220. To find the difference in dates. 1. What length of time elapsed from the discovery of America by Columbus, Oct. 21, 1492, to the Declaration of Independence, July 4, 1776? OPERATION. yr. mo. da. 1776 7 4 1492 10 21 283 8 13 SOLUTION. We place the earlier date under the later, writing first on the left the number of the year from the Christian era, next the number of the month, counting January as the first month, and next the number of the day from the first day of the month, then subtract. 2. George Washington was born Feb. 22, 1732, and died Dec. 14, 1799. What was his age? Ans. 67 yr. 9 mo. 22 da. 3. How much time has elapsed since the Declaration of Independence of the United States? 4. How many years, months, and days is it from you birthday to this date; or what is your age? 5. How long was it from the battle of Bunker Hill, June 17, 1775, to the battle of Waterloo, June 18, 1815? Ans. 40 yr. 1 da 6. What length of time will elapse from 20 minutes past 2 o'clock, P.M., June 24, 1892, to 10 minutes before 9 o'clock, A.M., January 3, 1897 ? Ans. 4 yr. 6 mo. 8 da. 18 h. 30 min 7. How many days is it from any day of April to the same day of August? Of December? Of February? 8. How many days is it from the 6th of November to the 15th of April? Ans. 160 days. 9. How many days is it from the 20th of August to the 15th of the following June ? Ans. 299 days. 10. What length of time elapsed from the death of Henry Wadsworth Longfellow, March 24, 1882, to that of James Russell Lowell, Aug. 12, 1891 ? 221. To subtract denominate fractions. 1. From of an oz. take of a pwt. 3. From £ take of a league take of a mile. Ans. 1 mi. 193 rd. 11. ft. 7.9 in. + 5. From 8 cwt. take 27 lb. Ans. 8 cwt. 62 lb. 94 oz. 6. From of a week take of a day. Ans. 1 da. 4 h. 48 min. 7. Two persons, A and B, start from two places 120 miles apart, and travel towards each other; after A travels, and B, of the distance, how far are they apart? Ans. 41 mi. 289 rd. 8 ft. 71⁄2 in. 8. From a cask containing 96 gallons, leaked out, and of the remainder was sold. How much still remained in the cask? Ans. 25 gal. 2 qt. 3 gi. 9. From of a gross subtract of a dozen. 10. From of a mile take of a rod. 11. From the sum of 4 of 3 mi. and 174 rd. take 5 fur. 12. From the sum of lb. 4 oz. and 13 pwt. take the difference between oz. and 7 pwt. 13. From the sum of take 49 min. of 365 da. and 4 of 5§ wk. MULTIPLICATION. EXAMPLES. 222. 1. A farmer has 8 fields, each containing 4 A. 107 P. How much land has he in all? OPERATION. A. P. 4 107 8 37 56 SOLUTION.-Eight times 107 P. are 856 P., equal to 5 A. 56 P. We write the 56 P. under the number multiplied. Eight times 4 A. are 32 A., and 5 A. added make 37 A., which we write under the same denomination in the multiplicand, and the answer is 37 A. 56 P. RULE.-I. Write the multiplier under the lowest denomination of the multiplicand. II. Multiply as in simple numbers, and carry as in addition of compound numbers. 2. How many acres of land are there in 4 fields, each containing 2 acres 160 rods? It is generally better to reduce the lower denominations to the form of a fraction of the higher. 3. How many square yards of cloth are there in a piece 40 yards long and 1 yard 18 inches wide? 4. In 6 barrels of grain, each containing 2 bu. 3 pk. 5 qt., how many bushels are there? Ans. 17 bu. 1 pk. 6 qt. 5. If a man travels 29 mi. 150 rd. 15 ft. in 1 day, how far will he travel in 8 days? 6. If a woodchopper can cut 3 Cd. 48 cu. ft. of wood in one day, how many cords can he cut in 12 days? Ans. 40 Cd. 7. What is the weight of 48 loads of hay, each weighing 1 T. 3 cwt. 50 lb.? 8. If 1 acre of land produces 45 bu. 3 pk. 6 qt. 1 pt. of corn, how much will 64 acres produce? Ans. 2941 bu. 9. How much will 120 yards of cloth cost, at £1 9s. per yard? DIVISION. EXAMPLES. 223. 1. If 4 acres of land produce 102 bu. 2 pk. of wheat, how much will 1 acre produce? OPERATION. bu. pk. qt. 4)102 2 0 25 2 4 SOLUTION. We divide 102 bu. by 4, and obtain a quotient of 25 bu., and a remainder of 2 bu. We write the 25 bu. under the denomination of bushels, and reduce the 2 bu. to pecks, making 8 pk., and the 2 pk. of the dividend added make 10 pk. Dividing 10 pk. by 4, we obtain a quotient of 2 pk. and a remainder of 2 pk.; writing the 2 pk. under the order of pecks, we next reduce 2 pk. to quarts, making 16 qt., which divided by 4 gives a quotient of 4 qt. By using the fractional form, the following more simple operation may be performed. RULE. -I. Divide the highest denomination as in simple numbers, and each succeeding denomination in the same manner if there is no remainder. II. If there is a remainder after dividing any denomination, reduce it to the next lower denomination, adding in the given number of that denomination, if any, and divide as before. III. The several partial quotients will be the quotient required. 1. When the divisor is large and is a composite number, we may shorten the work by dividing by the factors. 2. When the divisor and dividend are both compound numbers, they must both be reduced to the same denomination before dividing, and then the process is the same as in simple numbers. 4. Divide 358 A. 57 P. 6 sq. yd. 2 sq. ft. by 7. Ans. 51 A. 31 P. 8 sq. ft. 5. Divide 336 yd. 4 ft. 33 in. by 21. Ans. 16 yd. 23 in. 6. Divide 77 sq. yd. 5 sq. ft. 82 sq. in. by 13. Ans. 5 sq. yd. 8 sq. ft. 106 sq. in. 7. Divide 1986 mi. 3 fur. 20 rd. 1 yd. by 108. 8. Divide 365 da. 6 h. by 240. 9. Divide 3794 cu. yd. 20 cu. ft. 709 cu. in. by 331. 10. Divide 121 lb. 3 3 23 10 4 gr. by 13. 11. Divide 28° 51′ 27.765" by 2.754. 12. Divide 1950 da. 15 h. 155 min. by 100. 13. How many casks, each containing 2 bu. 3 pk. 6 qt., can be filled from 356 bu. 3 pk. 5 qt. of cherries? 14. I bought 6 large silver spoons, which weighed 11 oz. 3 pwt. What was the weight of each spoon? 15. A man traveled by railroad 1000 miles in one day. What was the average rate per hour? Ans. 41 mi. 213 rd. 5 ft. 6 in. 16. If a family uses 10 bbl. of flour in a year, what is the average amount used each day? Ans. 5 lb. 5 oz. 17. The aggregate weight is 57 T. 19 cwt. 42 lb. 14 oz. per hogshead? of 123 hogsheads of sugar What is the average weight Ans. 9 cwt. 42 lb. 10 oz. 18. How many times are £5 10s. 10d. contained in £537 10s. 10d.? Ans. 97 times. 19. A cellar 50 feet long, 30 ft. wide, and 6 ft. deep was excavated by 5 men in 6 days. How many cubic yards did each man excavate daily? Ans. 11 cu. yd. 3 cu. ft. 20. If a town 5 miles square is divided equally into 150 farms, what will be the size of each farm? Ans. 106 A. 106 P. 20 sq. yd. 1 sq. ft. 72 sq. in. 21. How many times are 4 bu. 3 pk. 2 qt. contained in 336 bu. 3 pk. 4 qt.? Ans. 70 times. |