when practicable, to units of the next higher denomination; and all units of the same denominaton are collected into one (§ 23). sum. EXERCISES. 1. Add together 125£, 13 s. 5 d., 19£, 4s. 10 d. 2 qr., and 12£, 16 s. 8 d. 3 qr. Ans. 157£, 15s. 0 d. 1 qr. 16 dwt., 36 lb. 5 oz. 8 dwt. 16 gr., Ans. 360 lb. 4oz. 14 dwt. 5 gr. 2 qr. 16 lb., 10 T. 15 cwt. 1 qr., Ans. 68 T. 12 cwt. 3 qr. 8 lb. 2. Add together 23 lb. 8 oz. and 300 lb. 2 oz. 9 dwt. 13 gr. 3. Add together 3 T. 9 cwt. and 54 T. 7 cwt. 3 qr. 20 lb. 4. Add together 56 lb, 7 3,5 3, 29, 13 gr., 25 lb, 63, and 5 tb, 103, 33, 19, 19 gr. 73, Ans. 88b, 13, 03, 19, 12 gr. 5. Add together 13 bu. 2 pk. 7 qt. 200 bu. 3 pk. 5 qt. pt. 6. Add together 3 hhd. 20 gal. 3 200 hhd. 12 gal. 1 qt. 1 pt., 150 bu. 1 pk. 5 qt., and Ans. 365 bu. O pk. 2 qt. qt., 29 hhd. 13 gal. 2 qt., and Ans. 232 hhd. 46 gal 2 qt. 7. Add together 4 m. 5 fur. 20 p., 29 m. 3 fur. 16 p. 4 yd., and 34 m. 7 fur. 13p. 1 yd. 8. Add together 15 yd. 3 qr. 100 yd. 1 qr. na. 1 in. Ans. 69 m. 0 fur. 9 p. 5 yd. 1 na., 75 yd. 3 qr. 3 na. 1 in., and Ans. 192 yd. 0 qr. 2 na. 2 in. 9. Add together 24 A. 3 R. 20 P., 100 A. 2 R. 16 P. 4 sq. yd., and 95 A. 1 R. 29 P. 20 sq. yd. Ans. 220 A. 3 R. 25 P. 24 sq. yd. 10. Add together 200 A. and 500 A. 3 R. 19 P. 16 sq. yd. Ans. 751 A. 3 R. 4 P. 53 sq. yd. 11. A farmer raised from one field 150 bu. 3 pk. of wheat, from another 75 bu. 1 pk. 7 qt., and from another 200 bu. 5 qt. What quantity did he raise in all? Ans. 426 bu. 1 pk. 4 qt. 12. A merchant has in one piece 34 yd. 3 qr. of cloth, in another 21 yd. 2 qr., and in two others each 19 yd. 3 qr. How many yards has he in the four pieces? Ans. 96 yd. 13. An agriculturist sold at one time 3 T. 19 cwt. 2 gr. of hemp, at another 5 T. 13 cwt., and at another 2 T. 16 cwt. 3 qr. 20 lb. What amount did he sell? Ans. 12 T. 9 cwt. 1 gr. 20 lb. SUBTRACTION OF POLYNOMIALS. RULE XXXVIII. $194. For Polynomial or Compound Subtraction. 1. Set the less polynomial under the greater, with similar terms one under the other. 2. Proceeding from right to left, subtract each lower term from the one above it, and underneath set the remainder. 3. If the lower term exceed the upper, add to the upper term that number of its own denomination which makes a unit of the next higher; from the sum subtract the lower term, and add 1 to the next lower term, before subtracting it. EXAMPLES. 1. To subtract 85£, 13 s. 7 d. from 250£, 9 s. 10 d. Having set the less polynomial under the greater, with pounds under pounds, &c., we subtract 7d. from 10d., and set down the remainder 3 d. The next lower term 13 s. being greater than the upper term 9 s., we add 20 s. to 9 s., since 20 s. 1£. From the sum 29 s. we subtract 13 s., and set down the remainder 16 s. Then adding 1 to the 5, we say 6 from 10 leaves 4, &c. As we cannot take 3d. from 0 d., we add 12 d. 1 s., and say 3 d. from 12 d. leaves 9 d. Then 1 to 7 s: makes 8 s., and since we cannot take 8 s. from 0 s., we add 20, and say 8 s. from 20 s. leaves 12 s. Then 1 to 5 makes 6, and 6 from 10 leaves 4, &c. The difference between two polynomials is not changed by adding, to any upper term, a quantity equal to the unit added to the next lower term. EXERCISES. 1. From 60£, 17 s. subtract 35£, 13 s. 6 d. Ans. 25£, 3 s. 6 d. 、 2. From 200 lb. 9 oz. 1 dwt. subtract 180 lb. 10 oz. Ans. 19 lb. 11 oz. 1 dwt. 3. From 150 T. 13 cwt. subtract 75 T. 3 cwt. 1 qr. Ans. 75 T. 9 cwt. 3 qr. 4. From 433 b, 3 3, 2 3, subtract 93 b, 10 3. Ans. 339 tb, 5 3,2 3. 5. From 100 bu. 2 pk. subtract 21 bu. 1 pk. 1 qt. Ans. 79 bu. 0 pk. 7 qt. 6. From 21 T. 2 hhd. 3 gal. subtract 3 T. 13 gal. Ans. 18 T. 1 hhd. 53 gal. 7. From 275 L. 2 m. subtract 75 L. 1 m. 5 fur. Ans. 200 L. 0 m. 3 fur. 8. From 150 yd. 3 qr. 2 na. subtract 2 qr. 3 na. Ans. 150 yd. 0 qr. 3 na. 9. From 123 A. 2 R. subtract 30 A. 3 R. 13 P. Ans. 92 A. 2 R. 27 P. 10. From 200 A. 3 R. 20 P. subtract 30 A. 50 P. Ans. 170 A. 2 R 10 P. 11. A jeweler purchased 34 lb. 9 oz. 13 dwt. of silver ware, of which he has sold 19 lb. 4 oz. 18 gr. What quantity has he remaining? Ans. 15 lb. 5 oz. 12 dut. 6 gr. 12. An agriculturist raised 30 T. 13 cwt. 1 gr. of hemp, of which he has sent to market 21 T. 15 cwt. 21 lb. What quantity of hemp has he still on hand? Ans. 8 T. 18 cwt. 0 qr. 7 lb. 13. A farmer raised 500 bu. 3 pk. 7 qt. of wheat. Having sold 300 bu. 2 pk. 5 qt. of this crop, what quantity of wheat has he still unsold? Ans. 200 bu. 1 pk. 2 qt. 14. A vintner purchased 3 T. 1 hhd. 40 gal. 2 qt. of wine, of which he has sold 1 T. 3 hhd. 47 gal. 1 pt. What quantity of wine has he yet unsold? Ans. 1 T. 1 hhd. 56 gal. 1 qt. 1 pt. 15. A merchant bought a bale of cotton containing 400 yd. 3 qr. Having sold 139 yd. 3 qr. 2 na. of this purchase, how many yards of the cotton remain on hand? Ans. 260 yd. 3 qr. 2 na. 16. A speculator bought a tract of land containing 960 A. 2 R. 26 P. Having sold from the tract to the amount of 509 A. 3 R., how many acres of it remain unsold? Ans. 450 A. 3 R. 26 P. 17. A merchant bought at one time 4 T. 19 cut. of hemp, at another 3 T. 2qr., and at another 1 T. 13 cwt. 3 qr. 10 lb. Having sold at different times to the amount of 5 T. 10 cut. 1 qr. 20 lb., how much hemp has he still unsold? Ans. 4 T. 2 cwt. 3 qr. 18 lb. 18. A person who undertook a journey of 900 miles, traveled the first day 39 m. 3 fur., the second 40 m. 7 fur., the third and fourth each 43 m. 6 fur. How many miles of his journey then remained to be traveled? Ans. 732 m. 2 fur. 19. A manufacturer put into one bale 335 yd. 3 qr. of cotton, into another 400 yd., and into two others each 421 yd. 1 qr. having sold to one person 100 yd. 2 qr. from the first bale, and 200 yd. from each of the others, how many yards remain ? Ans. 877 yd. 3 qr. 20. A gentleman's fortune is estimated at 10000£ sterling. If he give to each of his three sons 2000£, 15 s., and to his only daughter the remainder, what will be the daughter's portion? Ans. 3997£, 15 s. 21. A planter has one tract of land containing 3000 A., and two others containing each 1500 A. 1 R. 16 P. If he sell from the first tract 400 A. 2 R., and from the other two together 305 A. 3 R. 25 P., how many acres will remain to him? Ans. 5294 A. 1 R. 7 P. 22. A miller bought at one time 200 bu. 3 pk. of wheat, at another 313 bu. 1 pk., and at another 194 bu. Having manufactured 405 bu. 1 pk. of these purchases into flour, what quantity of wheat has he still on hand? Ans. 302 bu. 3 pk. 23. A grocer bought from one distillery brandy, from another 40 gal., and from Having sold to the amount of 50 gal. 1qt. remains unsold? 34 gal. 3 qt. 1 pt. of another 31 gal. 1 qt. pt., what quantity Ans. 55 gal. 3 qt. 1 24. Farmer A has 300 A. 1 R. 40 P. of land; B has 100 A. 2 R. 13 P. more than A, and C has 39 A. 10 P. more than B, while D has 75 A. 2 R. 20 P. less than the other three together. How much land has B, C, and D, respectively? Ans. B, 401 A. 13 P.; C, 440 A. 23 P.; D, 1066 A. 16 P. Interval of Time between two given Dates. § 195. In subtracting a prior from a later date, add to the number of days elapsed in the month of the later date (when requisite,) as many as make the month of the prior date, and allow 12 months to a year. EXAMPLE. To find the interval between the 20th day of March, 1823, and the 10th day of April, 1848. y. m. da. 1848 4 10 1823 3 20 25 0 21 March being the 3d, and April the 4th month in the year, we designate them by these numbers, respectively. Since March has 31 days, 11 days of it remained after the 20th. Adding these 11 da., to the 10 da. of April, we have 21 da.; and it is plain that whatever number of months might intervene between the months of the two given dates, the surplus days would be found in a similar manner. But 31-20+10=10+31—20; hence the 21 da. (and the surplus days in every case) will be found, most readily, by the direction above given. (§ 195). $196. The interval of time, found as above, will include the particular day of the later date, but not that of the prior one. Thus in the Example given, the 10th of April is included in the interval 25 y. 21 da., but not the 20th of March,-as is obvious from the explanation. 25. Find the interval of time between May 16th, 1834, and September 4th, 1848. Ans. 14y. 3 m. 19 da. 26. A person was born on the 3d of April, 1807: required his age on the 15th of December, 1848. Ans. 41 y. 8 m. 12 da. 27. How long was it from the discovery of America, October 21st, 1492, to the founding of Jamestown, May 23d, 1607 ? Ans. 114y. 7 m. 2 da. 28. How long was the founding of Jamestown prior to the birth of Washington, February 22d, 1732; and what was Washington's age at his death, December 14th, 1799? Ans 124 y. 8 m. 30 da., and 67 y. 9 m. 21 da. |