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1221, remainder.

REM. 1.—When the dividend is not the exact product of two integral numbers, there will be a remainder, and the dividend is equal to the product of the quotient and divisor plus the remainder.

REM. 2.-When there are the same number of zeros in dividend and divisor, beginning with the order of units they may be canceled ; and when there are zeros in the divisor only, they may be omitted, and also the same number of figures in the dividend, which after the division is performed must be brought down as a part or the whole of the remainder.

EXAMPLES.

235643 by

345678 by

234567 by

1. Divide

2. Divide

3. Divide

4. Divide

1357916 by

5. Divide 369875432 by

123.

234.

891.

248.

1768.

625.

1234.

2345.

6. Divide 487698425 by 7. Divide 987654321 by 8. Divide 876543219 by 9. Divide 678956732 by 10. Divide 34567890 by 11. Divide 786954321 by 176543.

1546.

2564.

12. Divide 678900432 by 1004000.

The student must not proceed until he is familiar with division.

EXAMPLES.

1. What cost 5 lbs. of sugar at 10 cts. per lb.?

2. At 10 cts. per lb., how many lbs. can be bought for 50 cts.?

3. What cost 10 lbs. of sugar at 10 cts. per lb. ?

4. At 10 cts. per lb., how many lbs. can be bought for 100 cts.?

5. What cost 15 lbs. of sugar at 10 cts. per lb. ?

6. At 10 cts. per lb., how many lbs. can be bought for 150 cts. ?

7. What cost 20 lbs. of sugar at 10 cts. per lb.?

8. At 10 cts. per lb., how many lbs. can be bought for 200 cts.?

9. What cost 25 lbs. of sugar at 10 cts. per lb. ?

10. At 10 cts. per lb., how many lbs. can be bought

for 250 cts.?

11. What is the cost of 4 barrels of molasses at 18 dollars a barrel?

12. What is the cost of 9 barrels of sugar at 15 dollars a barrel?

13. What is the cost of 25 pounds of beef at 9 cents a pound?

14. What is the cost of 33 pounds of butter at 21 cents a pound?

15. What is the cost of 147 pounds of cheese at 16 cents a pound?

16. What is the cost of 123 barrels of cider at 4 dollars a barrel?

17. What is the cost of 436 barrels of flour at 8 dollars a barrel?

18. What is the cost of 432 tons of coal at 6 dollars a ton?

19. In an orchard there are 9 rows of trees and 43 trees in each row; how many trees are there in the orchard?

20. Bought 6 pieces of cloth, each containing 42 yards, at 6 dollars a yard; how many yards were there, and what did the whole cost?

21. Bought 9 pieces of cloth, each containing 43 yards, at 5 dollars a yard, and 25 barrels of flour at 6 dollars a barrel; what did the whole cost?

22. If 4 barrels of flour cost 32 dollars, what is that per barrel?

23. A man paid 320 dollars for two horses; what was the price of each?

24. A man owning 480 acres of land, wishes to divide it equally among his 4 sons: how many acres will each get?

25. A farm of 120 acres is laid off into six fields of equal size; how many acres in each?

26. A man is 45 years old, and he is three times as old as his son. How old is the son?

27. A farmer sold 325 bushels of wheat for 650 dollars. What was the rate per bushel?

28. In an orchard there are 625 trees, and there are 25 trees in a row. How many rows are there?

29. In a garden there are 100 heads of cabbage in ten rows, and an equal number in each row. How many heads in each row?

30. A farmer sowed five bushels of clover-seed on

forty acres of land. How many acres to a bushel

of seed?

31. A man dying, bequeathed his estate of 580,640 dollars, as follows: 60,000 dollars to each of two daughters, 125,000 dollars to a son, 22,000 dollars to each of his four sisters, and the remainder to his grandson. What was the grandson's share?

32. Four persons enter into partnership; the first invests 8564 dollars, the second 500 dollars more than the first, the third as much as the first and second, and the fourth 645 dollars less than the third. What was the whole amount invested?

33. Bought silk for 1600 dollars, lace for 960 dollars, shoes for 356 dollars, a shawl for 30 dollars, and some ribbon for 5 dollars. Paid at one time 500 dollars, at another 685 dollars, and at a third 800 dollars. How much is still owing?

34. A man bought a carriage and two horses for 963 dollars; the horses were valued at 450 dollars. What

was the value of the carriage, and how much more was the carriage than the horses?

35. Bought molasses for 2634 dollars, sugar for 965 dollars, and coffee for 1589 dollars; sold the molasses at a gain of 500 dollars, the sugar at cost, and lost 100 dollars on the coffee. Did I gain or lose, and how much?

36. Washington was born in 1732 and died in 1799; how old was he when he died?

37. The pyramids of Egypt were built 337 years before the founding of Carthage; Carthage was founded 49 years before the destruction of Troy; Troy was destroyed 431 years before Rome was founded; Carthage was destroyed 607 years after the founding of Rome and 146 years before the Christian era. How many years before Christ were the pyramids built?

38. What is the cost of 5 pounds of sugar, at 12 cents a pound?

39. What is the cost of 15 pounds of sugar, at 11 cents a pound?

40. What is the cost of 335 pounds of sugar, at 9 cents a pound?

41. What is the cost of 23 tons of hay, at 14 dollars a ton?

42. What is the cost of 435 acres of land, at 43 dollars per acre?

43. What is the cost of 753 bushels of oats, at 35 cents per bushel?

44. If 5 lbs. of sugar cost 60 cents, what is it per lb.? 45. If 15 lbs. of sugar cost 165 cents, what is it per lb.? 46. If sugar at 9 cents per lb. cost 3015 cents, how many pounds were there?

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