19. Reduce 13 bu. 2 pk. 7 qt. 1 pt. to pints. 20. Reduce 47 miles to feet. 21. Reduce 72 lb. 10 oz. 15 pwt. 7 gr. to grains. 22. Reduce 43 T. 13 cwt. 20 lb. to pounds. 23. Reduce 365 d. 5 h. 48 min. 50 sec. to seconds. 24. How many cubic inches in 8 cu. yd. 10 cu. ft. 728 cu. in.? 25. How many seconds in 45° 28' 54" ? 26. How many cubic feet in 25 cd. ? 27. How many gills in 40 gal. 3 qt. O pt. 2 gi. ? 28. How many minutes in 67 wk. 6 d. 9 h. 52 min. ?

29. How many sheets of paper in 4 bundles 1 ream of paper ?

30. What is the value of 1 A. 80 sq. rd. of land at 5 cents a square foot ?

31. What will be the cost of grading 3 m. 195 rd. of road at $ 5.50 a rod ? 32. Change ] of a mile to feet.

660 Solution. — 1 mile=5280 ft. ; [ mi. = of 5280 ft., or} X 5289 ft. = 4620 ft.

33. Reduce do of a mile to yards.
34. What part of a grain is gelio of a pound troy ?
35. What part of a second is gotoo of a day?
36. What part of a gill is zig of a gallon ?
37. Reduce its of a bushel to quarts.
38. Reduce 1.375 gallons to pints.
1.375 (gal.)
4 qt.

Solution. — 1 gal. = 4qt.; 1.375 gal.=1.375 5.500 (qt.)

X 4 qt., or 5.5 qt. . 2 pt.

1 qt. = 2 pt. ; 5.5 qt. = 5.5 X 2 pt., or 11

pints. 11.000 pt.

39. Reduce .024 of a ton to pounds.
40. Reduce .0075 of an acre to square feet.
41. Reduce .3945 of a day to minutes.
42. How many square yards in 1.364 acres ?

To change Denominate Numbers to Larger Denominations.

ORAL EXERCISES. 43. How many feet in 84 inches ? In 66 inches ? 44. How many gallons in 160 gills ? In 88 gills ? 45. How many pounds troy in 36 ounces? In 103 ounces? 46. How many hours in 260 minutes ? In 315 minutes ?

47. How many reams in 200 quires of paper ? In 76 sheets of paper how many quires ?

48. How many weeks in 90 days ? In 81 days ?
49. How many pecks in 24 quarts? In 72 quarts ?

189. Reduction Ascending is changing denominate numbers to larger denominations.

WRITTEN EXERCISES. 50. Change 410 feet to larger denominations. 3 ft. 410 ft.

Solution. — As in 5} yd. 136 yd. + 2 ft.

3 feet there is 1 yard,

there are as many 2

yards in 410 feet as 11 hf.-yd. 272 hf.-yd.

· times 3 feet in 410 | 24 rd. + 8 hf.-yd., or 4 yd. feet, which are 136,

and 2 feet remainder. As in 54 yards there is 1 rod, there are as many rods in 136 yards as times 54 yards in 136 yards, or times 11 half-yards in 272 balf-yards, or 12, and 8 half-yards, or 4 yards, remainder.

In 410 feet there are 24 rd. 4 yd. 2 ft.

51. Change 1279 dry pints to larger denominations. 52. Change 1311 cubic feet to larger denominations. 53. Change 35790 pounds to larger denominations.

. 190. Rule for Reduction Ascending. Divide the given number by the number of units it takes of that denomination to equal one of the next larger, and reserve the remainder, if any. Divide the quotient in like manner, and so proceed until the required denomination is reached.

The last quotient, and the several remainders, if any, will be the number sought.

Note. — Reduction Ascending and Reduction Descending, being reverse processes, are proofs of each other.

Change to larger denominations :
54. 562068 square feet. 61. 31556930 seconds.
55. 273749 cubic inches. 62. 391256 cubic inches.
56. 487 liquid pints. 63. 163734".
57. 879 dry pints.

64. 3200 cubic feet. 58. 248160 feet.

65. 1306 gills. 59. 419887 grains.

66. 684592 minutes. 60. 87320 pounds.

67. 4320 sheets of paper. 68. At 5 cents a square foot, how many acres and square rods of land can be bought for $ 3267 ?

69. At $5.50 a rod, how many miles and rods of road can be graded for $ 6352.50 ? 70. Change 3080 ft. to the fraction of a mile.

Solution. — 1 mi.=5280 ft. ; 3080 ft. • are 398mi., which, changed to smallest

terms, is į mi. 71. Reduce 88 yards to a fraction of a mile. 72. What part of a pound troy are 3000 grains ? 73. What part of a day are 12600 seconds ? 74. What part of a gallon are 24 gills ? 75. Reduce 44 quarts to a fraction of a bushel.

aco

76. Reduce 11 pints to a decimal of a gallon. 2) 11.000 pt. Solution. — As in 1 quart there are 2 pints, 4) 5 500 qt.

there are in 11 pints £ as many quarts, or

11 ; 2=5.5 quarts. 1.375 gal.

As in 1 gallon there are 4 quarts, there are in 5.5 quarts | as many gallons, or 5,5 = 4= 1.375 gallons.

77. Reduce 48 pounds to a decimal of a ton.
78. Reduce 326.7 square feet to a decimal of an acre.
79. What decimal of a day is 568.08 minutes ?
80. How many acres in 6601.76 square yards ?

To change Denominate Fractions to Integers of Smaller

Denominations.

ORAL EXERCISES. 81. How many quarts in of a peck ? 82. How many hours in & of a day? 83. How many feet and inches in of a yard ?

84. How many days and hours in of a week ? 85. How many ounces and pennyweights in .8 of a pound ? 86. How many quarts and pints in .6 of a gallon ?

191 A Denominate Fraction is a fraction of a denominate number.

WRITTEN EXERCISES. 87. Reduce { of a bushel to units of smaller denominations.

[] bu.=] of 4 pk. = 3} pk. Solution. ) pk. = 1 of 8 qt. = 0f qt. fqt. = 5 of 2 pt. = 1% pt.

Ans. 3 pk. O qt. 17 pt.

90. Reduce .53 rods to units of smaller denominations.

192. Rule for Reduction of Denominate Fractions to Integers.

Change the fraction, as far as possible, to an integer of the denomination next smaller. If there is a fraction in the result, proceed with it in like manner, and so continue as far as required.

Reduce to integers of smaller denominations : 91. of an acre.

95. .6725 of a cental. 92. g of a pound troy. 96. .282 of a ton. 93. Yr of a common year. 97. .875 of a rod. 94. ß of a mile.

98. .761 of a day.

To change Denominate Integers to Fractions of Larger

Denominations.

ORAL EXERCISES. 99. What part of a peck is 6 quarts ? 100. What part of a day is 21 hours ? 101. What fraction of a pound is 14 ounces ? 102. What fraction of a yard is 2 feet 6 inches ? 103. What fraction of a gallon is 2 quarts 1 pint ?