4. What will be the cost of 352 dozen eggs at 183 cents a dozen?

5. If a man can hoe a field in 74 days, how long will it take 3 men to hoe a field 23 times as large?

6. From a barrel of kerosene containing 41 gallons it was estimated that leaked out. If I paid $6.15 for it, at what price per gallon must I sell the remainder to balance the loss sustained by leakage?

7. James Henderson sold of his farm of 155 acres to Mr. Paine, and Mr. Paine soon sold of what he had bought, to Mr. Banker. How many acres did Mr. Banker buy?

8. Mr. A. built a block of stores which cost him $31221 for brick, $1368 for lumber, $3258 for labor, and $1325,5 for other expenses. He sold the block for $10000. Did he gain or lose, and how much?

9. There are 2724 square feet in a square rod. How many square feet are there in & of a square rod?

10. I sold a house and lot for $3215, which was 15 times what it cost me. How much did it cost?

11. How much will 8 carpenters earn in 6 days at $27 per day?

12. If a man walks 34 miles per hour, in how many hours can he walk 30 miles?

13. Mr. Jones left an estate valued at $19000. % of it was divided equally among 4 sons and the rest equally among 3 daughters. What was the share of each?

14. The price of maple sugar this year is only of what it was last year. How much more would I have received last year for 3140 pounds which I sold this year at $.20 a pound?

15. Custom millers take of the quantity of grain as pay for grinding it. How many bushels must a man carry to the mill so that he may bring back 14 bushels of ground provender?

16. If $45 is of my money, what part of it will that sum plus $41 be?

17. A farmer had two fields in which he kept his sheep. In one there was of the whole number of sheep, and in the other there were 148 sheep. How many sheep had he?

18. A merchant exchanged 21 barrels of flour worth $73 a barrel, for 24 cords of wood. What did the wood cost him per cord?

19. If I give A 1 of my money, B 4 of it, and C † of it, what part of my money have I left?

20. Mr. A. owns of a vessel valued at $18326. If he sells of his share to Mr. B., what part of the whole will he have left? What part will Mr. B. have? What is the value of Mr. A.'s share? Of Mr. B.'s share?

21. After buying a suit of clothes for $60 I found I had & of my money left. How much had I at first?

22. A man sold of 3 cords of wood for of $83. How much did he receive for it per cord?

23. How many tons of hay will be required to keep 7 horses for 6 months, if 9 horses eat 16 tons in that time? 24. If of a farm is sold for $8516, what would be the worth of the whole at the same rate?

25. A gentleman spent of his annual income traveling, and of the remainder in the purchase of books. The rest, which was $8526, he expended upon paintings and other works of art. What was his annual income?

26. Two men dug a ditch for $53; one man worked 31 days and dug 14 rods; the other worked as many days as the first dug rods per day. How much did each receive, if they shared in proportion to the time they worked?

27. Two brothers together own of a flouring mill valued at $13000. One owns as much as the other. What is the value of each one's share?

28. The loss caused by a fire was $3865. The sum was paid by an insurance company which insured the stock for What was the entire value of the stock?

of its value.

29. A can do a piece of work in 10 days. What part of it can he do in 1 day? If B can do the same piece of work in 8 days, what part of it can he do in 1 day? What part can both together do in 1 day? How many days would be required for both to do the work?

30. If A can do a piece of work in 5 days and B in 8 days, how long will it take both to do it?

31. If A and B can do a piece of work in 10 days, and A can do it alone in 15 days, how long will it take B to do it?

32. A tree 124 feet high was broken in two pieces by falling. of the length of the shorter piece, equaled of the length of the longer piece. What was the length of each piece? 33. A man who had spent his money and $ more, found that he had $21 left. How much money had he at first? 34. A, B and C can do a piece of work in 9 days. A can do it in 25 days, and B in 30 days. In what time can C do it?

35. Two ladders will together just reach the top of a building 75 feet high. If the shorter ladder is the length of the longer one, what is the length of each?

36. There are two numbers whose sum is 140, one of which is the other. What are the numbers?

37. In 1875 a merchant's profits were of his receipts; in 1876 they decreased, which diminished his profits $27561. What were his receipts in 1875?

of

38. A and B together had $5700. of A's money was equal to of B's. How much had each?

39. A man engaged to work a year for $240 and a suit of clothes. At the end of 9 months an equitable settlement was made by giving him $168 and the suit of clothes. What was the value of the clothes?

40. A and B can do a piece of work in 12 days. Assuming that A can do as much as B, how long will it take each to do it?

194. 1. If an apple be divided into ten equal parts, what part of the apple will one of these parts be? Two parts? Five parts?

2. If one-tenth of an apple be divided into ten equal parts, what part of the apple will one of these parts be? Two parts? What part of 1 is of ?

of?

of

3. If one-hundredth of a dollar be divided into ten equal parts, what part of a dollar will one of these parts be? Eight parts? What part of 1 is of do?

4. What part of one-tenth is one-hundredth? Of 2 tenths is 2 hundredths? Of 3 tenths is 3 hundredths? Of 9 tenths is 9 hundredths?

5. What part of one-hundredth is one-thousandth? Of 2 hundredths is 2 thousandths? Of 8 hundredths is 8 thousandths?

6. What are the divisons of any thing into tenths, hundredths, thousandths, ten-thousandths, etc., called? Ans. Decimal divisions.

DEFINITIONS.

decimal divisions of a unit.

The word decimal is derived from the Latin word decem, which signifies ten.

9

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Decimal fractions, for the sake of brevity, are usually called decimals.

196. Since tenths are equal to ten times as many hundredths, and hundredths are equal to ten times as many thousandths, thousandths to ten times as many ten-thousandths, etc., it is evident that decimals have the same law of increase and decrease as integers, and that the denominator may therefore be indicated by the position of the figures.

According to the decimal system of notation, figures decrease in tenfold ratio in passing from left to right; therefore a figure at the right of units will express tenths, at the right of tenths, hundredths, at the right of hundredths, thousandths, etc., as is exhibited by the following expressions:

From this mode of expressing decimal fractions the following principles are deduced:

197. PRINCIPLES.-1. Decimals conform to the same principles of notation as integers.

2. Each decimal cipher prefixed to a decimal diminishes its value tenfold, since it removes each figure one place to the right. 3. Annexing ciphers to a decimal does not alter its value, since it does not change the place of any figure of the decimal.

4. The denominator of a decimal, when expressed, is 1 with as many ciphers annexed as there are orders in the decimal.