seconds wide. How many square feet do they contain? Ans. 1 plank contains 12ft. 9 in. 1 sec. 6"", and the whole number 153ft. lin. 6". 5. A sawyer having sawed 24 rafters 18 feet long, 4 inches wide, and 3 inches thick, demands how many square feet of sawing he must be paid for? Ans. 252 square feet 6. A glazier having glazed 24 sixteen light windows, each light being 8 by 10 inches, would know how many feet of glazing he must be paid for. 7. A joiner having wainscotted a room with cedar that measures 112 about and 9 feet 6 inches high, desires to know how many square yards of wainscotting it contains, allowing 9 square feet to each square yard. Ans. 118 yards 2 feet. 8. A carpenter having laid a floor that is 36 feet long and 24 wide, wishes to know how many squares, of 100 feet each, are contained on the said floor. Ans. 8 squares and 64 feet. 9. A plasterer having plastered the interior walls of a house that measures 120 feet round and 10 feet 6 inches high, would be glad to know how many square yards of plastering are contained thereAns. 140. on. COMPOUND DIVISION. Compound Division teaches us how to divide any given quantity, consisting of several denominations, by one common divisor; also, to find the price of an integer, when the whole number and value thereof are both given. GENERAL RULE. 1. Divide the first denomination on the left hand by Simple Division. 2. Multiply the remainder by as many of the second, or next lower denomination, as make one of the first, and add the number of the second denomination to the product. 3. Divide that sum by the same divisor, and proceed in like manner through all the denominations of the given quantity to the last. 4. If the first denomination be less than the divisor, reduce it to the next lower one by the second rule; then divide, and continue the process as above directed. 5. Prove the work by Compound Multiplication. CASE 1. When the divisor does not exceed 12. RULE. Divide the first denomination on the left hard by Short Division, and set the quotient directly under the said denomination; then continue the operation according to the general rule. EXAMPLES IN STERLING MONEY. EXAMPLES IN WEIGHTS AND MEASURES. 1. Divide 41 lb. 11 oz. 19 pwts. 23 grs. by 5. Ans. 8 lb. 4 oz. 15 pwts. 23 grs.+4 r. 2. Divide 91 tons, 16 cwt. 3 qrs. 27 lbs. by 6. Ans. 15 tons, 6 cwt. 0 qrs. 18 lbs. 8 oz.: 3. Divide 9 lb. 11 oz. 6 dr. 1 sc. 18 grs. by 7. Ans. 1 lb. 5 oz. O dr. 2 sc. 16 4. Divide 17 tods, 1 stone, 1 clo. 6 lbs. 8 oz. by 8. grs.+6 r. Ans. 2 tods, 0 sto. O clo. 6 lbs. 15 oz. Ans. 18 yds. 3 qrs. 3 na. Ans. 25 yds. 2 qr. 8 in. Ans. 33 F.E. 2 qrs. 6 in. Ans. 12 E.E. 4 qrs. 5 in. Ans. 15 Fr.E. 5 qrs. 8 in. Ans. 9 bls. 2 bus. 1 p. 0 g. 2q. 5. Divide 170 yds. 1 qr. 3 na. by 9. 6. Divide 257 yds. 0 qrs. 8 in. by 10. 7. Divide 372 F.E. 2 qrs. 3 in. by 11. 8. Divide 154 E.E, 4 qrs. 6 in. by 12. 9. Divide 143 Fr.E. 5 qrs. by 9. 10. Divide 75 bls. 3 bus. 2 pks. by 8. 11. Divide 601 bush. 2 pks. O g. 2 qts. by 7. Ans. 85 bush. 3 pks. 1 gal. 2 qts. 12. Divide 1 tun of wine by 6. Ans. 42 gallons. Ans. 8 deg. 21 miles, 5 fur. 31 poles. 15. Divide 187 A. 3 roo. 32 po. by 4. Ans. 46 A. 3 roo. 38 po. 16. Divide 1829 years by 12. Ans. 152 yrs. 5 mo. 1 w. 4 da. 18 h. 17. Divide 12 days, 5 hrs. 40 min. 45 sec. by 7. 18. Divide 11 signs, 20° 54' by 8. CASE 2. Ans. 1 da. 17 h. 57 m. 15 sec. Ans. 1 sign, 13° 51′ 45′′. When the given number of integers exceeds 12, and is the exact product of any two factors in the Multiplication Table. RULE. Divide the given price of the whole quantity by one of the said factors, and the quotient thence arising by the other one; the last quotient will be the answer required. When the divisor exceeds 12, and is not the exact product of some two factors in the Multiplication Table. RULE. Divide the greatest denomination of the given sum by Long Division, and proceed with the rest according to the general rule. £ S. 1. If 8 bushels of wheat cost 4 6 4, what will 1 cost? 0 10 91 11 3. If 20 lbs. of tobacco cost 1 2. If 12 yards of cloth cost 0 39 12 6, what will I cost? 4. If 24 yards of scarlet cost 28 4 0, what will 1 cost? 1 36 5. If 28 bushels of corn cost 5 5 0, what will 1 cost? 6. If 29 yds. of toileynet cost 10 17 6, what will 1 cost? 0 76 7. If 37 yds. of cassimere cost 19 17 9, what will 1 cost? 0 10 9 0 171 DIVISION OF CROPS. Division of Crops is supplemental to Compound Division, and is essentially necessary among planters and farmers in general. RULE. 1. Add all the whole shares and parts of a share together, and reduce the sum to one denomination for a divisor, by which divide the whole crop; the quotient will be such a part of a single share as the divisor was reduced to-that is, if the divisor was reduced into halves, quarters, or thirds, &c. of a share, the quotient will be one-half, one-quarter, or one-third part of a single share. 2. Multiply the quotient by such a number as will produce a single share-that is, if it be one-half share, multiply by 2; if it be onethird, multiply by 3; and if it be one-fourth, multiply by 4, &c. 3. Multiply the single share by the number of whole sharers that the employer has under the overseer. 4. If any sharer is allowed more than a single share, add such parts together as will make up his quota. 5. Add the employer's part, the overseer's share, and the remainder (if any) together, and the sum will be equal to the whole crop, if the operation is right. |