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59. of my money is invested in coal land, 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 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 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 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 10, 180;

(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.

5

75

4. Express decimally 1%, 100, 1000, 180, 180, 1880.

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:

5 3 5

4 5 5

9

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.

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19. 50.0745 is read 50 and 745 ten-thousandths.

How are both the integer and the decimal read? How is the decimal point read? What name is given to the last decimal place?

20. When is the decimal point read?

21. What determines the value of any figure in a decimal ?

22. In writing .5, .45, .075, .0075 as common fractions, what figure in each decimal tells us the size of the denominator?

A mixed decimal is a whole number and a decimal; as, 4.625.

23. What number in a mixed decimal is always read first? 24. How do the number of places in any decimal compare with the number of naughts in the denominator when the decimal is expressed as a common fraction?

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34. 5 thousandths calls for how many decimal places? What part of the decimal (5 thousandths) stands for the numerator of the fraction? what part of this decimal stands for the denominator?

35. Name the numerator and the denominator in the following decimals: .05, .0006, .000025, .045.

In writing a decimal write the numerator, and point off from the right as many decimal places as there are naughts in the denominator.

Write:

Written Work

1. 34 hundredths.

2. 675 ten-thousandths.

3. 16 and 75 millionths.

4. 400 and 45 thousandths.

5. 6006 and 66 ten-thousandths.

6. 89 and 5 thousandths.

7. Seven hundred forty-six ten-thousandths. 8. Nine hundred and 84 millionths.

9. 5 million 9 and 4 hundred 9 ten-millionths. 10. 5095 millionths.

11. 8 and 17 ten-thousandths.

12. 125 millionths.

13. 896 and 301 hundred thousandths.

14. One thousand and one thousandth.

15. 18051 and 957 thousandths.

16. 97 and 3 ten-thousandths.

17. 9864 millionths.

18. 2135 and 32 millionths.

19. One and one millionth.

20. One million and one tenth.

21. 90 thousand and 71 thousandths.

22. 1830 and 11684 hundred-thousandths.
23. 429 thousand and 46 ten-thousandths.

24. 7035 and 97 hundredths.

25. 67375 and 35 hundred-thousandths.

26. 5815 hundred-thousandths.

27. 375 and 69 thousandths.

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