5. Find the sum of 197 sq. yd. 4 sq. ft. 1044 sq. in., 122 sq. yd. 2 sq. ft. 274 sq. in., 5 sq. yd. 8 sq. ft. 23 sq. in., and 237 sq. yd. 7 sq. ft. 128 sq. in. Ans. 563 sq. yd. 4 sq. ft. 118.825 sq. in. When common fractions occur, they should be reduced to a common denomi. nator, to decimals, or to integers of a lower denomination, and added according to the usual method. 6. If a printer one day uses 4 bundles 1 ream 15 quires 20 sheets of paper, the next day 3 bundles 1 ream 10 quires 10 sheets, and the next, 2 bundles 13 sheets, how much does he use in the three days? Ans. 10 bundles 1 ream 6 quires 19 sheets. 7. A tailor used, in one year, 2 gross 5 doz. 10 buttons, another year 3 gross 7 doz. 9, and another year 4 gross 6 doz. 11. How many did he use in the three years ? Ans. 10 gross 8 doz. 6. 8. A ship, leaving New York, sailed east the first day 3° 45' 50"; the second day, 4° 50' 10"; the third, 2° 10' 55"; the fourth, 2° 39". east from the place of starting? How far was she then Ans. 12° 47' 34". 9. A man, in digging a cellar, removed 127 cu. yd. 20 cu. ft. of earth; in digging a drain, 6 cu. yd. 25 cu. ft. t.; and in digging a cistern, 17 cu. yd. 18 cu. ft. What was the amount of earth removed, and what the cost at 16 cents a cu. yd.? Ans. 152 cu. yd.; $24.37}. 10. A farmer received 80 cents a bushel for 4 loads of corn, weighing as follows: 2564 lb., 2713 lb., 3000 lb., and 3109 lb. How much did he receive for the whole? 3. What is the sum of of a mile, 281 rods? shilling? of a pound and § of a Ans. 138. 10d. 23 far. 5. What is the sum of 3 of a ton and 3 of 1 cwt.? Ans. 12 cwt. 42 lb. 131⁄2 oz. 6. What is the sum of 3 of a day added to an hour? Ans. 9 h. 30 min. 7. What is the sum of 1⁄2 of a week, & of a day, and of an hour? Ans. 1 da. 22 h. 15 min. 8. Add of a hhd. to of a gal. 9. What is the sum of 4 of a cwt., 81⁄2 lb., and 3 oz. by long ton table? Ans. 73 lb. 1 oz. 10. What is the sum of 3 of a mile, & of a yard, and 3 of a foot? 11. I sold 4 village lots; the first contained of ↓ of an acre; the second, 603 rods; the third, of an acre; and the fourth, & of of an acre. How much land was there in the four lots? Ans. 146 sq. rd. 12645 sq. ft. What 12. A farmer sold three loads of hay; the first weighed 1 T., the second, 13, T., and the third, 18 cwt. was the aggregate weight of the three loads? Ans. 3 T. 5 cwt. 91 lb. 10 oz. SUBTRACTION. EXAMPLES. 219. 1. If a grocer buys 25 gal. 2 qt. 1 pt. of vinegar and sells 18 gal. 3 qt., how much has he left? OPERATION. 18 3 0 Ans. 6 3 1 SOLUTION. Writing the subtrahend under the minuend, placing units of the same denomination under one another, we begin at the right hand, or lowest denomination. The remainder is 1 pt. As we cannot take 3 qt. from 2 qt., we add 1 gal. or 4 qt. to 2 qt., making 6 qt., and taking 3 qt. from 6 qt., we write the remainder, 3 qt., under the denomination of quarts. Adding 1 gal. to 18 gal., we subtract 19 gal. from 25 gal., as in simple numbers, and write the remainder, 6 gal., under the column of gallons. The example may be performed by reducing the lower denominations to fractions of a gallon, according to the usual custom in business, as illustrated below: 61 RULE. I. Write the subtrahend under the minuend, so that units of the same denomination stand under one another. II. Beginning at the right hand, subtract each denomination separately, as in simple numbers. III. If the number of any denomination in the subtrahend exceeds that of the same denomination in the minuend, add to the number in the minuend as many units as make one of the next higher denomination, and then subtract; in this case add 1 to the next higher denomination of the subtrahend before subtracting. Proceed in the same manner with each denomination. 6. A Boston merchant bought English goods to the amount of £4327 13s. 71⁄2d., and he paid £1374 10s. 113d. How much did he then owe? 7. From 300 miles take 198 mi. 305 rd. 2 yd. 1 ft. 10 in. Ans. 101 mi. 14 rd. 2 yd. 2 ft. 8 in. 8. What is the difference in the longitude of two places, one 75° 20' 30" west, and the other 71° 19′ 35′′ west? Ans. 4° 55". 9. From 1892 yr. 5 mo. 19 da. take 1846 yr. 6 mo. 13 da. 10. The apparent periodic revolution of the sun is made in 365 da. 6 h. 9 min. 9 sec., and that of the moon in 29 da. 12 h. 44 min. 3 sec. What is the difference? Ans. 335 da. 17 h. 25 min. 6 sec. 11. From 160 acres of land, a farmer sells 16 acres 120 rods. How much does he retain ? 12. A section of land containing 640 acres is owned by four men ; the first owns 196 A. 961 P.; the second, 200 A 60 P.; the third, 177 A. 36 P. How much does the fourth own? Ans. 65 A. 127.75 P. 13. From a pile of wood containing 753 Cd. were sold at one time 16 Cd. 5 cd. ft.; at another, 24 Cd. 6 cd. ft. 12 cu. ft.; at another, 27 Cd. 112 cu. ft. mained in the pile? How much re Ans. 6 Cd. 3 cd. ft. 4 cu. ft. 14. If from a hogshead of molasses 10 gal. 1 qt. 1 pt. are drawn at one time, 15 gal. 1 pt. at another, and 14 gal. 3 qt. at another, how much will remain ? 15. An excavation 58 ft. long 37 ft. wide and 6 ft. deep is to be made for a cellar. After 471 cu. yd. 16 cu. ft. 972 cu. in. of earth have been removed, how much more remains to be taken out? In subtracting time when hours are to be obtained, we reckon from 12 at night, and if minutes and seconds, we write them at the right of hours. In finding the time between two dates, or in computing interest, 12 months are considered a year, and 30 days a month. When the exact number of days is required for any period not exceeding one ordinary year, it may be readily found by the following table: TABLE. Showing the number of days from any day of one month to the same day of any other month within one year. TO THE SAME DAY OF THE NEXT. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 153 184 214 245 275 122 153 183 214 244 92 123 153 184 214 122 153 183 92 123 153 365 31 59 90 120 151 181 212 243 273 304 334 If the days of the different months are not the same, the number of days of difference should be added when the earlier day belongs to the month from which we reckon, and subtracted when it belongs to the month to which we find the time. If the 29th of February is to be included in the time computed, one day must be added to the result. |