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34. If it takes 4 men 9 days to do a piece of work, how long will it take 6 men, at the same rate, to do the work ?

35. If 4 of a farm is valued at $1240, what is the value of of the farm ?

36. A lady spends of her income for board, and of the remainder for clothes and travel. If she saves $160 per year, what is her income?

37. A farmer has 600 bushels of wheat, which is of 3 of what his neighbor has. How many bushels has his neighbor ?

38. A house was sold for $1800, which was of its cost. What was the loss ?

39. If 20 men can dig a ditch in 25 days, how long will it take 5 men ?

40. A farmer sold 36 head of cattle, which was 6 more than of all he owned. How many had he remaining ?

41. If a man works of a day and receives $1.50, how much should he receive for 4 of a day?

42. I purchased an overcoat for $ 45, and found I had of my money left. How much had I at first ?

43. James and John have together $40, and John has seven times as much money as James. How much does each have ? SOLUTION. — Once James's money = James's money.

7 times James's money = John's money.
8 times James's money = amount of both, or $40.
Once James's money = $5.
7 times James's money = $35, or John's money.

44. There are two numbers whose sum is 40; one number is of the other. What are the numbers ?

HAM. SCH. ARITH. -5.

45. A man invests 1 of his money in a mill, in a farm, . and the remainder, which is $900, he deposits in a bank. How much is he worth ?

46. A town has 3000 people. The number of pupils in the school is i of the remaining population. How many pupils are there in the school ?

47. In a farm of 500 acres the woodland is of the cleared land. How many acres are there of each ?

48. A miller has 360 bushels of wheat. of the number of bushels of wheat equals of the number of bushels of corn. How much is the corn worth at 50 cents per bushel ?

49. If of a clerk's salary for the year is $800, how much is of his salary?

50. f of 21 is fo of what number ?
51. of 20 is of what number?
52. of of a number is 16. What is the number?

53. 1 of C's farm equals of D's, and C has 100 acres. How many acres has D ?

54. There are two numbers: of the first is of the second. The first number is 18. What is the second ?

55. A and B agree to do a piece of work for $80. If A works 7 days and B 9 days, how much should each receive ?

SUGGESTION. — Together they work 16 da. Hence A should receive it of $80, and B 1 of $80.

56. Sarah earns $10 a week, and 4 of what Sarah earns is of what Edna earns. How much does Edna earn ? · 57. of % of 160 is of what number?

58. If of ã of a farm costs $2500, how much does the farm cost?

59. of my money is invested in coal land, i of the remainder in building lots, and the remainder, which amounts to $800, is in the bank. How much have I invested in coal lands ?

60. A man sold a horse for $120, which was less than the horse cost him. Find the cost.

61. If 24 is of a number, 21 is what part of that number? 62. I spend } of my monthly salary for board and room,

of the remainder for clothing, and save the remainder, which is $20. What is my salary?

63. If of a piece of work can be done in 9 days, how long will it take to complete the work after has been done ?

64. By selling land at $120 an acre, I gain 1 of the cost. Find the cost.

65. If of the value of a farm is $900, what is the value of / of the farm ?

66. , If 41 tons of coal cost $27, how much will 3 tons cost ? 67. What is the difference between of and of 1 ?

68. If I can do a piece of work in 7 days, what part can I do in 1 day ? in 3 days ? in of a day ? in 14 days?

69. A fruit grower sold 200 bushels of apples, which was

of his crop. How much did he realize from the sale of his crop at $1.20 per bushel ?

70. An heir gets & of an estate and invests of his share, and still has $1600. What is the value of the estate ?

71. A tank holds 120 gal. and is full of the quantity is drawn off. How many gallons will it take to fill the tank ?

72. One man bids 7 of the cost of an article, another man bids of the cost of the article. The difference between their bids is 70 cents. Find the cost of the article,

DECIMAL FRACTIONS

1. What is the largest common fractional unit ?

2. Show that an integral unit may be divided into any number of fractional units.

3. Name the different fractional units from 1 to in order of their size.

4. What fractional unit divides the integral unit into 10 equal parts ? into 100 equal parts ? into 1000 equal parts ?

The divisions of an integral unit into 10ths, 100ths, 1000ths, etc., are called decimal divisions.

There are three ways by which decimal divisions may be expressed :

(1) by words, as nine tenths ;
(2) by common fractions, as %, Tod;

(3) by decimals, as .9, .75. A decimal fraction is any number of 10ths, 100ths, 1000ths, etc. of an integral unit. When expressed after a decimal point and without a written denominator, it is usually called a decimal.

A decimal point is a period placed after ones' place and before tenths' place.

5. What is the largest decimal unit? the second largest? the third largest?

In any decimal system 10 x 1 unit in any place=1 unit of the next higher place. 6. Show that United States money is a decimal system.

NOTATION AND NUMERATION OF DECIMALS 1. Since the first decimal division of an integral unit is tenths, what is the first place to the right of the decimal point?

2. What is the second place called ? the third place ?

3. Five tenths is written .5; five hundredths is written .05; five thousandths is written .005, etc. Write 7 tenths, 6 hundredths, 8 thousandths.

4. Express decimally io 10, 10% 166, 167, 176o.

Every decimal contains as many decimal places as there are naughts in the denominator of the equivalent fraction.

Table of places and names of integral and fractional units :

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5. In .555 what figure stands for tenths ? for hundredths ? for thousandths ? It is read 555 thousandths.

6. Is the decimal point named in reading a decimal ? Observe that the decimal is read as an integer and that the last figure is given the required denomination. Read: 7. .25 11. .101

15. .60745
8. .05
12. .0045

16. .678705 9. .005

.4045

17. .0065
10. .375
14. .0002

18. .60005

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