58. How many times 7 cents are there in $430.78 ? 7)430.78 We divide $430.78 as if the figures stood to express the whole in cents. 61 54 The quotient is the number of times.. 59 How many times 6 cents are there in $20.22? 60. How many times 15 cents are there in $11.10? 61. How many times 90 cents are there in $27.00 ? 62. How many times $4.06, [406 cents,] are there in $190 146 04, [19014604 cents]?

63. How many lead pencils can you buy for $3.44, when they are sold at 8 cents apiece?

64. How many pounds of butter, at 21 cents per pound, can be bought for $3.57?

65. A laborer earned $53.75, by working at $1.25 a day. How many days did he work?

66. If 84 cents should be divided equally among 6) boys, what would each boy receive?

67. If $28.71 [2871 cents] be divided equally among 9 men, what will each man receive?

68. If $205 58 be divided equally among 38 men, what will each man receive?

€9. If $637 be divided equally among 24 men, what will each man receive?

71. 8 men received $230 for performing a piece of work. What was each one's share of the money?

72. An insurance office, whose stock was owned in 1000 shares, divided among the stock-holders, $1586. How much was paid on one share?

73. The expense of a village school, for 6 months, was $466.80; and it was paid in equal shares by 4C gentlemen. What was each one's share?

74. Add together $9.87, 50 cents, $705.30 and $390: subtract from this sum, 606 dollars and 7 cents: multiply the remainder by 45: divide the product by 37. What is the quotient, and the remainder?

75. A shoe-maker paid $1.58 apiece for 10 calf-skins, and 22 cents a pound for 3 sides of sole leather, each side weighing 35 pounds. From this stock he made 48 pairs of shoes, which he sold at $1.75 a pair. What did he get for his work?

76. Suppose a man, whose income is $400 a year, should spend $3.90 a week, how much would he save in 2 years; there being 52 weeks in 1 year?

77. Suppose wheat to be worth $1.05 per bushel, and rye 70 cents per bushel: how many bushels of rye must be given for 550 bushels of wheat?

Questions to be answered Orally.

(1) What is Federal money? (2) State the denominations of Federal money. (3) State the number of mills in a cent, the number of cents in a dime, &c. (4) How many cents make a dollar? (5) By what short inethod do you find the number of cents in any number of dollars? (6) How do you distinguish the number of dollars, that there are in any number of cents? (7) In writing dollars and cents together, how many figures express the cents? (8) When the cents to be written with dollars are less than 10, what is to be done? (9) Suppose you are dividing dollars, and a remainder occurs, what is to be done, in order to divide the remainder?

Questions to be answered Orally.

(1) How many kinds of operations are practised. on numbers? (2) What are they called? (3) What is Addition? (4) What is Subtraction? (5) What is Multiplication? (6) What is Division? (7) Propose a question that you would solve by addition. (8) Propose a question that you would solve by sub(9) Propose a question that you would solve by multiplication. (10) Propose a question that you would solve by division. (11) How can a question in multiplication be solved by addition? (12) How can question in division be solved by subtraction?

traction.

SECTION 5.

MISCELLANEOUS EXAMPLES.

1. The population of the world has been estimated to be as follows. North America, twenty-six millions; South America, twelve millions; Europe, two hundred and twenty millions; Asia, five hundred millions; Africa, thirty-eight millions; Australia, four millions. What is the whole number?

2. In 1830, the national debt of the United States was 48 565 406 dollars; in 1831 it was 39 123 191 dollars. How much was paid in one year?

3. The national debt of England cannot be less than 1 900 000 000 dollars. How many years would it take to pay this debt, allowing ten millions of dollars to be paid annually?

4. What would be the expense of laying a rail-way from Louisiana to Maine; the distance being 1800 miles, and the rail-way costing 14 000 dollars a mile?

5. In how many days could a passage be effected from Maine to Louisiana, on the proposed rail-way; allowing a car to run 25 miles an hour, day and night?

6. How many days would it take a man to ride on horseback from Maine to Louisiana, riding 5 miles an hour, and 10 hours a day?

7. Light passes from the sun to the earth-a distance of 95 millions of miles-in about 8 minutes. What distance does light move in a minute?

8. The diameter of the earth is 7912 miles; and the diameter of the sun is 112 times as great. What is the diameter of the sun?

9. The income of the Bishop of Durham, in England, is 106 560 dollars per annum. How many clergymen would this support, on a salary of 800 dollars per annum?

10. Five men and three boys found a sum of money, and divided it so that each man had 43 dollars and each

boy 26 dollars. What sum did they find?

11. If a trader buy 558 barrels of flour at 5 dollars a barrel, and pay 14 dollars for storage, for how much must he sell the flour, to gain 160 dollars?

12. Suppose 5 bushels of wheat to make a barrel of flour, how many barrels of flour can be made from 12 bins of wheat, each bin containing 95 bushels?

13. In 12 times 95, how many times 5?

14. If a farmer sell 45 acres of land at 38 dollars an acre, and divide the money equally among 4 sons and I daughter, what is each one's share?

15. A man, who owned 520 acres of land, purchased 376 acres more, and then divided the whole into 8 equal farins. How many acres did each farm contain?

16. In 520 plus 376, how many times 8?

17. If a man's income be 1349 dollars a year, and his expenses 3 dollars a day, how much will he lay up in a year; there being 365 days in a year?

18. A merchant gave 39 240 dollars for a cargo of sugar, and after selling it, found he had gained 1671 dollars. For how much did he sell it?

19. A merchant gave 18 dollars a hogshead for 245 hogsheads of molasses, and then sold the whole for 4000 dollars: did he gain or lose; and how much?

20. A lot of land was divided into 8 farms, and each. farm contained 150 acres. How many acres were there

In the whole lot?

21. If a man's expenses are 2 dol. a day, and his Dcome 17 dol. a week; what will he save in 7 weeks?

L

58. How many times is 8 contained in 9150; and how many are there over?

59. Suppose 568 to be a dividend, and 7 the divisor; what is the quotient, and the remainder?

60. Suppose 1953 to be a dividend, and 7 the divi sor; what is the quotient, and the remainder?

61. Divide 564 by 7, and prove the work to be right. The remainder, in division, is an undivided part of the dividend: therefore, the remainder must be added to the product of the divisor and quotient, to make the product equal to the dividend.

62. Divide 109 by 6, and prove the work to be right. 63. Divide 817 by 5, and prove the work to be right.

SECTION 3.

The method of dividing taught in the two preceding sections, is called Short division: the method taught in this section; is called Long division. In long division, we place the quotient on the right hand of the dividend, and perform some operations under the dividend, heretofore performed in the mind.

1. How many times is 4 contained in 95307?

Dividend

Divisor

8

15

12

Quotient

Perceiving that 4 is contained in 9, twice, we place 2 in the quotient, multiply the divisor by 2, and subtract the product (8) 4)95307(23826 4)95307 (23826 from 9. This is the same as saying in short divisien, '4 in 9, 2 times, and I over.' Now. since the 1 over must be joined with the 5, we bring the 5 down to the right of the 1: and then, perceiving that 4 is contained in 15, 3 times, we place 3 in the quotient, multiply the divisor by 3, and subtract the product as before. Thus we proceed to bring down every figure of the dividend, and unite it with the previous remainder.

33

32

10

8

27

24

Remainder 3