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25. A man bequeathed of his money to his son, of the remainder to his daughter, and the remaining $5,000 to his wife what was the value of his estate? 26. A, B and C entered into partnership. A furnished of the capital; B, and C the remainder, which was $7,000: what was the aggregate capital?

27. A grocer bought 56 pounds of sugar at 61 cents a pound; it dried out 3 pounds in weight and he sold the remainder at 7 cents a pound: what did he gain? 28. If of 9 acres of land cost $1,140, what is the cost of of 2 acres?

29. If peaches are worth of a dollar a basket, and a man sells them at of a dollar a basket, how many baskets will it take to yield a profit of $81?

30. Quintin bought a farm for $7,200, and sold of it to Moses, and the remainder to John; what was the value of the remainder?

31. If at 3 P. M., a pole 371⁄2 feet high casts a shadow 581 feet long, how tall a pole will it take to cast at the same hour, a shadow of 67 feet?

32. How many jars holding of a gallon can be filled from a cask containing 15 gallons?

33. Illustrate by an original problem, addition of fractions.

34. Illustrate by an original problem, subtraction of fractions.

35. Illustrate by an original problem, multiplication of fractions.

36. Illustrate by an original problem, division of fractions.

37. Illustrate by an original problem, addition and subtraction of fractions.

38. Illustrate by an original problem, multiplication and division of fractions.

39. A's farm is of B's farm. They both together have 640 acres: how much has each ?

40. The product of three numbers is 2488. 7 and 8 are two of them: what is the other one?

41. A farmer sold 24 pounds of butter at 373 cents a pound; 25 bushels of corn at 423 cents; 125 bushels of oats at 25 cents; 150 bushels of rye at 58 cents: how much money

did he receive for all ?

42. How does it affect the value of a proper fraction to add the same number to both of its terms? Explain this.

43. A bin that will hold 190 bushels contains 87 bushels of wheat: how many bushels more will it hold?

44. If $3 pays for of a bushel of clover seed, what part of a bushel will $2 buy?

45. A man's wages are $2 a day; he pays $4 a week for his board; his other expenses are $12 a month: how much money can he save in a month?

46. How many bushels of oats at $ a bushel will pay for of a barrel of flour at $51?

47. A boy bought 3 dozen eggs at the rate of 6 cents for dozen: how much did they cost?

48. A merchant bought 159 yards of cloth for $2703; 78 yards for $1417; 1131 yards for $2011; 574 yards for $785 how many yards did he buy, and what was the entire cost?

49. If 48 is of some number, what is of the same number?

50. Divide (84) x (8-4) by (13-7) × (6+2).

51. A tailor made two suits for a man. In the first he used 21 yards of cloth, 3 yards of cassimere, and of a yard of satin; in the second, 21 yards of cloth, 24 yards of cassimere, and 1 yard of satin: how many yards of material did he use for both?

Decimal Fractions.

If a unit be divided into 10 equal parts, what is one of the parts called?

If a tenth be divided into 10 equal parts, what is one of the parts called?

If a hundredth be divided into 10 equal parts, what is one of the parts called?

If a thousandth be divided into 10 equal parts, what is one of the parts called?

How many thousandths make a hundredth? How many hundredths make a tenth? How many tenths make a unit, or one?

ART. 164.-A Decimal Fraction is one whose denominator is 10, or 10 multiplied by itself one or more times.

A decimal fraction, for convenience, is written without the denominator and with a point after the units' place. Thus, 1, 180, 1000, and 10800, are written decimally .8, .08, .008, .0008.

8

The point is called the decimal point, and the fraction thus written is called a decimal.

The decimal point separates the decimals on the right from whatever whole numbers may be written on the left of it.

ART. 165.—A Mixed Decimal is an integer and decimal written together; as, 8.08; 245.32.

ART. 166.—A Complex Decimal is a decimal fraction and common fraction written together; as, .481⁄2 ; .212; 45.42.

For brevity, mixed decimals and complex decimals are called decimals.

The

ART. 167.—As we proceed from left to right in whole numbers, their value decreases in a tenfold ratio. same law governs the value of decimal fractions.

Beginning at the decimal or unit point, the first place to the right is tenths; the second, hundredths; the third, thousandths; the fourth, ten-thousandths; the fifth, hundred-thousandths; the sixth, millionths, and so on.

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ART. 168. In reading decimals, first read the figures representing them as whole numbers; then give the decimal order of the last figure as a name for the entire decimal. Thus, .315 is first read as 315; then as the 5 or last figure stands in thousandths place, we read the decimal as 315 thousandths. Use the word and only between the whole number and the decimal. Thus, 24.056 is read twenty-four and fifty-six thousandths.

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Express decimally :

1. 4 tenths.

2. 1 tenth.

3. 12 hundredths. 4. 9 hundredths.

5. 25 hundredths.

6. 75 hundredths.

7. 146 thousandths. 8. 65 thousandths.

9. 2364 ten-thousandths. 10. 769 ten-thousandths.

11. 11 ten-thousandths.

12. 87 hundred-thousandths.

23. Seventy thousand seven and three thousand seven hundred-thousandths.

24. One thousand one and one thousand one millionths.

25. One and one hundred one ten-thousandths.

26. Nine thousand and nine tenths.

27. Seventeen and seventeen hundred-thousandths.

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19. One hundred five ten- 31. Seven thousand and seven

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