QUESTIONS FOR EXAMINATION.*

ADDRESSED TO THE LEARNER AND CANDIDATES FOR SCHOOL-KEEPING.

TO BE ANSWERED WITHOUT THE SLATE.*

CXVIII. Q. 1. What is Quantity? See page 26. How is it estimated? Illustrate it by an example. How are different quantities expressed?

Q. 2. What is Number? 3. How is it represented? What are Concrete and Abstract Numbers? 26. Simple and Compound Numbers? 27. What is meant by denomination?

Q. 3. What is Arithmetic? 27. What are its fundamental rules? Describe the different methods of representing numbers? 28. Q. 4. What is Numeration? 32. Notation and its rule? Repeat Numeration Table III. What is the greatest number that can be formed by thirty 5s?

Q. 5. What is addition? 37. Its rule? Why do you carry 1 for every 10 36. What is the proof and the reason for it? 37.

Q. 6. What is Subtraction? 41. Its terms? Rule? Why do you borrow from one figure and pay to another? 40. What is the proof and the reason for it? 42.

Q. 7. What is Multiplication? 45. Its terms? Which terms are called factors and why? When may Addition be performed by Multiplication? How do you multiply by 12 or less?-by 13 or more?-by a composite number?-by 10, 100, &c. ?-3700 by 210?

Q. 8. What is Division? 52. Its terms? What rule is proved, and what one is performed, by Division? What is Short Division? 53. Rule? Long Division? 54. Rule 57. Rule for dividing by 10, 100, &c. 60. Rule for dividing 888 by 800 in the most concise manner?

subtrahend found when the minuend and How may the multiplier be found with the How may the remainder be found with

Q. 9. How is the remainder are given? multiplicand and product? the dividend and quotient?

Q. 10. What is the amount of 35 and 7500 and 30000 and 4200000 added together? When the minuend is 400 and the remainder 40, what is the subtrahend? When the multiplier is 8 and the product 4000, what is the multiplicand?

Q. 11. What are the results of 34398 multiplied by 100 and the same divided by 100? When the quotient is 50 and the dividend 2504, what is the remainder?

For the benefit of the Teacher the answer to each example is given in the key, to gether with reasons for the more difficult operations.

† All questions without numbers annexed, refer to the page indicated by the last pre ceding number.

Q. 12. Two men are traveling in the same direction, one at the rate of 36 miles a day, and the other 40 miles; in how many days will the latter be 100 miles forward of the other?

Q. 13. Suppose a fox, which is 120 rods before a greyhound, runs at the rate of 4 rods in 2 seconds, and the dog 13 rods in 6 seconds. How far must the dog run to catch the fox, and how long will he be in doing it?

Q. 14. If the minuend be 600 and the difference between the remainder and subtrahend 100, what are the last two terms?

Q. 15. Two men having met on a journey, found that they had both traveled 1,200 miles; but one had traveled 200 miles more than the other. What was the distance each traveled?

Q. 16. Suppose four boys together weigh 435 pounds, and that it should so happen that three of them go in the same notch, but the other in a notch 15 pounds higher; what would be the weight of each boy?

Q. 17. Divide 600 dollars so that A may have 50 dollars more than B, and C 100 more than B.

Q. 18. Said Harry to Dick, my purse and money are worth 100 dollars; but the money is worth 19 times more than the purse. How much money was in the purse?

Q. 19. If a clerk, whose salary for 4 years amounted to 2,000 dollars, had received 50 dollars advance for each successive year after the first, what was his annual salary?

Q. 20. Suppose that C resides 3 times as far from Boston as A, and D 5 times as far as C, and that to meet in that city they must all travel 380 miles. What distance from Boston does each reside?

Q. 21. A man bought a horse, saddle and bridle for 318 dollars, and paid 20 times as much for the horse as for the saddle, and 5 times less for the bridle than for the saddle. What did the bridle and saddle both cost?

Q. 22. Fifteen years ago I was three times as old as my eldest son, who was then but 15, but am now only twice as old. What are our present ages?

Q. 23. A company at a tavern spent $3, and each of them had as many dimes to pay as there were persons in the company; how many persons were there?

Q. 24. What is the difference between twice twenty-five and twice five and twenty?

Q. 25. A snail in going up a May-pole 22 feet high, ascended 41 feet every day, and descended every night 23 feet; how long would it be in getting to the top of the pole?

26. What is Federal Money? 73. What is the rule for Addition of Federal Money? 75. For Subtraction? 76. For Multiplication? 77. For Division? 78.

Q. 27. Suppose you sell 4 bushels of oats at 37 a bushel, and pay 62 cents for 5 pounds of cheese, and lay out the balance in pins

at 6 cents a paper; how many papers of pins will you have, and how much will the cheese cost by the pound?

Q. 28. If you purchase 29 yards of ribbon at 6 cents per yard, and give the shop keeper a five dollar bill, how much change must he give you? What will 2 barrels of pork cost at 12 cents per pound? -at 10 cents per pound?

Q. 29. What will 6,404 articles of any thing cost at 6 cents each? at 12 cents?—at 1 shilling?-at 25 cents ?-at 50 cents?at 75 cents?

Q. 30. What is Reduction? 74. Reduction descending and its rule? 89. Reduction Ascending and its rule? What is Compound Addition and its rule? 97. Compound Subtraction and its rule? 101. Compound Multiplication and its rule? 104. Compound Division

and its rule? 107.

Q. 31. What are Fractions? 110. What is the denominator? Numerator? How is the integer found from having its fraction given? What is the integer of which is 20? What is the value of a fraction? 111.

Q. 32. What part of 48 is 36? What is the rule and reason for it? 112. What are the two ways for multiplying a fraction, and why? 113. What for dividing fractions, and the reason? 114.

11

300

Q. 33. What is the product of multiplied by 47?— multiplied by 202-20 divided by 16?- divided by 3? 53

9

Q. 34. What is meant by a common measure or a common divisor? 116. What by a common multiple? 118. What are the rules for finding both? 117, 120. What is the greatest common divisor of 48 and 24? What is the least common multiple of 5

and 20?

Q. 35. What is a Vulgar Fraction? 121. Describe the different sorts of Vulgar Fractions? How are mixed numbers reduced to improper fractions? 125. Compound and complex fractions to single ones? 123, 127. Rule, and the reason of it for the reduction of fractions to their lowest terms? 122. For finding the least common denominator? 127.

Q. 36. What fraction of a dollar is equal to 3 of a pound? What is the rule for it? 131. What are the rules for Addition of Fractions 133. For Subtraction? 134. For Multiplication? 136. For Division? 139.

Q. 37. A man being asked how long he had been in business, replied that the time he spent at school was 6 years, and that of that period is just 3 of the time he had been in business; what was a direct answer to the question?

Q. 38. of 21 is of what number? of 22 is of what number?

Q. 39. One drover said to another, I have 20 cows. Well, said the other, of 3 of your drove is only of mine. How many cows had both?

Q. 40.
Q. 41.

of 24 is

of how many times 8.

of 24 is

of how many eighths of 40?

Q. 42. What number added to 2 of 16, will make 3 of 60 ?

Q. 43. A man bought 2 bushels of rye at one time, and 1 bushels at another. He sold 3 bushels; how much had he left?

Q. 44. A man bought a sheep for 5 dollars and a calf for 7 dollars; what did he give for both, and what was the difference in their cost? What fraction added to and will make a unit?

Q. 45. There is a mast erected so that of it stands in the ground, in the water, and 28 feet out of the water; how long is the mast?

Q. 46. Suppose A having taken a job of work does of it in 1 day, of it the second day, and the third day; how much of it does he do in the three days?

Q. 47. Suppose A can mow a certain field in 2 days, and B in 4 days; what part of the field would each mow in one day? What part would both mow in one day? How long would it take both together to mow the field?

Q. 48. Suppose a cistern has three spouts, and that one will fill it in 2 hours, another in 3 hours, and another în 4 hours; in how many hours would it be filled by them all together?

Q. 49. Suppose a cistern is filled by two spouts in 4 and 12 minutes respectively, and is emptied by a tap in 16 minutes; how many minutes will have elapsed before it is filled, when they are all left open or running, the influx and efflux being uniform?

Q. 50. What is one half the quarter of? What part of three pence is a third part of two pence?

Q. 51. If a herring and a half cost a penny and a half, how many may be had for 11 pence? What number is that of which 9 is? Q. 52. What number is that, the 3d and 4th parts of which, taken together, make 24? What part of a dollar is a 3d part of a cent? Q. 53. What would of a hogshead of molasses cost at 50 cents a gallon?- of a cwt. of sugar cost at 10 cents per pound?

Q. 54. What part of an eagle is a fourth part of a dime? How many pecks are of a bushel?

Q. 55. The aggregate of and of a debt is 60 dollars; what is that debt? What fraction multiplied by 3 of 3 of 3 will make ?

Q. 56. A person having of a coal mine, sells of his share for 600 dollars; what is the whole mine worth?

Q. 57. A can do a piece of work in 5 days, B in 3 days, and C in 10 days; how long would they jointly be in doing it?

Q. 58. If the trees in an orchard bear apples, pears, plums, 40 of them peaches, and 10 cherries, what number of trees does the orchard contain? What is that number of which++ is 45? bushels of oats cost 22 dollars, what is the price

Q. 59. When 5

by the bushel? What number is that, to which, if its half be added, the sum will be 12

Q. 60. What number is that, to which, if its half, its third, and its fourth, be added, the sum will be 25? The double and the half of a certain number, increased by 5 more, will make 26; what is that number?

Q. 61. If a horse will eat 8cwt. of hay in a month, a cow 4cwt., and a calf 3cwt., in what time will they all consume a load of hay? Q. 62. A person being asked how much money he had, replied evasively as follows-If and of it, with 18 dollars more, be added to it, the sum would be 4 times as much as he had. What sum had he? Q. 63. What number is that, which, if increased by its half, its third, and 2 more, will be doubled?

Q. 64. A man spent one third of his life in England, one fourth in Scotland, and the remainder, which was 20 years, in the United States. To what age did he live?

Q. 65. A person, after paying away one third of his money, together with ten dollars, finds that he has remaining 15 dollars more than its half; what sum of money had he?

Q. 66. A man having purchased a drove of cattle, was driving them to market, when he was met by a gentleman, who inquired of him where he was going with his 100 head of cattle. Sir, said he, I have not 100, but if I had as many more as I now have, as many more, and 71⁄2 head of cattle, I should have 100. How many had he?

Q. 67. What are Decimal Fractions? 145. What decimals are equal to ?-to-to-to ?-What is the rule for these reductions? 149.

Q. 68. What decimal of a pound is 2s. 6d.? What is the value of £125 Rules for the last two examples? 152, 153.

Q. 69. What is the general method of proceeding in decimal rules, and why? 153. Rule for Addition of Decimals? 154. Subtraction? 155. Multiplication? 156. Division? 158.

Q. 70. What is the sum of .6 and .03 and .004 and .0005? How much does unity exceed .123456789 ?

Q. 71. Multiply 1.234 by 10;-by 100;-by 1,000.

Q. 72. Divide 123.4 by 10;-by 100;-by 1,000.

Q. 73. How is Reduction of Currencies performed? 161. What number of shillings make a dollar in the different states? What number of pence is equal to 12 cents in these same states?

Q. 74. What is Rate per Cent.? 163. Rule for finding the per centage? When 5 yards of broadcloth, that cost 6 dollars per yard, sells for 25 per cent. profit, how many dollars does it sell for ?

Q. 75. What price must be put on molasses that cost 30 cents a gallon, to gain 20 per cent. on the sale of it?

Q. 76. What are Stocks? 166. When you buy stocks, the par value of which is $500, for 10 per cent. advance, and sell them for 15 per cent. discount, what is your loss in the transaction?