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4. 12 is ; of what number? of what number of what number?

5. 4 is of what number of what number? 6. is of what number of what number? 7. 24 is 4 of what number? ANALYSIS.Since 24 is of a certain number, 1 fifth of the number is . of 24, or 6; and since 6 is } of the number, the number must be 5 times 6, or 30. Hence 24 is of 30. 8. 24 is of what number? 56 is ? of what number? 을

} 9. 18 is z of what number? 49 is į of what number? 10. 24 is į of what number? 42 is of what number? 11. 45 is of what number? 96 is 13 of what number? 12. 4 is of what number?

ANALYSIS.—Since 4 is į of a certain number, } of the number is } of f, or $; and since } of the number is ļ, the number must be 3 times f, or 4. Hence 4 is 3 of 4.

13. 14 is of what number? is 11 of what number? 14. j is of what number? 24 is of what number? 15. 4! is is of what number? 3 is of what number? 16. Mis is of what number? % is 1o of what number?

REVIEW EXERCISES.

193. 1. Mr. B. bought a barrel of flour for $78, a cord of wood for $57, and gave the clerk a twenty-dollar bill. How much change should Mr. B. receive?

2. A merchant bought 360 pounds of sugar at 11} cents a pound, 50 pounds of tea at 62 cents a pound. How much did he pay for both ?

3. If a man can cut in one day 1 of a field containing 7 acres of wheat, how many acres can he cut in of a day?

4. What will be the cost of 31. dozen eggs at 184 cents a dozen?

5. If a man can hoe a field in 71 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, $32587 for labor, and $1325 for other expenses. He sold the block for $10000. Did lie 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

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per day?

in how many

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12. If a man walks 34 miles per hour,

hours can he walk 30.2 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 $45 be?

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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 $7} a barrel, for 24; cords of wood. What did the wood cost him

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per cord.?

19. If I give A } of my money, B of it, and C d of it, what part of my money have I left?

20. Mr. A. owns 5 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 1 of 3} cords of wood for of $81. 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 16,1 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 141 rods; the other worked as many days as the first dug rods per day. How much did cach 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 s 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 j of its value. What was the entire value of the stock?

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 šof the length of the longer piece. What was the length of each piece? 33. A man who had spent 1 his money and $1 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 of $2756}. What were his receipts in 1875?

38. A and B together had $5700. Şof 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?

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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 12 of 1? * of 1.

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 iof 100?

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.

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DEFINITIONS.

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195. A Decimal Fraction is one or more of the decimal divisions of a unit.

The word decimal is derived from the Latin word decem, which signifies ten. 9

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