Operation by Slate illustrated. 1. A merchant bought a piece of cloth containing 10 yds 2 qrs. 3 na., and sold 7 yds. 3 qrs. 2 na.; how much had he left? OPERATION. 4 4 yds. qrs. na. 10 2 3 Ans. 2 3 1 Q. In this example, how are the num bers written down? A. The less under the greater, with nails under nails, quarters under quarters, &c., as in Compound Addition. Q. How do you get the 1 na, in the answer? A. I begin with nails, the least denomination, and say, 2 na. from 3 na. leaves 1 na. Q. How do you proceed to get the 3 qrs.? A. I cannot take 3 qrs. from 2 qrs., but I can borrow, as in Simple Subtraction, 1 yd. 4 qrs., from the yards; then say, qrs. joined or added to the 2 qrs. (the top figure) makes 6 qrs., from which taking 3 qrs. leaves 3 qrs. Q. But suppose that, instead of adding first, we subtract first how would you proceed? A. Taking 3 qrs. from 4 qrs. (borrowed) leaves 1 qr., and 2 qrs. makes 3 qrs. Q. How do you get the 2 yds.? A. I must carry 1 yd. (for the yard which I borrowed) to T yds., making 8 yds., which, subtracted from 10 yds., leaves 2 yds From this example we derive the following RULE. Q. How do you write the numbers down? A. The less under the greater, placing each denomination as in Compound Addition. Q. With which denomination do you begin to subtract? Q. How do you subtract each denomination? A. From the denomination above it, as in Simple Subtraction. Q. If the lower number in any denomination be greater than the upper, how do you proceed? A. Borrow as many units as make one in the next higher denomination, from which subtract the lower number. Q. What must the remainder be added to? A. The upper number. Q. How many do you carry in such cases? A. One. Q. How do you subtract the last denomination? PROOF. Q. How do you prove the operation? A. By adding the Remainder and Subtrahend together, as in Simple Subtraction, the amoun of which must be equal to the Minuend. More Exercises for the Slate. 2. If, from a piece of cloth containing 10 yds. 2 qrs., you cut off 2 yds. 2 qrs., how much will there be left? A. 8 yds. 3. A bought of B a bushel of barley for 8 s. 6d. ; he gave B 1 bu. of rye, worth 4 s. 3 d., and paid the rest in money; how much did he pay? A. 4s. 3 d. 4. A bought of B a bale of cotton for 20£ 4 s., and B. bought of A 4 tierces of rice for 15£ 18 s.; A paid B the rest in money; how much did he pay? A. 4£ 6 s. 5. A man bought a wagon for 6£ 10 s., and sold it for 12£ 18 s.; how much did he make by the trade? A. 6£8s. 6. A man bought one load of hay for 4£ 10 s., and another for 5£ 15 s.; how much more did he give for one than the other? A. 1£ 5 s. 7. A man bought two loads of hay, one weighing 18 cwt. 3 qrs. 25 lbs., and the other 17 cwt. 0 qr. 26 lbs.; how much did one weigh more than the other? A. 1 cwt. 2 qrs. 27 lbs. 8. A merchant bought a piece of broadcloth, containing 40 yds., from which he sold 36 yds. 1 qr. 2 na.; how much did he have left? A. 3 yds. 2 qrs. 2 na. 9. A grocer bought a hhd. of rum, containing 65 gals., and by accident 2 gals. 2 qts. 1 pt. leaked out; how many gallons did he have left? A. 62 gals. 1 qt. 1 pt. 10. A merchant bought a quantity of corn, weighing 20 cwt. 2 qrs. 15 lbs., of which he sold 10 cwt. 3 qrs. 12 lbs. ; how much had he left? A. 9 cwt. 3 qrs. 3 lbs. 11. A grocer retailed 10 gals. 3 qts. 1 pt. 1 gi. of rum from a hhd. containing 54 gals. 2 qts. 1 pt. 2 gi.; how much had he left? A. 43 gals. 3 qts. 0 pt. 1 gi. 12. If, from a box of butter, containing 20 lbs. there be sold 10 lbs. 8 oz., how much will there be left? A. 9 lbs. 8 oz. 13. If, from a field, containing 40 acres, 2 roods, 20 poles, there be taken 19 acres, 3 roods, 30 poles, how much will there be left? A. 20 acres, 2 roods, 30 poles. 14. William engaged himself in a store for 3 yrs.; after having staid 2 yrs. 2 mo. 2 w. 2 d., how much longer had he to stay? A. 9 mo. 1 w. 5 d. 15. A farmer, having raised 40 bu. of corn, kept 23 bu. 2 pks. for his own use, and sold the rest; how much did he sell? A 16 bu. 2 pks. 16. A farmer made in one year, from his orchard, 200 bbls. 14 gals. of cider, of which he sold precisely 118 bbls. 3 qts. 1 pt.; how much had he left for his own use? A. 82 bbls. 13 gals. 1 pt. 17. If, from a parcel of wood, containing 40 cords and 64 feet, there be sold 39 cords and 32 feet, how much will there be left? A. 1 cord 32 feet. 18. The distance from Providence to Norwich is 45 miles; now, when a man has travelled 30 m. 7 fur. 20 rods of the distance, how much farther has he to travel? A. 14. m. 20 rods. 19. From 14£ 15 s. 6 d. 2 qrs. take 12£ 15 s. 6 d. 3 qrs. A. 1£ 19 s. 11 d. 3 qrs. 20. From 1£ take 2 s. A. 18 s. A. 19 s. 10 d. take 3 sq. ft. A. take 50 cu.in. 32. From 1 yr. A. 6 sq. ft. 39 sol. ft. 1678 sol. in A. 11 mo. 3 w. 6 da. 12 h COMPOUND MULTIPLICATION. ¶ XXXII. 1. If one knife cost 9 d., how many shillings will buy 2 knives? Will buy 4? Will buy 6? Will buy 8? Will buy 12? 2. William, having a basket that would hold 1 qt. 1 pt., filled it with nuts; how many qts. can be put in a basket that will hold twice as much? 3 times as much? 4 times as much? 3. At 1s. 6 d. a bushel, how many shillings will 2 bushels of apples cost? Will 4 bu.? Will 6 bu.? Will 8 bu.? 4. Multiply 2 s. 6 d. by 2. 5. Multiply 2 pwts. 12 grs. by 2. 6. Multiply 2 bu. 4 qts. by 3. 7. Multiply 3 gals. 2 qts. by 2. 8. Multiply 20 m. 20 sec. by 3. 9. How many pence in 2 times 2 farthings? 4X2 farthings, or 2 qrs.? 4x3 qrs.? How many shillings in 2 times 6 d.? 2 X 12 d.? 4×6d.? 5×12 d.? 8×3d.? 4X7 d.? 3× 5 d.? 8 X 12 d.? 10. How many pounds in 4 times 10 s.? 3X 10 s.? 4 X 6 s.? Operation by Slate illustrated. 1. A merchant bought 5 yards of cloth for 2£ 6 s. 1 d. 3 qrs. per yard; what did the whole cost? Q. How do you get the 10 s.? Q. How do you get the 3 qrs. in the answer? A. 5 times 3 qrs. are 15 qrs. 3 d. 3 qrs., writing down the 3 qrs, and carrying 3 d. as in Compound Addition. Q. How do you get the 8 d.? A. 5 times 1 d. are 5 d., and 3 d. (to carry) makes 8 d. A. 5 times 6 s. are 30 s. 1£ 10 s., writing down the 10 s. and carrying the 1£. Q. How do you get the 11£? A. 5 times 2£ are 10£, and 1£ (to carry) makes 11£. From these illustrations we derive the following RULE Q. With which denomination do you begin to multiply? Q. How do you multiply that, and each denomination? PROOF. Q. What is the proof? A. As in Simple Multiplication. More Exercises for the Slate. 2. At 5 s. 6 d. a gallon, what will 2 gals. of rum cost? A. 11 s. 3. At 2s. 6d. I qr. a quart, what will 2 qts. of brandy cost?5-0-2. What will 3 qts. ?-7-6-3. What will 4 qts.?-10-1. What will 5 qts. ?-12-7-1. What will 6 qts. ?-15-1-2. A. 2£ 10 s. 5 d. 4. How much wine in 7 bottles, each containing 2 qts. 1 pt. 2 gills?-4-3-0-2. How much in 8 bottles?-5-2. In 9?-6-0-1-2. In 10-6-3-1. In 11?-7-2-0-2. A. 30 gals. 3 qts. 1 pt. 2 gills. 5. What is the weight of 3 doz. silver spoons, each doz. weighing 2 lbs. 6 oz. 12 pwts. 3 grs. ?-7-7-16-9. What will 4 doz. weigh? -10-2-8-12. What will 5 doz. ?-12-9-0-15. What will 6 doz. ?15-3-12-18. A. 45. lbs. 10 oz. 18 pwts. 6 grs. 6. Bought 4 loads of hay, each load weighing 1 T. 10 cwt. 2 qrs. 20 lbs. 5 oz. 15 drs.; what was the weight of the whole ?6-2-2-25-7-12. What would be the weight of 5 loads ?-7-13-1 17-13-11. Of 11 loads ?-16-17-2-0-1-5. Of 12 loads?-18-8-0-20-7-4. A. 49 T. 1 cwt. 3 qrs. 7 lbs. 14 oz. 7. At the rate of 36 lea. 2 m. 3 fur. a day, how far will a vessel sail in 6 days?-220-2-2. In 15 days?-551-2-5. In 10 days?367-2-6. In 9 days?-331-0-3. A. 1471 lea. 2 m. 8. In 8 bales of cloth, each bale containing 12 pieces, each piece 27 yds. 1 qr. 2 na., how many yards? A. 2628 yds. COMPOUND DIVISION. ¶ XXXIII. 1. William had 2 qts. 1 pt. of walnuts, which he wished to divide equally among his two little brothers; how many must he give each ? 2. James bought 2 books for 2 s. 6d. ; how much did he pay apiece? 3. If you pay 1 s. 6 d. for 2 inkstands, how many shillings would that be apiece? 4. A man bought 4 lambs for 6 shillings; how many pence did he pay apiece? 5. William has 3 pks. 4 qts. of walnuts, which he wishes to put into 4 little baskets, each of which will hold 7 qts.; will his baskets hold all his walnuts, or not? and inform me how you do it. 6. 3 men have 4 gals. 2 qts. of cider allowed them every day; how much is that apiece? |