tract the subtrahend from the figure borrowed, and add the difference to the minuend. Thus, in the above example, 14 from 20 leaves 6, and 4 is 10. The process in the foregoing example may be presented in the form of a RULE for the Subtraction of Compound Num bers: I. Write down the sums or quantities, the less under the greater, placing those numbers which are of the same denomination directly under each other. II. Beginning with the least denomination, take successively the lower number in each denomination from the upper, and write the remainder underneath, as in subtraction of simple numbers. III. If the lower number of any denomination be greater than the upper, borrow as many units as make one of the next higher denomination, subtract the lower number therefrom, and to the remainder add the upper number, remembering always to add 1 to the next higher denomination for that which you borrowed. Proof. Add the remainder and the subtrahend together, as in subtraction of simple numbers; if the work be right, the amount will be equal to the minuend. EXAMPLES FOR PRACTICE. 1. A merchant sold goods to the amount of 136 £. 7 s. 64 d., and received in payment 50£. 10 s. 42d; how much remained due ? Ans. 85£. 17 s. 12 d. 2. A man bought a farm for 1256 £. 10 s., and, in selling it, lost 87. 10 s. 6 d.; how much did he sell it for? Ans. 1168£. 19 s. 6 d. 3. A man bought a horse for 27£. and a pair of oxen for 19£. 12 s. 81 d. ; how much was the horse valued more than the oxen? 4. A merchant drew from a hogshead of molasses, at one time, 13 gal. 3 qts.; at another time, 5 gal. 2 qts. 1 pt.; what quantity was there left? Ans. 43 gal. 2 qts. 1 pt. 5. A pipe of brandy, containing 118 gal. sprang a leak, when it was found only 97 gal. 3 qts. 1 pt. remained in the cask; how much was the leakage? 6. There was a silver tankard which weighed 3 lb. 4 oz. ; the lid alone weighed 5 oz. 7 pwt. 13 grs.; how much did the tankard weigh without the lid ? 7. From 15 lb. 2 oz. 5 pwt. take 9 oz. 8 pwt. 10 grs. 8. Bought a hogshead of sugar, weighing 9 cwt. 2 qrs. 17 lb.; sold at three several times as follows, viz. 2 cwt. 1 qr. 11 lb. 5 oz.; 2 qrs. 18 lb. 10 oz.; 25 lb. 6 oz. ; what was the weight of sugar which remained unsold? Ans. 6 cwt. 1 qr. 17 lb. 11 oz. 9. Bought a piece of black broadcloth, containing 36 yds. 2 qrs.; two pieces of blue, one containing 10 yds. 3 qrs. 2 na., the other, 18 yds. 3 qrs. 3 na.; how much more was there of the black than of the blue? 10. From 28 miles, 5 fur. 16 r. take 15 m. 6 fur. 26 r. 12 st. 11. A farmer has two mowing fields; one containing 13 acres 6 roods; the other, 14 acres 3 roods: he has two pastures also; one containing 26 A. 2 r. 27 p.; the other, 45 A. 5 r. 33 p.: how much more has he of pasture than of mowing? 12. From 64 A. 2 r. 11 p. 29 ft. take 26 A. 5 r. 34 p. 132 ft. 13. From a pile of wood, containing 21 cords, was sold, at one time, 8 cords 76 cubic feet; at another time, 5 cords 7 cord feet; what was the quantity of wood left? 14. How many days, hours and minutes of any year will be future time on the 4th day of July, 20 minutes past 3 o'clock, P. M. ? Ans. 180 days, 8 hours, 40 minutes. 15. On the same day, hour and minute of July, given in the above example, what will be the difference between the past and future time of that month? 16. A note, bearing date Dec. 28th, 1826, was paid Jan. 2d, 1827; how long was it at interest? The distance of time from one date to that of another may be found by subtracting the first date from the last, observing to number the months according to their order. (¶ 37.) 17. A note, bearing date Oct. 20th, 1823, was paid April 25th, 1825; how long was the note at interest? 18. What is the difference of time from Sept. 29, 1816, to April 2d, 1819? Ans. 2 y. 6 m. 3 d. 19. London is 51° 32', and Boston 42° 23′ N. latitude; what is the difference of latitude between the two places? Ans. 9° 9', 20. Boston is 71° 3', and the city of Washington is 77° 43' W. longitude; what is the difference of longitude between the two places? Ans. 6° 40'. 21. The island of Cuba lies between 74° and 85° W. longitude; how many degrees in longitude does it extend? ¶ 40. 1. When it is 12 o'clock at the most easterly extremity of the island of Cuba, what will be the hour at the most westerly extremity, the difference in longitude being 11° ? Note. The circumference of the earth being 360°, and the earth performing one entire revolution in 24 hours, it follows, that the motion of the earth, on its surface, from west to east, is 15° of motion in 1 hour of time; consequently, 1° of motion in 4 minutes of time, and 1' of motion in 4 seconds of time. From these premises it follows, that, when there is a difference in longitude between two places, there will be a corresponding difference in the hour, or time of the day. The difference in longitude being 15°, the difference in time will be 1 hour, the place easterly having the time of the day 1 hour earlier than the place westerly, which must be particularly regarded. If the difference in longitude be 1°, the difference in time will be 4 minutes, &c. Hence,-If the difference in longitude, in degrees and minutes, between two places, be multiplied by 4, the product will be the difference in time, in minutes and seconds, which may be reduced to hours. We are now prepared to answer the above question. 11° 44 minutes. Hence, when it is 12 o'clock at the most easterly extremity of the island,, it will be 16 minutes past 11 o'clock at the most western extremity. 2. Boston being 6° 40′ E. longitude from the city of Washington, when it is 3 o'clock at the city of Washington, what is the hour at Boston? Ans. 26 minutes 40 seconds past 3 o'clock. 3. Massachusetts being about 72°, and the Sandwich Islands about 155° W. longitude, when it is 28 minutes past 6 o'clock, A. M. at the Sandwich Islands, what will be the hour in Massachusetts ? Ans. 12 o'clock at noon; MULTIPLICATION & DIVISION OF COMPOUND NUMBERS. T 41. 1. A man bought 2 yards of cloth, at 1 s. 6 d. per yard; what was the cost? 2. If 2 yards of cloth cost 3 shillings, what is that per yard? 3. A man has three pieces of cloth, each measuring 10 yds. 3 qrs.; how many yards in the whole ? 4. If 3 equal pieces of cloth contain 32 yds. 1 qr., how much does each piece contain ? 5. A man has five bottles, each containing 2 gal. 1 qt. 1 pt.; how much wine do they all contain? 6. A man has 11 gal. 3 qts. 1 pt. of wine, which he would divide equally into five bottles; how much must he put into each bottle? 7. How many shillings are 3 times 8 d.? 5 X 2 qrs.? 3 x 9 d.? 3 x 10 d.? -4 × 7 d. ? 9. At 1£. 5 s. 8 d. per yard, what will 6 yards of cloth cost? 10. If 6 yards of cloth cost 7. 14 s. 4 d., what is the price per yard? Here, as the numbers are large, it will be most convenient to write them down before multiplying and dividing. 6 times 3 qrs. are 18 qrs.ner of short division, 6 is con4 d. and 2 qrs. over; we set tained in 7£. 1 time, and 1£. down the 2 qrs.; then, 6 times over; we write down the 8 d. are 48 d., and 4 to carry quotient, and reduce the remakes 52 d. 4s. and 4 d. mainder (1.) to shillings, over, which we write down; (20 s.,) which, with the given again, 6 times 5 s. are 30 s. shillings, (14 s.,) make 34 s. ; and 4 to carry makes 34 s. 16 in 34 s. goes 5 times, and 4 s. 1£. and 14 s. over; 6 times over; 4 s. reduced to pence 1£. are 6£., and 1 to carry = 48 d., which, with the makes 7., which we write given pence, (4 d.,) make 52 down; and it is plain, that the d.; 6 in 52 d. goes 8 times, and united products arising from 4 d. over; 4 d. = 16 qrs., the several denominations is which, with the given qrs. the real product arising from (2) 18 qrs. ; 6 in 18 qrs. goes the whole compound number. 3 times; and it is plain, that the united quotients arising from the several denominations, is the real quotient aris ing from the whole compound number. 11. Multiply 3£. 4 s. 6 d. by 7. = 12. Divide 22£. 11 s. 6 d. by 7. 13. What will be the cost 14. At 2. 12 s. 6 d. for 5 of 5 pairs of shoes at 10 s. 6 d. pairs of shoes, what is that a a pair ? 15. In 5 barrels of wheat, each containing 2 bu. 3 pks. 6 qts., how many bushels? 17. How many yards of pair? 16. If 14 bu. 2 pks. 6 qts. of wheat be equally divided into 5 barrels, how many bushels will each contain ? 18. If 9 coats contain 39 cloth will be required for 9 yds. 3 qrs. 3 na., what does 1 coats, allowing 4 yds. 1 qr. coat contain? 3 na. to each? 19. In 7 bottles of wine, 20. If 5 gal. 1 gill of wine each containing 2 qts. 1 pt. 3 be divided equally into 7 bottles, how much will each con gills, how many gallons? 21. What will be the tain? 22. If 8 silver cups weigh weight of 8 silver cups, each 3 lb. 9 oz. 1 pwt. 16 grs., what weighing 5 oz. 12 pwt. 17 is the weight of each? grs. ? 23. How much sugar in 12 24. If 119 cwt. 1 qr. of su hogsheads, each containing gar be divided into 12 hogsheads, how much will each hogshead contain ? 9 cwt. 3 qrs. 21 lb. ? 25. In 15 loads of hay, each weighing 1 T. 3 cwt. 2 qrs., how many tons? 26. If 15 teams be loaded with 17 T. 12 cwt. 2 qrs. of bay, how much is that to each team? |