18. If of a cwt. of sugar cost $5.40, what is the value of of a cwt.?

ILLUSTRATION.

If of a cwt. cost $5.40, will cost of $5.40, or $1.80; and 4, or a cwt., will cost 4 times $1.80, or $7.20. Now, if lewt. cost $ 7.20, of a cwt. will cost of $7.20, or $0.80; and 7 will cost 7 times $ 0.80, or $ 5.60, Ans.

19. If of a pound of ipecacuanha cost $2.52, what is the value of of a pound? Ans. $1.76. 20. When $80 are paid for of an acre of land, what cost of an acre? 21. If of a carding-mill are worth $631.89, what are of it worth? Ans. $401.20.

Ans. $93.333.

22. If of a ship and cargo are valued at $141.52, what are 2 of them worth? Ans. $30.50. 23. If the value of of a farm containing 1787 acres. is $1728, what is the price of of the remainder?

Ans. $2304.

24. E. Carter's garden is 17 rods long, and 11 rods wide. He disposes of of it for $82.80; what is the value of remainder?

of the Ans. $ 41.40. 25. When 26£ 12s. 6d. are paid for § of a bale of cloth, what sum should be paid for of the remainder?

Ans. 18£ 12s. 9d.

26. If 7cwt. of sugar cost $28.14, what will 9gcwt. cost?

ILLUSTRATION.

If 7cwt. cost $28.14, 1cwt will cost of $28.14, or $4.02. In 95cwt. there are cwt.; and if 1cwt. cost $4.02, cwt. will cost of $ 4.02, or $ 0.67, and 52 will cost 59 times $0.67, or $39.53, Ans.

27. If three tons of hay cost $ 49, what will 7 tons cost? Ans. $120.27. 28. Gave $78.80 for 11 tons of coal; what should I give for 3 tons ? Ans. $24.673.

29. Paid 37£ 18s. 10d. for 3 bales of velvet; what was the cost of 5 bales? Ans. 67£ 19s. 611d. 30. Gave $40 for 5 yards of broadcloth; what was the price of 19 yards? Ans. $156.574. 31. Paid $360 for 20 barrels of beer; what must be given for 43% barrels ? 32. If 7 bushels of rye cost $8.75, what cost 187 bushels? Ans. $23.29.

Ans. $789.

33. Paid $19.80 for 3 yards of broadcloth; what sum must be given for 11 yards? Ans. $76.374.

34. If 9cwt. of sugar cost $39.53, what must be paid for 7cwt.?

ILLUSTRATION.

In 98cwt. there are 52cwt. If 52cwt. cost $39.53, ewt. will cost of $ 39.53, or $ 0.67; and 8, or 1cwt., will cost 6 times $ 0.67, or $4.02; and 7cwt. will cost 7 times $4.02, or $ 28.14, Ans.

Τ

What Ans. $1376.

35. When $187 are paid for 3cwt. of sugar, how much may be purchased for $1? How much for $78? Ans. 12cwt. 36. If 3 tons of potash cost $276.18, what will be the value of 1 ton? Of 75 tons? Ans. $6041.431. 37. If 7 acres of land cost $875, what will one acre cost? What will 75 acres cost? Ans. $8912.0319. 38. If 48 tons of coal cost $70, what will 1 ton cost? will 86 tons cost? 39. For 27 acres of land there were paid $375; what cost 1 acre? What cost 69 acres? Ans. $932.4337. 40. If 4 tons of hay cost $80.50, what costs 1 ton? What cost 15 tons? Ans. $262.50. 41. If 7cwt. of sugar cost $62.37, what will lcwt. cost? What cost 19cwt.?

Ans. $160.93.

42. If 7 yards of cloth cost $13.95, what will be the value of 11 yards?

ILLUSTRATION.

In 7 yards there are 1 of a yard. If 31 of a yard cost $13.95, will cost of $13.95, or $0.45; and 4, or 1 yard, will cost 4 times $ 0.45, or $1.80. In 114 yards there are 10% of a yard. If 1 yard cost $1.80, of a yard will cost of $ 1.80, or $ 0.20; and 18 will cost 103 times $0.20, or $ 20.60, Ans.

43. When $668.50 are paid for 17

the value of 89 acres?

acres, what would be Ans. $3457.30.

44. If $1738 are given for 193 tons of iron, what will be the cost of 37 tons?

Ans. $3288.

45. Paid $11 for 1128 feet of boards; how many could I have purchased for $119?

Ans. 11480 feet.

46. For 3 tons of potash I received 116cwt. of sugar; required the quantity of sugar that may be received for 113 tons of potash. Ans. 376cwt.

47. For 11 tons of potash I received 376cwt. of sugar;

required the quantity of sugar that should be received for 3 Ans. 116cwt.

tons.

48. When $8 are paid for 13 yards of broadcloth, how much must be given for 8 yards? Ans. $49. 49. Gave $414 for 20 acres of land; what shall be given for 11 acres? Ans. $236.

MISCELLANEOUS QUESTIONS BY ANALYSIS.

1. Sold a small farm for $ 896.50; what was received for of it? For of it? For 1 of it?

2. Gave $17 for 3 barrels of flour; What 37 barrels ?

it?

Ans. $815. what cost 1 barrel? Ans. $213.0333.

3. Sold a house for $3687; what sum was received for of Ans. $3226.121. 4. Bought 17 tons of hay for $187; what is the cost of of a ton?

Ans. $7.61254. $13; what cost of Ans. $30.52.

Ans. $0.213.

6. When $37 are paid for 100 gallons of molasses, what cost of a gallon? 7. When 12 cents are paid for of a gallon of molasses, what will 48 gallons cost? Ans. $16.01%. 8. If of a barrel of flour cost $34, what will 63 barrels cost? Ans. $4811

9. When $236 are paid for 11 acres, what will be paid for 2017 acres?

Ans. $414.

10. Paid in Liverpool 974£ for 3 bales of cloth; how many bales should be received for 1073%£? Ans. 33 bales.

11. If 63 barrels of flour cost $48141, what will

of a barrel Ans. $3.284.

cost? 12. If 3 pounds of coffee cost 34 cents, what sum must be paid for 744 pounds? Ans. $6.90. 13. If 2 tons of hay cost $ 63, what will be the cost of 16 tons? Ans. $38118. 14. If a piece of land 3 rods square cost $17, what will be the cost of 4 square rods? Ans. $7. 15. Paid $314 for 23cwt. of iron; required the sum to be paid for 689cwt. Ans. $76809. 16. For 63 cords of wood J. Holt paid $ 63; what sum must

be paid for 18 cords?

Ans. $170.10.

17. Gave $243 for 96 barrels of tar; what quantity could be purchased for $1000? Ans. 394133 barrels.

18. Paid $7888.30 for 83+ acres of wild land; what sum did I pay for each acre, and what would be the cost of 7 acres? Ans. $660.80.

19. Gave 132£ 12s. for 75 tons of starch; what cost 127 tons? Ans. 224£ 5s.

20. For 17 days' work I paid $ 25.44; what should be paid for 894 days' labor? Ans. $128.64. 21. Sold 77 bushels of apples for $7.28; what should I receive for 1911 bushels? Ans. $19.12. 22. Paid $4355.52 for 49 pieces of carpeting; what did 37 pieces cost? Ans. $3294.72. 23. If of of the cost of the Capitol at Washington was $300,000, what was the whole cost? Ans. $2,000,000.

13

24. Purchased 7 thousand of boards for $135.80; what must be paid for 19 thousand? Ans. $359.45. 25. My wood-pile contains 6 cords and 76 cubic feet. If I dispose of of it, what is the value of the remainder at 4 cents per cubic foot? Ans. $23.143.

26. I have a field 30 rods square, and having sold 18 square rods to S. Brown, and 82 square rods to J. Smith, what part of the field remained unsold? Ans. §. 27. Bought 7T. 12cwt. 3qr. 18lb. of iron, and having sold 3T. 18cwt. 1qr. 20lb., what is the value of of the remainder at 53 cents per lb.? Ans. $242.594. 28. Bought 37 tons of iron at $68.50 per ton, for 2 of which I paid in coffee at $8.50 per cwt., and for the remainder I paid cash. Required the amount of cash paid, and also the value of the coffee.

Ans. Cash, $633.621; Value of the coffee, $1900.87. 29. A man, having received a legacy of $7896, spent of it in speculations, and the remainder he put in the savings bank, where it continued 15 years. It was then found that the sum deposited had doubled. Required the sum in the bank.

Ans. $3948. 30. Bought a piece of broadcloth for $88, and sold of it to J. Smith, and of the remainder to O. Lake; what is the value of the part unsold? Ans. $37.49.

31. A gentleman gave of his estate to his wife, of the remainder to his oldest son, and of what then remained to his daughter, who received $750; required the whole estate.

Ans. $12,000.

32. From an acre of land I sold two house-lots, each 100 feet square; what is the value of the remainder, at 8 cents per square foot? Ans. $1884.80.

DECIMAL FRACTIONS.

175. A Decimal Fraction is a fraction whose denominator is 10, or the product of several 10's.

Decimal fractions are commonly expressed by writing the numerator only, with a point (.), called the decimal point, before it, care being taken to put a cipher in any decimal place not requiring a significant figure; thus,

=

99

=

999

By examining the foregoing fractions, it will be seen that, .9 can occupy only one place while it remains in the form of a proper fraction; .99, only two places; and 10 .999, only three places; for, if their numerators are increased respectively by o.1, To= .01, Tooσ = .001, each fraction becomes a unit or whole number. Hence,

The first figure or place of any decimal on the right of the point is tenths, the second hundredths, the third thousandths, &c.

The denominator of a decimal fraction is 1 with as many ciphers annexed as the numerator has places.

177. Decimal fractions originate from dividing the unit, first, into 10 equal parts, and then each of these parts into 10 other equal parts, and so on indefinitely. Thus, 1÷ 10

÷ 10 TOO

=

= .1; .001. Hence,

The unit in decimal fractions is divided into 10, 100, 1000, &c., equal parts.

175. What is a decimal fraction? How are decimal fractions commonly expressed? What is the first figure or place of any decimal? The second? The third? &c. Why? What must be done when a decimal place has no significant figure to fill it?-176. What is the denominator of a decimal fraction? 177. How do decimal fractions originate?