S. How much cloth in 25 pieces, each measuring 27 yd. Ans. 681 yd. 1 qr. 1 qr.? 9. How much land in 9 fields, each containing 14 A. 1 R. 25 sq. Ans. 129 A. 2R. 25 sq. rd. rd.? 10. How many bushels of apples in 144 casks, each containing 3 bush. 3 pk.? Ans. 540 bush. 11. Find the difference between 100 Julian, and 100 Ans. 18h. 40 min. Solar years. COMPOUND DIVISION, Is when the dividend consist of different denominations. RULE. 1. Set down the divisor at the left hand of the dividend, as in Simple Division. 2. Divide the highest denomination of the dividend by the divisor, as in Simple Division, and the quotient will be a part of the answer, of the same denomination. 3. If there is any remainder after the division of the highest denomination, reduce that remainder to the next lower denomination, and add to it the given number (if any) of this denomination in the dividend. Then divide this a mount by the divisor, as before; and so proceed till the lowest denomination has been divided; and the several numbers of the quotient, taken together, will be the answer.* *To divide a number consisting of several denominations by any simple number, is the same as dividing all the parts or members of which the compound number is composed, by the simple number. And this will be true when any of the parts are not an exact multiple of the divis or; for, by conceiving the number, by which it exceeds that multiple, to have its proper value by being placed in the next lower denomination, the dividend will still be divided into parts, and the true quotient found, as before: Thus 411. 17 s. 6d. divided by 6, will be the same as 36 l. 114 s. 42 d. divided by 6, which is equal to 67. 19 s. 7 d., as by the Rule. Note 1.-Each particular or partial quotient, and each remainder, will be of the same denomination as the dividend. When the lowest denomination of the dividend is not the lowest of its kind; then, if there is a remainder after the division of this denomination, it may be reduced to the next lower denomination, and then divided by the given divisor; and so on. PROOF.-Compound Multiplication and Division prove each other. Rem. 6 20 120 17 14 244.. 17.. 8 Proof. Explanation.-I first divide the 244 pounds by 14; and the quotient is 17 l., and 67. remain. The remainder I multiply by 20, to reduce it to shillings, and add to the product the 17s. of the given dividend, and the sum is 137 s. This sum I divide by 14, and the quotient is 9s. and 11s. remain. The re137(9 s. mainder I multiply by 12, to reduce it to 126 pence, and add to the product the 8 d. of the dividend, and the sum is 140 d. This sum I divide by 14, and the quotient is 10 d.; and as this is the lowest denomination of the given dividend, and nothing remains, the work is 132 done. So the whole quotient, or answer, is 177. 9 s. 10 d. Then, to prove the work, I multiply the quotient by the divisor; and the 140(10d. produ ct being the same as the dividend, I conclude the work is right. Rem. 11 14 12 0 Note 2. When the divisor does not exceed 12, the di - vision may be performed after the manner of Short Division; as in the 2d and 3d examples. 5. Divide 3767. 11 s. 4 d. by 11. Ans. 347. 4 s. 8d. Ans. 257. 19 s. 6d. 3q.+ 6. Divide 961 l. 4 s. by 37. (8) Weights and Measures. lb. oz. dr. 4)59.. 15.. 4 Quot. 14. 15.. 13 Ans. 5ș. 4d. (9) 10. Divide 280 miles, 4 furlongs, by 16. Ans. 17 m. 4. fur. 10 rd. 11. Divide 570 yd. 2 qr. 1 na. by 47. Ans. 12 yd. 0 qr. 2 na.+ 12. Divide 2 acres and 10 sq. rods by 6. 13. Divide 15 sq. ft. 120 sq. in. Ans. 1R. 15 sq. rd. by 12. Ans. 1 sq. ft. 46 sq. in. 1585 cub. in. by 7. Ans. 7 Cd. 75 cub. ft. 967 cub. in. 14. Divide 53 cords, 16 cub. ft. 15. Divide 69 gallons, 3 qt. by 8. Ans. 8 gal. 2 qt. 1 pt. 3 gil. 16. Divide 51 bush. 3 pk. 6 qt. 1 pt. by 25. Ans. 2 bush. 2 qt. 1 pt. 17. Divide 5 bushels by 8. Ans. 30 da. 10 h. 30 min. 19. Divide 4S. 5°.. 45' by 9. Ans. 13..58' .. 20". CONTRACTIONS. I. When the divisor exceeds 12, and is a composite num ber, you may divide successively by its component parts, instead of the whole divisor at once. Ans. 87. 1232 s., or 87. 12 s. 4 d. 2 q. 3. Divide 1285 acres and 32 sq. rd. by 144. Ans. 8 A. 3 R. 28 sq. rd. 4. Divide 11426 bush. 1 pk. by 1320. 12×11×10=1320. Ans. 8 bush. 2 pk. 5 qt. II. When the divisor is large, and is not a composite number, you may reduce the dividend to the lowest denomination of which it consists, and then divide it by the divisor; and the quotient will be the answer; which may be brought into a higher denomination, if necessary. EXAMPLES. 1. Divide 657 l. 6 s. 11 d. by 79. 657l. 6s. 11d.=157763 d.; and 157763÷79–1997 d., and 1997 d. 87. 6s. 5 d. Ans. Here, I first reduce the given dividend to pence, and find it to be 157763 d. I then divide those 157763 d. by 79, and the quotient is 1997 d., which I reduce to pounds, and have 87. 6s. 5 d. for the answer. Ans. 81. 17s. 4d. 2. Divide 505 l. 8 s. by 57. Ans. 6 oz. 8 dr.+ 4. Divide 506 yd. 2 ft. 9 in. by 711. Ans. 2ft. 1 in. 2b.c. PRACTICAL QUESTIONS, to exercise the learner in Compound Division and the preceding rules. 1. An estate, valued at 8615 l. 12 s. is to be divided equally among 4 heirs : What is each share? L. S. 4)8615.. 12 Ans. 2153. 16 2. A certain house is worth 850 Z., and I own of it: What is my part worth? L 850 4)2550 S. Ans. L 637.. 10 Ans. 7s. 6d. 3. If 75 bushels of wheat be worth 287. 2s. 6 d., what is the value of 1 bushel? 4. If 8 cheeses weigh 162 lb. 8 oz., what is the average weight of each? Ans. 20 lb. 5 oz. 5. A farmer has three farms: the first contains 125 acres, 3 roods; the second 175 acres and 10 sq. rods; and the third 200 acres, 2 roods, 18 sq. rods. He intends to divide these farms equally between his two sons: What will be the share of each son? Ans. 250 A. 2 R. 34 sq. rd. 6. Bought 110 lb. of cheese, for 27. 10 s. 8d., and 140lb. more, for 31. 14 s. 4 d.: What did the whole cost me a lb.? Ans. 6 d. 7. If a man drinks 4 barrels of cider,(each 31 gallons,) in a year, or 365 days, how much does. he drink in a day? Ans. 1 qt. 3 gil.+ 8. In 487. 6 s. how many guineas, at 21 shillings each? 48 l. 6 s. 966 s., and 966÷21-46 guineas, Ans. 9. How many moidores at 36 shillings each; guineas at 28 s., and pistoles at 22 s., are there in 283l. 16 s., and the number of each equal? 283 l. 16 s.-5676 s., and 36+28+22=86: then, 5676÷ 86-66, the Ans. 10. If11 s. 3 d. sterling be equal to 22 dollars, how much sterling money is equal to 1 dollar? S. d. 11..3 2 24×2=5)22 6 Ans. 4..6 Here the divisor contains a fraction, and I perform the division according to the rule given in the Supplement to Simple Division. 11. The sun is about 95000000 miles from the earth, and a cannon ball, at its first discharge, flies about a mile in 7 seconds: How long would a cannon ball be, at that rate, |