denomination; and so proceed until the given number is changed to the denomination required. III. The last quotient, and the remainders, if any, written in their order from the highest denomination to the lowest, will be the result required. Written Exercises. Change to integers of higher denominations — 1. 756 in. to yards; 792 ft. to rods; 960 rd. to miles. 2. 3620 in. to rods; 1220 feet to mi.; 1000000 in. 3. 864 sq. in. to square feet; 1089 sq. ft. to square yards. ft.; 4. 65340 sq. ft. to square rods; 26620 sq. yd. to acres. 5. 100000 sq. in. to A.; 200000 sq. 2000000 sq. yd. 6. 15552 cu. in. to cubic feet; 3375 cu. ft. to cubic yards. 7. 45678 cu. in. to cu. yd.; 7986 cu. ft.; 46356 cu. in. 8. 123 gi. to quarts; 756 gi. to gallons; 1234 pt. to gallons. 9. 1000 gi. to gal.; 2000 pt. to bbl.; 30000 gi. to hhd. 10. 136 pt. to pecks; 320 qt. to pecks, and to bushels. 11. 2016 pwt. to lb.; 200 oz.; 10000 gr.; 200000 gr. 12. 3200 oz. to hundred-weight; 5000 lbs. to cwt.; to tons. 13. 20000 oz. to T.; 30000 lb.; 1000000 oz.; 4567800 lb. 14. 3600 sec. to hours; 10000 min. to days; 367 da. to yr. 15. 10000 sec.; 20000 min.; 30000 hr.; 1000000 min. 2 2 3 11 2 11 4 33 EXPLANATION.-Since 3 feet are 1 yard, there is as many yards as feet, or of a yard. yd. ===rd. Since 54, or of a yard are 1 rod, there are as many rods as yards, or of a yard. 33 17. 144 in. to ft.; to yd.; to rd.; to mi. 18. 144 sq. in. to sq. ft.; to sq. yd.; to sq. rd. 19. 2000 cu. in. to cu. ft.; to cu. yd.; to cd. 55 yd. to mi. 8 sq. ch. to A. 36 cu. ft. to cd. 20. of a gi. to pt.; to qt.; to gal. qt. to pk.; to bu. 21. 4% of a pk. to bu.; 10 gr. to oz.; 123 min. to hr. 22. 12 pwt. to the decimal of a pound Troy. 12 put. = SOLUTION. .6 oz. = .6 ÷ 12 .05 lb. EXPLANATION. - Since 20 penny weights are 1 ounce, there is as many ounces as pennyweights, or .6 oz. Since 12 ounces are 1 lb., there is as many pounds as ounces, or .05 lb., the decimal required. 23. 20 gr. to oz.; to lb. ; 24 to oz.; 6 oz. to lb. 24. 250 oz. to cwt.; 25 lb. to cwt.; to T.; 8 cwt. to T. 25. 5 mills to $; 3 qr. to s. ; to £; 8 s. to £; 10 s. 6 d. to £. 26. 60 sec. to hr.; to days; 3 da. to wk.; to years. 27. 110 in. to rd.; 55 yd. to mi.; 121 sq. in. to sq. yd.; 103 sq. rd. to A.; 144 cu. in. to cu. ft.; 31⁄2 cu. ft. to cu. yd. 28. If sound travels 1142 feet in a second of time, how many miles will it travel in a minute? 29. How long will it take a clock, ticking once every second, to tick a million times? To tick 3050500 times? 30. If a rifle-ball weighs an ounce, how much lead is needed to cast 50000 rifle-balls? To cast 1000000 balls? 31. A carter feeds 6 quarts of shelled corn a day. How much must he buy for his horse in a year? A leap year? 32. At $1.50 a rod, how many miles of fence can be made for $900? For $1200? For $2250? For $5000? 33. How many ounces of calomel are needed to make 3 gross of pills, each weighing 5 grains? 34. If 47 gal. 1 qt. of vinegar be put into barrels, and sold at $10 a barrel, what will be received for it? 35. The circumference of the earth is about 25000 miles. At 4 miles an hour, how long will it take to walk that distance? 36. At 10 cents a quart, how many bushels of cherries can be bought for $7.50? For $11.25? SECTION XXII. ADDITION OF COMPOUND NUMBERS. 422. Addition, subtraction, multiplication, and division of compound numbers depend upon the same general principles that govern similar operations in simple numbers. Written Exercises. 423. Example. - Find the sum of 3 rd. 4 yd. 10 in., 4 yd. 2 ft. 8 in., 7 rd. 5 yd. 1 ft., and 3 rd. 3 yd. 2 ft. 8 in. SOLUTION. 3 rd. 4 yd. 0 ft. 10 in. 0 4 2 8 7 5 1 0 3 3 2 8 16 1 2 Since only like orders of units can be added, write the numbers so that units of the same denomination shall stand in the same column (81). Begin with the lowest denomination, and add each column separately. The sum of the inches is 26 inches, or 2 feet 2 in. Write 2 inches under the column of inches, and add 2 feet with the column of feet. The sum of the feet is 7 feet, or 2 yd. 1 foot. Write 1 foot, etc. The sum of the yards is 18 yd., or 3 rd. 14 yd. Write 11⁄2 yd., etc. The sum of the rods is 16 rods, which write under the column of rods. 1 half-yard changed to lower denominations equals 1 foot 6 in., which, added to 1 foot 2 inches, gives the entire sum, 16 rd. 1 yd. 2 ft. 8 in. 424. Rule for Addition of Compound Numbers. I. Write the compound numbers so that units of the same denomination shall stand in the same column. II. Begin with the lowest denomination, and add each column separately. III. If the sum is less than one of the next higher denomi nation, write it under the column added. If the sum is equal to, or greater than, one of the next higher denomination, change it to that higher denomination, write the remainder under the column added, and add the ones of the higher denomination with the column of that denomination. 4. 10 mi. 75 rd. 5 yd. 2 ft. ; 150 rd. 3 ft.; 100 mi. 100 rd. 5. 75 mi. 200 rd. 5 yd.; 200 mi. 4 yd.; 95 mi. 2 ft. 6. 75 A. 10 sq. rd.; 100 sq. rd. 5 sq. ft.; 130 A. 10 sq. yd. 7. 175 A. 30 sq. yd.; 98 A. 8 sq. ft.; 765 A. 25 sq. yd. 8. 99 cu. yd. 20 cu. ft.; 25 cu. ft. 88 cu. in.; 500 cu. yd. 1700 cu. in.; 44 cu. yd. 30 cu. ft. 732 cu. in. 9. 85 T. 75 lb.; 137 T. 15 cwt. 101⁄2 oz.; 76 T. 50 lb.; 876 T. 19 cwt. 81 oz.; and 976 T. 18 cwt. 85 lb. 81 oz. 10. 10 T. 4 cwt. 90 lb.; 50 T. 95 lb. 8 oz.; 100 T. 10 cwt.; 500 T. 2 cwt. 90 lb.; 20 cwt. 80 lb. 12 oz.; 90 lb. 153 oz. 11. Add 11 lb. 3 oz. 2 pwt.; 10 oz. 18 gr.; 15 lb. 5 pwt. 10 gr.; 25 lb. 6 oz. 15 pwt.; 8 lbs. 21 oz. 15 pwt. 183 gr. 12. 100 cd. 8 cu. ft.; 500 cd. 17 cu. ft. 1400 cu. cd. 20 cu. ft.; 1000 cd. 25 cu. ft. 1700.25 cu. in. in. ; 210 13. How much coal are in five cars containing 17 T. 10 cwt. 73 lb. of coal; 15 T. 15 cwt. 80 lb. ; 18 T. 99 lb.; 17 T. 18 cwt.; and 16 T. 10 cwt. 75 lb. ? 14. Philadelphia is in longitude 75° 8′ 42′′ W., and Rome 12° 27' E. How far apart are they? 15. Washington is in latitude 38° 53′ 20′′ N., and Rio Janeiro 22° 56' S. How many degrees between them? 16. In a farm there are three fields: the first contains 10 A. 40 sq. rd.; the second 25 A. 30 sq. yd.; and the third 20 A. 100 sq. rd. 20 sq. yd. How large is the farm? SECTION XXIII. SUBTRACTION OF COMPOUND NUMBERS. Written Exercises. 425. Example.- From 25 mi. 80 rd. 4 yd. take 16 mi. Since 5 yd. cannot be taken from 4 yd., take 1 rod, or 5 yd., from 80 rd., leaving 79 rd., and add the 5 yd. borrowed to the 4 yd., making 9 yd. 5 yd. from 91 yd. are 4 yd., which write under the column of yards. Since 100 rods cannot be taken from 79 rods, take 1 mile, or 320 rods, from 25 miles, etc. 16 miles from 24 miles are 8 miles, which write, etc. 1 half-yard changed to lower denomination equals 1 foot 6 in., which gives the entire difference, 8 mi. 299 rd. 4 yd. 1 ft. 6 in. 426. Rule for Subtraction of Compound Num bers. I. Write the subtrahend under the minuend so that units of the same denomination shall stand in the same column. II. Begin with the lowest denomination, and subtract each column separately. III. If the units of any denomination of the subtrahend are less than the units of the same denomination in the minuend, write the difference under the denomination subtracted. If the units of any denomination of the subtrahend are greater than the units of the same denomination in the minu |