7. Reduce 3qr. 3na. to the fraction of a yard. 8. What part of 7lb. is 13oz. 14dr. ? 9. What part of 576 grammes is 43 centigrammes ? 10. Reduce 6sq. ft. 130sq. in. to the fraction of a rood. TO REDUCE LOWER DENOMINATIONS TO THE DECIMAL OF A HIGHER. X Reduce 10oz. 15dwt. 22gr. to the decimal of a th. 22 gr.=?i dwt.=.916dwt. Therefore, 15dwt. 22gr.=15.916dwt.=15.916oz. =79583oz. Then, 10oz. 15dwt. 22gr.=10.79583oz.=10.7958 38. =.899652716. RULE. Commence with the lowest denomination, annex decimal o's, and reduce each denomination to the decimal of the next higher, by dividing as in ordinary reduction. In the following examples, the numbers are all to be reduced to the decimal of the highest denomination mentioned. 1. Add £11 11s. 11d. ; £4 3s. 7d. ; 2s. 6d. 3qr.; and 9s. 6d. 2. Add 6gal. 3qt. Ipt. 3gi.; 2qt. Ipt. 1gi. ; 5gal. 3gi.; X and 4gal. 1qt. 3. From 19T. 10cwt. subtract 15cwt. 3qr. 141b. 8. Reduce £591 98. 3d. to Federal Money, at $4.85 per £. 9. Reduce 28 ducats 9 carlins 7 grains of Naples, to dollars and cents, at 83cts. per ducat. 10. Reduce 28C. 7C. ft. 4c. ft. to cords and decimals of a cord. 11. What is the value of 94 francs 79 centimes, at 184 cts. per franc? 12. What is the value of 75 milrees 2 crusades, at $1.15 per milree? COMPOUND ADDITION. EXAMPLE FOR THE BOARD. 11 66 £. qr. What is the sum of £20 16s. 9d. 3qr.; 20 “ 1666 966 3 £11 7d. lqr.; and £9 19s. 11d. 2qr.? Writ 066 7 66 1 ing the numbers as in Simple Addition, 9 6 19 6 11 6 2 placing those of the same denomination in the same perpendicular column, I commence 41 “ 17 6 4 66 2 with the column of farthings, and find its sum, 6qr.=ld. 2qr. I write the 2qr. beneath the column of gr., and carry the 1d. to the column of d. The sum of the column of d. is 28d.=2s. 4d. Write the 4d. beneath the column of d. and carry 2s. to the column of s. There are 375.=£1 178. Write 17 beneath the column of s. and carry £l to the column of £. The sum of the £ is 41, which is written down, as there is no higher denomination. RULE. Write the numbers as in Simple Addition, placing those of the same denomination in the same vertical column. Commence at the right hand to add, and reduce the sum of each column to the next higher denomination. Write the remainder underneath, and carry the quotient to the next column. 1. Add 9Qr. 1C. 2bu. 3pk; 4Qr. 1bu. 1pk. Igal. ; 3bu. 3pk. 1qt. ; and 5Qr. 2 pk., and reduce the result to quarts. 2. Add 3Cong. 70. 15f3 7f3 59 m.; 7 Cong. 3f 3 ; 40. 9f3 4f3; and 2Cong. 4f3 1 m, and find the weight of the whole. 3. Add 116gal. 3qt. 1 pt. ; 59gal. 1pt. 3gi.; 76gal. 2qt. and 291gal. Iqt. 1pt. lgi., and reduce the result to gallons and decimals of a gallon. 4. Add 14T. 9cwt. 3qr. 171b. ; 9T. lqr. 25lb. 50%. ; 1616. 3oz. 14dr. ; and 17 T. 18cwt. Iqr. 277b. 2dr. 5. Add £19 7s. 6d. 3qr. ; £276 19s. 11d. ; 14s. 3qr.; £278 138.; and £190 58. 5d. 2qr. 6. Add 515. 113 73 29 18gr.; 71. 14gr ; 33 33 ; and 1515. 43 19gr. and reduce the 3, &c., to the fraction of a lb. 7. Add 55yd. 3qr. 3na.; 7yd. Ina. 1 in.; 4yd. 2qr. lna.; 63yd. 2na.; and 175yd. iqr. 2na. 2in., and reduce the result to decimal yards. 8. Add 3C. 7C. ft. 15c. ft. 1719c. in.; 14C. 3c. ft. 96c. in. ; 2C.ft. 14c. ft. ; 47C. 6C. ft.; and 19C. 9. Add 9sq. m. 627 A. 3R. 30r. ; 3sq. m. 248 A. 39r. ; 41 sq. m. 27r.; and 163 A. 2R. 12r, and reduce the result to rods. 10. Add 17m. 7fur. 39r. 4yd. 2ft. llin.; 19m. 3fur. 3yd. ; 6fur. 18r. ift. 9in.; and 41m. 24r. 2ft. 7in. 11. How many deniers in 4 Louis d'ors 1 ecu 5 livres +13 Louis 2 livres 19 sous 10 deniers +2 livres 7 sous + 4 livres 13 sous 9 deniers ? 12. Add 19 ducats 8 carlins 7 grains; 12d. 3c. 5gr. ; 9c. &gr.; and 29d. 2c, and find their value at 81 cts. per ducat. 13. Add 19 ft. 11' 8" 5'' ; 3 ft. 4" 9'"'; 10' 10"; 8ft. 6'; 15ft.; and 29ft. 27" 11". COMPOUND SUBTRACTION. EXAMPLE FOR THE BOARD. bu. pk. qt. pt. From 39bu. 1 pk. 3qt. Ipt. take 19bu. 2pk. 39 6 1 6 3 66 1 5qt. 1 pt. Commencing at the right hand, as 19 66 2 6 5 1 in Simple Subtraction, I say Ipt. from 1pt. leaves Opt. 5qt. cannot be taken from 3qt., 19 2 6 - 0 I therefore increase both numbers by lpk. or 8qt. and say, 5qt. from 1lqt. leaves 6qt., 3pk. from 5pk. leaves 2pk., and 20bu. from 39bu. leaves 19bu. 66 RULE. Write the numbers as in Compound Addition, and commence at the right hand to subtract. If the number representing any denomination in the minuend, is less than that in the subtrahend, increase each by one of the next higher denomination, and proceed as in ordinary subtraction. 1. From 28chal. 3bu. lpk. take 18chal. 31bu. 2 pk. 70t. 2. What is the difference between 187gal. 3qt. 1pt. 3gi. and 216gal. 2gi.? 3. Subtract 7Y. 191d. 18h. 59min. 2 sec. from 8 Y. 32d. 17h. 4. From 19 Cong. subtract 70. 1183 383 41 712, and reduce the remainder to M. 5. A grocer purchased 19cwt. Iqr. of sugar. How much had he left after selling 11cwt. 2qr. 17lb. 12oz. ? 6. A man sold his horse for £40, which was £9 8s. 6d. more than it cost him. What did he give for the Š horse? 7. Subtract 9]$ 73 73 12 11gr. from 165 33 9gr. 8. Subtract 19yd. 3qr. 3na. from 117yd. Iqr. 2na. 9. A ship left port Nov. 29th, 1841, and returned Aug. 18th, 1844. How long was her voyage ? 10. From a lot of land containing 490 Acres, 163A. 3R. 17r. were sold. How much was left ? 11. From a board measuring 13ft. 9' 11", a piece was sawed containing 4ft. 0' 3" 8''. How much was left? 12. How many seconds elapsed from 20min. past 5 A. M. 8th mo. 18, 1829, to 17min. past 3 P. M. 5th mo. 3, X 1831 ? 13. Subtract 9 marcs 13 schillings 11 pfennings Hamburg, from 10m. 3sch., and reduce the remainder to the fraction of a marc. 14. From 7m. 3fur. Sch., subtract 7fur. 3p. 181., and X reduce the remainder to miles and decimals of a mile. COMPOUND MULTIPLICATION. EXAMPLE FOR THE BOARD. yd. ft. in. Multiply Syd. 2ft. llin. by 15. Multiplying 9 6 2 6 11 the inches by 15, we find 165in.=13ft. 9in. 15 Write 9in. below the line, and carry 13ft. 15 times 2ft.=30ft. and 13ft. to carry, make 43ft. 149 1 9 =14yd. 1ft. Write 1fi. in the column of feet, and carry 14yd. 15 times 9yd.=135yd. and 14yd. to carry, make 149yd. RULE. Commence with the smallest denomination, and reduce each product to the next higher denomination, writing the remainder underneath, and carrying the quotient as in Compound Addition. 1. Multiply 13 Y. 79d. 18h. 43m. 12s. by 43. X 2. Multiply 19m. 7fur. 4r. 4yd. llin. by 81. 3. Multiply £96 11s. 11d. lqr. by 57. 4. Multiply 41yd. 2qr. 3na. lin. by 79. 8. How many acres, roods, &c., in 73 pieces of land, each of which is 73.8 rods long, and 31.3 rods wide ? 9. How many cords, &c., of wood, in 61 piles, each pile being 12.5ft. long, 4ft. wide, and 8.75ft, high? 10. How many seconds in 13 times 4Y. 18d. 13h.? 11. How many feet, primes, &c., in 86 times 39' 0" 4" ? 12. Multiply 7m. 3fur. 5ch. by 17, and reduce the fur. and ch. to the fraction of a mile. 13. Multiply 19 4' 2" 11'" by 29, and reduce the result to ". 14. Add 4251b. 13oz. 15dr. ; 371b. 14oz. ; 91lb. 2oz. 11 dr. ;-subtract 50016, 1502, 14dr. 2sc. from the sum;multiply the remainder by 11, and reduce the result to grains. COMPOUND DIVISION. EXAMPLE FOR THE BOARD. yd. ft. in. Divide 19yd. 2ft. 9in. by 5. Dividing the 5)19 - 26 9 19yd. we have a quotient of 3yd. with a re mainder, 4yd. The 4yd. undivided, are equi3 " 2 " 113 valent to 12ft., which, added to the 2ft. make 14ft. 14ft. -5=2ft. with a remainder, 4ft. The 4ft. undivided, are equal to 48 inches, which, added to the 9 inches, make 57 inches. 57 in. -5=11; in. RULE. First divide the highest denomination. Whenever there is any remainder, reduce it to the next lower denomination, and add it to the number (if any) already in that denomination. Then divide as before, and so proceed until the division is completed. If both the divisor and the dividend are compound numbers, reduce them to the same denomination, and divide as in simple division. 1. What is the price of a qr. of sugar, at £2 3s. per cwt. ? |