6 gr. (2) the ounces. Subtract 9 lb. from 13 lb., and write 4 lb., the difference, under pounds. The difference is 4 lb. 18 pwt. 8. A farmer raised 7 bu. 1 pk. 4 qt. of clover-seed, and sold 5 bu. 6 qt. 1 pt.: how much had he left? 9. A man bought a farm containing 356 A. 2 R. 25 P., and sold 148 A. 3 R. 36 P.: how much land had he left? 10. Washington is 77° 2' 48" W. longitude, and San Francisco 122° 26' 15" W. longitude: how much farther west is San Francisco than Washington? 11. From a stack of hay containing 5 tons, a farmer sold 3 T. 12 cwt. 65 lb.: how much hay remained unsold? 12. From a hogshead of molasses containing 63 gallons, a grocer sold 38 gal. 3 qt. 1 pt.: how much molasses remained in the hogshead? 13. A silversmith bought a bar of gold weighing 1 lb. 5 oz. 12 pwt., and a bar of silver weighing 3 lb.. 8 oz. 16 pwt. 10 gr.: how much more silver than gold did he buy? 14. A company contracted to build 65 mi. 4 fur. of railroad, and completed the first year 27 mi. 7 fur. 20 rd. how much remained to be built? 15. A note was given July 23, 1863, and paid Sept. 15, 1869: how long did it run? 16. What is the difference of time between Oct. 23, 1856, and June 15, 1866? 17. How long from April 12, 1861, to May 22, 1865? 18. Abraham Lincoln was born Feb. 12, 1809, and died April 15, 1865: what was his age? 19. The American Revolution began April 19, 1775, and ended Jan. 20, 1783: how long did it continue? 20. America was discovered Oct. 14, 1492, and the Declaration of Independence was signed July 4, 1776: how much time elapsed between these two events? 21. The laying of the Atlantic Cable was consummated July 28, 1866, and the Pacific Railroad was completed May 10, 1869: how much earlier was the first event than the second? 22. Andrew Jackson died at Nashville, Tenn., June 8, 1845, aged 78 yr. 2 mo. 23 days: what was the Idate of his birth? DEFINITION AND RULE. Art. 134. Compound Subtraction is the process of finding the difference between two compound numbers of the same kind. Art. 135. RULE.-1. Write the subtrahend under the minuend, placing terms of the same denomination in the same column. 2. Beginning at the right, subtract each successive term of the subtrahend from the corresponding term of the minuend, and write the difference beneath. 3. If any term of the subtrahend be greater than the corresponding term of the minuend, add to the term of the minuend as many units of that denomination as equal one of the next higher, and from the sum subtract the term of the subtrahend, writing the difference beneath. 4. Add one to the next term of the subtrahend, and proceed as before. NOTE.-Instead of adding one to the next term of the subtrahend, one may be subtracted from the next term of the minuend. LESSON III. Multiplication of Compound Numbers. 1. Multiply 34 gal. 3 qt. 1 pt. by 9. PROCESS. gal. qt. pt. 34 3 1 9 313 gal. 3 qt. 1 pt. Write the multiplier under the lowest denomination of the multiplicand. 9 times 1 pt. are 9 pt., equal to 4 qt. 1 pt. Write the 1 pt. under pints, and reserve the 4 qt. to add to the product of quarts. 9 times 3 qt. are 27 qt., and 4 qt. added are 31 qt., equal to 7 gal. 3 qt. Write the 3 qt. under quarts, and reserve the 7 gal. to add to the product of gallons. 9 times 34 gal. are 306 gal., and 7 gal. added are 313 gal. Hence, 9 times 34 gal. 3 qt. 1 pt. 8. If a barrel of sugar weigh 2 cwt. 45 lb. 8 oz., how much will 6 barrels weigh? 9. How much gold will make a dozen rings, each weighing 7 pwt. 15 gr.? 10. If a pupil study 4 h. 30 min. each day, how many hours will he study in 12 school weeks of 5 days each? 11. If a ship sail 3° 25′ 33′′ in 1 day, how far will it sail in 15 days? 12. If 1 man can build 5 rd. 4 yd. 2 ft. of fence in a day, how many yards can 8 men build? 13. How much wheat in 12 bins, if each bin contain 50 bu. 2 pk. 5 qt.? 14. John's age is 7 yr. 9 mo. 16 d., which is onefifth of the age of his father: how old is his father? 15. If a load of wood contain 6 cd. ft. 12 cu. ft., how much wood will 15 loads make? 16. If a family use 2 gal. 3 qt. 1 pt. of milk a week, how much will it use in a year? 17. How much hay is there in 6 stacks, each containing 4 T. 16 cwt. 70 lb. ? 18. What is the distance round a square field, each side of which is 24 rd. 3 yd. 2 ft.? 19. If a printer use 3 reams 15 quires 12 sheets of paper each day, how much paper will he use in 4 weeks of 6 days each? 20. If a man walk 2 mi. 7 fur. 32 rd. an hour, how far will he walk in 12 hours? 21. A field contains 25 rows of corn: if each row yield 5 bu. 3 pk., how much corn will the field yield? DEFINITION AND RULE. Art. 136. Compound Multiplication is the process of taking a compound number a given number of times. Art. 137. RULE.-1. Write the multiplier under the lowest denomination of the multiplicand. 2. Beginning at the right, multiply each term of the multiplicand in order, and reduce each product to the next higher denomination, writing the remainder under the term multiplied, and adding the quotient to the next product. NOTE. In both simple and compound multiplication the successive products are each divided by the number of units of their denomination which equals one of the next higher denomination, LESSON IV. Division of Compound Numbers. 1. Divide 15 w. 6 d. 13 h. 12 min. by 12. PROCESS. 12)15 w. 6 d. 13 h. 12 min. 1 w. 2 d. 7 h. 6 min. Write the divisor at the left of the dividend, as in simple division. 1 of 15 1 w., with 3 w. remainThe 3 w. remaining of 27 d. W. weeks. ing. Write the 1 w. under 2 d., with 3 d. remaining. Write the 2 days under days. 13 h. equal Write the 6 min. 85 h. of 85 h. 7 h., with 1 h. remaining. 7 h. under hours. The 1 h. remaining equals 60 min., and 60 min. and 12 min. equal 72 min. of 72 min. Write the 6 min. under minutes. The quotient is 1 w. 2 d. 7 h. 6 min. |