(as in 373), and we shall have Cd. Cd., which, reduced to its equivalent decimal, equals .4375 Cd., the same as before. Hence, RULE. Divide the lowest denomination given by that number in the scale which will reduce it to the next higher denomination, and annex the quotient as a decimal to that higher. Proceed in the same manner until the whole is reduced to the denomination required. Or, Reduce the given number to a fraction of the required denomination, and reduce this fraction to a decimal. EXAMPLES FOR PRACTICE. 1. Reduce 5 da. 9 h. 46 min. 48 sec. to the decimal of a week. Ans. .7725 wk. 2. Reduce 3° 27′ 46.44" to the decimal of a sign.375 3. Reduce 1 R. 11.52 P. to the decimal of an acre. 322 4. What part of 4 oz. is 2 oz. 16 pwt. 19.2 gr ? Ans. .71. 5. What part of a furlong is 28 rd. 2 yd. 1 ft. 11.04 in.?/2 6. Reduce 313 to the decimal of a pound.27083 7. Reduce 126 A. 4 sq. ch. 12 P. to the decimal of a township. Ans. .0054893+ Tp. 8. What part of a fathom is 33 ft.? Ans. .625 fath. 9. What part of 14 bushels is .45 of a peck? Ans. .09. 10. What part of 3 A. 2 R. is 1 R. 11.52 P.? Ans. .092. 11. Reduce of of 223 lb. to the decimal of a short ton. 0016 12. What part of a f3 is 5 f3 36 m? Ans. 7 f3. 13. Reduce 50 gal. 3 qt. 1 pt. to the decimal of a tun. ADDITION. Ans. .20188 + T. 375. Compound numbers are added, subtracted, multiplied, and divided by the same general methods as are employed in simple numbers. The corresponding processes are based upon the same principles; and the only modification of the operations and rules is that required for borrowing, carrying, and reducing by a varying, instead of a uniform scale. 376. 1. What is the sum of 50 hhd. 32 gal. 3 qt. 1 pt., 2 hhd. 19 gal. 1 pt., 15 hhd. 461 gal., and 9 hhd. 39 gal. 2 qt.? OPERATION. hhd. gal. qt. pt. 50 32 3 1 2 19 0 1 15 46 9 39 1 0 78 11 3 1 ANALYSIS. Writing the numbers so that units of the same denomination shall stand in the same column, we add the numbers of the right hand or lowest denomination, and find the amount to be 3 pints, which is equal to 1 qt. 1 pt. We write the 1 pt. under the column of pints, and add the 1 qt. to the column of quarts. The amount of the numbers of the next higher denomination is 7 qt., which is equal to 1 gal. 3 qt. We write the 3 qt. under the column of quarts, and add the 1 gal. to the column of gallons. Adding the gallons, we find the amount to be 137 gal., equal to 2 hhd. 11 gal. Writing the 11 gal. under the gallons in the given numbers, we add the 2 hhd. to the column of hogsheads. Adding the hogsheads, we find the amount to be 78 hhd., which we write under the left hand denomination, as in simple numbers. 2. What is the sum of 7 wk., da., and 3 h. the same denomination, (368 or 372), then add them, and find the value of their sum in lower denominations. 377. From these examples and illustrations we derive the following RULE. I. If any of the numbers are denominate fractions, or if any of the denominations are mixed numbers, reduce the fractions to integers of lower denominations. II. Write the numbers so that those of the same unit value will stand in the same column. III. Beginning at the right hand, add each denomination as in simple numbers, carrying to each succeeding denomination one for as many units as it takes of the denomination added, to make one of the next higher denomination. NOTE. The pupil cannot fail to see that the principles involved in adding compound numbers are the same as those in addition of simple numbers; and that the only difference consists in the different carrying units. 5. Add 1 T. 17 cwt. 8 lb., 5 cwt. 29 lb. 8 oz., 1 cwt. 42 lb. 6 oz., and 17 lb. 8 oz. Ans. 2 T. 3 cwt. 97 lb. 6 oz. 6. Add 6 yd. 2 ft., 3 yd. 1 ft. 8 in., 1 ft. 10 in., 2 yd. 2 ft. 61 in., 2 ft. 7 in., and 2 yd. 5 in. Ans. 16 yd. 2 ft. 1 in. 7. Add 4 Cd. 7 cd. ft., 2 Cd. 2 cd. ft. 12 cu. ft., 6 cd. ft. 15 cu. ft., 5 Cd. 3 cd. ft. 8 cu. ft., and 2 Cd. 1 cu. ft. -4-4 8. What is the sum of 13 hhd. 42 gal. 3 qt. 11 pt., § gal. 2 qt. pt., and 1.75 pt. Ans. 2 hhd. 23 gal. 2 qt. 3 gi. 9. What is the sum of 1453 A., 7 A. 2 R. 291 P., 1 A. 3 R. 16.5 P., and A. ? Ans. 156 A. 391 P. ? 10. Required the sum of 31 bu. 2 pk., 107 bu., 5 bu. 61⁄2 qt., 14 bu. 2.75 pk., and Ans. 62 bu. 1 pk. 5 qt. 13 pt. pk. 11. Required the value of 42 yr. 71⁄2 mo. + 10 yr. 3 wk. 5 da. +93 mo. + 1 wk. 16 h. 40 min. + 1⁄2 mo. + 33 da. Ans. 53 yr. 7 mo. 9 da. 23 h. 52 min. 12. Add 3 S. 22° 50′, 24° 36′ 25.7", 17' 18.2", 1 S. 3° 12′ 15.5", 12° 36′ 17.8", and 57.3". Ans. 6 S. 3° 33′ 14.5′′. 13. How many units in 11 gross 7 doz., 3 gross 12 doz., 2 of a great gross, 61 doz., and 4 doz. 7 units? Ans. 2183. 14. What is the sum of 240 A. 6 sq. ch., 212.1875 sq. ch., and 5 sq. ch. 104 P.? Ans. 262 A. 3 sq. ch. 13.8 P. 15. Add 3 Pch. 18 cu. ft., 84.6 cu. ft., § Pch., and 39 cu. ft. 16. Add $33, $251, $127, $23, and $2.543. Ans. $47.0725. 17. What is the sum of 3 tb 53 43 29 17 gr., 2 tb 53 12 gr., 43 23 19 16 gr.? Ans. 5b 10 3 4 3 29 5 gr. 18. A N. Y. farmer received $.60 a bushel for 4 loads of corn; the first contained 42.4 bu., the second 2866 lb., the third 36% bu., and the fourth 39 bu. 29 lb. How much did he receive for the whole? Ans. $100.848. 19. Bought three loads of hay at $8 per ton. The first weighed 1.125 T., the second 13 T., and the third 2500 pounds; how much did the whole cost? Ans. $30.20. 20. A man in digging a cellar removed 140 cu. yd. of earth, in digging a cistern 24.875 cu. yd., and in digging a drain 46 cu. yd. 201 cu. ft. What was the amount of earth removed, and how much the cost at 18 cts. a cu. yd.? Ans. 212.425 cu. yd. removed; $38.24-cost. SUBTRACTION. 378. 1. From 18 lb. 5 oz. 4 pwt. 14 gr. take 10 lb. 6 oz. 10 subtract 10 pwt. from 4 pwt., we add 1 oz. or 20 pwt. to the 4 pwt., subtract 10 pwt. from the sum, and write the remainder, 14 pwt., underneath. Having added 20 pwt. or 1 oz. to the 6 oz. in the subtrahend, we find that we cannot subtract the sum, 7 oz., from the 5 oz. in the minuend; we therefore add 1 lb. or 12 oz. to the 5 oz., subtract 7 oz. from the sum, and write the remainder, 10 oz., underneath. Adding 12 oz. or 1 lb. to the 10 lb. in the subtrahend, we subtract the sum, 11 lb., from the 18 lb. in the minuend, as in simple numbers, and write the remainder, 7 lb., underneath. 2. From 12 bar. 15 gal. 3 qt. take 7 bar. 18 gal. 1 qt. the less value from the greater, and find the value of the remainder in integers of lower denominations. 379. From these illustrations we deduce the following RULE. I. If any of the numbers are denominate fractions, or if any of the denominations are mixed numbers, reduce the fractions to integers of lower denominations. II. Write the subtrahend under the minuend, so that units of the same denomination shall stand under each other. III. Beginning at the right hand, subtract each denomination separately, as in simple numbers. |