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43. Cost of 224 bbl. flour, at $6.75 per bbl.? 44. Find cost of 40 gal. molasses, worth $.37 per gal. 45. Value of 160 acres of land at $15.75 per A.? 46. Value of 36 oz. pure gold, worth $20.672 per oz.? 47. Value of 45 oz. standard gold, worth $18.605 per oz.? 48. Cost of 18 cwt. of tobacco, worth $75 per cwt.? 49. Cost of 325 bu. rye, worth 6214 per bu.?

50. Cost of 70 perch of stone, at $45 per perch?

51. What is the cost of 360 bbl. flour, if 17 bbl. cost $102?

52. What is the cost of 37 cords of wood, if 9 cords cost $29.25?

53. Cost of 532 bu. wheat, if 13 bu. cost $16.25?

54. Cost of 181 T. coal, if 5 tons cost $25?

55. Cost of 30 acres of land, if 5 acres cost $33? 56. Cost of 52 reams of paper, if 26 reams cost $78? 57. Cost of 5 cu. yd. of earth, if 3 cu. yd. cost $2.25? 58. Value of 8 yd. cloth, if 214 yd. cost $42.50? 59. Value of 24 miles of wire, if 2 miles cost $42? 60. Value of 57 acres of land, if 160 A. are worth $400?

61. Find cost 30 bu. of beans, at $1.124 per pk.
62. Find cost of 21 gal. cider, at 444 per qt.
63. Find cost of 3 T. nails, at 34 per lb.

64. Find cost of 33 sq. rd. of land, at $640 per A. 65. Find cost of 320 sq. yd. of oil-cloth, at 16¢ per sq. ft. 66. What is the value of 14 sq. miles of land, at $.30 per sq. rd.?

67. Value of 17 quires of paper, worth $2.40 per ream? 68. Value of 5 acres of land, worth $.50 per sq. ft.? 69. Value of 3 cu. yd. of stone, worth $6.40 per cord? 70. Cost of 5 hhd. vinegar, worth 84 per qt.?

71. Find cost of 2 yd. 1 ft. 6 in. of chain, at 50¢ per yd. SUGGESTION.-Reduce the ft. and in. to fractions of a yd.

per cd.

72. Find cost of 4 A. 40 sq. rd. of land worth $60 per A. 73. Find cost of 6 cd. 32 cu. ft. of wood at $4 74. Find cost of 20 perch 8 cu. ft. of stone, at $3.30 per perch.

75. Find cost of 400 cu.

masonry, at $1.75 per cu. yd.

yd. 13 cu. ft. 864 cu. in. of

76. Value of 15 bbl. 15 gal. 3 qt. spirits, worth $150 per bbl.?

77. Cost of 85 bu. 3 pk. corn, at $.50 per bu.?

78. Cost of 32 T. 2 cwt. 50 lb. of iron ore, worth $12 per T.?

79. Value of 7 oz. 15 pwt. of gold, worth $20.50 per oz.? 80. Cost of 4 gr. gross 8 gross buttons, at $2.50 per gr. gross?

ADDITION AND SUBTRACTION.

213. 1. Find the sum of 3 yd. 1 ft. 7 in.; 2 ft. 8 in.; 1 yd. 1 ft. 10 in.

PROCESS.

yd. ft. in.

3

1

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2

8

1

1

10

6

0

1

ANALYSIS.-1. Write the numbers to be added so that units of the same denomination shall stand in the same column.

2. Find the sum of the numbers in the column of the lowest denomination (inches), which is 25 inches 2 ft. 1 in. Write the 1 in. under the column of in.; add the 2 ft. to the column of ft.

3. Find the sum of the column of ft., which is 6 ft.=2 yd. 0 ft. Write the 0 under the column of ft.; add the 2 yd. to the column of yd.

4. Find the sum of the column of yd., which is 6 yd.

NOTE.-By comparing the analysis of addition of simple numbers, page 41, it will be seen that the same principles underlie the addition of both simple and compound numbers. In the addition of simple numbers, the sum of each column is always divided by 10, the remainder written, and the quotient added to the next higher column. In the addition of compound numbers, the sum of each column is divided by the number of units which equal one of the next higher denomination, the remainder written, and the quotient added to the next higher column. In subtraction, multiplication and division, the same principles are applied.

Rule for Addition of Compound Numbers.

I.

Write the numbers to be added so that units of the same denomination shall stand in the same column.

II. Find the sum of the numbers in the column of the lowest denomination.

III. If this sum is less than the number required to equal a unit of the next higher denomination, write it under its own column. If the sum is greater than the number required to equal a unit of the next higher denomination, divide it by this number; write the remainder, if any, under its column, and add the quotient to the next higher column.

IV. So proceed. Under the highest column write its

sum.

2. Add 5 T. 8 cwt. 10 lb. 6 oz.; 2 T. 16 cwt. 45 lb. 8 oz.; 75 lb. 10 oz.

3. Add 10 bu. 1 pk. 2 qt.; 7 bu. 3 pk. 5 qt.; 20 bu. 4 qt. 4. Add 5 m. 140 rd. 3 yd.; 2 m. 10 rd. 2 ft. 5 in.; 4 yd. 1 ft. 11 in.; 10 m. 100 rd. 5 yd. 8 in. 5. Add 25° 39′ 40′′;

72° 16′ 56′′; 120° 45′ 17′′; 28′ 34′′. 6. Add 5 A. 120 sq. rd. 7 sq. ft. 129 sq. in.; 20 A. 140 1 sq. m. 50 A. 100 sq. rd.

sq. rd. 25 sq. yd. 8 sq. ft.; 7. From 18 gal. 2 qt. 1 pt. 3 gi.

PROCESS.

gal. qt. pt. gi.

2

18 2

1

10

1 1

3

8 0

1

3

1 pt. 2 gi. subtract 10 gal. 1 qt.

ANALYSIS.-1. Write the subtrahend under the minuend, units of the same denomination in the same column.

2. Subtract, beginning with the lowest denomination. Since it is impossible to take 3 gi. from 2 gi., take from the minuend the 1 pt.=4 gi., and add to the 2 gi.; 2 gi.+4 gi.=6 gi.; 6 gi.—3 gi.=3 gi., which write under the column of gi.

3. Since the 1 pt. of the minuend has been taken, 0 pt. remain, and it is impossible to take the 1 pt. of the subtrahend from 0 pt. of the minuend. Therefore, take 1 qt. from the 2 qt. of the minuend, and reduce it to pt.; 1 qt. 2 pt.; 2 pt.-1 pt. 1 pt., which write under the column of pt.

4. Since 1 qt. has been taken from the 2 qt. of the minuend, 1 qt. remains. 1 qt.-1 qt.=0 qt., which write under the column of qt. 5. 18 gal.-10 gal.=8 gal.

Result, 8 gal. O qt. 1 pt. 3 gi.

Rule. The pupil may easily deduce a rule from the analysis, or from an example.

8. From 10 yr. 7 mo. 8 d. subtract 5 yr. 9 mo. 20 d.

9. From 20 bu. 3 pk. 1 qt. 1 pt. subtract 15 bu. 2 pk.

6 qt. 1 pt.

10. From 1 T. take 5 cwt. 25 lb. 10 oz.

11. From 1 cd. take 50 cu. ft. 200 cu. in.

12. From 1 bbl. 5 gal. 3 qt. take 25 gal. 1 qt. 1 pt. 13. From a quadrant take a sextant.

14. From 5 lb. 8 oz. 16 pwt. take 3 lb. 9 oz. 5 pwt. 16 gr.

MULTIPLICATION.

214. 1. Multiply 3 pk. 7 qt. 1 pt. by 9.

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ANALYSIS.-1. Beginning with the lowest denomination, 9 times

1 pt. 9 pt. 4 qt. 1 pt.

2. 9 times 7 qt.=63 qt.; 63 qt.+4 qt.=67 qt.=8 pk. 3 qt.

3. 9 times 3 pk.=27 pk.; 27 pk.+8 pk.=35 pk.=8 bu. 3 pk. NOTE.-In the 2nd process the work is more extended.

Rule.-Let the pupils deduce a rule, and compare it with the rule for multiplication of simple numbers.

2. Multiply 8 yd. 2 ft. 5 in. by 7.

3. Multiply 13 lb. 10 oz. Av. by 20. 4. Multiply 24° 15′ 28′′ by 18.

5. Multiply 7 lb. 5 oz. 12 pwt. 8 gr. by 24.
6. Multiply 129 cu. ft. 524 cu. in. by 32.

7. Multiply 3 bales, 7 reams, 9 quires by 12.
8. Multiply 25 cu. yd. 17 cu. ft. 84 cu. in. by 40.
9. Multiply 5 T. 3 cwt. 40 lb. 8 oz. by 28.

DIVISION.

215. 1. Divide 7 lb. 3 oz. 11 pwt. by 4.

[blocks in formation]

2. 3 lb. 36 oz.; 36 oz.+3 oz.=39 oz.; one fourth of 39 oz. is 9 oz.

with remainder of 3 oz.

3. 3 oz. 60 pwt.; 60 pwt.+11 pwt.=71 pwt.; one fourth of 71 pwt. is 17 pwt. with remainder of 3 pwt.

4. 3 pwt. 72 gr.; one fourth of 72 gr. is 18 gr.

Rule. -I. Divide the number of the highest denomination given. The quotient is the first term of the result sought.

II. Reduce the remainder, if any, to the next lower aenomination. Find the sum of the reduced remainder and the number, if any, of the same denomination of the dividend.

III. Divide as before, and so proceed.

2. Divide 16 yd. 2 ft. 10 in. by 3.

3. Divide 1 T. 18 cwt. 50 lb. 8 oz. by 4.

4. Divide 60° 27′ 40′′ by 12.

5. Divide 8 bu. 3 pk. 7 gt. by 6.

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