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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 Centered into partnership. A furnished 3 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 31 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 24 acres ?

29. If peaches are worth 4 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 374 feet high casts a shadow 584 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 2483. 7 and 8f are two of them: what is the other one?

41. A farmer sold 24 pounds of butter at 374 cents a pound; 25 bushels of corn at 42 cents; 125 bushels of oats at 25 cents; 150 bushels of rye at 584 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 871 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 $25 a day; he pays $4} a week for his board; his other expenses are $124 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 1593 yards of cloth for $2704; 78,5 yards for $1417%; 1134 yards for $2014; 574 yards for $783 : 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 (8+4) R (8-4) by (13-7) x (6+2).

51. A tailor made two suits for a man. In the first he used 2; yards of cloth, 31 yards of cassimere, and / of a yard of satin ; in the second, 24 yards of cloth, 21 yards of cassimere, and 1 yard of satin : how many yards of material did he use for both ?

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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, 10, 187, 10*07, and 10807, are written decimally .8, .08, .008, .0008.

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, .48}; .2125 ; 45.427.

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

ART. 167.-As we proceed from left to right in whole numbers, their value decreases in a tenfold ratio. The 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.

3.

units.
.3 tenths.
.03

hundredths.
.003 thousandths.
.0003 ten-thousandths.
.00003 hundred-thousandths.

.000003 millionths. 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.

Read the following: 1. .

13. 10.07 2. .67

14. 30.094 3. 4.8

15. 214.214 4. 5.32

16. .0361 5. 6.07

17. .0178 6. 31.015 18. 741.09 n. 21.0048 19. 31.9019 8. 315.326 20. .00007 9. 43.5178 21. 500.05 10. .00864 22. 7000.007 11. .101 23. 900.0009 12. .9019 24. 4100.0195

25. 9.09
26. .400
27. .004
28. 50.0005
29. 701.0701
30. 3400.043
31. 6000.006
32. 4000.0007
33. 70.009
34. 61010.101
35. 41720.0019
36. 10000.00001

Express decimally:

seven

1. 4 tenths.

23. Seventy thousand seven 2. 1 tenth.

and three thousand 3. 12 hundredths.

hundred-thou

sandths. 4. 9 hundredths.

24. One thousand one and 5. 25 hundredths.

one thousand one mill6. 75 hundredths.

ionths. 7. 146 thousandths.

25. One and one hundred 8. 65 thousandths.

one ten-thousandths. 9. 2364 ten-thousandths.

26. Nine thousand and nine 10. 769 ten-thousandths.

tenths. 11. 11 ten-thousandths.

27. Seventeen and seventeen 12. 87 hundred-thousandths. hundred-thousandths. 13. 2002 hundred-thou - 28. Seven and seventeen sandths.

thousandths. 14. 5007 millionths.

29. One hundred thousand 15. 1001 ten-millionths.

and one hundred-thou16. Sixty-five thousandths. sandth. 17. Seven hundred

30. Two hundred thousand hundred-thousandths.

two and two hundred 18. Eight ten-thousandths.

two ten-thousandths. 19: One hundred five ten- 31. Seven thousand and seven millionths.

millionths. 20. Three thousand and 32. Eighty thousand and

three hundred thou eight hundred-thollsandths.

sandths. 21. Four hundred four and 33. One million and one ten

ten thousand five mil thousandth.
lionths.

34. One hundred million ten 22. Five million and five and ten thousand one millionths.

hundred-millionths.

seven

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