15. How many times is 35 contained in 45 817?

35)45817(1308

35

108

105

317

280

37

Here we have chosen 8 for the last figure of the quotient; but, after subtracting 8 times 35 from 317, there remains, 37. This remainder will contain 35, once more; therefore, we must rub out the 8 and the work resulting from it, and must put 9 in the place of 8. 16. How many times is 47 contained in 804? 17. How many times is 53 contained in 1625 ? 18. How many times is 68 contained in 94 605 ? 19. How many times is 71 contained in 661 419 ? 20. How many times is 108 contained in 216 ? 21. How many times is 325 contained in 7134 ? 22. How many times is 476 contained in 92 107 ? 23. How many times is 504 contained in 1008 ? 24. How many times is 651 contained in 43 126 ?

RULE FOR DIVISION. When the divisor does not exved 9, draw a line under the dividend, find how many times the divisor is contained in the left hand figure, or two left hand figures of the dividend, and write the figure expressing the number of times underneath: if there be a remainder over, conceive it to be prefixed to the next figure of the dividend, and divide the next figure as before Thus proceed through the dividend.

When the divisor is more than 9, find how many times it is contained in the fewest figures that will contain it, on the left of the dividend, write the figure expressing the number of times to the right of the dividend, for the first quotient figure; multiply the divisor by this figure, and subtract the product from the figures of the dividend considered. Place the next figure of the dividend on the right of the remainder, and divide this number as before. Thus proceed through the dividend.

PROOF. Multiply the divisor and quotient together, and to the product add the remainder the sum will be equal to the dividend, if the work be right.

25. Divide 46242 by 252, and prove the operation

26. Divide 74 201 by 625, and prove the operation 27. Divide 408 732 by 9, and prove the operation. 28. Divide 15 362 by 88, and prove the operation. 29. Divide 57 026 by 492, and prove the operation 30. Divide 982 700 by 53, and prove the operation 31. Divide 162 941 by 256, and prove the operation 32. Divide 648 035 by 14, and prove the operation. 33. Divide 106 401 by 333, and prove the operation. 34. Divide 62 509 by 4423, and prove the operation. 35. Divide 1 071 400 by 29, and prove the operation. 36. How many acres of land, at 22 dollars an acre, can be bought for 8514 dollars?

37. Suppose a man to earn 35 dollars a month; how many months will it take him to earn 490 dollars?

38. If a man travel 48 miles a day, in how many days will he perform a journey of 3264 miles?

39. If 774 dollars be divided equally among 18 sailors, how many dollars will each sailor receive?

40. If a man's income be 2555 dollars a year, how much is it a day, there being 365 days in a year? 41. The income of the Chancellor of England, is 99 280 dollars a year. How much is it per day? 42. 63 gallons of water will fill a hogshead. How many hogsheads will 5166 gallons fill?

43. How many hogsheads can be filled from 19721 gallons? and how many gallons will there be left?

44. Suppose a regiment of 512 men have 8192 pounds of beef; how many pounds are there for each man?

45. If a dividend be 46 319, and the divisor 807, what is the quotient?—and what the remainder?

SECTION 4.

ABBREVIATIONS.

When there are ciphers on the right hand of a divisor, cut them off, and omit them in the operation; also cut off and omit the same number of figures from the right hand of the dividend. Finally, place the figures cut off from the dividend, on the right of the remainder.

1. How many times 900 are there in 741 725?

900)741725

824 125

We divide 7417 by 9; there remains 1, to which we annex the 25, making the true rem. 125. 2. How many times 70 are there in 8 563 512 ? 3. How many times 300 are there in 6374 ? 4. How many times 5000 are there in 46 578 ? 5. How many times 40 are there in 80 603? 6. How many times 600 are there 675 700? 7. How many times 8000 are there in 16 000 ? 8. Divide 65 237 by 50, and prove the operation. 9. Divide 567 289 by 400, and prove the operation. 10. How many times 570 are there in 35 871? 11. How many times 280 are there in 6423? 12. How many times 4200 are there in 91 621? 13. How many times 9060 are there in 287 000 ?

When the divisor is 10, 100, 1000, &c., cut off as many figures from the right hand of the dividend, as there are ciphers in the divisor; the other figures of the dividend will be the quotient, and the figures cut off will

be the remainder.

14. How many times 10 are there in 240?

15. How many times 10 in 435; and how many over? 16. How many times 100 are there in 4000?

17. How many times 100 in 748; and how many over 18. 100 cents are equal to 1 dollar. How many dollars are there in 5400 cents?

19. In 642 cents, how many dollars are there; and now many cents over?

20. In 1937 cents, how many dollars are there; and how many cents over?

When factors of the divisor can be found, (that is, when two numbers can be found, which, being multiplied together, produce the divisor,) you may divide the dividend by one of the factors, and the quotient thence arising by the other: the last quotient will be the true one.

21. In a certain school there are 36 scholars, among whom 540 quills are to be equally divided. How many will 1 scholar receive?

Let us suppose the school to be divided into 4 classes, allowing 9 scholars to be in each class. Then we will find how many quills 1 class will receive, and from this number, find how many 1 scholar will receive.

4)540 number of quills for the school.

9)135

15

number of quills for 1 class.

number of quills for 1 scholar.

Observe in the above example, that the divisors 4 and 9, are the factors of 36: and, if we had divided first by the 9, and then by the 4, our last quotient would have been the same it now is.

22. Divide 11 376 by 72; using the factors of 72. 23. If 1024 dollars be divided equally among 64 men, how many dollars will 1 man receive?

24. How many times is 42 contained in 1176 ?

25. If 27 yards of cloth cost 216 dollars, how many dollars does I yard cost?

26. Suppose 1952 to be a dividend, and 32 the divisor: what is the quotient?

To obtain the true remainder, where factors have been used as divisors, multiply the last remainder by the first divisor, and to the product add the first remainder.

27. Suppose 622 to be a dividend, and 35 the aivi sor; what is the quotient; and what the remainder? 28. Suppose 99 to be a dividend, and 25 the divisor, what is the quotient; and what the remainder?

29. Suppose 4862 to be a dividend, and 81 the divisor; what is the quotient; and what the remainder? 30. Divide 1739 bv 56

Questions to be answered Orally.

(1) When we say, '3 is contained in 20, 6 times, and 2 over,' which of these numbers have we for the dividend? Which for the divisor? Which for the quotient? Which for the remainder? (2) What is meant by the dividend? (3) What is meant by the divisor? (4) What is meant by the quotient? (5) What is meant by the remainder ? (6) Can the remainder ever be equal to, or greater than the divisor? Why? (7) Suppose you have a number of dollars to divide among a number of men; which number do you make the dividend;-and which the divisor? -If there be a remainder, will it be so many dollars, or so many men? (8) Recite the rule for division. (9) How do you proceed when there are ciphers on the right hand of the divisor? (10) How do you divide by 10, 100, 1000, &c.? (11) How can you divide by means of factors? (12) When you have divided by the factors of the divisor, how do you find the true remainder? (13) How do you prove an operation in division?

Perform the following examples by either of the foregoing methods, which may be found convenient.

31. Suppose it takes 7 bushels of apples to make a barrel of cider, how many barrels of cider can be made from 945 bushels of apples?

32. Suppose an acre of land properly cultivated, to produce 38 bushels of corn; how many acres must be cultivated to produce 4902 bushels ?

33. If 50 dollars will pay for an acre of land, how many acres can be bought for 6900 dollars?

34 How many days will a ship be in sailing from New York to Liverpool; allowing the distance to be 3000 miles, and the ship to sail 100 miles a day?

35. A vintner wishes to put 6615 gallons of wine into hogsheads that will hold 63 gallons apiece;-how many hogsheads must he have?