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. OPERATION. bar. gal. qt. 12 15 3 7 18 1 4 28/ 2 4 29 3. From ANALYSIS. Proceeding as in the last operation, we obtain a remainder of 4 bar. 281 gal. 2 qt. But, gal. = 2 qt., which added to the 2 qt. in the remainder makes 1 gal., and this added to the 28 gal. makes 29 gal.; and the answer is 4 bar. 29 gal. of a rod subtract of a yard. 3 yd. = OPERATION. 4 yd. 0 ft. 4 in. = 3rd. 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 frac fans to integers of lower denominations. Write the subtrahend under the minuend, so that units of the denomination shall stand under each other. I. Beginning at the right hand, subtract each denomination parately, as in simple numbers. IV. If the number of any denomination in the subtrahend exceed that of the same denomination in the minuend, add to the number in the minuend as many units as make one of the next higher denomination, and then subtract; in this case add 1 to the next higher denomination of the subtrahend before subtracting. Proceed in the same manner with each denomination. 5. Subtract 15 rd. 10 ft. 31 in. from 26 rd. 11 ft. 3 in. Ans. 11 rd. 11 in. 6. From 1 T. 11 cwt. 30 lbs. 6 oz. take 18 cwt. 45 lb. 7. Subtract .659 wk. from 2 wk. 3§ da. Ans. 1 wk. 6 da. 5 h. 17 min. 16 sec. 8. From 11 hhd. take .90625 gal. 9. From of 3 A. take 142.56 P. 10. Subtract lb. Troy, from 10 lb. 8 oz. 8 pwt. 11. From a pile of wood containing 36 Cd. 4 cd. ft., there was old 10 Cd. 6 cd. ft. 12 cu. ft.; how much remained? 12. From 5 barrels take of a hogshead. Ans. 4 bbl. 11 gal. 1 qt. 13. Subtract 887 of a day from of a week. 14. From § of a gross subtract 15. From of a mile take Ans. 4 da. 49 min. 30 sec. of a dozen. Ans. 6 doz. of a rod. 16. Subtract 2 A. 125.76 P. from 5 A. 64.24 P. Ans. 2 A. 98.48 P. 17. Subtract .0625 bu. from pk. Ans. 4 qt. 18. From the sum of 5 of 3651 da. and 3 of 55 wk. take 49% Ans. 33 wk. 1 da. 1 h. 10 min. min. 19. From the sum of 2 of 33 mi. and 174 rd., take 2133 rd. 727 20. From 15 bbl. 3.25 gal. take 14 bbl. 24 gal. 3.54 qt. 21. A farmer in Ohio having 200 bu. of barley, sold 3 loads, the first weighing 1457 lb., the second 1578 lb., and the third 1420 lb.; how many bushels had he left? Ans. 107 bu. 9 lb. 22. Of a farm containing 200 acres two lots were reserved, one containing 50 A. 136.4 P. and the other 48 A. 123.3 P.; the remainder was sold at $35 per acre. How much did it bring? Ans. $3513.19+ 23. An excavation 58 ft. long, 37 ft. wide, and 6 ft. deep is to be made for a cellar; after 471 cu. yd. 16 cu. ft. 972 cu. in. of earth have been removed, how much more still remains to be taken out? 5 cu. yd. 7 cu. ft. 756 cu. in. 24. From the sum of 4 lb., 45 oz., and 31 pwt., take the differ Ans. 1 lb. 3 oz. 8 pwt. 21 gr. Ans. ence between oz. and 7 pwt. 25. From the sum of 5 A., P., take 4 A. 25 P. 12 sq. yd. of 64 A., 30 P., and † of 2† Ans. 5 A. 125 P. 6 sq. yd. 380. To find the difference in dates. 1. How many years, months, days and hours from 3 o'clock P. M. of June 15, 1852, to 10 o'clock A. M. of Feb. 22, 1860? yr. OPERATION. mo. da. h. 1860 2 22 10 1852 6 15 15 ANALYSIS. Since the later of two dates always expresses the greater period of time, we write the later date for a minuend and the earlier date for a subtrahend, placing the denominations in the order of the descending scale from left to right, (300, NOTE 8). We then subtract by the rule for subtraction of compound numbers. 7 8 6 19 When the exact number of days is required for any period not exceeding one ordinary year, it may be readily found by the following TABLE, Showing the number of days from any day of one month to the same day of any other month within one year. TO THE SAME DAY OF THE NEXT FROM ANY DAY OF Jan. Feb. Mar. Apr. | May June July. Aug. Sept. Oct. | Nov. Dec. December....... 31 62 90 121 151 182 212 243 274 304 335 365 If the days of the different months are not the same, the number of days of difference should be added when the earlier day belongs to the month from which we reckon, and subtracted when it belongs to the month to which we find the time. If the 29th of February is to be included in the time computed, one day must be added to the result. EXAMPLES FOR PRACTICE. 1. War between England and America was commenced April 19, 1775, and peace was restored January 20, 1783; how long did the war continue? Ans. 7 yr. 9 mo. 1 da. 2. The Pilgrims landed at Plymouth Dec. 22, 1620, and Gen. Washington was born Feb. 22, 1732; what was the difference in time between these events? 3. The first settlement made in the U. S. was at Jamestown, Va., May 23, 1607; how many years from that time to July 4, 1860? 4. How long has a note to run, dated Jan. 30, 1859, and made payable June 3, 1861 ? 4 mo. 3 da. Ans. 2 yr. 5. How many years, months, and days from your birthday to this date? 6. What length of time elapsed from 16 minutes past 10 o'clock, A. M., July 4, 1855, to 22 minutes before 8 o'clock, P. M., Dec. 12, 1860 ? Ans. 1988 da. 9 h. 22 min. 7. What length of time will elapse from 40 minutes 25 seconds past 12 o'clock, noon, April 21, 1860, to 4 minutes 36 seconds before 5 o'clock, A. M., Jan. 1, 1862? 8. How many days from the 4th September, to the 27th of May following? Ans. 265 da. MULTIPLICATION. 381. 1. Multiply 5 mi. 178 rd. 15 ft. by 6. in simple numbers, and carry from lower denominations to higher, according to the ascending scale of the multiplicand, as in addition of compound numbers. Hence, 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. NOTES.1. When the multiplier is large, and is a composite number, we may shorten the work by multiplying by the component factors. 2. The multiplier must be an abstract number. 3. If any of the denominations are mixed numbers, they may either be reduced to integers of lower denominations before multiplying, or they may be multiplied as directed in 193. 4. The multiplication of a denominate fraction is the most readily performed by 193, after which the product may be reduced to integers of lower denominations by 369. 382. As the work of multiplying by large prime numbers is somewhat tedious, the following method may often be so modified and adapted as to greatly shorten the operation. |
