1. Let it be required to divide 67389 by 700.

multiply by the first divisor, 100, and then add 89, forming the true remainder, 189: to the quotient, 96, we annex 189 divided by 700, for the entire quotient. Hence, the following

Rule.

I. Cut off the ciphers by a line, and cut off the same number of figures from the right of the dividend.

II. Divide the remaining figures of the dividend by the remaining figures of the divisor, and find the true remainder. III. To the quotient before found, annex the true remainder, divided by the divisor, for the true quotient.

79. Abstractly, the object of Division, is to find how many times one number is contained in another. Practically, all questions are reduced to three classes:

1. To find the value of any equal part of a number, or of any number of things.

2. Knowing the entire cost of a number of things, and the price of a single thing, to find the number of things.

78. How do you divide when the divisor is any digit, with ciphers on the right of it?

8. Knowing the number of things, and their entire cost, to find the price of a single thing.

The three analyses on pages 54 and 55, give the following

Rules.

1. To find the value of each part.

Divide the number of things by the number of parts into which they are to be divided: the quotient will be the value of each part.

2. To find the number of things.

Divide the entire cost by the price of a single thing: the quotient will be the number of things.

3. To find the price of a single thing.

Divide the entire cost by the number of things: the quotient will be the price of a single thing.

Applications in the previous Rules.

1. Mr. Jones died, leaving an estate worth 4500 dollars, to be divided equally among 3 daughters and 2 sons: what was the share of each?

2. The owner of an estate sold 240 acres of land, and had 312 acres left: how many acres had he at first?

3. The sum of two numbers is 3475, and the smaller is 1162 what is the greater?

4. The difference between two numbers is 1475, and the greater number is 5760: what is the smaller?

5. A gentleman bought a house for two thousand twentyfive dollars, and furnished it for seven hundred and six dollars; he paid, at one time, one thousand and ten dollars, and at another time, twelve hundred and seven dollars: how much remained unpaid?

6. At a certain election, the whole number of votes cast

79. What is the object of Division, abstractly? Practically, to how many forms are all questions reduced? What are they? What are the rules?

for two opposing candidates, was 12672; the successful candidate received 316 majority: how many votes did each receive?

7. What number must be multiplied by 124, to produce 40796?

8. The sum of 19125 dollars is to be distributed equally among a certain number of men, each to receive 425 dollars: how many men are to receive the money?

9. A merchant has 5100 pounds of tea, and wishes to pack it in 60 chests: how much must he put in each chest? 10. The product of two numbers is 51679680, and one of the factors is 615: what is the other factor?

11. Bought 156 barrels of flour for 1092 dollars, and sold the same for 9 dollars per barrel: how much did I gain?

12. Mr. James has 14 calves, worth 4 dollars each; 40 sheep, worth 3 dollars each; he gives them all for a horse, worth 150 dollars: what does he make or lose by the bargain?

13. Mr. Wilson sells 4 tons of hay, at 12 dollars per ton, 80 bushels of wheat, at 1 dollar per bushel, and takes in payment a horse, worth 65 dollars, a wagon, worth 40 dollars, and the rest in cash: how much money did he receive? 14. If the remainder is 17, the quotient 610, and the dividend 45767, what is the divisor?

15. If the product of two numbers is 346712, and one of the factors is 76, what is the other factor?

16. If the quotient is 482, and the dividend 135442, what is the divisor?

17. There are 31173 verses in the Bible: how many verses must be read each day, that it may be read through in a common year?

18. The distance around the earth is computed to be about 25000 miles: how long would it take a man to travel that distance, supposing him to travel at the rate of 35 miles a day?

19. A person having a yearly salary of 1500 dollars, saves at the end of the year, 405 dollars: what were his average daily expenses, allowing 365 days to the year?

20. The salary of the President of the United States is 25000 dollars a year: how much can he spend daily, and save of his salary, 4925 dollars at the end of the year?

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21. A speculator bought 512 barrels of flour for 3584 dollars, and sold the same for 4608 dollars: how much did he gain per barrel ?

22. Mr. Place purchased 15 cows; he sold 9 of them for 35 dollars apiece, and the remainder for 32 dollars apiece, when he found that he had lost 123 dollars: how much did he pay apiece for the cows?

23. If a man's salary is 800 dollars a year, and his expenses 425 dollars, how many years will elapse before he will be worth 10000 dollars, if he is worth 2500 dollars at the present time?

24. How long can 125 men subsist on an amount of food that will last 1 man 4500 days?

25. The income of the Bishop of Durham, in England, is 292 dollars a day: how many clergymen would this support on a salary of 730 dollars per annum?

26. The diameter of the earth is 7912 miles, and the diameter of the sun, 112 times as great: what is the diameter of the sun?

27. By the census of 1850, the whole population of the United States was 23191876; the number of births for the previous year was 629444, and the number of, deaths, 324394 supposing the births to be the only source of increase, what was the population at the beginning of the previous year?

28. A farmer purchased a farm, for which he paid 18050 dollars; he sold 50 acres for 60 dollars an acre, and the remainder stood him in 50 dollars an acre: how much land did he purchase?

29. A merchant bought a hogshead of molasses, containing 96 gallons, at 35 cents per gallon; but 26 gallons leaked out, and he sold the remainder at 50 cents per gallon: did he gain or lose, and how much?

30. Mr. James bought of Mr. Johnson two farms, one con

taining 250 acres, for which he paid 85 dollars per acre; the second containing 175 acres, for which he paid 70 dollars an acre; he then sold them both, for 75 dollars an acre: did he make or lose, and how much?

31. A farmer has 279 dollars, with which he wishes to buy cows at 25 dollars, sheep at 4 dollars, and pigs at 2 dollars apiece, of each an equal number: how many can he buy of each sort,?

32. Two persons counting their money, found that together they had 342 dollars; but one had 14 dollars more than one-half of it how many dollars had each ?

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33. Mr. Bailey has 7 calves, worth 4 dollars apiece, 9 sheep, worth 3 dollars apiece, and a fine horse, worth 175 dollars. He exchanges them for a yoke of oxen, worth 125 dollars, and a colt, worth 65 dollars, and takes the balance in hogs, at 8 dollars apiece: how many hogs does he take?

34. How many pounds of coffee, worth 12 cents a pound, must be given for 368 pounds of sugar, worth 9 cents a pound?

35. If 600 barrels of flour cost 4800 dollars, what will 2172 barrels cost?

36. Mr. Snooks, the tailor, bought of Mr. Squires, the merchant, 4 pieces of cloth; the first and second pieces each measured 45 yards, the third, 47 yards, and the fourth, 53 yards; for the whole he paid 760 dollars: what did he pay for 35 yards?

37. What is the difference between the cost of a flock of sheep containing 175, at 4 dollars apiece, and a drove of 97 cattle, at 85 dollars apiece?

38. A miller bought 320 bushels of wheat for 576 dollars, and sold 256 bushels for 480 dollars: what did the remainder cost him per bushel?

39. A merchant bought 117 yards of cloth for 702 dollars, and sold 76 yards of it at the same price for which he bought it: what was the value of the cloth sold?

40. If 46 acres of land produce 2484 bushels of corn, how many bushels will 120 acres produce?