CASE II. 330. To reduce a compound number to a common fraction of a higher denomination. 1. Reduce 3 s. 6 d. 2 far. to the fraction of a pound. SOLUTION.-By reduction we find 3 s. 6 d. 2 far. equal to 170 far., and also £1=960 far.; one farthing is of a pound, and 170 far. equals 170 times, which reduced to its lowest terms, equals . Therefore, etc. OPERATION. 3s. 6 d. 2 far.=170 far. £1960 far. 178=17, Ans. Rule. Reduce the number to its lowest denomination, and write under it the number of units of this denomination which make a unit of the required denomination; and then reduce the resulting fraction to its lowest terms. WRITTEN EXERCISES. 2. Reduce 3 oz. 8 pwt. 12 gr. to pounds. 3. What part of 2 bushels is 1 bu. 4 qt. ? 7. Of 3 years is 3 wk. 6 da. 20 h.? Ans. 1. Ans. f. Ans. Ans. ff. Ans. T Ans. 187. Ans. ; 2. 8. What part of 4 inches square is 4 square inches? What part of a 2 inch cube is 2 cu. in.? CASE III. 331. To reduce a compound number to a decimal of a higher denomination. 1. Reduce 1 bu. 2 pk. 4 qt. to the decimal of a busbel. of SOLUTION.-There are 8qt. in 1 pk., hence the number of quarts equals the number of pecks; of 4 equals .5, which, with 2 pk. equals 2.5 pk.; there are 4 pk. in a bushel, hence of the number of pecks equals the number of bushels; of 2.5 equals 625, which, with 1 bu., equals 1.625 bu.; hence 1 bu. 2 pk. 4qt. equals 1.625 bu. OPERATION. 814 4.2.5 1.625 Ans. Rule.-I. Divide the lowest term by the number of units which equals one of the next higher, and annex the decimal quotient to the integer of the next higher denomination. II. Proceed in a similar manner until the whole 18 re duced to the required denomination. NOTE.-It may also be done by reducing to a common fraction, and the common fraction to a decimal. Reduce WRITTEN EXERCISES. 2. 5 oz. 10 pwt. 12 gr. to the decimal of a lb. Ans. .4604166 lb. +. 3. 3 pk. 4 qt. 1 pt. to the decimal of a bu. Ans. .890625 bu. 1. 93 13 20 8 gr. to the decimal of a b. Ans. .76875 lb. 5. 286 rd. 1 yd. 38 in. to the decimal of a mile. Ans. .894375 mi. 6. What decimal part of 5 gal. is 1 qt. 3 gi.? Ans. .0725. 7. Reduce 295 rd. 3 yd. 2 ft. 8 in. to the decimal of a mile. Ans. .92408459 mi.+. 8. Reduce 91 lb. 127 oz. to the decimal of a ton. Ans. .04590234375 ton. MENTAL EXERCISES. MISCELLANEOUS EXAMPLES. 1. How many seconds are there in the circumference of a carriage wheel? 2. A lady put up 50 quart cans of strawberries; how many pecks did she put up? 3. When the sun has seemed to pass over 4 signs, how many seconds has he appeared to move? 4. How many pages of an octavo volume can be printed on 3 quires of paper? 5. A hostler at a hotel stable fed out 48 half-peck measures of oats; how many bushels did he feed? 6. Sarah picked a peck of cherries, and sold them at 4 cents a pint; how much did she receive for them? 7. A sailor took the sounding, and found the water 75 feet deer; how many fathoms was it? 8. My grandfather's age is "three-score years and ten;" how many years old is he? 9. A merchant buys dozen hand-saws, at $20 a dozen; how shali he sell them to gain 50 cents apiece? 10. I paid $3.20 for a bushel of huckleberries; how shall I seD them to gain 2 cents a quart 11. A merchant bought dozen shovels, at $9.60 a dozen; how shall he retail them to gain 20 cents apiece? 12. What must I pay a gross for hair-pins, that I may sell them for 5 cents a dozen, and gain 2 cents a dozen? 13. How many cubic inches in a 2-inch cube? in a 4-inch cube ? in a 6-inch cube? 14. In 6 francs how many centimes? How many in 8 france? in 10 francs? 15. How many leap years in every century? At what time did the 19th century begin? 16. What part of a circumference is 90°? 60°? 180°? Number of degrees in a quadrant? 17. A grocer paid $6.40 for a bushel of cranberries; how shall he sell them a quart to gain 2 cents a pint? 18. A huckster woman sold one day a bushel of pea-nuts by the half-pint glass, at 5 cents a glass; how much did she receive? 19. A lady bought 2 pairs of vases, 3 sets of chairs, and a dozen knives and forks; how many individual articles did she buy? 20. If Henry Clay spoke 90 words in a minute, how many words would he speak in an address of one hour? 21. Bought paper collars at 40 cents a box, each box containing a dozen; how much will I gain on each collar by selling them for 5 cents apiece? WRITTEN EXERCISES. MISCELLANEOUS PROBLEMS. 1. If 8 barrels of flour cost £24 12 s. 8 d., what will 12 barrels cost at the same rate? Ans. £36 19 s. 2. If 7 bales of goods weigh 20 cwt. 75 lb., what will 56 bales of the same size weigh? Ans. 166 cwt. 3. What cost 8 cords of wood, at the rate of £11 5 d. for 5 cords? Ans. £16 12 s. 2 d. 4. What cost 8 yd. of cloth, at the rate of $4.50 per yard? Ans. $39.37. 5. Multiply 8 d. by 6.334, and from the product take 28. 6 d. Ans. 1s. 11g d. 6. Add .003 sq. yd., .044 sq. ft., and .0008 sq. in. Ans. 18.1808 sq. in 7. Reduce 1 shilling, 11 pence and 1.0384 farthings to the decimal of a guinea. Ans. .0923 guinea 8. How many cubic feet in 75.125 cords? How many cubic inches in the same? Ans. 9616 cu. ft. 9. How much gold may be obtained from a ton of quartz rock, if it yields .0016 of its weight in gold? Ans. 3.2 lb. 10. How much is the cost of 24 cwt. 87 lb. of sugar, at $6.50 per hundredweight? Ans. $161.65. 11. A man bought 4 hhd. 28 gal. 3 qt. of wine at $4.50 a gallon; what did it cost? Ans. $1263.375 12. A grocer shipped 6120 eggs to Philadelphia in 6 barrels; how many did he pack in a barrel? Ans. 85 doz. 13. An apothecary bought 16 lb. 10 oz. of drugs, at $12.25 a pound; required the cost. Ans. $204.039. 14. Since 9 o'clock the sun has seemed to pass over 4° 23' 24"; what time is it? Ans. 9 h. 17 min. 33 sec. 15. A druggist purchased 20 lb. 8 oz. of opium at 48 cents an ounce; what did it cost? Ans. $160.265+. 16. What is the weight of $1,000,000 in gold dollars at 25.8 gr. each? What is the weight in silver half-dollars at 192.9 gr. each? Ans. 4479 lb. 2 oz.; 66979 lb. 2 oz. 17. If I start at St. Louis, latitude 38° 37' 28" N., and travel due north 1800 miles; what latitude do I reach ? Ans. 64° 39' 3"+. 18. What cost 31 lb. 14 oz. of drugs, if 6 lb. 6 oz. cost $31.40? Ans. $157. 19. What cost 5 cwt. 65 lb. of sugar, if .96 of a cwt. cost $7.50? Ans $44.14. 20. What cost 10 cwt. 81 lb. of hay, if 5 cwt. 55 lb. cost £2 10 s. 6 d.? 21. If £124 16 s. 6 d. are worth lars are £136 10 s. 6 d. worth? Ans. £4 18 s. 4 d.+. $599.16, how many dolAns. $655.32. 22. In what time will a man walk 120 mi. 160 rd. if he goes 12 mi. 16 rd. in 3 h. 20 min. Ans. 33 h. 20 min. 23. If A travels 24 mi. 198 rd. 4 yd. in 6 h. 30 min., how far will he go in 9 h. 45 min.? Ans. 36 mi. 298 rd. 1ft. 6 in. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 24. How many centals of wheat are equivalent to 1200 bushels? How many centals in 150 bar. ? Ans. 720; 294. 25. How many bushels of buckwheat in Kentucky are equivalent to 520 bu. in Illinois ? To 650 bu. in Pennsylvania? (See Art. 286.) Ans. 400; 600. 26. A merchant bought in Connecticut 32 bushels of oats at 2, a pound. and sold them in New York at 80 a bushel; what was his profit? (See Art. 286.) Ans. $4.48. 27. If-B digs 863 rd. 7 yd. of ditch in 35 wk. 5 da., how long will it take to dig 910 rd. 84 yd., working 12 h. a day, 6 da. a week, and 4 wk. a month ? Ans. 22 mo. 1 wk. 8 da. 28. If a river current carries a raft of lumber at the rate of 4 mi. 265 rd. per hour, how long will it be in carrying it a distance of 309 miles? Ans. 2 da. 16 h. 29. Mr. Owen sold 15 bu. 3 pk. 4 qt. of apples at $2.75 a bushel, and took his pay in flour at 3} a pound, receiving only an exact number of barrels, and in sugar at 12 a pound for what remained; how many barrels of flour and how many pounds of sugar did he receive? Ans. 6 barrels; 2077 lb. 30. Two men start from different places on the equator, and travel toward each other till they meet; on comparing their watches with the time of the place of meeting, it is found that the first is 45 minutes slow and the second 1 h. 15 min. fast; how far apart were the points at which they started, and in what direction did each travel? Ans. 2074.8 mi. 31. The distance from a certain toll-gate east to a tavern is 3 mlles; from the toll-gate west to a school-house is 45}} rods; half way between the tavern and the school-house is a creek 100 yards wide; how far from the toll-gate to the middle of the creek; to the further bank of the creek? Ans. 1 mi. 195 rd. 2 yd. 2 ft. 9 in.; 1 mi. 204 rd. 3 yd. 1 ft. 3 in. 32. A balloon started from Paris with despatches for Tours, and alighted near Bourges, 119 mi. 266.663 rods from Paris. Its actual route was 11 times this distance, which it made at the rate of 51 mi. 80 rd. an hour. Starting at 4 A. M., when did it alight? Ans. 6 h. 48 min. 21 sec. A. M. |