulgar fraction, or a decimal. 
 
 The Percentage is the number, or quantity, which is the 
 given per cent, of the given base. 
 
 Exercise 130. 
 
 Find the loss on :- 
 
 1. 200 apples, if 6 (8, 1 1) in every hundred rot. 
 
 2. 300 oranges, if 7 (4, 16) in every hundred spoil. 
 
 3. 500 cattle, if 5 (9, 12) in every hundred die. 
 
 4. 800 soldiers, if 4 (15, 25) are killed in every hundred. 
 6. 700 peaches, if 12 (14, 18) spoil in every hundred. 
 
 6. 600 eggs, if 10 (13, 17) are broken in each hundred. 
 
 7. 1000 sheep, if 8 (12, 16) die in every hundred. 
 
 Exercise 131. 
 
 Find the loss on 
 
 1. 150(250, 350^ 
 
 2. 250(450, 750) 
 
 3. 350 (650, 950) 
 
 4. 125(225,425) 
 6. 325 (725, 625) 
 
 6. 160(240, 480) eggs, if 5 (15, 25) in every hundred 
 are broken. 
 
 7. 320 (430, 560) lambs, if 10 (20, 30) in every hundred 
 die. 
 
 apples, if 6 in every hundred rot. 
 cattle, if 4 in every hundred die. 
 soldiers, if 12 in every hundred die. 
 peaches, if 8 in every hundred spoil, 
 sheep, if 16 in every hundred die. 
 
 00 
 
 -•'^-y^-'-'mirfxfs^-m 
 
 ryo^Mf*'. '. re?-*^-:z'-»*-^-^'- 
 
56 
 
 MENTAL ARITHMETIC. 
 
 5%. 
 
 24%. 
 
 15%. 
 
 48%. 
 
 35%. 
 
 96%. 
 
 55%. 
 
 i^%. 
 
 95%. 
 
 36%. 
 
 25%. 
 
 72%. 
 
 75%. 
 
 84%. 
 
 25%. 
 
 33j%. 
 
 iiU- 
 
 i%. 
 
 125%. 
 
 66r%. 
 
 22^%. 
 
 i%. 
 
 37l%- 
 
 i6:t%. 
 
 55f%. 
 
 1%. 
 
 62j%. 
 
 8i%. 
 
 88«%. 
 
 u. 
 
 Syn- 
 
 4»H%. 
 
 14?%. 
 
 Uj 
 
 61%. 
 
 83.U. 
 
 28f%. 
 
 l^ff%* 
 
 3V/o- 
 
 100%. 
 
 7}%. 
 
 l\/^' 
 
 Exercise 133. 
 
 Write down the fractions (i) vulgar, (2) decimal, 
 which are equivalent to the following percentages : — 
 
 1. io%. 
 
 2. 20%. 
 
 3. 40%. 
 
 4. 80%. 
 
 5. 60%. 
 
 6. 30%. 
 
 7. 90%. 
 
 Exercise 133. 
 
 1. I gain 20 cents on every hundred. How much will 
 I gain on 200 pears ? 300 plums ? 500 books ? 600 eggs ? 
 
 2. I lose twenty cents per hundred plums. How much 
 will I lose on 100 plums? 50 plums ? 25 plums ? 75 plums ? 
 
 3. I gain 20 per cent. What is my gain on icx> papers ? 
 10 papers ? 30 papers ? 60 papers ? 90 papers ? 40 papers ? 
 
 4. I have 80 sheep. How many are 10% of my flock ? 
 20%? 40%? 80%? 60%? 30%? 90%? 45%? 15%? 5%? 
 
 6. What per cent, of mv flock is 6 sheep out of 12 ? of 
 24 .? of 30 ? of 60 ? of 1 20 ? of 1 5 ? of 45 ? of 75 ? of 90 ? 
 
 6. What % is 8 eggs out of 16? of 32? of 40? of 20? 
 of 10? of 80 ? of 160 ? of 24 ? of 64 ? of 48 ? of 72 ? of 96 ? 
 
 Exercise 134* 
 
 What percentage is equivalent to : — 
 
 1. i? V i.^ i? i? V ii* ^^ T^u? 
 
 tV.^ 
 
 10 . 
 
 /2 ? 
 
 3_? 
 
 2. §? f? V i? F f? i? ^ 
 
 3. i'^? VV? \V rh^ irJ 3^? W ^? ^? 1^? 
 
 4. .04? .08.? .06? .09? .37.? .45.? .63? .25? .75? 
 
 5. .125.? .625? .375? .875? .425? -345? .695? 
 
 6. .3325? .4725.? .5625.? .3825? ,0625? .0125 ? .64125? 
 
 7. .3? .6? .5? .16? .09? .63? .142857? .285714? 
 
1. 
 
 2. 
 3. 
 4. 
 6. 
 6. 
 
 ^of8 = 
 
 3 of 9 = 
 ^of25 = 
 I of 24 = 
 §of3o = 
 f of63 = 
 
 PERCENTAGE. 
 
 Exercise 135. 
 
 . I of 60= .05 of 200= 
 
 .7 of 80= 
 .9 of 40= 
 .6 of 45 = 
 .8 of 85 = 
 
 .4 of 75 = 
 
 Exercise 
 
 25 of 300= 
 1 5 of 400 = 
 35 of 500 = 
 65 of 8o3= 
 95 of 700 = 
 
 136. 
 
 57 
 
 •33jof45 = 
 .66|of36 = 
 .12.} of 48 = 
 • 371 of 64 = 
 .ii^of8i = 
 .I4f of63 = 
 
 1. 
 2. 
 3. 
 
 4. 
 5. 
 6. 
 
 7. 
 
 1. 
 2. 
 3. 
 4. 
 6. 
 6. 
 7. 
 
 1. 
 2. 
 3" 
 4. 
 6. 
 7. 
 
 What is : — 
 10% of $50? $80? $7.50? $13.60? 90 sheep? 
 20% of $85 ? $75 ? $4.25 ? 95 girls ? 65 apples ? 
 25% of $100? $84? $160 ? 360c. ? 840 acres? 236 pigs ? 
 5o%of$2C50? $96? $1.50? 48 sheep? 64 weeks? 
 75% of $300? $30? $3.00? 60 yards? 84 miles? 
 I2j% of $400? $40? $4.00? 96 reams? 88 hrs. ? 
 i6^% of $300? $30? $3.0D? 36 gal. ? 48 tons ? 
 
 Exercise 137. 
 
 8% of $25 = 
 5% of $40= 
 6% of $50= 
 
 12% of $75 = 
 24% of $25 = 
 
 48% of $75 = 
 72% of $50= 
 
 Exercise 138 
 
 What per cent, is : — 
 $5 of $10? $20? $25? $40? $50? $75? $100? 
 6 of 12? 30? 48? 24? 36? 72? 100? 50? 96? 
 $8 of $16? $32? $64? $96? $24? $48? $72? 
 3 quarts of 4 qts. ? 6 qts. ? 9 qts. ? 8 qts. ? i gal. ? 
 1 gallon of 4 gal. ? 8 gal. ? i pk. ? 2 pk. ? i bush. ? 
 12 hours of 6 hrs. ? 4 hrs. ? 16 hrs. ? 20 hrs. ? I day? 
 
 10% of 30= 
 20% of 80 = 
 50% of 64 = 
 25% of 48 = 
 75% of 84 = 
 45% of 60 = 
 15% of 40= 
 
 33)^% of 48 sheep = 
 i6§% of 72 eggs = 
 I2.J% of 64 hens = 
 37j%of 48 1ambs = 
 ii^% of 63 geese = 
 872% of 80 cows = 
 14^% of 49 acres = 
 
58 
 
 M KNTA L A KITH M E TIC. 
 
 Exercise 139. 
 
 1. A man had 45 lambs, and sold 20% (40%, 60%) of 
 them. How many did he sell ? How many had he left ? 
 
 2. I had 64 sheep, and 25% (50%, 75%) of them died. 
 How many have I still? 
 
 3. A man had 360 acres, and sold 35% (45%, 85%) of 
 his farm. Find the size of his present farm. 
 
 4. A man bought 480 bushels of potatoes, and sold 
 25% (30%, 35%) of them. How much had he left ? 
 
 6. I had 48 bushels of apples, and sold I2.\% (i6§%, 
 8J%) of them. Find the value of the rest at $1 a bushel. 
 
 6. A man earned $800, and saved 12^% (37^%, 62]%). 
 How much did he save ? How much did he spend ? 
 
 7. I earned $720 a year, and saved 1 1§% (12^%, i6§%) 
 of it. How much do I spend? Howmuch lessdo I save? 
 
 8. A school class of 84 pupils is 25% (33^%, i6g%) 
 boys. How many girls are in the class ? 
 
 Exercise 140. 
 
 1. A clerk who received $7. 50 a week had his wages 
 raised 20% (33g%, i6§%). Find his present wages. 
 
 2. A clerk received $9 a week, and spent 50% (25%, 
 12^%) of his wages. How much did he save ? 
 
 3. A clerk who received $12 a week had his wages 
 reduced 25% (30%, 15%). Find his present wages. , 
 
 4. A person received $75 a month. He spends 40% 
 (33g%, 83 J%). How much does he save? 
 
 6. A man gets $960 a year, and spends 75% (66g%, 
 of it. How much does he save ? 
 
 6. A man gets $750 a year, and spends 30% (35%, 
 45%) of it. How much more than that does he save ? 
 
 7. My house and lot cost $2,400. The lot cost 25% 
 (30%; 37^%) of the whole. Find the cost of each. 
 
 8. 32 sq. rds. is what per cent, of 40 sq. rds. ? 64 sq. 
 rds. ? 80 sq. rds. ? 128 sq. rds. ? i acre ? 5 acres ? 
 
 Ml 
 
PERCENTAGE. 
 
 59 
 
 Commission. 
 
 Commission is the charge made by an agent for buying or 
 selling goods — usually a percentage on the value of the goods. 
 
 A Commission Merchant is one who buys or sells goods 
 intrusted to him. A Consignment is goods sent to a com- 
 mission merchant to be sold. The Consignor is the person 
 who sends the goods. The Consignee is the person to whom 
 the goods are sent. The Net Proceeds is the amount for 
 which the goods were sold, less ihe commission. 
 
 Exercise 141. 
 
 How much will an agent get for selling goods for : — 
 
 1. $800 ($700, $1,200), if his com. be 7% (8%, 10%)? 
 
 2. $450(5750, $1,250), if his com. be 8 (10, 20)%? 
 
 3. $325 ($825, $1,275), if his com. be 8 (12, 24) % ? 
 
 4. $360(1480, $720), if his com. be I2| (37 .J, 62^) %? 
 6. $420 ($630, $936), if his com. be 33I (66|, 162) % ? 
 6. $490 (1630, $880), if his com. be 14? (i 4, 9^) % .? 
 
 Exercise 14 a. 
 
 1. What is the commission for selling a house for $7ck 
 ($800, $1,600) at 5% .? 8% ? 10% ? 
 
 2. How •much would a man receive for collecting a 
 note of $450 at 2% ? 2^% ? 3^% ? 
 
 3. How much would I receive for a house which my 
 agent sold for $1,500 ($2,400, $3,500) on a com. of 4% ? 
 
 4. Find the cost of a vessel which my agent bought for 
 $1,250 ($1,500, $4,500) on 8% com. 
 
 6. Find the net proceeds from 4oobbls. flour @ $4.50, 
 if ihe commission merchant gets 2| (7|, I2h) %. 
 
 6. What commission would I receive for selling 750 
 bbls. apples @ $2 a bbl., at l%? 1%} 1^% ? 
 
 7. Find the com. at i^ (2.], 3I) % I must pay an agent 
 for buying 300 bales cotton, each 800 lbs., @ 6c. a lb. 
 
 8. Find com. at 6;^ (6J, 7I) %, for selling 48 bbls. 
 apples @ $5 ^ bbl. 
 
6o 
 
 MENTAL AUITHMETIC. 
 
 Exercise 143* 
 
 Goods Sold. 
 
 1. $800. 
 
 2. $450. 
 
 3. $623. 
 
 Goods Bo't. 
 
 Com. Net Proceeds. 
 
 Com. 
 
 Net Cost. 
 
 4. 
 6. 
 
 $750- 
 $840. 
 
 1. 
 
 Rate of Com. 
 
 4 (5, 9) %. 
 6(8, 12)%. 
 
 8(10,20)%. 
 
 Rate of Com. 
 10 (20, 40) % 
 
 2S(i2l37l)% 
 
 Exercise 144. 
 
 I received $75 commission for selling a house @ 5 
 ('o> 7'\%)' What was the selling price? 
 
 2. I received $45 for selling a house on a commission 
 of 1 1^ (9lV» 6j) %. How much did the owner get ? 
 
 3. Find net proceeds from selling 24 kegs butter, 
 each 26 lbs., ® 25c. a lb. : commission 2 (5, 10) %. 
 
 4. How much would I have to pay my agent for 48 
 bbls. apples® $3.50, commission 14^^%? J2^%? i6§% ? 
 
 5. How much must I remit my agent, that he may buy 
 me a house for $1,200 ($750, $1,225), ^"d have 2% com. ? 
 
 6. My agent remitted $1,176 ($1,440, $1,710) when 
 selling 300 bbls. flour @ $4 ($5, $6) a bbl. Find (i) his 
 commission ; (2) his rate of commission. 
 
 7. Bought 360 bbls. flour @ $4 a bbl. Sold |: of it @ 
 25 (50, 20) % gain, and the remainder @ 10(25, 20) % 
 
 Find the gain. 
 
 Exercise 145* 
 
 Value. Commission. Rate. Net Proceeds. 
 
 $600. $24 ($36, $45) 
 
 $500 $45o($-, o, $250). 
 
 .... $21 ($56, $75) $679 ($744, $675). 
 
 .... $45 ($72, $95). I2i%. 
 
 25%. $i5o($48o,$75o). 
 
 10 (25, 40) %. $900. 
 
 am. 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 
PKRCENTACE. 
 
 6l 
 
 Trade Discount. 
 
 A Discount is a reduction made from the nominal price of 
 an article. The List Price of an article is its usud retad 
 price. A Trade Discount is a reduction from the list price, 
 made to the retail dealer, by the wholesale merchant or the 
 manufacturer. A Cash Discount is a reduction from the list 
 price, for prompt cash payment. An Invoice is a statement, 
 in detail, of goods sold by one dealer to another. 
 
 Exercise 146. 
 
 What is the discount if the invoice price is : - 
 
 1. $300 ($450, $7.50) and discount 10% ? 20% ? 30% ? 
 
 2. $600 ($360, $4.80) and discount 5% ? 15% ? 35% ? 
 
 3. $800 ($250, $12.50) and discount 8% ? 16% ? 48% ? 
 
 4. $500 (S350, $4.50) and discount 6% ? 12%? 24%? 
 
 5. $900 ($720, $8.40) and discount 33!% ? i6§% ? 8J% ? 
 
 6. $400 ($640, $8.80) and discount 25%? 12^%.? 37.^%? 
 
 Exercise 147. 
 
 What is the cost if the marked price is : — 
 
 1. $500 ($750, $6.25) and discount 4% ? 8% ? 12% ? 
 
 2. $400 ($850, $3.25) and discount 6% ? 10% ? 20% ? 
 
 3. $600 ($720, $6.40) and discount 5% ? 15% ? 25% ? 
 
 4. $800 ($480, $9.60) and discount 25%? 12^%? 6^%? 
 6. $900 ($540, $3.24) and discount 33^% ? 663% ? i6§ ? 
 6. $450 ($729, $6.48) and discount 1 4% ? 22^%? 5;^%? 
 
 Exercise 148. 
 
 Find the net cost if the list price is : — 
 
 1. $500, and the trade discounts 20%, 10% and 10%. 
 
 2. $600, and the trade discounts 33 J%, 25% and 2%. 
 
 3. $7.50, and the trade discounts i6-g%, 20% and 3%. 
 
 4. $9.60, and the trade discounts 12^%, 14^% and 5%. 
 
 5. $640, and the trade discounts 25%, 33^% and 75%. 
 
 6. $6.25, and the trade discounts 20%, 10% and 3j%. 
 
62 
 
 List Price. 
 
 1. $300 ($450). 
 
 2. $500 ($750) 
 
 3. $600 ($720). 
 
 4 
 
 6 
 
 6 
 
 MKNTAI. ARITHMETIC. 
 
 Exercise 149. 
 
 Rate()*"Disc. Discount. 
 
 (6)% 
 
 $50 ($150). 
 
 $225 ($84). 
 
 Net Cost. 
 
 $450 ($480). 
 
 25 (20) %. 
 10(30)%. 
 
 $720 ($84). 
 $360 ($375). 
 
 $90 ($250). 
 
 Exercise 150. 
 
 • 1. I buy goods at 25 (20, 40)% discount, and sell at 
 list prices. Find my gain %. 
 
 2. I gain 20 (25, 33J) % by selling goods at list prices. 
 Find the discount allowed me. 
 
 3. What single discount is equivalent to a discount of 
 25%and33j%.' 20% and 25%? 12?,% and 14^ % ? 
 
 4. What is the difference between a discount of 20% 
 and 25%, and a discount of 25% and 20% ? 
 
 6. I am allowed 20% and 10% discount and pay $360 
 ($792, $5.76) for goods, Find the list price. 
 
 6. Find the difference between a discount of 30% and 
 a discount of 20% and 10% on $500 ($250, $425). 
 
 7. I sent my agent $630 ($715, $720) to buy goods at 
 5 (10, i2|) % CO I). Find the value of the goods. 
 
 8. I sell wheat @ 3% com., and buy goods @ 2%, and 
 get $200. Find the value of ( i) the wheat ; (2) the goods. 
 
 Exercise 151. 
 
 List Price. Discount. Rate. Net Cost. 
 
 1. $3oo($4.8o) 33hm)% 
 
 $50 ($4. 50) 
 
 2. $400 ($7. 20) 
 
 3. $800 ($9.00) 
 
 4 
 
 6. 
 
 6 $9 ($.09) 
 
 $45 ($.28) 6i(2'-)% 
 
 1 (!y °/ 
 
 $750 ($8). 
 
 $398 ($3-97)- 
 $591 ($2.31). 
 
PERCENTAGE. 
 
 ^>3 
 
 Loss and Qain. 
 
 The cost is what is paid for an article. 
 
 The selling price is what is got for an article. 
 
 Goods sold at an advance on cost are sold at a gain. 
 Goods sold at less than cost are sold at a loss. The loss or 
 gain is the difference between the cost price and the selling 
 price. The loss or gain % is always computed on the cost. 
 
 Exercise 15 a. 
 
 Find the gain and the selling price if: — 
 
 1. Cost $100: gain 6%, 8%, 25;^, 6]%, 7.]%, 37.]%. 
 
 2. Cost $75: gain 20%, 40%, 30%, 50%, 25%, 33.]%. 
 
 3. Cost $250: loss 10%, 16%, 20%, 24%, 32%, 40%. 
 
 4. Cost $4.80: loss 5%, 7i%. 12.]%, 165%, 33j%, 8J%. 
 6. Cost $6.30: gain 14%, 22g%, ssU. 14?%. 28i%. 
 
 6. Cost $9.60: gain 50%, 25%, 20%, 40%, i2i%, 37.!%. 
 
 7. Cost $2.50: loss 20%, 10%, 5%, 2.]%, ii%, 1%. 
 
 Exercise 153. 
 
 1. Apples cost $2 40 a bbl. What is the selling price 
 togain2o%? 2,%? 3o%?33i%.^ 12^/0? 163% r 6]%? 
 
 2. I bought flour @ $4.80 a bbl. What was the selling 
 price if I lost 10% ? 15% ." 26% r 20% t 12.^%? 165% ? 
 
 3. Bought lambs at $3.00. What was the gain %, if I 
 sold@$3.3o? $3.60? $4.20? $4.50? $4,001' $5.00? 
 
 4. What is the gain % on buying land @ $24 an acre 
 and selling @ $30 1 $36 ? $27 ? $32 ? $40 ? $48 ? $72 ? 
 
 6. Find the loss % on buying wheat @ 72 cents and 
 sell ng @ 54c. ? 36c. ? 48c. ? 63c. ? 60c. ? 66c. ? 45c. ? 
 
 6. What is the gain or loss % on buying cloth @ $4 
 and selling @ $5 ? $6? $7? $3? $2/ $3.60? $4.80? 
 
 7. Find the cost of cloth which sold ©$4.50, at a loss 
 of 10%, 25%, 50%, 75%, 66§%, 33j%, i6§%. 
 
 8. Find the cost of flour which sold @ $6 a bbl. at a 
 gain of 20%, 25%p, 100%, ii^%, 9iV%, 33^/. 66a%, 14?%. 
 
 9. Iff of the selling price = cost, find gain %. 
 
64 
 
 MKNTAL ARITHMETIC. 
 
 Exercise 154. 
 
 What is the gain or loss %, if the cost is : — 
 
 1. $200 and selling price $220 ? 230? $250? $275? 
 
 2. $300 and selling price $330 ? $345? $360? $270? 
 
 3. $450 and selling price $495 ? $540? $600? $750? 
 
 4. $750 and selling price $735 ? $675 ? $600 ? $690 ? 
 
 5. $625 and selling price $750? $875? $500? $612.50. 
 
 6. $3.20 and selling price $4.00 ? $4.80 ? $2.40 ? $2.80 ? 
 
 7. $7.20 and selling price $8.00? $6.40? $9.60.? $8.40? 
 
 Exercise 155* 
 
 1. I gained 25 (12J, u^) % by selling machines for 
 $75 ($63, $8.50). Find the cost of each, 
 
 2. I lost 20 (i6g, 14^) % Ijy selling cattle @ $48 ($75; 
 $9.60). How much did each cost me ? 
 
 3. I gained $5 ($8, $2.50) by selling some sheep for 
 $20 ($20, $1 5). What was the gain % ? 
 
 4. I lost $5 ($10, $2.50) by selling my land @ $20 
 ($15, $17.50) an acre. What was the loss % ? 
 
 5. I gained 10 (33^, i6§) % by selling chairs @ $22 
 ($24, $2.80). Find gain % by selling @ $2 5 ($20, $3). 
 
 6. I lost 12J (9^, 37|) % by selling for $35 ($40, $6). 
 Find my gain or loss % by selling for $48 ($33, $8.40). 
 
 7. I received $300 ($450, $450) for 50 (90, 100) bbls. 
 flour— a gain of 20 (25, 12J) %. Find cost per bbl. 
 
 Exercise 156. 
 
 Selling Price. Gain. , Rate. 
 $io($i5, $15) 
 
 $3 
 
 ••, 25(12^,37^)%. 
 
 $15 ($18, $21). $6 
 
 $2 5 ($30, $36). .. 25(20,12.1)%. 
 
 $5 i6e(33j,iii)%. 
 
 Cost. 
 
 1. $8 ($10, $12). 
 
 2. $8 ($9, $15). 
 
 3. $6 ($16. $24). 
 
 4 
 
 6 
 
 8 
 
PERCENTAGE. 
 
 65 
 
 Exercise 157. 
 
 Cost Selling Price. Loss. Rate. 
 
 1. $2.50. $2 ($1.50) 
 
 2. $4.50. $.5o($i.5o) 
 
 3. $9.60 i2H6j)%. 
 
 4 $3.60 ($4.80). $.60 ($.60) 
 
 5 $7.5o($5.5o) i4f('6|)%. 
 
 6 $.45 ($-75). 9f'i(8:^)%- 
 
 Exercise 158. 
 
 1. A man bought 450 (375, 525) bbls. apples and sold 
 them at a gain of 20%. Find the gain. 
 
 2. I bought 350 (420, 640) bbls. flour, and sold at a 
 loss of 15 (25, 37^) %. Find the loss. 
 
 3. A man bought 320 (440, 760) bbls. potatoes @ $.80 
 ($.96, $.60) and sold them at a loss of 15 (25, i6§) %. 
 Find total loss. 
 
 4. B had a flock of 640 sheep, and the increase this 
 year is 25 (12^, 87^%. Find the present flock. 
 
 6. How many gals, water must be mixed with 9 ( 1 2, 15) 
 gals, wine that 25 (20, i6§) % of the mixture is water.? 
 
 6. I bought cloth ® $75 a yard and sell it to gain 
 15 (25, 45) % on each yard. Find gain % on 32 yds. 
 
 7. Bought cloth @ $.50 ($.60, $.80) a yard. Find the 
 marked price, so that I may give 20% (25%, 10%) dis- 
 count, and slill make a gain of 20% (10%, 12.5%). 
 
 Exercise 159. 
 
 What is the number which is : — 
 
 1. 480 when increased 50% ? 25%? 20%? 60%.? 140%? 
 
 2. 880 when increased 10% ? 25% .? 33^% ? 665 ? 14^% ? 
 
 3. 480 when decreased 50% ? 25% ? 33?^% ? 20%? i iS% ? 
 
 4. 420 when decreased 25% ? 20% ? 16^% ? Mf % ? i2.l% ? 
 6. $840 when increased 33^% ? 25%? 20%? i6|% ? 
 
 6. $840 when decreased 163% ? i4f % .? 12^%? 1 1,1% ? 
 
66 
 
 MKNTAL ARITHMETIC. 
 
 Exercise i6o. 
 
 1. What % is gained by selling 15 oz. for i lb.? 35 
 inches for i yd. ? 1750 lbs. for i ton? 
 
 2. At what % above cost must I mark goods to gain a 
 discount of 10% and yet gain 8(17, 26) % t 
 
 3. My flock increased 50% in three successive years, 
 and then I had 270 sheep. Find each year's increase. 
 
 4. The population of a city decreased 10% in each of 
 three successive decades, and now is 7290. Find the 
 population at each census. 
 
 6. Find my gain % by buying at a discount of 20%, 
 and selling at an advance of 10 (20, 25) % on list prices. 
 
 6. Iff f|, t'^) of the selling price is 10 (4, 2) % less 
 than cost, find the gain % at which the goods are sold. 
 
 7. I bought 8 (16, 20) cattle @ $25. Four of thern die, 
 and I sell the others @ $40. Find ga'n or loss %. 
 
 Exercise 161. 
 
 1. I sell 5 sheep for what 6 (7, 4) cost me. Find the 
 gain or loss %. 
 
 2. I sell goods to A at to% profit, who sells to B at 
 20% profit. Find my gain % had B bought from me. 
 
 3. I sold a horse for $72 ($63, $170), losing 20 (10, 
 15) %. Find the price to gain 20 (10, 15) %. 
 
 4. I lost TO (20, 25) % by selling a horse. Had I 
 received $3o($25, $15) more I had gained 5%. Find cost. 
 
 6. I sold two lots @ $300 ($450, $180), gaining 20 
 (16;^, 12^) % on one and losing 20 (10, 10) % on the other. 
 Find gain or loss. 
 
 6. By selling what cost $90 C$80, J75), I gain 10 (20, 
 25) % of the selling price. Find the selling price. 
 
 7. By selling what cost $90 ($80, $84) I lose 12J (33^, 
 i6§) of the selling price. Find the selling price. 
 
 8. In two successive decades the population increased 
 20%, and now is 2880. Find the population 20 years ago. 
 
PERCENTAGE. 
 
 (^1 
 
 Insurance. 
 
 Insurance is a system in which one party, on receiving a 
 certain sum from another, undertakes to pay a specified sum 
 to the owner of a propeny, in case of loss by fire, water, etc., 
 within a certain time. 
 
 The Premium is the amount paid to secure the insurance. 
 
 The Policy is the written agreement or contract. 
 
 The Risk is the amount promised in case ^f loss. It is 
 usually less than the value of the property. 
 
 Exercise i6a. 
 
 Amount of Risk. Rate of Ins. Premium. 
 
 1. $500 (f 750, $960). ia2)%- 
 
 2. $800 ($640, $960). \k%1)7o- 
 
 3. $600 ($720, $750). 
 
 4. $900 ($450, $480) 
 
 5 
 
 $3 ($5.40, $6). 
 $6 ($6.75, $6). 
 $4 ($7.50, $10). 
 $9 ($7.50, $10). 
 
 8 \.,' 'a/ /o* 
 
 6 fa,2|)%. 
 
 Exercise 163. 
 
 1. Find the premium to insure a property worth 
 $ 1 200 ($750, $960) for 3 of its value ® f (i, 1 J) %. 
 
 2. Find the value of my property if I paid $6 ($7.50, 
 $13.50) to insure it for f of its value @ \ (i|, 2]) %. 
 
 3. I paid $9 ($6.40, $2 1) to insure my property for ^ of 
 its value @f (|, if) %. Find the val'ie of my property. 
 
 4. What part of the value of a property worth $ 1 500 
 is insured, if the premium @ § (|, 1;^)% is $8 ($8, $15)? 
 
 6. For how much must I insure a vessel worth $9, 500 
 ($19,500, $6,345) @ 5 (2J, io)% to get the value of ship 
 and the premium, in case of loss. 
 
 6. Find the greatest gain (loss) a company can have 
 by insuring a house for $750 ($1250) @ ^ (2) %. 
 
 7. $45 ($75, $50) is p^id to secure a risk of $2500 for 
 3 years. What is the yearly ra;e ? 
 
68 
 
 MENTAL ARITHMETIC. 
 
 \ 
 
 Hxercise 164— Bankruptcy. 
 
 1. A man has $3000 ($4500, $4800) to pay $6ocx) 
 ($7500, $6400). How much can he pay on the $ ? 
 
 2. A bankrupt's Habilities are $4500 : his assets are 
 $2250 ($1500, $3375). Find his dividend. 
 
 3. A's assets are $750 ($960, $981) and he pays 20 
 (25, 45) cents on the $. Find his liabilities. 
 
 4. B's liabilities are $6480, and he pays 25 (50, 62 J) 
 cents on the $. Find his assets. 
 
 6. C owes me $720 ($492, $976), and I get 25 
 (37h ^2.}) cents on the $. How much do I lose ? 
 
 6. A man owes $7500, and his creditors lose $2500 
 ($5000, $1875). Find assets and dividend. 
 
 7. A gets $300 ($112.50, $337.50) on a debt of $450. 
 How much will B lose on a debt of $960 ? 
 
 Exercise 165 -Partnership. 
 
 1. A and B have equal shares in a business. The 
 gain is $750 ($4325, $3475). Find the share of each. 
 
 2. A mvests $500 and B $750. The gain was $750 
 ($1250, $960). Find the gain of each. 
 
 3. A and B invest 3*700 ($924, $6475) in business, in 
 the ratio of 3 : 4. A's loss is $750 ($963, $73.50). Find B s. 
 
 4. A and B gain $2250 ($1500, $3,000) on $4,500 in- 
 vested. A received $450 ($600, $720). How much did 
 B invest in the business ? 
 
 5. A invested $500 ($600, $750) for 4 years ; and B 
 $500 i$8oo, $2000) for 3 years. Find the share of each 
 in a gain of $4500 ($2896, $9675). 
 
 6. The rent of a field is $30. A puts in 6 (2, 14) cows 
 and B 4 (8, 16) cows. Find share each pays. 
 
 7. A and B rent a pasture for $24 ($35, $40). A puts 
 in 12 (9, 10) sheep for 4 months, and B 8 (8, 20) sheep 
 for 6 months. Find share each should pay. 
 
 8. A and B paid $[500 for a house, and sold it for 
 $1800(12125). A gained $100 ($125). What did B pay ? 
 
PERCENTAGE. 
 
 69 
 
 s assets are 
 
 Exercise 166— Taxes. 
 
 What are the taxes on a property assessed at : — • 
 
 1. $800 ($600, $900) @ 1% ? i% ? i% ? f % ? f % ? f % ? 
 
 2. $800 ($1200, $4800)® i^%? ii%? i.]%? i3%? 2^%? 
 
 3. $900 ($750, $875) @ 2 (4, 6, 8, ID, 12) mills on the $ ? 
 
 4. $900 ($1250, $625)® 3(5, 7, 9, II, 15) mills onthe$? 
 
 5. $1200(3840, $960) @ 1} (2^, 3f, 4|) mills on the $ ? 
 
 6. $1200 ($750, $1800) @ 4 (2§, 3j, 65) mills on the $? 
 
 Bxercise 167. 
 
 1. A man whose property is assessed at $1500 ($2400, 
 $3000) pays $12 ($12, $22.50) taxes. Find the rate. 
 
 2. A town assessed at $2,500,000 raises $10,000 
 ($ 1 5,000, $3, 500) taxes. Find the rate of taxation.- 
 
 3. What is the rate on an assessment of $350,000, to 
 build a school worth $1400? $2100? $5250? 
 
 4. A pays $6 ($7.50, $18) on an assessment of $ 1 500 ; 
 how much should B pay on property assessed for $4200? 
 
 5. On what part of my income of $750^31200, $2000) 
 do I pay if the tax® 8 mills on the$ is $4 ($4.80, $14)? 
 
 6. What part of my income of $1200 is exempt, if I 
 pay $4 ($6, $12) taxes, at 8 (12, 15) mills on the $. 
 
 7. A collector receives 2 (3, 5) %. Find the taxes 
 raised in a town to pay $490 ($970, $3,800) for a bridge. 
 
 8. With $700 exempt, I have $1195 ($2182, $1684) 
 after paying a tax of 10 (12, 16) mills on the $. Find 
 income. 
 
 Exercise 168— Income Taxes. 
 
 Find the income tax ($700 exempted) on : — 
 
 1. $iooo($85o)@2%, 3%, i%, i%, 1%, f%. 
 
 2. $i2oo($94o)@ij%, 1,1%, 2i%, 3-J%, 4%, 7i%. 
 
 3. $ 1 500 ($ 1 2 50) @ 2 (3, 4, 6, 9, 1 2, 1 5) mills on the $. 
 
 4. $1800 ($1525)® 1 (3, 5, 7, 9, 4, 8, 16) mills on the $. 
 
 5. $2300 ($.900) @ 1 1 (2], 3.1, 2]:, 5l, SI) mills on the $. 
 e. $2 500 ($1450) @ I J (2 J, 3^, 6|, 8 J, 1 60 mills on the$. 
 
70 
 
 MENTAL ARITHMETIC. 
 
 Valuation. 
 
 1. $900 ($750). 
 
 2. $700 ($[,250). 
 
 3 
 
 4. $800 ($650). 
 
 6. $1,200 ($17.50). 
 6 
 
 Exercise 169. 
 
 Rate on $. 
 5 (6) mills. 
 
 Amount of Taxes. 
 
 6 (9) mills. 
 
 7 5 (6.4) mills. 
 
 $5.60 ($10). 
 $42 ($8.64). 
 
 $4.20 ($9.10). 
 $7.50 ($10.32). 
 
 6H8.6) mills. 
 
 Exercise 170— Customs and Excise. 
 
 1. Distinguish excise and customs ; direct and indirect 
 taxation ; specific and ad valorem duty. 
 
 2. Find the duty on books valued at $700 ($450, $3.75) 
 at 5 (10, 20) % ad valorem. 
 
 3. Find the duty on dry goods invoiced at $1,200 
 ($750, $2.25) at 12J (25, 33^) % ad valorem. 
 
 4. Find the duty on 640 yds. tweed @ 75 cents, at an 
 ad valorem duty of 20 (25, 37^) %. 
 
 6. Find the specific duty on 750 gals, wine worth $3 a 
 gal., if the rate be 36 (48, 64) cents a gal. 
 
 6. Find duty on 480 gals, wine @2. 50 ; the specific duty 
 is 25 (35, 75)centsagal ; the ad val. duty is 25 (33 J, i6|)%. 
 
 7. I paid $40 ($90, $.70) customs on goods, valued at 
 $800 ($750, $3.5o,>. Find the ad valorem duty. 
 
 8. Find the duty on goods invoiced at ^450 12s. 6d.y 
 if the ad val. duty be 10 (20, 25) %. 
 
 Exercise 171. 
 
 Value of Goods. Rate of Duty. Amount of Duty. 
 1. $600 ($7 50, $8,75). 12(16,20)% 
 
 2. $500 ($650, $6.25). 
 
 $60 ($130, $1.50) 
 
 3 15(25,75)%. .$30 ($7. 50, $3-75). 
 
 4. $8oo($84o,$4.8o). I2?j(i4f, i6§)%. 
 
 6. $900 ($960, $4.50) 
 
 6 2J(6}, 6^)%. $25 ($7.50, $.48). 
 
 $200 ($320, $.375). 
 
PERCENTAGE. 
 
 71 
 
 Simple Interest. 
 
 Interest is the money paid for the loan of money. 
 
 The Principal is the money loaned. 
 
 The Unit of Time is one year. 
 
 The Rate per cent, is the interest on $ioo for i year. 
 
 The Amount is the principal + the interest. 
 
 Exercise 172. 
 
 1. I borrow $100 for a year. How much interest 
 must I pay at 3% .? 4% ? 5% ? 8% ? 9% ? 12% i 7% ? 
 
 2. Money is going at 4%. How mucji interest a year 
 do I pa,y for $100.'* ^200? $500? $700? $900? $1200? 
 
 3. What is the yearly interest on $200 @ 5% ? $300 @ 
 6% ? $500 @ 7% ? $600 @ 8% .? $900 @ 9% ? $400® 12% ? 
 
 4. What is the interest ® 6% /<?ra«««w on $400 for 
 I year ? 2 years ? 3 years ? 4 years ? 7 years ? 5 years ? 
 
 6. What is the interest @ 6% per an. on $800 for i 
 year ? ^ yr. ? J yr. ? f yr. ? J yr. r § yr. ? \ yr, ? |)t. ? 
 
 6. At 8% per an. what is the interest on $600 for i 
 year ? 6 mos. i 3 nios. ? 9 mos. ? 4 mos. ? 8 mos. ? 
 
 7. At 6% per an. find the interest on $800 for i^ yrs., 
 2^yrs., ijyrs., 2J yrs., i^yrs., 3 J yrs., 6| yrs. 
 
 8. What is the interest ©9% on $800 for i yr., 6 mos. ? 
 I yr., 3 mos. ? 2 yrs., 9 mos. ? 3 yrs.^ 4 mos. ? 
 
 Exercise 173. 
 
 Find the simple interest on : — 
 
 1. $100 for I year® 4%, 6%, 10%, 8%, 9%, 7%. 
 
 2. $200 for I year® 5%, 8%, 7%, 10%, 6%, 9%. 
 
 3. $200 for 2 years @ 4%, 6%, 8%, 5%, 7%,.9%- 
 
 4. $7oofor2years@i%, 1%, f%, ii%, 2?.%, 4^%- 
 6. $300 for 2 years @ 4l %, S\7o. 6i%, 7.]% 12.]%. 
 
 6. $400 for 2 years ® 4^%, 5lX 62%, 8]%, 3^%, 6§%. 
 
 7. $800 for I year® 6%, 8%, 5%, 7%, 4], 6J, 8^%. 
 a $6ooforiiyears®6%, 8%, 5%, 9%, 3^%, 6i%. 
 
72 
 
 MENTAL AKITHMETIC. 
 
 Exercise 174. 
 
 What is (i) the interest on ; (2) the amount of: — 
 
 1. $250 @ 6% for I yr. ? (2, 3, 5, 7, 6, 9) yrs. ? 
 
 2. $350 @ 8% for I yr. ? (I f , |, f, |, |) yrs. ? 
 
 3. $750 @ 9% for 4 mo. ? (8, 12, 6, 3, 9) mo. ? 
 
 4. $450 @ 5% for 73 days ? (146, 219, 292) days. 
 6. $960 @ 8% for 1 J yrs. ? (2|, 2^, 3J, 3I) yrs. ? 
 
 6. $480 (<i) 6% for I yr., 6 mo. ? 3 yrs,, 4 mo. ? 
 
 7. $1250 @ 10% for I yr. 219 da. ? i yr., 146 da. ? 
 
 * Exercise 175. 
 
 1. In what time will a sum of money double itself at 
 (4, 5, 6, 8, 10, 9, 7) %, simple interest ? 
 
 2. At what rate % would a sum of money double itself 
 in 2 (4, 5, 8, 6, 3, 7, 9, 10, 20) years ? 
 
 3. At 6 %, to what fraction of itself will a sum of 
 money amount in 3 yrs., 4 mo. ? 4 yrs., 6 mo. ? 
 
 4. In 3 yrs., 4 mo. what fraction of the principal will 
 the interest be @ 3 (6, 9, 15, 1 2) % ? 
 
 6. What is the interest on ^600 16.S. Sd. for i (2, 3) 
 year at 4% ? 5% ? 6%.? 10%.? 8% ? 7-!%? I2.J%? 
 
 6. What is the amount of £7So 12s. dd. in i (2, 3)- 
 year® 8% ? 4%? 6%.? 5%? 121%? 6-}% .? 
 
 Exercise 176. 
 
 Principal. Rate. Time. Interest. Amount. 
 
 1. $100(200) 6(7% I yr 
 
 2. $300 (600) I yr. $27 (36) 
 
 3. $400 (900) 5 (6)% .... $60 (io8) 
 
 4. $400 (700) 2 (3) yrs $448 (784). 
 
 5 5(7)% 2 (3) yrs. $60 (84) ...: 
 
 6 6(5)% .... $144(70). $774(770). 
 
 7. $500 (800) 4 (5)% $580 (920). 
 
 8 1 1 yrs. $72(90) $672(840). 
 
 
 
 8(6)% 2^ yrs ^300(345). 
 
PERCKNTAtiK. 
 
 73 
 
 Exercise 177 -Bank Discount. 
 
 Find the bank discount on a note for : — 
 
 1. $400 ($750, $625) due 
 
 2. $600 ($450, $640) due 
 
 3. $500 ($800, $320) due 
 
 4. $800 ($750, $640) due 
 
 5. $700 ($650, $62|) due 
 
 6. $900 ($550, $325) due 
 
 7. $350 ($960, $360) due 
 
 in I year at 4 (6, 8) %. 
 in 6 mo. at 6 (8, 5) %. 
 in 3 mo. at 8 (6, 10) %. 
 in 9 mo. at 6 (8, 10) %. 
 in -jz da. at 10 (5, 6) %. 
 in 146 da. at 6 (7, g) %. 
 in 292 da. at 7.1 (12^, 8J) %. 
 Exercise 178. 
 
 1. How much will I receive for a note for $450 
 (S75» $37-50) due in 2 (6, 4) mo.— discount 6 (8, 12)% .? 
 
 2. A note for $259, due in 3 (4, 6) mo., is discounted 
 at 6%. How much 'does the bank pay for it ? 
 
 3. A note for $356 ($750, $360), due June 15, is dis- 
 counted at 5 (6, 8) % on April 4. Find the bank's gain. 
 
 4. I lose $2 ($1.80, $3) by discounting^ a note for $75 
 ($60, $37.50) due in 4 (6, 8) mo. Find rate of discount. 
 
 6. On July 8, the bank discounts a note for $50 at 6 
 (8, 10) %, paying $49.40 ($48.40, $48). When is it due ? 
 
 6. Find the discount and the proceeds of a note for 
 ;^45o Zs. 4flf., due in 3 (8, 6) mo., at 8 (7^, 6) %. 
 
 Exercise 179. 
 
 Face of Note. 
 
 1. $300(450). 
 
 2. $600(750). 
 
 Time. Rate. Discount. Proceeds. 
 
 I year. 7 (9)% 
 
 6 mo $18 (30) 
 
 3. $800(350) 5(8)%. $10(7). 
 
 4. $500 (850). 8 mo. 
 
 6. $900(750) 7(6)% 
 
 6 73 da. 6(8)%. $8.40(12) 
 
 7 146 da. 5 (5)% $882 (441). 
 
 8 6(9)%. $12(27). $388(423). 
 
 9 Z\r^o $15(25)- $785(775)- 
 
 $480 (799). 
 $858 (735)- 
 
74 
 
 MENTAL AKHHMEl'IC. 
 
 Exercise 180— True Discount. 
 
 1. Find the amount of $400 ($750, $836) in i year at 
 6 (8, lo)%, simple interest. 
 
 2. What sum will amount to $212 ($648, $49.50) in i 
 year at 6 (8, io)%, simple interest ? 
 
 3. Find the present value of a deot of $224 ($290, 
 $72.90) due in 2 years, if money is worth 6(8, I2.j)%. 
 
 4. Find the present worth of a note for $327 ($330, 
 $36.30) due in i.^ (i|, i J) years at 6 (8, 12) %. 
 
 6. Find the true discount on $612 ($721, $420) due in 
 3 (4, 6) mo. @ 8 (9, 10) %. 
 
 6. Find difference between true and bank discount 
 on $510 ($520, $530) due in 6 (8, 9) mo. at 4 (6, 8) %. 
 
 7. The difference between the true and the bank dis- 
 count on a sum of money due in 4 (6, 10) mo. at 6 
 (10, 6) % is $. 16 ($1.50, $2^. Find the sum of money. 
 
 Exercise 181. 
 
 Find(i) the true discount ; (2) the present worth, of: — 
 
 1. $220 ($440, $550) due in i year at 10%. 
 
 2. $336 ($560, $784) due in 2 years at 6%. 
 
 3. $312 ($364, $468) due in 6 months at 8%. 
 
 4. $416 ($260, $572) due in 146 days at 10%. 
 
 Exercise i8a. 
 
 Face of Note. Time. Rate. True Dis. Pres. Worth 
 
 1. $420 (636). I year. 5 (6)% 
 
 2. $545(345)- 2 yrs $45(45) 
 
 3. .$412(260) 6.8)%. $12(10) 
 
 4. $424 (386). 8 mo 
 
 6. $742(675) 8(12)% 
 
 6 73 da. 5(io)%- $3(i.)- 
 
 7 2 19 da. 10%. 
 
 8 6 (8). Us (90)- 
 
 $400 (350). 
 $700(625). 
 
 9. 
 
 2,j yrs 
 
 » • * • 
 
 $36 (60). 
 
 $750 (450). 
 $500(750). 
 $360 (400). 
 
PKKCKNTAOK. 
 
 75 
 
 Exercise 183— Compound Interest. 
 
 What is the compound interest on : — 
 
 1. $100 for 2 years ® 10% ? 8% ? 6% ? 
 
 2. $200 for 2 years @ 5% ? 6% ? 8% ? 
 
 3. $400 for 2 years © 10% ? 6j % ? 1 2.1 % ? 
 
 4. $500 for 3 years @ 6% ? 8% ? 20% ? 
 
 6. $500 for 7. years @ 8 (6) % payable half-yearly. 
 
 6. $800 for I year % 10 (8) % payable quarterly. 
 
 7. $750 for I.]- years @ 8 ([2) % payable half-yearly. 
 
 Exercise 184. 
 
 1. I deposit $100 ($200, $500) in the bank each New 
 Year's Day. What will stand to my credit at the end of 
 two yeais, if the interest is 5%, compounded yearly? 
 
 2. Find the difference between the simple and the 
 compound interest on $800 (f6oo, $640) in 2 years at 5 
 (10, 12.})%. 
 
 3. The difference between the simple and the com- 
 pound interest on a sum of money for two years @ 5 
 (4, 10)% is $.25 ($.64, $4). Find the sum of money. 
 
 4. The difference between the simple and the com- 
 pound interest on $[25 ($625, $640) for two years is $.80 
 ($i.oo, $10). Find the rale %. 
 
 Exercise 185. 
 
 Principal. Time. Rate. Interest. Amount. 
 
 1. $200(250) 2yrs. 5(6)% 
 
 2. $500(750) 2yrs $40.8(124.8) 
 
 3. $400(350) .... 5(4)% $4[(28.56) 
 
 4. $300(450) 2yrs $363(544.5). 
 
 6. $600(800) .... 10(5)% $726(882). 
 
 6 2 yrs. 10% $105(84) 
 
 7 2 yrs. 10% $847(1936). 
 
 8 412.])% $51 (170) $676(810). 
 
 9 2yrs $114(159) $739(784). 
 
76 
 
 MKNTAL ARITHMKTIC. 
 
 Exercise i86— Partial Payments. 
 
 1. I borrow $100 ($200, $300) at 4 (6, 8)%. How 
 much is due at the end of one year ? Of two years ? 
 
 2. I borrow $200 at 4 (5, 6)%. In a year, I pay 
 $100. How much is due at the end of the second year? 
 
 3. I borrow $200 ($300, $500) at $10%. In a year, I 
 pay $150 ($200, $300). How much is due at the end of 
 another year ? 
 
 4. I borrow $400 ($500, $800) at 6%. In 6 mo. I pay 
 $200 ($250, $500). How much is due at the end of the 
 year. 
 
 6. I borrow $300 ($600, $700) at 4 (6, 8)%. At the 
 end of 6 mo. I make a payment and at the end of the 
 year there is $102 ($412, $237.12; due. Find the first 
 payment. 
 
 6. I borrow $200 ($300, $400)® 8%. In three months 
 
 1 make a payment, and $106 ($212, $265) is due at the 
 end of the year. Find the payment I made. 
 
 Exercise 187 —Equation of Payments. 
 
 1. I owe $300 due in 5 (6, 7) mo , and $600 due in 
 
 2 (3, 4) mo. When may I pay both at once ? 
 
 2. I owe $500 ($800, $900) due in i year. I pay $200 
 ($400, $300) now. When is the balance due ? 
 
 3. I pay $300 ($400, $750) in one payment instead of 
 $50 ($ioo, $75) a month. When should I pay it ? 
 
 4. I have 3 notes : $400 due in 8 mo. ; $600 due in 3 
 mo. ; and $500 due in 2 mo. What single payment will 
 discharge all? 
 
 6. What single note is equivalent to a note for $300 
 ($600, $800) due in 10 mo., and one for $400 ($200, 
 $200) due in 3 (2, 5) mo. ? 
 
 6. What single payment equals $300 ($400, $250) due 
 June 4, and $300 ($800, $750) due June 28 ? 
 
 7. Find the equated time for $30 due Jan. 15 ; $80 due 
 Jan. 27 ; $70 due Feb. 8 ; and $60 due Feb. 24. 
 
*^t 
 
 PERCENTAGK. 
 
 77 
 
 Exercise i88— Stocks and Bonds, 
 
 1. Find the cost of 24 (50, 63) shares ($100) stock at 
 par ; at 10% prem. ; at 20% discount. 
 
 2. Find the cost of 24 (36, 48) shares of railroad 
 stock at 75 (125, 175). 
 
 3. How much do I realize by selling 25 (30, 48) shares 
 bank stock at a discount of 40 (16, 25) %. 
 
 4. How much must I pay for 16 (20, 25) shares of 
 msurance stock quoted at -25 (30, 44) % premium. 
 
 6. How much stock going at a discount of 10 (25, 
 35) % must I sell to realize $900 ($975, $780) ? 
 
 6. I buy stock at a discount of 8 (12, 16) % and sell at 
 a premium of 5 (11, 10) %, gaining $130 (S253, $936;. 
 How much stock do I buy ? 
 
 7. Find the cash value of $800 ($900, $1600) stock 
 quoted at 87 J (66^, 62^). 
 
 Exercise 189. 
 
 1. Find my income from 30(48, 160) shares of bank 
 stock paymg a dividend of 8 (10, 12.}) %. 
 
 2. How much must I invest in 6 (7, 8) % consuls at 
 75 (83, 87 J) to have an income of $600 ($630, $640) ? 
 
 3. What rate of interest do I receive by iiivesting in 
 8 (6, 5)% consuls going at 80 (120, 62|)? 
 
 4. I invest in stock at 20 (25, 40) % premium, and 
 receive a half-ye;»rly dividend of 6 (5, 7) %. What rate 
 pf interest do I receive ? 
 
 6. Which is the better investment, 6 (5, 7) % stock at 
 75 (62^, 87^, or 8% stock at par (20% prem., 20% disc.) ? 
 
 6. At what price must 6 (8, 10) % stock be selling that 
 I may get 8 (5, 12 J) % interest on my investment. 
 
 7. What do I pay for stock that I may gain 20 
 (25» 33^) % by selling at 2 (5, 8) % prem. 
 
 8. Sold 40 shares of 6 (8, 5) % bonds at 90 (120, 62 J), 
 and invest in 4% (6, 12) % bonds at 60 (80, 125). 
 
78 
 
 MKNTAL ARITHMETIC. 
 
 Exercise 190— Brokerage. 
 
 1. Find the cost of stock quoted at 87^ (67!^, 74|)— 
 brokerage l(h i) %- 
 
 2. How much do I receive for stock sold at 62^ 
 (83I, ii2^)-brokerage 1 (^ f) % ? 
 
 3. Find the brokerage at ^ (j, ^) %, on selling 72 
 (80, 96) shares railroad stock, going at 75I (ii2|^, 187^). 
 
 4. Find the proceeds from selling 20 (24, 36) shares 
 of bank stock at 62^ (75f , 8o|)— brokerage I (§, |) %. 
 
 6. My broker buys $6400 stock for me at 62f (87^, 
 99^)— brokerage | (|, f) %. How much do I pay ? 
 
 6. I receive $2400 ($2800, $2000) for stock at 76 
 (88, 62I)— brokerage i (|, f) %. How much stock was 
 sold? 
 
 7. I pay $2Aoo ($2700, $3000) for $3600 stock. Find 
 price of the stock, if the brokerage is | (J, ^) %. 
 
 Exercise 191. 
 
 1. Find the sales to give $25 brokerage at } (J, |) %. 
 
 2. How much stock @ 88} must be sold to realize 
 $700 ($875, $i75o)» brokerage | % ? 
 
 3. How many shares, $100 each, must be sold at 37 
 (12, 24^)% discount to realize $625 ($1050, $1125), 
 brokerage ^ %. 
 
 4. A broker sells 50 (64, 96) shares stock @ ^ % brok- 
 erage, and remits $3125 ($2400, $8400). Find price of 
 the stock. 
 
 5. A broker remits $2322 ($1295, $3150) for 36 shares 
 of stock @ 62^ (37h 9°)' Find brokerage and rate. 
 
 C. Find cost of $800 in gold at 112^ (io8|, lost), 
 brokerage | (|, |) %. 
 
 7. Bou;,;ht 36 shares canal stock at 87^ and sold at 
 io8|^. Find gain, brokerage ^ % in each case, 
 
 8. At what price must I buy 10(12, 15)% stock that 
 it may yield the same income as 6% stock @ 90 ? 
 
PERCENTAGE. 
 
 79 
 
 Exercise 192— Review. 
 
 1. A gallon is what % of a peck ? A bushel? 
 
 2. A has $36 ; B, $24. What % has each of the others ? 
 
 3. A lost f (f, I) of his money. What % remains ? 
 
 4. What monthly rent will allow 4 (6, 7^) % on a house 
 that cost $3600 ? 
 
 6. What part taken from a numl^er is equal to 25% 
 (•35> f) of the remainder? 
 
 6. A book was sold for ^ (f, .87) of the cost. Find 
 the gain or loss %. 
 
 7. A earned $800, and saved 15% (25%, 37^%) of it. 
 How much did he spend ? 
 
 8. Teas @ 35, 40 and 45 cents are mixed equally, and 
 sold @ 50 (60, 65) cents a pound. Find the gain %. 
 
 9. A shed [24' X 36' X 16'] contains 27 (81, 72) cords 
 of wood. What fraction (decimal, %) of it is empty ? 
 
 Exercise 193. 
 
 1. A merchant uses a yard stick i inch too short. 
 Find his gain %. On a sale of $10.80. 
 
 2. After paying an income tax of 15 mill;3 on the $, I 
 have $788 ($1 182, $985) left. Find taxes and income. 
 
 3. My income tax ($400 exempt) at 8 (10, 12) mills on 
 the $, is $12 ($16, $18). Find my income. 
 
 4. A owns $40 less than ^ of the stock. The gain is 
 $300, and B gets $120. Find A's gain and the stock 
 each has. 
 
 5. Bought chestnuts @ $2 a bu. and sold @ 5c. a pint. 
 Find the gain or loss %. 
 
 6. The difference between a 35% discount and a dis- 
 count of 30% and 5%, is 60c. Find the amount of the 
 invoice. 
 
 7. I lent A $500 ($700, $800) for 3 mo., and $500 ($300, 
 $3oor) foj- 7 mo. For how long should he lend me $1000 
 ($600, $900) to return the compliment ? 
 
So 
 
 MENTAL ARITHMKTIC. 
 
 Exercise 194— Theory. 
 
 1. Give the four ways of denoting per cent. 
 
 2. Give the various ways of finding the % of a number. 
 
 3. Name the applications of percentage which involve 
 time. Name some which do not involve time. 
 
 4. What are aj,ents, commission merchants, brokers, 
 assessors, collectors ? 
 
 6. Show the relation between the cost price, the sell- 
 ing price, and the gain or the loss. 
 
 6. What is a tax ? An income tax ? A poll tax ? A 
 property tax ? An exemption from taxation ? 
 
 7. Distinguish direct from indirect taxation, and give 
 examples of each. 
 
 8. Upon what base is brokerage computed ? 
 Upon what base is commission computed ? 
 Upon what base is the loss or gain computed ? 
 
 9. What is an invoice ? For what purpose is a certi- 
 fied invoice required ? 
 
 Exercise 195. 
 
 1. Distinguish simple interest fromcompoand interest. 
 
 2. What is true discount ? Bank discount ? 
 Which is the greater ? How much the greater ? 
 Distinguish both from trade discount. 
 
 3. In business, how many days are considered as a 
 month ? 
 
 4. What is meant by 3 days of grace ? 
 
 6. Distinguish between when a note is nominally due 
 and legally due. 
 
 6. Define assets, liabilities, dividends. 
 
 7. Distinguish commission from brokerage. 
 
 8. Show that a fraction represents the quotient of the 
 numerator by the denominator, 
 
 9. What is meant by quoting greenbacks at 93, or by 
 saying gold is at a premium ? 
 
MECHANICAL MEASUREMENTS. 
 
 6 feet 4 inches is usually written 6' 4". 
 
 X chain =100 links = 4 rods = 2i yards = 66 feel. 
 
 X mile = 320 rods = 1 760 yards = 5280 feet. 
 
 X acre = 10 sq. ch. = 160 sq. rods = 4840 sq. yds. 
 
 Lumber is sold by the M — 1000 feet. A board i' x i' x 1", 
 or its equivalent, is i foot of lumber. If less than an inch 
 thick it is counted as i inch thick. If more than an inch thick, 
 the amount of lumber is proportional to the thickness. 
 
 Ditching is paid for by the foot, yard, or rod. 
 
 Painting is paid for by the square yard. 
 
 Bricks are usually 2" x 4" 8", and are sold by the M. 
 
 Drain Tiles are usually 12" long, and are sold by the M. 
 
 Plastering is counted by the square yard. Half the area 
 of the doors and windows is usually deducted, and the nearest 
 square yard counted as the area. 
 
 Lathing— deduct area of the doors and windows and esti- 
 mate I bundle la^hs for each 5 sq yds. of surface. 
 
 Flooring— a square = 10 feet square = 100 sq. ft. 
 
 Shingling— 1000 shingles (4 bundles) cover one s(]uare 
 = TOO sq. ft. An average shingle is 4 inches wide, and laid 4 
 inches to the weather. 
 
 Carpeting — Carpet is sold by the linear yard, and the com- 
 monest widths are 27", 30" and 36". The strips are usually laid 
 lengthwise of the room, and must be matched. If part of a 
 strip is required, the whole strip must b<;: taken ; but any fraction 
 of a yard may be purchased. 
 
 Wall Papering — A single roll is 24 feet long ; a double 
 roll is 48 feet long. The commonest width is 18 inches, but 
 several other widths are manufactured. The width of thi 
 doors and windows is deducted from the perimeter of the room 
 in calculating the number of str ps required for the walls of the 
 room. The border is sold by the yard. 
 
 Excavating— I cubic yard of earth is considered a load. A 
 cord of rough stone is 128 cubic feet = 4 loads. 
 
 81 
 
82 
 
 AIKNTAL ARITHMETIC. 
 
 IBxercise 196 Cost of ilaterial. 
 
 What is the cost, at the given price per M, of: — 
 
 1. 500(250, 960) ft. lumber @ $10? $20? $30? 
 
 2. 900 (750, 840) ft. lumber @ $5 .? $15 ? $25 .? 
 
 3. 700(1250, 720) ft. lumber @ $12.? $14.? $16? 
 
 4. 800(1750, 528) ft. lumber ©$12.50? $22.50? $32.50? 
 
 5. 1,200(880, 672) ft. lumber® $7.50? $17.50? $27.50? 
 
 6. 1,600(650, 1 260) ft. lumber® $12.50? $15.00? $17.50? 
 
 7. 2,400(480, 2472) ft. lumber @$i 1.25? $21.25? $ 13-75? 
 
 Exercise 197. 
 
 1. What is the value of 500 rails ® $8 per M ? $4? 
 $12? $16? $20? $10? $30? $15? $45? $90? $9? 
 
 2. What will a man get for hauling 4,800 bricks @ 
 $2.5operM? $1.25? $.50? $1.00? $1.50? $.75? $2.25? 
 
 ^ What will I receive for laying 3,200 tiles @ $1.25 
 pevM? $2.50? $3.75? $7.50? $15? $5? $1.50? $.75? 
 
 4. What will a man receive for pihng 1,250 ft. lumber 
 O $1.00 per M? $.50? $.25? $.75? $1.50? $2.25? 
 
 6. At $2.50 per M, how much will I get for making 
 400 bricks ? (800, 200, 600, 300, 900, 450) bricks ? 
 
 6. At $[2.50 per M, what do I get for splitting 800 
 rails? (1600, 400, 100, 500, 1500, 300, I2CO, 120) rails? 
 
 7. At $7.50 per M, how much do I get for laying 400 
 bricks ? (40, 80, 160, 320, 640, 960, 480, 120, 840) bricks? 
 
 Exercise 198. 
 
 What is the cost, at the given price per M, of: — 
 
 1. 700 (750, 720) bricks @ $10? $20? $40? $50? 
 
 2. 600 (250, 640) bricks @ $5 ? $25? $35? $75? 
 
 3. 500(1750, 960) bricks® $12? $22? $32? $52? 
 
 4. 400(480, 996) bricks @ $12.50? $22.50? $52.50? 
 6. 800 (650, 990) tiks @ $4 ? $6 ? $8 ? $7 ? $9 ? 
 
 6. 1,200(1250, 1750) tiles® $12? $14? $16? $18? 
 
 7. 2,000(1500, 2500) tiles @ $22? $24? $36? $48? 
 
 8 
 
 H 
 
 1. 6 
 
 2. 9 
 
 3. 7 
 4 
 5 
 6 
 7. 
 8. 
 9. 
 
 1. 
 
 24' X 
 48' x< 
 56' X 
 
 2. 
 
 27'? 
 
 36'? 
 
 54'? 
 
MECHANICAL MEASUREMENTS. 
 
 83 
 
 Exercise 199 -Fencing. 
 
 How long a fence would enclose a field : — 
 
 1. 
 2. 
 
 3. 
 4. 
 5. 
 6. 
 7. 
 8. 
 9. 
 
 6 ch. X 4 ch. ? 
 9 rds. x6 ids. ? 
 
 7 ch. X 8 ch. ? 
 
 8 rds. X 9 rds. ? 
 
 35 yds. square ? 
 48 yds. square } 
 57 rds. square ? 
 65 ch. square? 
 84 rds. square ? 
 
 36 yds. X 64 yds. ? 25 yds. x 45 ft. ? 
 75 yds. x 85 yds. ? 45 yds. x 60 ft. ? 
 
 87 rds. X 63 rds. ? 
 95 rds. x75 rds, ? 
 
 16 yds., 2 ft. 
 
 23 yds., I ft. 
 
 75 yds. x 60 ft. .? 
 24 rds. X 24 yds. ? 
 X 13 yds., I ft. .? 
 X 26 yds., 2 ft. ? 
 45 yds., I ft. X 21 yds., i ft. } 
 24 ch., 2 rds. X 10 ch., 2 rds, } 
 36 ch., 3 rds. X 23 ch., i rd. ? 
 
 Exercise 200. 
 
 1. How many posts, 8' apart, to fence a field : — 
 24' X 40' ? 24 yds. X 32 yds. } 8 rds. x 16 rds. ? 
 48' X 64' ? 64 yds. X 80 yds. ? 8 rds. x 24 rds. ? 
 56' X 72' ? 88 yds. x 96 yds. ? 16 rds. x 32 rds. .? 
 
 2. How many posts, 9 feet apart, for a straight fence : — 
 27'.? 9 yds..? 12 yds..? 18 rds. .? 3 ch. ? 15 ch. .? 
 36' ? 18 yds. ? 24 yds. 1 36 rds. ? 6 ch. ? 30 ch. .? 
 54'? 45 yds.? 15 yds.? 72 rds. ? 9 ch. ? 45 ch. ? 
 
 3. How much inch lumber for a close-board fence : — 
 350 ft. long and 5 it. high ? 275 ft. long and 4 ft. high ? 
 280 yds. long and 4 ft. h igh ? 3:? 5 yds. long and 6 ft. high ? 
 
 20 rds. long and 4 ft. hiyh ? 40 rds. long and 6 ft. high ? 
 
 Exercise 201. 
 
 Find the length of a fence enclosing a field : — 
 
 1. 45' X 64' 64 yds. X 56 yds. 46 ch. x 84 ch. 
 
 2. 25 yds. X 55 ft. 20 rds. x 90 yds. 
 
 3. I5ch. x2ords. 18 ch. X 28 rds. 
 
 4. 5 ch. X 90 yds. 8 ch. x 64 yds. 
 
 5. 5 ch. X 70 ft. 10 ch X 140 ft. 
 
 6. 6 yds., 2 ft. square. 
 
 7. 1 1 yds.. 2 ft. square. 
 
 10 rds. X 35 ft. 
 ko ch. X 36 rds. 
 12 ch. X J 36 yds. 
 15 ch. X no ft. 
 7 ch., 2 rds square. 
 10 ch., 40 ft. square. 
 
84 
 
 MKNTAL AUiTMMKTIC. 
 
 Exercise ao3. 
 
 Find the cost of fencing a field : — 
 
 1. [36' X 64'] @ 5c. a ft. [16 rds. x 24 rds.] @, 2c. a yd. 
 
 2. [42' X 48'] @ 6c. a ft. [25 rds. x 35 ids.] @ 4c. a yd. 
 
 3. [35' X 45'] @ 8c. a ft. [28 rds. x 42 rds.] @ 2c. a yd. 
 
 4. [53' X 67'] @ 6c. a yd. 24 rds. square @ $.94 a rd. 
 5' [36' X 54] @ 7*^- ^ y*^- 27 rds. square @ $1.02 a rd. 
 Q- [75' X 75'] @ 9c. a yd. 28 rds. square @ $ 1 . 1 8 a rd. 
 
 7. [12 rds., 4 yds. x 16 rds., 2 yds.] @- 2c. a yd. 
 
 8. [18 rds., I yd. x 16 rds., 2 yds.] @ 3c. a yd. 
 
 Exercise 303. 
 
 1. How much wire will make a 5-strand fence around 
 a field 36 rds. X 44 rds. ? 48 rds. x 52 rds. ? 135' x 165'? 
 
 2. Find weight of the wire for a 6-strand fence around 
 a field 24 yds. x 36 yds., if 5 yards of wire weigh a lb. 
 
 3. Find cost of the fence for a lo-mile railway @ 50c. 
 a rd. ; @, 20c. a yd. ; @ loc. a ft. ; @ $2 a ch. 
 
 4. It cost $20 ($150, $28.80) to fence a square field @ 
 25 (75,60) cents a rod. Find the dimensions of the field. 
 
 6. Find the cost of fencing a 10 (9, 7) acre field, which 
 is 40 rods long, @ 10 cents a foot. 
 
 6. A field is 2 (3, 4) times as long as wide. The fence 
 . t $15 ($20, $25) @ 25 cents a rod. Find dimensions. 
 
 7. A field is 48 (64, 80) rds. long and contains 12 (16, 
 20) acres. Find the perimeter of the field. 
 
 Exercise 304. 
 
 How much inch lumber is required to fence a field : — 
 
 1. 125' X 175' with a 4-ft. close-board fence? 
 
 2. 120 yds. X 80 yds. with a 5-ft. close-board fence ? 
 
 3. 16 rds. X 24 rds. with a 4-ft. close-board fence.? 
 
 4. 125 feet square with a 6-ft. close-board fence ? 
 f). I2C yards square with a 5-ft. close-ljoard fence ? 
 0. 20 rods square with a 5-ft. close-board fence? 
 
MECHANICAL MEASUREME-NTS. 
 
 85 
 
 |!xercise 205— Ditching. 
 
 1. Find the co&t of digging a ditch 60 (i 50, 750) yards 
 long @ $.75 ($1.50, $.84) a yard. 
 
 2. How much will it cost to dig a ditch 60 (150, 400) 
 rods long @ 20 (30, 28) cents a yard ? 
 
 3. What is the cost of the ditches for a mile of road 
 @ $2.50 a ch. ? @ 75c. a rod? @ 20c. a yard ? 
 
 4. I paid $90(5105, $48.75) for digging a drain (di 25 
 (35, 75) cents a rod. Find length of drain. 
 
 6. Find the cost of digging a ditch 600 ft. long, 2 
 (3, 4) feet wide, and 2 feet deep at 6c. a cub. ft. 
 
 6. Find the cost of digging a ditch 630 feet long, 5 
 (6, 9) feet wide at the top, 3 (4, 5) feet wide at the bot- 
 tom, and 3 feet deep, @ loc. a cub. yd. 
 
 7. It cost $10 ($20, $75) to dig a ditch 3 (6, 9) feet wide 
 and 3 (4, 6) feet deep at 10 (25, 50) cents a cub. yd. How 
 long was it ? 
 
 Exercise 2q6. 
 
 1. How many tiles, 12" long, will be needed for a drain 
 50 (85, 165) feet long f 
 
 2. How many tiles 12" long, will be needed for a drain 
 60 (75, 325) yards long ? 
 
 3. How many tiles, 1 2" long, will be needed for a drain 
 across and along one side of a .field [24 rd:'. x 36 rds.] ? 
 [36 rds. X 44 rds.].? [16 ch. x 24 ch.].? 
 
 4. How many tiles, 12" long, would be needed for a 
 drain across each end of a field 25 (50, 60) rods wide.? 
 
 6. At $12. 50 per M, find the cost of the tiles 1 2 (lb, 18) 
 inches long, needed for a dra'n 800 ft. (320 yds., 40 rds.) 
 long? 
 
 6. At $15 per M, it costs 4)9.60 for the tiles for a drain. 
 Find the length of the drain if the tiles arc 12" (15", 24") 
 long. 
 
 7. At 10 cents a yard, it costs $;^.^ ($44, $49.50) to dig 
 a drain across and along one side of a Hold 24 (36, 40) 
 rods wide. How long is it ^ 
 
86 
 
 MENTAL ARITHMETIC. 
 
 Exercise 307— Painting, Etc. 
 
 Find the cost ©9(12, 15) cents a sq. yd., of painting 
 the floor, or the ceiling, of a room : — 
 
 1. 12' X 15'. 
 
 2. 15'x 18'. 
 
 3. 16' X 18'. 
 
 4. i8'x2r. 
 6. 21' X 24'. 
 6. 25' X 27'. 
 
 10' X 15'. 
 12' X 16'. 
 
 15'x 16'. 
 
 16' X 18'. 
 1 2' X 20'. 
 15' X 22'. 
 
 8'4"x 12' 
 I2'6"x 12' 
 i3'6"x 15' 
 i6'6"x 15' 
 i6'6"x 21' 
 I9'6"x24' 
 
 2. 12' X 15' X 9'. 
 
 3. 13' X 14' X 10'. 
 
 4. 14' X 16' X 12'. 
 
 5. 16' X 17' X 15'. 
 
 6. 22'X28'X 18'. 
 
 io'6"x 7'6" 
 
 X 
 
 9' 
 
 io'6"x io'6" 
 
 X 
 
 9' 
 
 ii'6' X I2'6" 
 
 X 
 
 9' 
 
 I2'3"xi4'9" 
 
 X 
 
 10' 
 
 7'6" X 12'. 
 io'6"x 12'. 
 I3'6"x 18'. 
 
 9'6"x 12'. 
 i6'6"x 18'. 
 22'6" X 24'. 
 
 Exercise 208. 
 
 Find the cost, @ 3 (5, 6) cents a sq. yd., of kalsomin 
 ing the walls of a room : — 
 1. 9'xi2'x 9'. io'6"xi2'x 9'. 
 
 io'6"xi5'x 9'. 
 
 i3'6"x 15'x 12'. 
 
 i4'6"x 10' X 12'. 
 
 i6'6"xi8'x 12' 
 
 I9'6"x24' X 15'. 
 
 Exercise ao9. 
 
 1. A room is 15' x i2''x 9'. Find cost of tinting ceil- 
 ing @ 10 (12, 15) c, and walls @ 8 (9, 12) c, a sq. yd. 
 
 2. What will it cost to paint a 2 (3, 4) foot wainscot 
 around a room 1 1' 3" x 1 1^ 3" @ 1 5 (20, 25) c. a sq. yd. ? 
 
 3. Find the cost, @ 20 cents a sq. yd., of painting the 
 roof of a barn 75^ long and 36^ from eav*^s to gable. 
 
 4. I paid $5 ($10.50, $8.75) for painting a floor 15 
 (21, 21) feet long at 25 cents a sq. yd. Find width of room. 
 
 5. At 8 (10, 15) c. a sq. yd. it cost $9.60 ($16, $30) to 
 tint the walls of a room 24'' x 36'' . How high is the room ? 
 
 6. Find cost, @ 9 (12, 15) c. a sq. yd., of painting one 
 side of a 5-lt. close-board fence, 36 (48, 90) yards long. 
 
 7. Find cost of painting a 6-ft. close-board fence 
 around a field 24 rds. x 36 rds. @ 10 (12, 15) c. a sq. yd. 
 
 i2'7"x i4'5" X 12' 
 18' 8" x 174" X 15' 
 
MECHANICAL MKASUREMENTS. 
 
 87 
 
 Exercise aio— Plastering. 
 
 How many square yards of plastering will be counted 
 for the ceiling of a room : — 
 
 1. 9'xi2'xio'? io'xi2'x9'? 
 
 10' X 15' X 9'? 
 
 12' X 16' X 9'? 
 
 15' X 16' X 10' ? 
 
 15' X 20' X 10'? 
 
 20' X 30' X 10'? 
 
 Exercise an. 
 
 How many yards of plastering will be counted for the 
 walls of a room : — 
 
 2. 9' X 15'x 10'? 
 
 3. 12' X 15' X 10'? 
 
 4. 12' X 18' X 11'? 
 
 5. 15'x 18' X 12'? 
 
 6. i8'x24'x 16'? 
 
 10' X I2'6"x9'? 
 12' X I2'6"x9'? 
 16' X I2'6"x9'? 
 16' X i5'6"x 10'? 
 20' x 22' 3" X 12'? 
 2o'x24'9"x 16'? 
 
 10' X 12' X 10'? 
 
 ■? 
 
 10' 6" X I4'6"x9'? 
 12' 6"xi7'6"x 12'? 
 14' 3" X I5'9"x 12'? 
 17' 4" X 14' 8" X 15'? 
 17' 3"x2o'3"x 15'? 
 16' 2" X 21' 4" X 18'? 
 
 1. 10' X 12' X 9'? 
 
 2. 12' X 15'x 9'? 10' X 15'x 10' 
 
 3. 12' X 15'x 10'? 14' X 16' X 12'? 
 
 4. 12' X 15'x 12'? 12' X 18' X 12'? 
 6. 15'x i8'xi2'? 15'x 15'x 16'? 
 6. 16' X 20' X 14'? 15' X 20' X 16? 
 
 Exercise aia. 
 
 1. How many yards of plastering will be counted for a 
 room [12' X 15'x 9']? [i5'xi8'xi2'|? [i2'xi8'x9]? 
 
 2. What is the cost, @ 15c. a sq. yd., of the plastering 
 of a room [15' x 21' x 12] ? [15' x 18' x 12']? 
 
 3. How many yards of plastering in a room having a 
 12-inch base-board and measuring [i2'xi5'xio']? 
 
 4. How much plastering will be counted for a room 
 having a 3' wainscot and measuring [12'x i2'x9']? 
 [12'x I5'x9']? 12'x 15'x 12']? [14'x i6'x i3'J? 
 
 5. Find the cost, @ 1 5 rents a square yard, of plaster- 
 ing a room 15' x 18' x 12' (18'' x 24** x 12') having 4 
 windows 3' x 6' , and 2 doors 7' 6''^ x 4' . 
 
 6. The cost of plastering the ceiling of a room 24 feet 
 long @ 20c. a sq. yard was $8 ($9.60, $1 1.20). Find the 
 width of the room. 
 
 I 
 
1 
 88 
 
 M KNT A r , A i< rr h m k r i c. 
 
 1. 
 2. 
 3. 
 
 5. 
 6. 
 
 Exercise J13 - Lathing. 
 
 How many bundles of laths are required : — 
 
 ( 1 ) For the ceiling of a room : - 
 9' X 10' X 9' ? 12' 6" X 10' X 9' ? 1 2' 3" X 12' X 10' ? 
 9'xi5'xio'? 15' 6" X 20' X 12'? 12' 4" X 15' X 12'? 
 
 i2'xi5'xio'? 17' 6" X 20' X 15'? 12' 8" X 15' X 12'? 
 
 (2) For the walls of a room : — 
 
 4. i5'xi2'xio'? 9'6"xi3'xi2'? 1 1' 8"x i5'4" x 10' ? 
 ii'xi6'xio'? i5'6"x i6'x 12'? i5'3"x2o'9"x 10'? 
 i6'x2o'xio'? i6'6"xi5'xi2'? i4'3"xi7'3"xio'? 
 
 Exercise 214. 
 
 How many bundles of laths for a room : — 
 
 1. 12' X 15' X 12' having a 12" base-board around room ? 
 
 2. 1 2' X 1 8' X 1 3' 6" having a 1 2" base-board ? 
 
 3. 15' X 18' X 12' 6" having a 2' '^ainscot around room? 
 
 4. 12' X 15' X 10 ; doors 2 [7' x 4'] ; windows 2 [6' x 3'] ? 
 6. I2'xi5'x 1 2' ; doors 2 [7' 6" X 4] ; windows 4 [3' x 5' 6"]? 
 6. 1 5' 6" x 1 8' x 1 2' ; doors 2 [8' 6" X 4']; wind's 6 [4' x 7' 6']? 
 
 Exercise ai5 - Roofings 
 
 1. Find the surface of the roof of a barn 50(60, 75) 
 feet long, and 30 (40, 45) feet from eaves to ridge. 
 
 2. How many squares in the roof of a shed 36 (48, 72) 
 feet long, and 25 feet from eaves to ridge ? 
 
 3. How many bundles of shingles are needed for a 
 roof 24 (32, 40) feet long, and 25 feet from eaves to ridge? 
 
 4. Find cost, @ $1.25 a bundle, of shingles ne»*ded 
 for a roof 75 (64, 80) feet long, and 36 (25, 40) feet wide. 
 
 6. How many shingles, 4" wide, and laid 4" to the 
 weather, are needed for a roof [32' x 16''].? [36'' x 20'] ? 
 
 6. How many slates, S^^ wide, and laid S^^ to the 
 weather, are needed for a roof 2 [32 ' x 25 *] ? 2 [40 ' x 25 '] ? 
 
 7. Find distance, from eaves to ridge, of a roof 24 
 (36, 64) feet long, requiring 24 {2% 128) bundles shingles. 
 
 N 
 
MECHANICAL MEASURKMKNTS. 
 
 89 
 
 64 rds. X 25 cli. ? 
 48 rds. X 25 ch. ? 
 24CI1. X 20 rds. ? 
 25 rds. X 16 ch. ? 
 
 Exercise ai6— Land Areas. 
 
 How many acres in a field :— 
 
 1. 24 rds. X 40 rds. ? 12 ch. x 15 ch. .'^ loch. x 24 rds. ? 
 
 2. 36 rds. X 40 rd*. .-' 15 ch. x 18 ch. ? 36 rds. x 10 ch. ? 
 
 3. 40 rds. A 28 rds. ? 16 ch. x 20 ch. ? 32 rds. x 20 ch. ? 
 
 4. 32 rds. x 80 rds. ? 18 ch. X25 ch. ? 
 
 5. 48 rds. X 80 rds. ? 15 ch. x 24 ch. ? 
 
 6. 25 rds. X 32 rds. ? 25 ch. x 32 ch. ? 
 
 7. 64 rds. X 25 rds. ? 64 ch. x 75 ch. ? 
 
 Exercise 217. 
 
 1. From a field 12 ch. x 15 ch. I sell a field 24 rds. 
 X 40 rds. How much land remains ? 
 
 2. A field is 40 (80, 64) rds. wide, and contains 
 7 (12, 14) acres. How wide is it? 
 
 3. My farm is I mile wide and contains 80 (100, 160) 
 acres. Find the length of the fence which encloses it. 
 
 4. A square field contains 900 (1600, 3600) sq. rds. 
 Find its dnnensions and its perimeter. 
 
 6. A square field contains 10 (40, 90) acres. P'ind its 
 dimensions and the length of its fence. 
 
 6. My farm, i mi. square, is in square 40-acre fields. 
 How many fields have I ? 
 
 Find the length of fence which is required to en- 
 close these fields. 
 
 Exercise ai8. 
 
 What are the dimensions of a field whose sides are to 
 each other as : — 
 
 1.2:1 and which contains 2 ac, 130 sq. rds. ? (5) ac. ? 
 
 2. 3 : I and which contains 7 ac, 5 sq. ch. ? (7 J) ac. ? 
 
 3. 2 : 3 and which contains 3 ac, 120 sq. rds. ? (3^) ac ? 
 
 4. 3 : 4 and which contains 7 ac, 80 sq. rds. ? (i|) «c ? 
 
 5. 2 : 5 and which contains 2 ac , 40 sq. rds. ? (6}) ac ? 
 
 6. 4 : 5 and which contains 3 ac, 20 sq. rds. ? (4j)ac. ? 
 
^. 
 
 
 IMAGE EVALUATION 
 TEST TARGET (MT-3) 
 
 k 
 
 5/ i^V^ 
 
 
 &'. 
 
 /. 
 
 II I.I 
 
 11.25 
 
 ■SO "^^ II^H 
 
 1.6 
 
 j.4 
 
 III 
 
 
 \^>: '/» 
 
 Photographic 
 
 Sdences 
 Corporation 
 
 ^ 
 
 !C« 
 
 v 
 
 4^ 
 
 i\ 
 
 \ 
 
 
 23 WEST MAIN STREET 
 
 WEBSTER, N.Y. 14580 
 
 (716) 872-4503 
 
 
 6^ 
 
90 
 
 MENTAL ARITHMETIC. 
 
 2 : 3. The fence 
 Find the cost of 
 
 Exercise 319. 
 
 1. How many sods 2' x i' will be required for a lawn 
 24 (36, 48) ft. long, and 20 (30, 40) ft. wide ? 
 
 2. How many sods will be required for a lawn 36 
 yds X 48 yds., if each is [2' x 3 J ? [3' x 18"] ? [18" x 24"] ? 
 
 3. How much will it cost to pave a court 12 (24, 36) 
 yards square with flags [2' x 3'] at 75c. each ? 
 
 4. How many flags 2 (3, 4) feet square will be required 
 for a court yard 64 (75, 80) yards .square ? 
 
 6. It required 300 sods, each 2' x 3' (24" x 36") to sod 
 a lawn 60 (90) feet long. How wide was it ? 
 
 6. A lawn is twice as long as it is wide. The fence 
 around it is 600 (450, 750) feet long. Find the cost of 
 sodding the lawn @ 9 cents a sq. yd. 
 
 7. The dimensions of a iavyn are as 
 around it is 100 (150, 250) yds. long, 
 sodding it @ 2 cents a sq. ft. 
 
 Exercise 220. 
 
 1. How many sods i' 6" x 2' 6" will be required for a 
 lawn [36* X 60] ? [48' X 75'] ? [75' X 100'] ? 
 
 2. How many flags i'4''x i' 8" v/ill be needed for a 
 court [16' X 2o'J? [32' x 40'] ? [32 yds. x 40 yds.] ? 
 
 3. How many bricks, laid on edge, will be required 
 for a walk 32 (48, 80) feet long, and 6 feet wide ? 
 
 4. How many bricks, laid on edge, will be needed for 
 a road 400 yards long and 4 (6, 8) feet wide ? 
 
 6. How many paving stones each 4" x 9" will be 
 needed for a road 600 yards long and 6' (5' 3", 6' 9") wide ? 
 
 6. How long a swath 4' wide will cut 100 sq. yards ? 
 40 sq. rods ? i acre ? 
 
 7. A man turns a furrow 9" (12", 16") wide. How far 
 will he walk in plowing 4 sq. rods ? 40 sq. rods ? i acre ? 
 
 8. A man is plowing a square lo-acre field. If he 
 turns a 12" furrow how far will he have walked when the 
 work is done ? 
 
MECHANICAL MEASUREMENTS. 
 
 91 
 
 Exercise aai—Lumber. 
 
 How much lumber in a board : — 
 
 1. 
 2. 
 3. 
 
 4. lo'xi'xi", 
 
 6. I0'X2'X l" 
 
 I x rx I . 
 3'xi'xi". 
 6'xrxi". 
 
 6. I2'x2'x 1'. 
 
 7. 15' x 2' XI". 
 
 I2'XI2"XI". I2'XI'X2". I2'XI'XJ". 
 
 1 2' X 6" X i". 16' X I' X 2". 12' X 2' X I". 
 
 i6'x6"x i". 15'x i'x3". I2'x2'x iV'. 
 
 16' X 3" X i". 1 2' X 8" X 3". 16' X 2' X 2I". 
 
 16' x 9" XI". i6'x6"x3". i8'x2'x2|". 
 
 18' X 4" XI". i6'x9"x3". i6'x2'x2|". 
 
 18' X 8" X i". 1 5' X 8" X 3". 20' X 3' X 3I". 
 Exercise 22a. 
 
 1. How many feet of lumber in 3 (5, 8) inch-boards, 
 each 12 '(16', 1 8) long and i'(i5", 16") wide? 
 
 2. How much lumber in 8 (12, 20) scantlings 12' 
 (15', 24') long, 4" wide, and 2 (3, 2^) inches thick r 
 
 3. How much lumber in 10(15, 20) planks, i2'(i6', 20') 
 long, 1 2" (15", 18") wide, and 2^ inches thick? 
 
 4. How much lumber in a close-board fence 4' (5 ', 6') 
 high and 30 ft. (60 yds., 20 rds.) long ? 
 
 6. How much lumber in a 4 (6, 8) foot walk, 60 ft. 
 (50yds., 40 rds.) long— the planks 2" (3", 2}") thick ? 
 
 6. How many boards 12' x 6" x i" would make a pile 
 of lumber 4 (5, 8) ft. broad and 2 ft. high? 
 
 7. How many planks S''' ( 1 2'''', i6''0 wide, and 2''' (y^^ 
 $Y0 thick, would make a 16ad 4 ft. wide and 3' 6''' high ? 
 
 Exercise 223. 
 
 How much lumber is needed for a floor : — 
 
 1. 8' X 12'. 
 
 2. 10' X 15'. 
 
 3. 12' X 15'. 
 
 4. 15'x 18'. 
 6. i8'x25'. 
 
 6. 20' x 28'. 
 
 7. 25' X 32'. 
 
 22' X 28'. 
 23' X 27'. 
 25' X 25'. 
 24' X 26'. 
 21' X 29'. 
 
 31' 5^39'. 
 32' X 38'. 
 
 I2'6"x 16'. 
 13' 6" X 16'. 
 i5'6"x2o'. 
 17' 6" X 20'. 
 22' 3" X 16'. 
 22' 8" X 15'. 
 
 27' 9'' X20'. 
 
 93x99. 
 
 10' 4" X 10' 8". 
 
 14' 5" X 14' 7". 
 19' 2" X 19' 10". 
 19' 6':x 19' 6". 
 24' 4" X 24' 8". 
 29' 6" X 29' 6". 
 
92 
 
 MENTAL ARITHMETIC. 
 
 Exercise 324— Flooring, etc, 
 
 1. How much inch-lumber is in a floor ri6'x25']? 
 [36'x4o']? [32'x45']? [35'x48']? [25'x64']? 
 
 2. How much lumber is in a close-board fence 6 feet 
 high and 36 (45, 64, 75, 175) feet long ? 
 
 3. How much inch-lumber is in a 5 (4, 6)-foot close- 
 board fence around a lot [30' x 64 '] ? [148 ' x 252 '] ? 
 
 4. How much lumber in a 4 (5, 6)-foot walk made of 
 2" (3", 4") planks, and 25 (36, 72) yds. long? 
 
 6. How much lumber is in an 8-foot walk made of 2.J 
 (2I, 2f )-inch planks, and 20 rods long ? 
 
 6. Find the thickness of the lumber, if I used 600 
 (900, 750) feet, in making a floor [24' x 25 '] ? 
 
 7. I used 1800 (2250, 2025) feet of lumber in making 
 1 50 feet of 6 ' sidewalk. Find thickness of planks used. 
 
 Exercise 325. 
 
 1. Find cost, @ $12.50 per M, of the inch-lumber used 
 to make a floor [25 ' x 32 '] ; [25 ' x 48 '] ; [30 ' x 40 ']. 
 
 2. Find the cost of the 2|-inch planks in a 5' walk 320 
 (480, 640) feet long, @ $15 per M. 
 
 3. I use boards 4" wide to make a floor 16 (24, 36) feet 
 wide. How many boards do I use ? 
 
 4. How m?ny boards 4" wide, having a half-inch 
 tongue and groove, will be used for a floor 14 (21, 28) 
 feet wide ? 
 
 6. How much lumber will be required for a floor 
 [24' X 25'], made of boards 3 (4, 6) inches wide, and hav- 
 ing a half-inch tongue and groove ? 
 
 6. I used 1440 (1800, 1620) feet of inch lumber for a 
 close-board fence 120 yds. long. How high is it ? 
 
 7. At $15 per M, I paid $7.^^ ($12, $30) for the lumber 
 in a 5' close-board fence Find length of the fence. 
 
 8. I used 1000(1080, 1200) feet of inch -h' ber for a 
 4-foot close-board fence around a lot 25 yards long. How 
 many feet wide was it ? 
 
MECHANICAL MEASUREMENTS. 
 
 93 
 
 Exercise 226— Carpeting. 
 
 How many strips of 3-foot carpet, running lengthwise 
 of the room, are required for a room : — 
 
 1. 9'xi2'? 
 
 2. 12' X 15'? 
 
 3. I5'xi8'? 
 
 4. i8'x24'? 
 
 5. 30' X 36' ? 
 
 lo'xis'? 9'xi4'? ii'x2o'? 
 
 I4'xi8'? I2'xi6'? i6'x25'? 
 
 I6'X2I'? I8'X25'? 20'X28'? 
 
 2o'x24'? 24'X32'? 25'x32'? 
 
 32' X 36' ? 27' X 40' ? 28' x 40' ? 
 
 How many yards of carpet are required for each ? 
 
 Exercise aaj. 
 
 How many strips of 27-inch carpet, running length- 
 wise of the room, are required for a room : — 
 
 1. 9'xi2'? ii'xis'? 6'9"xi2'? 
 
 2. i8'x24'? 
 
 3. 27'x36'? 
 
 4. 36'x45'? 
 
 5. 45'x48'? 
 
 15' X 18'? 
 20' X 24' ? 
 28'x33'? 
 30' X 36' ? 
 
 7'6"x 10'? 
 12' 3" X 15'? 
 15' 6" X 18'? 
 21' 9" X 24'? 
 22' 3" X 27' ? 
 
 II' 3' X 15'!' 
 13' 6" X 15'? 
 15' 9" X 18'? 
 20' 3" X 24' ? 
 How many yards of carpet are required for each ? 
 
 Exercise aa8. 
 
 1. Find the width of a room which requires 3 (4, 7, 
 9» 8, 6, 5) strips of 3-foot carpet. 
 
 2. Find the width of a room which requires 4 (8, 6, 
 io» 5» 9» 7) strips of 27-inch carpet. 
 
 3. A room 12-feet wide requires 20 (24, 33^) yds. of 
 3-foot carpet. How long is the room ? 
 
 4. A room 13' 6" wide requires 25 (35, 28 J) yds. of 
 27-inch carpet. Find the length of the room. 
 
 5. Find width of a room 15 (18, 20) feet long, which 
 requires 25 (30, 40) yds. of 3' (27", 30") carpet. 
 
 6. A room is 15 feet square. How many yards of 3' 
 (27", 30*^ carpet would it require. 
 
 7. Which is the cheaper way to run a 3' (27", 30") 
 carpet in a room 20' x 24' ? Find the saving @ $1 a yd. 
 
 I it 
 
 ■: I 
 
94 
 
 MENTAL ARITHMETIC. 
 
 20' X 18' 6"? 
 15' X 14' 6"? 
 20' X 28' 6"? 
 30' X 15' 6"? 
 
 Exercise aap. 
 
 If the strips run lengthwise of the room, how many 3' 
 (2', 18") patterns must be taken for rooms 
 
 1. io'xi2'? 10' X 15'? 12' 6" X 12'? 
 
 2. 12' X 18'? 12' X 16'? 13' 6" X 12'? 
 
 3. 15' X 18'? I5'x2r? 16' 6" X IS'? 
 
 4. 2o'x24'? i8'x25'? 25'6"xi8'? 
 Find the length of each strip. 
 
 How much will be lost on each strip in matching ? 
 
 Exercise 230. 
 
 1. How many yards carpet are needed for 16 (18, 24) 
 steps each 8" high and 10" (12", 14") broad ? 
 
 2. What length of border carpet is needed for a room 
 I2'xi5'? I4'xi6'? II' 6" x 15' 6"? 17' 2" X 20' 4".? 
 
 3. Find cost of 27" carpet for a room 1 5' x 20' ; strips to 
 run lengthwise of room, and i' is lost in matching each. 
 
 4. Find difference in cost between carpeting a room 
 15' square with 27" carpet @ $1, and 3' carpet @ $1.25. 
 
 6. Find the width of the 75-cent carpet used for a 
 room 18' X 24', if the cost is $36 / $48 ? 
 
 6. It cost $15 ($17.50, $47.25) to carpet a room with 
 carpet 3' (30", 27") wide @ 50 (50, 75) cents. Had the 
 room been 6' (6', 4' 6") wider, it would have cost $21 
 ($24.50, $60.75). i^ind the size of the room. 
 
 Exercise 231. 
 
 Find the cost of carpeting a room : — 
 
 1. 9' X 12' with 3' (30", 27") carpet @ $.50 a yard. 
 
 2. 15' X 18' with 3' (30", 18") carpet @ $1.25 a yard. 
 
 3. 18' X 24' with 3' (27", 18") carpet @ $.75 a yard. 
 
 4. 11' 3" X 18' with 3' (27", 30") carpet @ $1.50 a yard. 
 6. 20' 3" X 24' with 3' (30", 27") carpet @ $1.25 a yard. 
 
 6. 13' 6" X 17' 6" with 3' (27", 18") carpet @ $.90 a yard. 
 
 7. 15' 9" X 22' 6" with 3' (27", 30") carpet @ $1.20 a yard. 
 
MECHANICAL MEASUREMENTS. 
 
 95 
 
 Exercise 23a— Wall-Papering. 
 
 1. How many strips of 2-foot wall-paper are needed 
 for a, ceiling which is 8 (12, 18, 15, 25) feet wide? 
 
 2. How many strips of 18-inch wall-paper are needed 
 for a ceiling which is 9(12, 15, 10, 14, 16) feet wide ? 
 
 3. How many strips of 18-inch wall-paper are needed 
 for a ceiling l7'(/'x(^']? [io'6''' x 12']? [13^6^'' x 15']? 
 
 4. How many strips of 18-inch wall-paper are needed 
 for the walls of a room [9 'x 12']? [12' x 15'J? [15'x 18']? 
 
 5. How many strips of wall-paper can be made of a 
 double roll, for a ceiling [9' x 12']? [12'x 16']? [i8'x24']? 
 
 6. How many double rolls of 18" wall-paper are needed 
 foraceiling [(/ x 12']? [12'x 16']? [12'x 15'] ? [12'x 20']? 
 
 7. How many double rolls of 1 8" wall-paper are needed 
 for the walls of a room [9' x 12' x 8'] ? [12' x 1 5' x 12'] ? 
 
 Exercise 233. 
 
 How many double rolls of 18" wall paper are required 
 for the ceiling of a room : — 
 
 1. 9'xi2'? 7'6"x8'.? io'xi2'? 
 
 7'6"x 12'? 10' x 16'? 
 
 10' 6" X 12'? I4'xi6'? 
 
 10' 6" X 16'? i6'x24'.? 
 
 13' 6" X 16'? 2o'x24'.? 
 
 How much border paper is needed for each room ? 
 
 Exercise 334. 
 
 How many double rolls of 18" wall-paper will be re- 
 quired for the walls of a room : — 
 
 1. 9'xi2'x8'.? 10' 6" X 12' X 8'.? 7' 6" X 10' 6" X 8'.? 
 
 2. 9' X 12'x 9'.? 10' 6"xi5'x9'? io'6"xi3'6"x9'? 
 
 3. I2'xi2' x9'? i3'6"xi5'xio'? 10' 6" X 16' 6" X 10'? 
 
 4. 12'x 15'x 12'? I3'6"xi8'xii'? io'3"xi6'9"xio'? 
 6. I2'xi8'xi2'? 16' 6" x 21' X 12'? I3'4"xi6'8"xi2'? 
 6. I5'xi8'xi6'.? i6'6"x24'x 15'? 16' 5" x I9'7"xi2'? 
 
 2. 12'x 12 ? 
 
 3. 12'x 16'.? 
 
 4. 15'x 16'.? 
 6. i8'x24'? 
 
 10' X 15' 6"? 
 12'x 14' 6".? 
 14' X 15' 9".? 
 16' X II' 4"? 
 
 20' X 22' 7"? 
 
 % 
 
96 
 
 MKNTAL ARITHMETIC. 
 
 Exercise 235. 
 
 1. Find cost, @ i^ cents a yard, of the border for the 
 walls of a room 1 5' x 1 8' ? 1 6' 4''' x 1 9^ 8'-' ? \f(/^ square ? 
 
 2. Find the length the strips of wall-paper will be for 
 a room 10 feet high, if the pattern is 2' (30", i'6", i yd.) 
 long. 
 
 3. How many rolls of 1 8-inch wall-paper will be needed 
 for the walls of a room [15' x 18' :; 1 1'], if the paper used 
 has a pattern 2' (3', 2' 6% i' 6") long ? 
 
 4. How many rolls of 18-inch wall-paper will be needed 
 for the ceiling of a room [12' x 15' x 12'], if the paper 
 used has a 2' (3', 2' 6", i' 6") pattern ? 
 
 6. Find the number of double rolls of 18-inch wall- 
 
 fiaper required for the ceiling and walls of a room 
 15' X 24' X 10'], having a 12-inch base-board. 
 
 6. Find the number of double rolls of 18 inch wall- 
 
 fiaper needed for the ceiling and walls of a room 
 12' X 18' X io'6"], if the pattern on the paper is 3' long. 
 
 . ■ Exercise 2136. 
 
 1. Find the cost, @ 20 cents a roll, of the 18-inch wall- 
 paper required for the ceiling' of a room [i 3' 6" x 1 5' x 10'] ? 
 [I3'6"xi6'x 12']? [i7'6"x24'x i6']?[2o'x22'9"xi6J? 
 
 2. Find the cost, @ 20 cents a roll, of the 18" paper 
 needed for the walls of a room [15' x 18' x 12'], having 2 
 doors 4' wide, and 4 windows 3' 6" wide. 
 
 3. What is the cost, @ 1 2 cents a yard, of the border 
 
 fiaper required for a room [i5'xi8']? [i6'xi4']? 
 i5'6"x 1/6"]? 
 
 4. How many double rolls of wall-paper will be re- 
 quired for the walls and ceiling of a room [12' 6" x 15' 6" 
 X 9'] if there is a door 4' wide, 3 windows 3' wide, and a 
 12" base-board around the room? 
 
 6. The border paper, ©15 cents a yard, for a room 9 
 high, and whose sides are as 2 : 3, cost $3. How many 
 double rolls of 18" wall-paper will be required for the 
 walls and ceiling of the room, if the width of the doors 
 and windows is 20 feet ? 
 
MECHANICAL MEASUREMENTS. 
 
 97 
 
 Exercise 237 - Excavating, etc. 
 
 1. How many cubic yards of earth must be removed 
 to make a cellar [12' X 15' x 6']? [15' x 18' x 8'J? 
 
 2. How manv loads of earth will be taken out to make 
 a cellar [12' X 18' X 7']? [15' x 18' x 9']? [12'x 18' x lo'l? 
 
 3. Find the cost-of drawing away the earth to form a 
 cellar 12' square aftd 6 (7, 8) feet deep, @ 75c. a load. 
 
 4. Find the cost of filling a cellar 15 feet square and 
 6 (8, 9) feet deep, ©45 cents a load. 
 
 6. At 25 cents a yard, I paid $15 ($12.50, $17.50) for 
 digging a cellar 1 5' long and 9' deep. How wide was it ? 
 
 6. A cellar 12' (15', 18') long is as deep as it is wide. 
 Find the width, if 36 (45, 96) loads of earth were removed 
 in forming it. 
 
 Exercise 238— Road-M^klng. 
 
 1. How many loads of gravel cv. ■ be taken from a 
 bank 24' long, 1 2* \yide at the bottom and 6' wide at the 
 top? 
 
 2. How many loads of gravel will put a 12" (6", 9") 
 layer on a road go yds. long and 1 5 feet wide ? 
 
 3. Find the cost of putting a 12" (4", 8") layer of gravel 
 on a road 150 yards long and 18 feet wide, @ 75c. a load. 
 
 4. At 75 cents a load, it cost $30 ($75, $37|) to put 
 a 6" layer of gravel on a road 18' wide. How long was it ? 
 
 6. It takes 10 (40, 50) loads more, to put a 12" layer 
 of gravel on a road 18' wide, than if it were 15' wider 
 Find the length of the road. 
 
 6. At 75 cents a load, it cost $270 ($180, $135) to 
 gravel a road 18' wide and 180 yards long. How deep 
 was the layer of gravel ? 
 
 7. Find the cost, per running foot, of a road 27 feet 
 wide @ 75 cents a square yard. 
 
 8. What length of road, 18 feet wide, will require 25 
 (75> 250) loads, for a 9-inch layer of gravel ? 
 
 % 
 
98 
 
 MENTAL ARITHMETIC. 
 
 Exercise 239— Review. 
 
 1. How many cent pieces, placed side by side, would 
 reach 5 feet ? 8 feet? 12 feet ? 25 yards? 10 rods ? 
 
 2. How many cent pieces, laid side by side, would 
 cover a surface tt" x 8" ? 2' x 3' ? 4' x 5' ? 6' x 10' ? 
 2 yds. X 4 yds. ? 6 feet square? 4 yds. square? 
 
 3. How many 2" cubes would form a 6" cube? An 
 8" cube? A 12" cube? A cubic foot? A cubic yard? 
 A cube 2 yards long ? 
 
 4. Find the height of a room 12' x 15' that contains 
 80 (100, 150) cubic yards of air. 
 
 6. What is the height of a room [16' x 20'] if the area 
 of the walls is 72 sq. yds. ? 80 sq. yds. ? 96 sq. yds. ? 
 
 6. It cost 48 cents to cut a log into 3 pieces. How 
 much will it cost to cut it into 2 (4, 7) pieces ? 
 
 7. The sides of a field containing 8 (6, 7) acres are as 
 4 : 5 (3 • 5» 7 • lo)' Find the length of the fence sur- 
 rounding it. 
 
 Exercise 240. 
 
 1. How much land, @ $^ a square rod, can be bought 
 for $36? 48? $75? $73.80? $ioo|? 
 
 2. What is the area of the surface of a brick 
 [2" X 4" X 8"] ? Of a six-inch cube ? Of a box [6' x 4' x 2'J ? 
 
 3. How many rotations will a wheel 11 feet in circum- 
 ference make, in going i mile ? 80 rods ? 240 rods ? 
 
 4. How many acres in a farm i mile square? 2 mi. 
 square ? 3 mi. square? i mi. x 2 mi. ? 2 mi. x 3 mi. ? 
 
 6. At $.75 a sq. ft, what is the cost of dressing the 
 top, front and enas of a stone [4' x 2' x i']? [6' x 3' x 2'] ? 
 [8'x'4'x2'j? 
 
 6. What is the cost, @ 12 cents a sq. yd., of painting 
 the outside of a box [3' x 2' x 2'] ? [4' x 3' x 2'] ? 4 feet 
 each side ? 
 
 7. Find the dimensions of a field containing 600 sq. 
 yds., and whose sides are as 3 : 2 ? As 6 : 1 ? As J : f ? 
 
MECHANICAL MEASUREMENTS. 
 
 99 
 
 Exercise 241— Review. 
 
 1. How much land will be rolled by a 9-foot roller in 
 going 1 50 feet ? 240 yards ? 40 rods i 
 
 2. How much land will be rolled in going around a 
 field 36 rods x 24 rods, with a roller 6 (8, 11) feet wide ? 
 
 8. How many 3-inch pickets, placed 3 inches apart, 
 will be needed for a fence around a lot 125 ft. x 175 ft. ? 
 
 4. How many sods, 1 2''' x i ^'\ will be needed to make 
 a 6-foot border around a flower-bed 24' x 36 ' ? 30' x 45 ' ? 
 
 6. How many panes of glass, 6" x 9", can be cut from 
 asheet ofglass 2'x3' ? 3'x4'? y'6"x6'g"? 
 
 6. Find the cost of a foot of lumber® $10 ($12, $12.50, 
 $15, $25, $30, $37.50) per M. 
 
 7. How many yards of satin, 2 (3, i^),feet wide, will 
 cover a box 1 3 ' x 4 ' x 2 '] ? 
 
 8. If 16 (24, ig\) bundles of laths were used in lathing 
 the walls of a room 16' x 20', how high is the roomi* 
 
 Exercise 242. 
 
 1. It took 45 (75, 50) flags 2' X 3' to cover a court- 
 yard. How many flags 15" x 18" would be required? 
 
 2. It cost $30 to carpet a room 1 5 ' x 18 '. How much- 
 would it cost to carpet a room 15 (18, 27) feet square with 
 the same carpet ? 
 
 3. It cost $40 to fence a square field @ 25 (50, 33J) 
 cents a rod. Find its value at $75 ($50, $32) an acre. 
 
 4. A square field contains 10 (3I, S^^j) acres. Find 
 the cost of fencing it @ $.50 ($1.25, $.75) a rod. 
 
 6. Find the cost of making a gravel walk, 3 (4, 5) feet 
 wide, around a bed 40' x 75' , @ 25 cents a square foot. 
 
 6. A mat 15 feet square is placed in the middle of a 
 floor 20^ X 24' . What part of the floor is covered ? What 
 part is uncovered ? 
 
 7. The cost of plastering the walls of a room 15 feet 
 long and 12 feet high, @ loc. a yard, was $6.40 ($7.20, $8). 
 Find its width. 
 
 I 
 
 m 
 
 .?Mi 
 
 ■1 
 
 f ft 
 
JOO 
 
 MKNTAL ARITHMETIC. 
 
 ExercUe 243— Review. 
 
 1. Find the perimeter of a field .625 mi. x .375 mi. 
 
 2. The sides of a rectangular field are as 2 : 3. Find 
 the dimensions if the area is 150 (384, 600) sq. rds. 
 
 8. Find the length of the fence around a field contain- 
 ing 3(12, 27) acres, if the sides are as 5 : 6. 
 
 4. Find the cost of fencing a square field containing 
 10 (2 J, 5|) acres @ 75 cents a lod. 
 
 6. A fence 36 yards long cost $18 ($15, $16) less than 
 if it were 48 yards long. Find its cost. 
 
 6. It cost $15 ($22.50, $30) to carpet a room 15 (18, 24) 
 feet long. If it had been 3 feet wider it would have cost 
 $16. 50 ($27, $36). Find its dimensions. 
 
 7. How many acres in a tract of land i\ miles square ? 
 
 8. Find the solid contents of a cube whose edge 
 measures 3 yds., i ft. Find its surface. 
 
 0. Find the value of a bin of wheat [5' x 8' x 12'] @ 75 
 cents a bushel. Find its weight if filled with barley. 
 
 Exercise 344. 
 
 1. What is the area of a square field whose perimeter 
 is 50 rods ? 62 rods ? 82 yds. ? 
 
 2. How many lo-acre fields in a farm 160 rds. square? 
 
 3. Find the cost of digging the post-holes, 8 feet 
 apart, around a square funn of 160 acres, @ 10 cents each. 
 
 4. How many rods of fencing will be required to en- 
 close a square 160-acre farm and divide it into 10 
 (20, 40) acre fields ? 
 
 6. How many acres in a field 15 ch. x 40 rods ? 
 
 6. Find the cost of sodding a plot 150 yds. x 75 @ 9 
 cents a square yard. 
 
 7. How long a pile of 16" (24", 30") wood will make a 
 cord, if piled 4 feet high ? 
 
 8. |f a bushel of wheat equals 1} cubic feet, how deep 
 must a bin 5' x 8' be to contain 300 bush. ? 400 bush. ? 
 
TYPE QUESTIONS. 
 
 Exercise 245— Short Methods. 
 
 1. 23x27= 
 
 2. 34x36= 
 
 3- 35x35 = 
 4. 32x38 = 
 
 6. 39x31"- 
 
 1. 2JX2J— 
 
 2. 3ix3f = 
 
 3. 4SX4J = 
 
 4. 5fx5f= 
 6. 6f x6f= 
 
 1. 2.5 X2.5 = 
 
 2. 3-25x3.75 = 
 
 3. 4.36x4.64= 
 
 4. 6.45x6.55 = 
 6. 7.27x7.73= 
 
 19 
 
 X2I = 
 
 28 
 
 X32 = 
 
 37 
 
 X43 = 
 
 65 
 
 X75 = 
 
 56: 
 
 <64= 
 
 Exercise 346, 
 
 ^l' 
 
 <2j = 
 
 3h 
 
 <2| = 
 
 6J 
 
 ><5^= 
 
 8^ 
 
 <7i = 
 
 9^ 
 
 <8H 
 
 Exercise 347. 
 
 1.75x2.25 = 
 2.95x3.05 = 
 3.85x4.15 = 
 6.55x7.45 = 
 5.64x6.36= 
 
 25x45 = 
 
 35x55 = 
 35x75 = 
 45x85 = 
 
 75x95 = 
 
 ijx35 = 
 2^x61 = 
 4ix6| = 
 3^x71 = 
 9|X3^ = 
 
 2.5x4.5 = 
 3.5x5.5 = 
 4.5x6.5 = 
 5.5x7.5 = 
 8.5x6.5 = 
 
 Exercise 348. 
 
 1. Find 73 X 770 - 53 X 570 ; 860 x 84 - 760 x 74. 
 
 2. Find 9| X 9j+ 19I X 19^ -f- 29-^ X 29J. 
 
 3. From 9.48 times 9.52 take 4.49 times 4.51. 
 
 4. Add 9j X 9|, 9.6 x 9.4 and 19.25 x 19.75. 
 
 5. Find the difference between the cost of 25 cows @ 
 $25 and 22 cows @ $28 ; 36 cows @ $34 and 26 cows at $24. 
 
 6. How much money must I give with 35 sheep @ 
 $7.50 to pay for 45 sheep @ $8; 50? 65 sheep ® $6.50.5* 
 45 lambs at $7.50? 
 
 101 
 
 I. 
 
 I 
 
 ■' •( !•! 
 
 i 
 
 ,i 
 
 ^f---^:.:..^.. 
 
MENTAL ARITHMETIC. 
 
 Exercise ^4 9 - Aggregates. 
 
 Find the aggregate of : — . ^ 
 
 1. 26, 34, 45, 28, 70, 92, 28, ^^, 39 and 35. 
 308, 547, 659, 783, 206, 865, 474 and 792. ' 
 
 2. 28 men, 36 men, 47 men, 65 men, 94 men and 53 men. 
 64 cents, 85 cents, 92 cents, yj cents and 78 cents. 
 
 3. $7.26, $4.35, $5.48, $8.54, $3.62 and $6.79. 
 $5, $2.86, $3.07, $4.50, $9, $.74 and $3.25. 
 
 4. 6' 4", 3' 9", 5' 6", 8' 2", 7' 5", 4' f and 9' 9". 
 3yds., 2 ft. ; 5 yds., 6 in. ;6ft., 4 in. ; 8 yds., 2 ft., 7 in. 
 
 6. £10 165., ;^24 I2J., ;^36 14J., ;^75 8^, and ^64 loy. 
 ^10 ids. 6</., ;^I5 loy. loflf., Ji^^d 125. 8^. 
 
 6. 4gal., 3qts. ; 5 gal.,2qts. ; 6qts., i pt. ; 3 gal., i pt. 
 4bu., 3pks. ;9bu., 3pks. ; 6pks., igal.;4bu., 1 gal. 
 
 7. 30%, 40%, 75%, 86%, 93%, 87%, 75% and 65%. 
 45%, 38%, 59%, 76%, 64%, 27%, 93% and 82%. 
 
 Exercise 250. 
 
 Find the aggregate of : — 
 
 \, I, f and f. 
 I, I, i and iV 
 2j, 3l, 32 and 2f . 
 45, 5f , 3f and 2f 
 
 1. I, \, \ and \. 
 §,f,^andi|. 
 
 2. i^, i^, I J and i^. 
 2I' 3l, 4t and 3i«2. 
 
 3. .47, .38, .64, 'IZ, .96, .85 and 59. 
 •324, -545, -768, .836, .687, .493 and .952. 
 
 4. .47, .386, .658, .56, .807, .74 and .925. 
 6.8, 4-93, 6.55, 6.8, .37, .42 and 5.08. 
 
 O. .3, .2, .9, .06, .5, .7, .88 ^nd .44. 
 
 .45, .36, .27, .63, .81, .72, .63 and. 18. 
 
 6. 4.3, 8.4, 9.27, 6.36, 7.09, 3.6 and 4.5. 
 
 .323, .040, .434, -545^6.282, 5.727 and .494. 
 
 7. .625, .375, .875, .25, .75, .125, .5 and .625. 
 
 ^11%. .75, 62.1%, f, 50%, ,375, .25, I2|%, 
 
TYPE QUESTIONS. 
 
 103 
 
 Exercise 351 Averages. 
 
 Find the average of : — ' 
 
 1. 6, 8, 9, 4, 3, 8, 7, 6, 5 and 4. 
 
 35, 28, 67, 49, 52, 73, 96, 84 and 56. 
 
 2. 45c., 86c., 29c., 64c., 53c., 78c., 97c. and 68c. 
 $23, $24, $25, $26, $27y $28, $29, $30 and $31. 
 
 3. $2.45, $3.26, $4.84, $5.63, $6.78, $7.39 and $4.65. 
 $3.25, $3.27, $3.29, $3.31, $3.33, $3.35 and $3.37. 
 
 4. 3^6^ 3^9^ 4^ 4'3^ 4^6^ 4^9^ 5', S' f' and 5^6;^ 
 3 yds., 2 ft., 7 in. ; 4 yds., 2 ft., 8 in. ; 3 yds., 9 in. 
 
 6. ;^24 I05. 6d. ; ^,36 i$s. gd. ; and ^^31 13s. gd. 
 ;^48 I05. 4d. ; ^50 14,?. yd. ; and £s^ ^^^' ^^d. 
 
 6. 4 wks., 2 d., 9 hrs. ; 5 wks., 4 d., 8 hrs. ; 2 wks., 7 hrs. 
 8 lbs., 130Z. ; 5 lbs., 12 oz. ; 3 lbs., 7 oz. ; and 18 lbs. 
 
 7. 48 bu., 36 lbs. ; 56 bu., 40 lbs. ; and 64 bu., 44 lbs. 
 16 bu., 17 lbs.; 32 bu., 29 lbs,; and 48 bu., 41 lbs. 
 
 Exercise 252. 
 
 Find the average of : — 
 
 1- h h \ and 
 h h f and 
 
 i 
 
 4' 
 
 and 
 
 12- 
 
 T2- 
 
 I, f, f and ^^. 
 
 '2. I, i h h h h t» i and 
 
 o» h \ 
 
 > 8» 2> 
 
 i i I, i» ij. ii» i}» and ij. 
 
 3. li, 2j, 3I, 4j, 5i, 6^, 7|, 9, iO¥» III and I2|. 
 i|, 2f, 4, sh (^h 7h 83, 9f and 11. 
 
 4. .44, 1.58, 2.72, 3.86, 5, 6.14, 7.28, 8.42 and 9.56. 
 1.45, i-53f I -61, 1.69, 1-77, 1-85, i-93» 2.01 and 2.09. 
 
 6. 1.23, 2.27, 3.31, 7.47, 8.51, 9.55, 6.43, 5.39 and4.35. 
 .64, .67, .7» -73. -625, .655» -685, .715 and .745. 
 
 6. 36%, 40%, 44%, 52%, 56%, 48%, 32%, 60% and 64%. 
 15%. 25%» 35%, 45%, 55%, 65%, 75%, §5% and 95%- 
 
 7. 62j%, 87U, 37r/o, 12.1%, 50%, 75% and 25%. 
 i6i%, 33^%, 50%, 83J, 662%, ,00% and ii6§%. 
 ni%, 33rA 661%, 22^%, 44U, 55f% and 77|%- 
 
 ■"i.I 
 
I04 
 
 MENTAL ARITHMETIC. 
 
 Exercise J53— Alligation. 
 
 1. I mix 2 (3, 4) lbs. sugar @ 6(9, 7) cents, with 4 
 (5, 6) lbs. @ 9 (7, 12) cents. Find average price per lb. 
 
 2. I mix 50 (25, 60) lbs. wool @ 13 (i i, 21) cents with 
 75 lbs. @ 8 (7, 12) cents. Find the average price per lb. 
 
 3. How many lbs. coffee @ 20 (35, 40) cents, must be 
 mixed with 4 (8, 9) lbs. @ 30 (20, 20) cents, to produce a 
 blend worth 25 (30, 35) cents a pound ? 
 
 4. How many lbs. tea® 75 cents, must be mixed with 
 25 (30, 20) lbs. @ 45 (40, 35) cents, to produce a blend 
 worth 50 cents a pound ? 
 
 5. A man mixed 4 (i, 8) gallons water with 8(9, 12) 
 gallons wine @ $3 ($2.50, $2^50). What is the mixture 
 worth a gallon ? 
 
 6. How many gallons of water must be mixed with 6 
 (8, 10) gal. wine @ $3 ($2.50, $4.50) to produce a mixture 
 worth $1.50 ($2, $2.50] a gallon ? 
 
 Exercise 254. 
 
 1. I buy sheep @ $3 and ® $4. Find the relative 
 number at each price, if the average cost was $3.25 
 ($3.20, $3.30). 
 
 2. I paid $600 ($540, $625) for 100 sheep, some ® $4, 
 and some @ $9 ($6, $7). How many did 1 buy at each 
 price ? 
 
 3. I sold 20 sheep for $85 ($76, $116), some ® $5 and 
 the others @ $4 ($3, $7). How many did I sell at each 
 price ? 
 
 4. I sold 10 (20, 30) lbs. tea and coffee for $6.50 ($11, 
 $18). If the tea sold @ $.75 ($.65, $.75) and the coffee @ 
 50 (45, 50) cents a lb., how many lbs. of each did I sell ? 
 
 5. I buy 3^ (7, si) lbs. tea and coffee for $2 ($2.05, 
 $3 65). How many lbs. of each do I buy if the tea costs 
 60 (40, 50) cents, and the coffee 40 (20, 40) cents a lb. ? 
 
 6. If3| lbs. tea and 6 J lbs. coffee cost $5.25 ($5, 
 $5.50), and 6} lbs. tea and 3| lbs. coffee cost $4.75 
 ($5, $6.50), find the price of each per lb. 
 
TYPE QUKSTIONS. 
 
 105 
 
 Exercise 355- Equations. 
 
 1. I f 3 geese and 4 turkeys cost $4.50 ($3.60, $7.25), 
 and 3 geese and 7 turkeys cost $6.75 ($5.40, $1 i.oo), find 
 the price of geese and tuikeys. 
 
 2. If 3 men and 2 boys earn $5.25 ($5.70, $8.35), and 
 5 men and 2 boys earn $7.75 ($8.70, $12.85), ^"^1 the 
 wages of each. 
 
 3. If 3 ducks and 4 hens cost $3. 10 ($3.80, $4.25) and 
 2 ducks and 3 hens cost $2.20 ($2.70, $3.00) find the 
 price of ducks and hens. 
 
 4. If 5 men and 3 boys earn $10.50 ($12.25, $6.50), 
 and 3 men and 4 boys earn $8.50 ($9.00, $5.00), find the 
 wages of each. 
 
 5. If 3 men arid 2 boys earn $6.00 ($7.50, $1 1) a day, 
 and 5 men and 4 boys earn $10.50 ($13, $19) a day, find 
 the daily wages of 3 men and 8 boys. 
 
 Exercise 256. 
 
 1. If 5 sheep and 4 pigs cost $39 ($53, $71), and 4 
 sheep and 9 pigs cost $66 ($83, $109), find the cost of 3 
 sheep and 5 pigs. 
 
 2. If 4 boys and 5 girls work 43 (85, 57) questions, 
 and 2 boys and 3 girls work 23 (47, 31) questions, how 
 many questions do a boy and a girl work ? 
 
 3. If 3 men and 4 women earn $10 ($17, $13.50) a 
 day, and 7 men and 2 women earn $16 ($25, $20.50) a 
 day, find the weekly wages of 6 men and 6 women. 
 
 4. To make 3 button holes and sew on 4 buttons takes 
 13 minutes ; to make 4 button holes and sew on 5 but- 
 tons takes 1 7 minutes. How long will it take to make a 
 dozen button holes and sew on the buttons ? 
 
 5. If 3 boys and 5 girls eat 29 (30, 55) apples, and 5 
 boys and 6 girls eat 46 (54, 73) apples, how many apples 
 will 10 boys and 10 girls eat ? 
 
 6. If 3 lbs. tea and 4 lbs. coffee cost $3.10 ($4-25, 
 $3.05), and 4 lbs. tea and 3 lbs. coffee are worth $3.20 
 ($4.50, $3.25), find the cost of 7 lbs. of each. 
 
 II! 
 (II 
 
io6 
 
 MKNTAL ARITHMETIC. 
 
 Exercise 357 Mixtures. 
 
 1. If 5 oz. green tea is mixed with 7 oz. black tea, How 
 many pounds of each will be in 72 (96, 27) lbs. of the 
 blend? 
 
 2. I blend 24 (48, 36) lbs. tea, @ 25 cents, with 16 
 (12, 44) lbs. @ 20(30, 36) cents, and sell® 30(40, S3) 
 cents. Find my gain or loss ?. 
 
 3. I bought 10 (8, 9) lbs. tea and 12 lbs. coffee for 
 $8.40 ($12, $11.70). Find the price of each, if the tea 
 cost 40 (25, 25) cents more, a pound, than the coffee. 
 
 4. If 24 lbs. of tea @ 50 cents, and coffee @ 30 cents, 
 are worth $9.60 ($10, $10.40), find the number of pounds 
 of each. 
 
 6. If 5 lbs. tea @ 40 (60, 80) cents be mixed with 7 
 (3, 3) lbs. @ 50 (80, 50) cents, and the blend sold ©55 
 (75, 55) cents, find the gain or loss %. 
 
 Exercise 358. 
 
 1. If 2 hens and 3 ducks are worth $2.30 ($1.85, $2.05) 
 and 3 hens and 5 ducks are worth $3.70 ($3, $3.30), find 
 the difference between the price of hens and ducks. 
 
 Find the cost of i hen and 2 ducks. 
 Find the cost of 5 hens and 8 ducks. 
 Find the cost of 8 hens and 12 ducks. 
 Find the cost of 7 ducks and 1 1 hens. 
 
 2. In a mixture of 60 gal., 20 % (25%, 33j%) is water. 
 How many gallons must be added so that 25 % (40%, 
 66|%) may be water? 
 
 8. In a mixture of 50 gal., 50% is water. What must 
 be added so that 25% (i6§%, i2|%)of the mixture may 
 be wine? 
 
 4. I mix 2Q gallons of water and 40 gallons, of wifte.. 
 What must be added so that ^ (.75, 87^°') ^^V be wine? 
 
 6. How much water must be added to a mixture of 12 
 (7» 9) gal. wine and 3 (4, 2) gal. water, so that § (.35. 
 75%) of the mixture may b6 wine ? 
 
TYPR Q IT EST IONS. 
 
 107 
 
 Exercise 359— Election Questions. 
 
 1. At an election, A got 3450 votes out of 7329 (4345, 
 8067) votes cast. How many did B get ? 
 
 2. A got 4325 votes, and B got 3864 (5729, 6500) 
 votes. Which was elected, and what was his majority ? 
 
 3. A got T487 votes out of 35 24 (3700, 3164) votes cast. 
 Find B's majority. 
 
 4. A and B, the candidates in »n election, received 
 4250 and 3200 (3427 and 4000 ; 4^56 and 3789) votes 
 respectively. Which was elected, and what was his 
 majority? 
 
 6. A and Fi were the candidates for mayor. A got 
 4352 (6478, 5369) and B got 5783, votes. Which was 
 successful, and what was his majority ? 
 
 6. In an election, A got a majority of 63 (85, i27Jout 
 of 725 votes cast. How many votes did B get ? 
 
 7. In an election, 2568 ballots were cast. A's major- 
 ity over B was 28 (74, 132). How many votes did each 
 get? 
 
 Exercise 260. 
 
 1. In an election, A got § (-55, 60%) of the votes, and 
 B received 540 (2 160, 9360) votes. How many did A get ? 
 
 2. A received ^ (.45, 37j%) of the votes and B's 
 majority was 75 (96, 72). Find the vote for each. 
 
 3. In an election, A got f (.75, 62^%) of the votes and 
 the majority was 640. How many votes did each get ? 
 
 4. In an election, the votes for A and B were as 2: 3, 
 (as 3 : 4, as 4 : 7) respectively, and the majority was 360. 
 Find the vote for each. 
 
 6. In an election, the number of ballots cast for A 
 and B were as 3 : 5 respectively, and B's majority was 
 96 (144, 720). Find the vote for each. 
 
 6. In an election, 8470 votes were polled for A and B 
 in the ratio of 3 : 4 (4 : 7, 6:5) respectively,. Find the 
 result of the election. 
 
 ; 
 i I 
 
 i 
 
lo8 
 
 MENTAL ARITHMETIC. 
 
 Exercise a6i— Remainders. 
 
 1. A man spent ^ (^, |) of his money, and had $750 
 left. How much had he at first ? 
 
 2. I paid J Qy ^) of my money for a cow, and ^ (J, ^) 
 of the remainder for a stove, and had $24 left. How 
 much had I at first? 
 
 3. A man spent § (J, j^) of his money, and lost J (3, h) 
 of the remainder, and had $25 ($35, $45) left. How much 
 had he at first ? 
 
 4. I gave $5 more than ^ (J, f)ofmy money for a 
 book, and had $7 left. How much had I at first ? 
 
 6. I gave $20 more than § (f, f) of my money for a 
 horse, and had $16 left. Find the cost of the horse. 
 
 6. I gave f (I, ^) of my money for a horse, J (^, ^) of 
 the remainder for a buggy, and ^ (J, ^) of what then 
 remained for a harness, and had $40 left. How much 
 had I at first ? 
 
 Exercise 262. 
 
 1. B spent $4 ($5, $8) more than ? (.6, 75%) of his 
 money and had $8 ($3, $2) moi j than | (f, 20%) of it 
 left. How much had he at first ? 
 
 2. I sold ^ (.7, 35%) of my flock and had 15 (36, 39) 
 sheep left. How many had I at first ? How many did 
 I sell ? 
 
 3. I sold 12 (9, 25) acres more than | (.5, 25%) of my 
 farm and have 7 (4, 30) acres less than } (.45, 80%) of it 
 left. Find size of the farm and how much I sold. 
 
 4. I spent J (,^, I) of my money and $5 ($4, $2) for a 
 hat, then $3 ($4, $2) less § (2, iV) of the remainder for a 
 coat and have $8 ($12, $10) left. Find the cost of each. 
 
 5. r gave $17 ($10, $4) more than § (f. |) of my 
 money for a horse, and $5 more than f (J, f ) of the 
 remainder for a harness, and had $10 ($10, $15) left. 
 Find cost of each. 
 
TYPE QUESTIONS. 
 
 Exercise 263— Work Questions. 
 
 109 
 
 1. A can do ^ (^, J) of a work in a day. B can do J 
 (}» \) of the work in a day. How long would it take A 
 and B to do the work ? 
 
 2. A can do a work in 2 (3, 5) days, and B in 3 (3, 6) 
 days. How much will the two do in one day ? 
 
 3. A can do a work in 2 (3, 4) days. B can do it in 3 
 (4, 5) days. How long would it take the two to do it 
 together ? 
 
 4. A can do a work in 2 (3, 4) days ; B in 3 (4, 3) 
 days ; C in 4 (5, 2) days. In what time would the work 
 be done by A and B ? B and C ? A and C ? A, B and C ? 
 
 6. A can do a work in 2^ (i J, i§) days ; B can do it in 
 3j i^h I J) f^ays ; C can do it in 4J (i^, 3]^) days. In 
 what time could any two do the work ? How long would 
 it take the three to do it ? 
 
 Exercise 264. 
 
 1. A can do a work in J (§, f) of a day ; B can do it 
 in ^ (I, f) of a day. How long would it take the two to 
 doit? 
 
 2. A can do a work in 5 (6, 8) days ; B can do it in 
 32 (^h ^1) days. How long will it take A to finish the 
 work after B has worked 2 days ? How long will it take 
 B to finish, after A has worked 3 days ? 
 
 3. A, B and C can do a work in ^§ (t\, i^j) hrs. ; 
 A and B in i^ (|, i^) hrs. ; A and C m i^ (f, ij) hrs. 
 How long would it take each ? 
 
 4. A and B can do f {^^, ^^g) of a work in a day. A 
 and C can do f (.}, -f^) of it in a day ; B and C, /g^ (^2» ^0) 
 of it in a day. How long would it take all to do it ? 
 How long would it take each to do it ? 
 
 5. A and B can do a work in i^ (i J, if) da. ; A and C 
 in i^ (i|, 1 1) da. ; B and C in if (2|, 2^) da. How long 
 would it take all ? How long would each take to do it 
 alone ? 
 
 il 
 
 ^i.'.'' 
 m. 
 
I lO 
 
 MENTAL ARITHMETIC. . 
 
 Bxercife 265 Miscellaneous. 
 
 1. A boy was to get $100 and a suit of clothes for a 
 year's work. At the end of 7 (8, 9) months he left and 
 received $50 ($48, $33) and the clothes. Find their value. 
 
 2. I have 75 (88, 78) books, pens and pencils. There 
 are 55 (65, 55) pensijnd pencils, and 50 (60, 51) books 
 and pencils. How many of each have I ? 
 
 3. A grocer sold 3 (4, 6) dozen eggs @ 3 cents each, 
 agreeing to get nothing and forfeit 5 cents for each bad 
 egg. How many were bad, if he got $.60 ($1. 12, $2) ? 
 
 4. For a ten-acre field, B offered to give $1 for the 
 first acre and to double the price for each successive 
 acre. Find price offered for the field. 
 
 5. B, who can row 8 (9, 12) miles an hour in still 
 water, takes 4 (4, 5) hours to row up a stream which runs 
 3 miles an hour. How long will he be returning ? 
 
 Exercise 266. 
 
 1. I bought 80 lbs. tea @ 34 cents. I sold 45 (25, 30) 
 lbs. © 40 cents, 25 (25, 40) lbs. @ 35 cents, and the rest 
 @ 30 cents. Find my gain or loss. 
 
 2. I bought 38(45, 39) chickens @ 32 (45, 31) cents. 
 I kept 2 (3, 4) of them for myself and sold the others @ 
 34 (48, 35) cents. Find my gain or loss. 
 
 3. I bought a number of chickens for $10 ($18.75, 
 $22.50). I gained $3.50 ($4.50, $2.50) by selling some 
 of them for $8.75 ($15.75, $17.50) @ 35 cents. How 
 many did I buy ? 
 
 4. The fore wheel of a carriage is 8 (9, 10) feet in cir- 
 cumference, and the hind wheel is 11 (12, 12) feet. How 
 far do they go if one revolves 90 (66, 264) times more 
 than the other ? 
 
 5. How many trees 66 feet apart will enclose a square 
 160-acre farm which is divided into square lo-acre fields? 
 
 6. If 2 horses are worth 3 oxen, and 4 oxen are worth 
 6 cows, and 8 cows are worth $256, find the value of 5 
 horses. 
 
TYPE QUKSTIONS. 
 
 Ill 
 
 Exercise 367— Train Questions. 
 
 1. Find how far a train travelling 15 (30, 30) miles an 
 hour will go in 30 (15, 45) seconds. 
 
 2. Find the rate of a train, if it travels 440 (220, 330) 
 yards in 1 5 (20, 40) seconds. 
 
 3. A train, 220 (440, 440) yards long, passes a point in 
 50 (30, 45) seconds. Find the rate of the train per hour. 
 
 4. A train travelling at the rate of 20 (30, 45) njiles an 
 hour, passes a point in 45 (30, 10) seconds. Find the 
 length of the train. 
 
 6. Find the length of a train which passes a point in 9 
 (18, 9) seconds while going at a rate of 20 (25, 35) miles 
 an hour. 
 
 6. How long will it take a train 160(140, 280) yards 
 long, and going at the rate of 30(45, 15) miles an hour, to 
 cross a bridge 60 (80, 160) yards in length ? 
 
 Exercise a68. 
 
 1. A train 220 yards long crosses a bridge in 45 
 (30, 45) seconds, while going at the rate of 20 (30, 40) 
 miles an hour. Find the. length of the bridge. 
 
 2. An express train, 160 yards long, passes a freight 
 train in a siding, in 30 (i 5, 45) seconds. Find the length 
 of the freight, if the rate of the express be 30 miles 
 an hour. 
 
 3. 1 wo trains of equal length, travelling in opposite 
 directions, at the rates of 20 and 30 miles an hour, meet 
 and pass in 45 (20, 30) seconds. Find the length of the" 
 trains. 
 
 4. Two trains, each 1 10 (220, 220) yards long, going 
 at the same rate, in opposite directions, pass each other 
 in 10 (20, 30) seconds. Find the rate of each. 
 
 5. How long will two trains, no and 220 yards long, 
 respectively, moving in the same direction at the rate of 
 15 and 30 miles an hour, be in passing ? How far will 
 each travel ? 
 
112 MENTAL ARITHMETIC. 
 
 Bxerolse 269— Stream Questions, etc. 
 
 1. I ride at the rate of 8 (6, 9) mi. an hour, arid walk 
 back at the rate of 4 (3, 6) mi. an hour. How far can I 
 go and return in 3 (4, 2|) hours ? 
 
 2. A walks to the city at the rate of 4 (5, 6) mi. an 
 hour, and returns at the rate of 3 (4, 4) mi. an hour. 
 Find the distance if he takes 2 (3, f) hours less to go 
 than to return. 
 
 3. A boat makes a round trip in 7 (9, f} hours, going 
 at the rate of 8 ( ro, 10) mi. an hour, and returning at the 
 rate of 6 (8, 6) mi. an hour. Find the distance between 
 the two points. 
 
 4. B rows 10 (9, 8) mi. an hour in still water. How 
 long should he be rowing 4 (8, 6) mi. down a stream and 
 returning, if the stream runs 2 (3, 4) mi. an hour ? 
 
 6. A boatman rows a distance down a stream running 
 2 (3, 4) mi. an hour in 20(12, 10) min., and returns in 
 60 (30, 30) rainutes. How far down stream does he go ? 
 
 Exercise 270— Raciog, 
 
 1. A can run 7 (8, 9) rods wh^e B runs 10 rds. How 
 far behind will A be in a race of 100 yds. ? 200 rds. ? 
 440 yds. ? 
 
 2. A can run 100 yards in 10 (12, 20) seconds. B 
 can run it in 12 (15, 25) seconds. What start should B 
 have to finish with A in a race of 100 (250, 440) yds. ? 
 
 3. A can run a mile in 5 (6, 8) minutes, and B can 
 run it in 6 (8, 10) minutes. Find A's handicap to make 
 their chances equal. 
 
 4. A and B run a mile race. A gains 2 (3, 5) yds. in 
 20 rods (176yds., 1056 ft.) How far behind will B come 
 in the race ? 
 
 5. A hare takes 5 (7, 9) leaps, each 3 (4, 5) feet, while 
 the hound takes i (2, 4) leap, i rod (5^ yds., 12 ft.) long. 
 How far will the hound go before he catches a hare hav- 
 ing a start of 50 (100, 220) yards ? 
 
TYPK QUKSTIONS. 
 
 n3 
 
 Exercise 271 -Clock Questions. 
 
 1. At what time after 11 (i, 3) o'clock will the hands 
 of a clock be together for the first time ? 
 
 2. When will the hands of a clock be together be- 
 tween 2 and 3 o'clock ? 3 and 4 o'clock ? 7 and 8 o'clock ? 
 
 3. When will the hands of a clock be opposite between 
 8 and 9 o'clock ? 10 and 1 1 o'clock ? 7 and 8 o'clock ? 
 
 4. When will the hands of a clock be opposite between 
 I and 2 o'clock ? 3 and 4 o'clock ? 4 and 5 o'clock ? 
 
 6. When will the hands of a clock be at right angles 
 to each other between 5 and 6 o'clock ? 6 and 7 o'clock ? 
 
 6. When will the hands of a clock be at right angles 
 to each other between 2 and 3 o'clock ? i and 2 o'clock ? 
 
 7. When will the bands of a clock be at right angles 
 to each other between 10 and 11 o'clock? 11 and 12 
 o'clock? 
 
 Exercise 272. 
 
 1. At what times are the hands of a clock 14(3, 15) 
 minute-spaces apart between 5 and 6 o'clock ? 
 
 2. At what times are the hands of a clock 20 minute- 
 spaces apart between 4 and 5 o'clock ? i and 2 o'clock ? 
 
 3. At what times after 2 (5, 7) o'clock will the hands 
 of the clock make an angle of 90° ? 
 
 4. At what time af er 4 o'clock will the hands of the 
 clock make an angle of 60" ? 120° ? 180° ? 270° ? 
 
 6. At what time after 3 (5, 8) o'clock will the hands 
 of a clock be equidistant from the figure 3 (5, 8)? 
 
 6. At what time past 4 (6, 9) o'clock will the minute 
 hand be twice as far from the figure 4 (6, 9) as the hour 
 hand is past it ? 
 
 7. At what time after 2 (3, 4) o'clock will the hour 
 hand be midway between the minute hand and the figure 
 
 2(3,4)? 
 
 8. At what times between midnight and noon are 
 the hands of a clock together ? 
 
114 
 
 MKNTAL ARITHMETIC. 
 
 ) 
 
 How 
 
 How 
 
 Exercise 273 -Age Questloiit, 
 
 1. In 8 (11, 25) years, I will be 36 years old. 
 Old will I be in 12(15, 28) years ? 
 
 2. Three years ago, I was 17 (20, 30) years old. 
 old will I be in 12 (19, 34) years? 
 
 3. If 'i (i, f) of A's age is his age 4 (7, 9) years ago, 
 how old will he be in 5 years hence ? 
 
 4. If I (§, §) of Mary's age is ^ (|, ?) of her age 8 
 (5, 4) years ago, find her age. 
 
 6. Find my age, if ^ (§, |) of it is 4 (5, 7) years more 
 thanf (^, f)ofit. 
 
 6. If ^ (§, f) of my age is § (2, ij) times what it was 
 6 (10, 10) years ago, how old am I ? 
 
 7. A's age and B s b 36 years. Four years ago A's 
 age was ^ (^, J) of B's. Find age of each. 
 
 8. A mother's age is 6 (5, 4) times her son's. In 6 
 (5, 4) years she will be 3 times as old. Find age of each. 
 
 Exercise 274— Time Questions. 
 
 1. What time is it when the time past three o'clock is 
 a ('}» f ) of the time past 2 o'clock ? 
 
 2. What time is it, when the time past 4 o'clock is ^ 
 (J, §) of the time to 5 o'clock ? 
 
 3. Find the hour, if the time past noon is ^ (^, J) of 
 the time to midnight. 
 
 4. Find the time, if f (f , ^) of the time past noon is 
 T (h i) of the time to midnight. 
 
 6. Find the time, if ^ (f , ^) of the time past midnight 
 is equal to § (5, f ) of the time to midnight. 
 
 6. How long does a person sleep, if § (f, f ) of the tifne 
 he sleeps is | (f, /,) of the time he is awake.? 
 
 7. Find the time a person sleeps, if i of the time he 
 sleeps is 36 (45, 45) minutes less than ^ (J, ^) of the time 
 he is awake ? 
 
 8. How long does a person sleep if the time he is 
 awake is to the time he is asleep as 3 : 9.'' 4:8? 3:8? 
 
TYPK QUKSTIONS. 
 
 115 
 
 Exercise 275 - Wages. 
 
 1. A man gettinjj $10 a week has his wages increased 
 $2 ($3, $5). What % was the increase ? 
 
 2. A man who got $8 a week now gets $10 ($12, $13). 
 What per cent, was his increase in wages ? 
 
 5. B got $2.50 a day, and his wages were increased 
 10% (20%, 25%). Find his weekly wages now. 
 
 4. A boy receiving $8J, ($12^, $i6§) a month has his 
 wages increased 25% (168%, 37j%). Find his yearly 
 wages now. 
 
 6. After having my salary increased 20% (33^%, 
 87.|%)» I get $900 ($840, $2250). Find my fon'ner 
 monthly salary. 
 
 6. I get $400 a year and am advanced 10% (20%, 25%) 
 a year. How much do I receive for 3 years ? 
 
 7. B spends 75% (66|%, 87^%) of his wages and saves 
 $372 a year. How much does he earn a month ? 
 
 Exercise 276— Sums and Differences. 
 
 1. The sum of two numbers is 60(11^, 14.6). Their 
 difference is 12 (3}, 1.8). Find the numbers. 
 
 2. The sum of two numbers is 62 (8J, 9). Half their 
 difference is 6 (i^, 1.25). Find the numbers. 
 
 3. Find the width of a field 48 (37^, 62^) yards long, 
 if the perimeter is 168 (135, 200) yards. 
 
 4. Find the length of a table 3 (2J, 2J) feet wide, if s 
 cord 54 (39, 60) feet long will reach 3 times around it. 
 
 6. The sum of two fractions is /jj (i^J, i/a)* ^'ve 
 times their difference is -^^ (J, ^). Find the numbers. 
 
 6. The sum of two numbers is 5f (Si'ij, uj). Four 
 times their difference is 3 (5^, 15). Find the numbers. 
 
 7. One number is f (4^, 6.75) of another. Their 
 difference is 12 (35, 23). Find the numbers. 
 
 8. One number is' ^ (2^, 3. 5) of another. Their sum 
 is 36(26, 22.5). Find the numbers. 
 
Ii6 
 
 MENTAL ARITHMETIC. 
 
 h 
 
 Exercise 277 - Populations. 
 
 1. Ten years ago a town had 5643 (2875, 3984) inhabi- 
 tants. Now it has 7000. Find the increase. 
 
 2. Ten years ago a town had 4758 inhabitants. The 
 increase has been 2864 (3549, 7682). Find its population. 
 
 3. The population of a town was 2200 (2432, 3245). 
 The increase has been -^ (.^5, 20%). Find population. 
 
 4. The population of A was 2500 (2250, 4820). The 
 decrease has been ^(.12, 25%). Find population now. 
 
 6. What population increased by ^ (.3, 12^%) amounts 
 102500(3965,6390).? 
 
 6. Ten years ago the population was 2500(2800, 3600). 
 Now it is 3000 (3500, 4800). Find the increase %. 
 
 7. Ten years ago the population was 3000 (3200, 
 7500). Now it is 2500 (2400, 5000). Find the decrease %. 
 
 8. Ten years ago a town had 6400 inhabitants. Now 
 it has 8000 (5600, 4800). Find increase or decrease %. 
 
 Exercise 278— Longitude and Time. 
 
 1. What is longitude? The greatest longitude possible? 
 
 2. When is it noon at any place north of the equator? 
 South of the equator? On the equator? 
 
 3. It is noon at one place i (2, 3) hour before it is noon 
 at another in the same latitude. How far apart are they ? 
 
 4. Find the difference between Greenwich time and 
 that of a point 1 5° (30", 60°) to the ( i ) east, (2) to the west. 
 
 6. At noon, Greenwich, what time is it at a place 
 whose longitude is 75' W. ? 120° W. ? 20° W. ? 35° W. ? 
 50° W.? 85° W.? 100° W.? i°W. ? 2°W? 
 
 6. At noon, Greenwich, what time is it at a place 
 whose longitude is 90° E. ? 105° E. ? 50° E. ? 7° 30' E. ? 
 22° 30' E. ? 32° 30' E. ? 17° 30' E. ? 2° 30' E. ? 
 
 7. Find the longitude of a place whose time, at noon 
 in Greenwich, is : — 
 
 I p.m. ? 2 p.m.? 4 p.m. ? 1,20 p.m.? 2.30 p.m. 
 
 II a.m.? 9 a.m.? 7 a.m.? 10.20 a.m? 9.40 a.m.? 
 
TYPE QUESTIONS. 
 
 H7 
 
 Bxercife 279 -Ratio. 
 
 1. What is ratio ? How is it expressed ? Distinguish 
 the antecedent from the consequent. 
 
 2. Express these ratios in their lowest terms : — 
 6:8, 12: 9, 15: 25, 16: 32, 25: 75. 
 
 3. Find the ratio, in the lowest terms, of: — 
 
 2 gal., 3 qts. : 3 gal , i qt. 3 yds., i ft. : 5 yds. 
 
 4. Divide $25 ($75, $9.60) between two men whose 
 shares shall be in the ratio of 2 : 3 (4 : i, 6 : 12). 
 
 6. Find the number which bears the same ratio to 1 5 
 ($35, £2 105) that 5 bears to 7. 
 
 6. Divide 45 ($37.80, ^3 \2S) into three parts, which 
 shall be to one another as i, 3 and 5. 
 
 7. A sum of money is divided into three parts in the 
 ratio of 2, 3 and 7. The smallest share is $16. Find 
 the sum. 
 
 Exercise 280 -Proportion. 
 
 1. What is a proportion ? How is it expressed ? What 
 are the means ? The extremes ? Show the relation of 
 the means to the extremes. 
 
 2. Find the other term of the proportion : — 
 
 6: 8: 
 
 : 9: 
 
 :$6 
 
 5:15: 
 
 : 7: 
 
 :$9 
 
 4: 9: 
 
 : =36 
 
 35: 
 
 8;i2: 
 
 : :27 
 
 %y. 
 
 3f 
 
 2}: 
 
 .75: -6} 
 :4.5 
 
 I 
 
 7!^ 
 
 /2 
 
 7-5 
 
 9- 
 
 •9 
 
 $30: $24 
 
 .^21: ;^27 
 
 $10: $12 
 
 15 : 24 
 
 3. What number bears the same relation to 3J that 7 
 bears to 8 (9, 12)? 
 
 4. If 14 (16, 21) men earn $35 ($24, $35) in a day, 
 how much will 20 (40, 1 5) men earn in a day ? 
 
 6. If 24 (15, 16) men can do a work in 20(16, 25) 
 days, how long would it take 16 (24, 40) men to do it .'' 
 
 6. A owns f (I, T^i) of a farm, and B owns the re- 
 mainder. Find the ratio of A's share to B's. 
 
 7. If § (J, 2.]) of A's farm equals f (f, 3f) of B's, find 
 the ratio of 15 s farm to A's. 
 
 ; I 
 
 I 
 
ii8 
 
 MENTAL ARITHMETIC. 
 
 Exercise a8i— Cancellation. 
 
 1. How many lambs @ $6 ($7^, $3|) are worth as much 
 as 33 (36, 24) sheep @ $8 ($5, $71)? 
 
 2. How many yards of print @ 9 (5^, 6^) cents, can 
 be bought for 24 (22, 8^) dozen eggs @ 12 (15, 15) cents ? 
 
 3. How many pounds of butter @ 21 (i2|, 17 J) cents, 
 must be given for 15 (16, 35) yds. cashmere @ 35 (37^, 
 45) cents ? 
 
 4. How many dresses each 8 (7^, 6|) yards can be 
 made of 12 (25, 18) pieces cloth, each 36(45, 15) yards 
 long ? 
 
 6. How many bushels of wheat will weigh as much as 
 45 (i2|, i8f) bushels of barley .? 
 
 6. If 36 (12}, 75) pounds of butter are given for 45 
 (35, 37^) yards cloth @ 24 (20, 48) cents, find the price 
 of the butter. 
 
 7. If 36 (48, 7) bushels of wheat weigh as much as 
 51 (60, 7l) bushels of another grain, what is the other 
 grain ? 
 
 Exercise 282. 
 Find the cost of : — 
 
 1. 4 tons, 15 cwt. hay @ $10 ($15, $12) a ton. 
 
 6 tons, 5 cwt. bran @ 40(60, 75) cents a cental. 
 
 2. 5 lbs., 8 oz. butter @ 10 (12, 14) cents a pound. 
 4 cwt., 75 lbs. beef® $8 ($6, $4.80) a cwt. 
 
 3. 9 tons, 5 cwt. coal @ $6 ($5, $6.40) a ton. 
 
 8 cwt., 25 lbs. flour @ $3 ($3.20, $4.80) a cwt. 
 
 4. 12 bu., 36 lbs. wheat @ 60 (75, 90) cents a bu. 
 15 bu., 36 lbs. barley @ 60 (72, 96) cents a bu. 
 
 6. 45 lbs., 12 oz. lard @ 8 (12, 16) cents a pound. 
 36 lbs., 14 oz. butter @ 24 (32, 40) cents a pound. 
 
 6. 42 doz. and 8 eggs @ 9 (12, 15) cents a dozen. 
 12 gr., 4 doz. eggs @ 12(15, ^^) cents a dozen. 
 
 7. 25 bu., 48 lbs. pease @ 75 (60, 95) cents a bushel. 
 12 stone, 7 lbs. oatmeal @ 20 (24, 36) cents a slope. 
 
TYPE QUESTIONS. 
 
 119 
 
 Exercise 283— Square Root. 
 
 1. Find the square root of : — 
 
 36, 81, 64, ICO, 225, 3025, 400, 121, 196, 256. 
 
 .49, .25, 6.25, 20.25, 5.76, .0441, .1225, .0169. 
 
 ^. 1%, T^*D If, Hh uh ih. 5% m, Hh m- 
 
 2h 61, 12I, 5i 301, 2|, 7I, iij, 3,V 
 
 2. What is the side of a square field whose area is 225 
 sq. rds. ? 400 sq. rds. ? 576 sq. rds. ? 3 ac , 145 sq. rds. ? 
 
 3. How many times is 6 (8, 9) cubic inches contained 
 in a 6 (8, 9) inch cube ? 
 
 4. Find the dimensions of a cube whose surface is 150 
 sq. in. ? 216 sq. in. ? 864 sq. in. ? 486 sq. in. ? 
 
 6. Divide a field 48 rds. x 64 rds. into square lots, the 
 largest possible. A field 36 rds. x 44 rds. A field 
 88 rds. X 99 rds. 
 
 6. How many square lots, the largest possible, can be 
 made of a field 72 rds. x 88 rods ? 50 rds. x 65 rds. ? 
 
 Exercise 284— Measures and Multiples. 
 
 1. Find the least distance which can be measured by 
 a 6' pole, an 8' pole, or a 9' pole. 
 
 2. Find the least distance which can be measured by 
 a pole 2' 6" long, 7' 6" long, or 12' 6" long. 
 
 3. Find the least quantity of milk which can be put 
 into cans holding 4 gal., 2 qts., or 6 gal., 3 qts. 
 
 4. Find the G.C.M. of $24, ^36, and 42 cents. 
 
 5. A man and his daughter walk together. He steps 
 3' (3' 30'X and she steps i' (2', 20"). How often will 
 they step together ? 
 
 6. Two boys walk together, taking steps of 18" and 
 24" (24" and 30", 30" and 36") respectively. How often 
 will they step together in 1 5 (30, 1 50) yards ? 
 
 7. The bells of a chime strike every second, two 
 seconds, three seconds, four seconds, five seconds, and 
 six seconds, respectively. How often will they strike 
 together.? How often will they strike together in five 
 minutes ? 
 
'I20 
 
 MENTAL ARITHMETIC. 
 
 Exercise J85— Aliquot Parts. 
 
 1. Give four aliquot parts of 20 (24, 36) which are 
 whole numbers. 
 
 2. Give the largest five aliquot parts of 100 (150, 240) 
 which can be expressed in whole numbers. 
 
 3. Give the greatest twelve aliquot parts of $1. 
 
 4. Give, in descending order of niagnitude, the ten 
 aliquot parts of ;^i which can be expressed in whole 
 numbers. 
 
 5. Write down the principal aliquot parts of i sq. yd. 
 which can be expressed in whole numbers. 
 
 6. Write down the principal aliquot parts of i bushel 
 which can be expressed in whole numbers. 
 
 7. Write down the principal aliquot parts of a bushel 
 of wheat. Of barley. Of potatoes. 
 
 8. What part of ;^i is 6s. 8d. ? 35. 4^. ? ly. 4^. ? 
 25. 6d. ? ys. 6d. ? 17s. 6d. ? 335. ^d. } 
 
 Exercise 286— Practice. 
 
 Find, by practice, the value of : — 
 
 1. I bu., 2 pks. @ 80 (72, 96) cents a bushel. 
 I gal., 3 qts. @ 10(12, 16) cents a gallon. 
 
 2. 3 gal., 3 qts., I pt. milk @ 8 (16, 20) cents a gallon. 
 
 5 bu., 3 pks., I gal. grain @ 64 (60, 75) cents a bushel. 
 
 3. 4 yds., 2 ft., 6 in. ribbon @ 12 (18, 20) cents a yard. 
 5 yds., I ft., 9 in. ribbon @ 12 (24, 30) cents a yard. 
 
 4. 3 lbs., 10 oz., 15 dwt @ 48 (96, 72) cents a lb. 
 9 lbs., II oz., 10 dwt. @ 72 (48, 36) cents a lb. 
 
 5. 2 sq. yds., 4 sq. ft., 72 sq. in. ® 12 (40, 72) c, a sq. yd. 
 
 3 sq. yds., 6sq. ft., 108 sq. in. @ 16 (24, 48) c. asq. yd. 
 
 6. 4 gal., 3 qts., I pt. milk ^ 20 (24, 15) cents a gal. 
 5 gal., I qt., I pt. milk @ 16 (20, 25) cents a gal. 
 
 7. 4 tons, 17 cwt., 2 qrs. hay @ $8 ($12, $20) a ton. 
 5 tons, 1275 lbs. coal ® $6 ($5.50, $7.50) a ton. 
 
 8. 6 tons, 12 cwt., 2 qrs. @ £2 \os. 6d, a ton. 
 
 4 tons, 7 cwt, 2 qrs. @ £6 ys. dd. a ton. 
 
TYPE QUESTIONS 
 
 121 
 
 Exercise aSy-Qeneral Review. 
 
 1. Find sum of the seven smallest composite numbers. 
 
 2. I sold 2o (i6, 48) cattle, averaging 725 lbs., @ 8 
 cents a pound. How much did I get for them ? * 
 
 3. How many days in 4 (8, 16) years of next century .-* 
 
 4. If 3 men or 5 boys do a work in 6 days, in what 
 time would 3 men and 5 boys do the work ? 5 men and 
 3 boys ? 3 men and 3 boys ? 
 
 6. How many plants, placed 9" (6", 15") apart, will 
 make a border for a bed [i 5' x 45'] ? 
 
 6. Find the number whose J (.75, 47%) is 10 greater 
 than its ^(.5, 27%). 
 
 7. Find the cost of 2 (5, 8) five-acre fields @ $a ($2^, 
 $3f ) an acre. 
 
 8. The marked price is 25% (33^%, 50%) above cost 
 and the discount is 10 (12^, 10) %. Find the gain %. 
 
 Exercise 288. 
 
 1. Find the sum of all the numbers ending in 48 
 (5o» 67) between 8000 and 90CX). 
 
 2. What is the difference between the squares of 6 
 and 7 ? 14 and 15? 24 and 25 ? 36 and 37 .? 84 and 83 ? 
 
 3. Arrange the digits in three columns, so that each 
 line added horizontally or vertically will be 15. 
 
 4. What fraction multiplied by 6 will give § .'' $4 ? 
 f gal. ? f mi. ? I ac. .? £^ ? 
 
 6. How far will a train run in 3 hrs., 45 min , 30 sec, 
 at the rate of 36 miles an hour ? 
 
 6. A pole is ^(.25, 35%) in the ground, I (.35, 35%) 
 in the water, and 15 (36, 48) feet in the air. Find its 
 length. 
 
 7. Divide 108 into two parts so that ^\ (.25, 25%) 
 of the first is I (.4, 20%) of the second. 
 
 8. I gained 25% (i6^%, 12!%) by selling cloth @ $.75 
 ($.84, $.90). Find the gain on a sale of $5 ($14, $45)? 
 
 ONTARIO COLLEGE OF EDUCWI 
 
122 
 
 MENTAL ARITHMETIC. 
 
 Exercise 289— General Review. 
 
 1. I lost 35 (24, 63) cents, by selling for f (.75, 87^%) 
 of cost. Find the selling price to gain ^ (.2, 20%). 
 
 2. What number increased by f (.625, 45%) of itself 
 amounts to 665 ($390, ;^87o) ? 
 
 3. What number decreased by f (.375, 14^%) of itself 
 leaves a remainder of 735 ($955, 636 sheep) ? 
 
 4. After spending § (.4, 25%) of my money, I found 
 that J (.5, 20%) of the remainder was $5 ($3.75, $7.50). 
 How much money had I at first ? 
 
 6. Find the cost of 1 1 (|, 4§) acres of land, if f (2^, 3^) 
 acres of land cost $45 ($75, $135). 
 
 6. A had 4 (5, 7) times as much money as B. He 
 gave B $12 ($12, $15) and then he had twice as much as 
 B. How much had each at first ? 
 
 Exercise 290. 
 
 1. How often does a watch tick in a second ? A min- 
 ute ? An hour? A day ? A week ? A fortnight ? 
 
 2. I buy 487 sheep® $4.75 and sell them ©$5.25 
 ($4.25, $5). Find the total gain or loss. 
 
 3. I get $600 ($750, $1000) a year, and spend as much 
 in 4 (5, 6) mo. as I earn in 3 (4, 4) mo. Find yearly 
 savings. 
 
 4. How many lambs @ 12/6 are worth £2$? £4$ ? 
 
 6. Three hams averaged 12 lbs., 8 oz. Two of them 
 averaged 1 1 lbs., 10 oz. Find the weight v>t the third. 
 
 6. Two trains, going at the same rate, meet and pass 
 in 20 (30, 50) seconds. The first train is 180 yards long, 
 and the second is 260 yards long. Find the rate of each 
 train. 
 
 7. In an election, A received ^ (.28, 54%) of the votes, 
 B received ^ (.55, 25%) of the votes, and C received 770 
 (1020, 1680) votes. Which was successful, and what 
 was his plurality? 
 
TYPE QUESTIONS. 
 
 123 
 
 Exercise 29 ■— General Review. 
 
 1. What number is as much above 425 (325, 48.3) as 
 it is less than 811 (983, 67.8)? 
 
 2. Find the gain or loss on buying a gross of oranges 
 ©25 cents a doz. and selling them @ 3 (4, 6) for 10 cents. 
 
 3. A 36-rod fence cost $9 more than a fence 42 (45, 48) 
 rods long. Find the cost of a 7 5 -rod fence. 
 
 4. If the divisor were ^ (^, j) of what it is, the quo- 
 tient would be 273 (428, 640). Find the quotient. 
 
 5. If 5 men do a work in 5 hrs., 45 min., how long 
 would it take i man ? 3 men ? 1 5 men ? 
 
 6. How far can I walk in 2| (2% 2^) hours at the rate 
 of 3 J (4I, 2§) miles an hour ? 
 
 7. Find the length of a pole if J (.35, 40%) of it is in 
 the ground, | (.4, 25%) of it is in water, and 15 (39, 90) 
 feet in the air. 
 
 8. A can do 2 (f, f) of a work in a day. In what part 
 of the next day should he finish it ? 
 
 Exercise 29a. 
 
 1. Find the product of 6, 8, 3 and o. 
 
 2. What is the gain or loss on buying a gross of pens 
 @ 3 for 4 cents, and selling them @ 4 for 5 cents ? 
 
 3. Find the cost of 33 (35, 42) sheep if 22 (14, 33) 
 sheep cost $30 ($35, $44). . ' 
 
 4. A and B have $75.90 in the proportion of 7 : 8. 
 How much has one more than the other ? 
 
 5. I mix 50 (25, 60) lbs. wool ©13(11, 21) cents, with 
 75 lbs. @ 8 (7, 12) cents. Find average price per pound. 
 
 6. A milkman has 42 gal., 3 qts., i pt. of milk, and 
 fills an equal number of pint, quart and half-gallon 
 bottles. How many bottles does he fill ? 
 
 7. By what must | (§, |«o) be divided to give | (f , f ) 
 as the quotient ? 
 
 8. A sum of money in 12 years at 5% amounts to $560. 
 In how many years will it amount to $595 ? 
 
124 
 
 MENTAL ARITHMETIC. 
 
 Exercise 393 -Qeneral Review. 
 
 1. Divide 756 successively by 3, 4 and 7. 
 
 2. How many sheep divided between A and B in the 
 proportion of 2 : 3 will give A 16 (24, 36) sheep ? 
 
 3. A carpet 8 feet long and 6 feet wide cost $16. 
 Find cost of a carpet 8' x 9' ; 10' x 12' ; 12' x 15'. 
 
 4. In the fraction .45, divide the 4 by the 5. 
 
 5. I paid $64 for tea supposed to be done up in pound 
 packages; but there were only 15 (15I, 15^)02. to the 
 pound. Hovv' much should I pay for the tea ? 
 
 6. Two brakesmen approach each other, each running at 
 the rate of 6 miles an hour, on the top of a train running 
 1 5 (24, 30) miles an hour. Find the rate at which each 
 moves. 
 
 7. Find the duty at 20% (25%, 33^%) on 360 boxes 
 raisins, each 30 lbs., @ 5 cents a pound. 
 
 8. Goods are marked at an advance of 25%. Find the 
 discount so as to gain 10%. 
 
 Exercise 294, 
 
 1. What two consecutive numbers give a quotient of 
 132? 210? 420.? 600.^ S70? 2450.? 
 
 2. What sum of money, divided between A and B in 
 the ratio of 3 : 4, will give B $25 ($36, $45) more than A ? 
 
 3. If 35 yds. of cloth cost $4.90 ($4.20, $6.30), what 
 will 45 (55, 25) yds. cost? 
 
 4. How many lengths, each .005 feet, can be cut from a 
 stick one yard long ? 
 
 6. A owned .6 (.8, .75) of a farm and sold f (.25, 40%) 
 of his share to B. What part does each now own ? 
 
 6. Find cost of 3 (4, 5) gal. milk @ i J (2^, 1 1) c. a pint. 
 
 7. Find value of a bin of wheat [5' x 8' x 12'] @ 75 
 cents a bush. Find weight of barley to fill it. 
 
 8. A sum of money, in 8 year? at 6 %, amounts to 
 $370 ($5 18, $6661 in how many years will it amount to 
 $550 ^$560, $747)? 
 
TYPE QUESTIONS. 
 
 125 
 
 Exercise 295— General Review. 
 
 1. Find the difiference between the largest and the 
 smallest number that can be expressed by the nine digits. 
 
 2. Write the prime numbers from 100 to 200. 
 Write the largcsl prime numbers of four figures. 
 Find the smallest multiple, of 3 figures, of 3 and 7. 
 
 3. What is the reciprocal of a number ? 
 
 4. Show the difference between long division and 
 short division. 
 
 6. What are the dimensions of a line ? A surface ? 
 A solid? 
 
 6. What is the difference between the length of a No. 
 3 shoe and a No. 4 shoe ? 
 
 7. Find the height of ahorse 15 (15^, 16J) hands high. 
 
 8. Find the cost of a firkin of butter @ 25 (22, 28) 
 cents a pound (56 lbs. = i firkin). 
 
 Exercise 296. 
 
 J 3_X2 3j-_2 _, 3-2. 
 
 5 
 
 1. Compare 
 
 and 
 
 5x2 5 + 2 5-2 
 
 2. Find the third proportional to 4 : 6. 
 Between what quantities can a ratio exis ? 
 Account for the name " Rule of Three. » 
 
 3. If'Jof a foot were 12 inches, what would § of a 
 yard be } 
 
 4. If there were 10 inches in a foot, and 4 feet in a 
 yard, how many inches would be in 5 yds., 3 ft., 4 in. ? 
 
 Multiply 6 yds., 2 ft., 7 in. by 5. 
 
 6. If 9 units made a ten, and 9 tens made a hundred, 
 and 9 hundreds niade a thousand, find the sum of 864 
 and 257, and the difference between 753 and 287. 
 
 6. When should I pay the year's rent in one payment 
 instead of on the first (last ) of each month ? 
 
 7. How many figures will be in the decimal part when 
 , reducing a vulgar fraction to a decimal ? How many 
 
 remainders can there be ? 
 
INDEX. 
 
 The Figures in Italics refer to Part 1. 
 
 Page. 
 
 Addition, Simple 11-26 
 
 — , Comfiound 88-/02 
 
 — , Fractions 35, 26 
 
 — , Decimals 44 
 
 -, Table 13,1s 
 
 Ages 3Si40, 4'» 43, Si, 1 14 
 
 Aggregates 44, 102 
 
 Aliciuot Parts c2o 
 
 Alligation 104 
 
 Analysis. ..7«'-7^, 106, 22, 27, 29, 34 
 
 Apothecaries^ VVeigh 96 
 
 Arabic Notation 57, 10 
 
 Areas 99, too, 47, icx) 
 
 Averages 82, 103 
 
 Avoirdupois Wei^fbc gs 
 
 Bank Discount.... 73 
 
 tianktuptcy od 
 
 Brokerage ^6 
 
 Cancellation 10, 118 
 
 Capacity 91,9^ 
 
 Carpeting 93, 94 
 
 Change i4. 42,62 
 
 Cloclu... 113 
 
 Commission 59i 60 
 
 Comparisons <S^i 2 (• 381 43 
 
 Compound Interest 75) 7^ 
 
 Cubes 9 
 
 Cubic Measure loi, 102 
 
 Customs and Excise /o 
 
 Days of the Week 39-43 
 
 Decimals 39~54 
 
 Numeration .-. 39> 40 
 
 Notation 41, 42, 43 
 
 Addition 44, 46 
 
 Subtraction 45> 46 
 
 Multiplicatioa 47i 48 
 
 Division 49 
 
 Denominate 50, 51 
 
 Reduction 50* 5 ^ 
 
 Circulating Dec 50 
 
 Theory 54 
 
 Discount, Bank 73 
 
 — , Truet- 74 
 
 Ditching. 85 
 
 Page. 
 
 Division, Simple 67-^) 
 
 — , Compound 87-110 
 
 — , Fractions 32, 33. 34. 35 
 
 — , Decimals 4^ 
 
 Dry Measure ^2 
 
 Earnings no, 1 75 
 
 Elections 107 
 
 Equations 105 
 
 Eq>>ntion of Paymentii 76 
 
 Excavating 97 
 
 Factors j6, 6, 7, ^4 
 
 Fencing n, 83 
 
 Finding Cosi.^;;, jj, 61, 62, 103, 106 
 30-34.47.83.118 
 
 Findmg Price ZJ", 49 
 
 Flooring 92 
 
 Fractions, Vulxar 19-38 
 
 Numeration 19 
 
 Notation 20 
 
 Reduction 20,21,23,24 
 
 Comparison. 24, 38 
 
 Addftion 25, 26 
 
 Subtraction 27-29 
 
 Multiplication 30-31 
 
 Division 32, 34 
 
 Complex Frs • .33 
 
 G.C.M 36 
 
 L.C.M 36 
 
 Simplifying 35, 26, 27, 30 
 
 .32, 33. 36 
 Theory 37,38 
 
 G.C.M. 
 Grain . . 
 
 7, 8, 9, 10-18, 36 
 J03,i04 
 
 Insurance.^ 67 
 
 Interest, Simple 71, 73 
 
 — (Compound 75, 76 
 
 Income Taxes 69 
 
 Land 89, 90 
 
 Lathing 88 
 
 LX.M 12, 13, 14-18, 36 
 
 Linear Measure 97, gS 
 
 Liquid Measure gt 
 
 m- 
 
INUKX Continiu'd. 
 
 ' Pagic 
 
 Longitude and Time 116 
 
 Lossand Gain 6^-66, j 10 
 
 Lumber Sa, 83, 84, 91, 92 
 
 Making Change 2^,42,62 
 
 Materials 82 
 
 Measures 5-1 1) i4'i8i "9 
 
 Mixtures.. 
 
 II, 104, 106 
 
 Money, Canadian 88 
 
 —, Enelish go 
 
 —, United States Sg 
 
 Multiples 12, 13, 14-18, 119 
 
 Multiplication, Simple <^7-<^ 
 
 — , Compound 8j-iio 
 
 — , Fractions 30, 31 
 
 — , Decimals 47, 48 
 
 —, Table 5' 
 
 Notation, Arabic S,(><7- 'o 
 
 — , Roman 8,g, 10 
 
 —(Fractions '9i 20 
 
 — , Decimals 39-43 
 
 Numeration J-'o, 19, 20, 39-42 
 
 Painting 86 
 
 Papering 95. 96 
 
 Partial Payments 76 
 
 Partnership 68 
 
 Percentage 55-58, 79 
 
 Plastering 87,88 
 
 Popalation 116 
 
 Posts 83 
 
 Powers 59 
 
 Practice 120 
 
 Products J6, 57, 61, 62, 6j 
 
 16, 30, 48 
 
 Proportion 117 
 
 Percentage 55-80 
 
 Commission 59i 60 
 
 Trade Diitcount 61, 62 
 
 Loss and Gain 63, 64, 65, 66 
 
 Insurance'. 67 
 
 Bankruptcy 68 
 
 Partnership 68 
 
 Taxes 69 
 
 Custoifts and Excise 70 
 
 Simple Interest 711 72 
 
 Bank Discount 73 
 
 True Discount 74 
 
 Compound Interest 75 
 
 Partial Payments 76 
 
 Equation of Payments 76 
 
 Stocks and Bonds. 77 
 
 Brokerage'. 78 
 
 PA(iE. 
 
 Review 79 
 
 Theory 80 
 
 Racing 17, iia 
 
 Ratio 117 
 
 Reduction 87-ito 
 
 — , Fractions 20, 2 1, 22, 23, 24 
 
 — , Decimals 4J 
 
 — , Percentage 56. 57 
 
 Remainders 27, 28, 45, 108 
 
 Roadmaking 97 
 
 Roofing 88 
 
 Roman Notation 8,g, to 
 
 Savings 29, 31 
 
 Sharing 7^t8o, toj, 34 
 
 Short Methods 61, 62, 63, loi 
 
 Simple Interest 7^-73 
 
 Simplifying 63, 81, 82, 83, 84 
 
 33. 34. 36. 46. 48, loi 
 
 Sodding 90 
 
 Solid Measure /o/, t02 
 
 Spending 29, 31, 108 
 
 Squares 9, 10 
 
 Square Measure 99, loo 
 
 Square Root 10, 37, 119 
 
 Stocks and Bonds 77) 78 
 
 Streams j/, 6/, 112 
 
 Subtraction, Simple 2j-4b 
 
 — , Compound 88-102 
 
 — , Fractions 27, 28, 29 
 
 — , Decimals 45, 46 
 
 —, Table 29 
 
 Sum and Difference 35, 28, 34 
 
 46, "5 
 Surface Measure gg, 100, 99 
 
 Table, Addition /J, /J 
 
 — , Subtraction 2g 
 
 — , Multipiication 5/ 
 
 Theory 10, 4s, 46, 66, 86, no 
 
 18, 37. 38, 54. 80, 125 
 
 Taxes 69, 70 
 
 Time. 9J, 9^, 114 
 
 Trade Discount 61, 62 
 
 Trains iii 
 
 Troy Weight 96 
 
 True Discount 74 
 
 Wages IIS 
 
 Wall Papering 95, 96 
 
 Weights and Measures ^-\xo 
 
 Working ^29, loq 
 
 Wheels. 17 
 
*SCHOOL HELPS" SERIES 
 
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