7. 1210 yards of shalloon, at 2s. 2d. per yard. CASE II. Ans. 1311. Is. 8d, If the multiplier cannot be produced by the multiplication of small numbers, find the nearest to it, either greater or less, which can be so produced; then multiply by the component parts as before; and for the odd parts, add or subs tract according as is required. EXAMPLES. 1. 17 elis of holland, at 7s. 8-d. per ell, 1 7s. 8d. 2. 23 ells of dowlas, at Is. 6d. per ell. Ans. 11. 15s, 5d, 3. 46 bushels of wheat, at 4s. 74d. per bushel. Ans. 10l. IIS. 9-d. 4. 59 yards of tabby, at 7s. 10d. per yard. Ans. 231. 2s. 2d. 5. 94 pair of silk stockings, at 12s. 2d. per pair. 6. 117cwt. of Malaga raisins, at 11. 2s. 3d. per cwt. Ans. 571. 3s. 8d. Ans. 130l. 3s. 3d. I 2 Vds. qr. nls. T. hhd. gal. pt. W. qr. bu. pe. 7 7 COMPOUND DIVISION, Compound Division teacheth to find how often one given number is contained in another of different denominations, RULE.** 1. Place the numbers as in simple division. 2. Begin at the left hand, and divide each denomination by the divisor, setting the quotients under their respective dividends, 3. But if there be a remainder, after dividing any of the denominations except the least, find how many of the next lower denomination it is equal to, and add it to the num ber, if any, which was in this denomination before; then divide the sum as usual, and so on, till the whole is finished. The method of proof is the same as in simple division. EXAMPLES * To divide a number consisting of several denominations, by any simple number whatever, is evidently the same as dividing all the parts or members, of which that number is composed, by the same simple number. And this will be true, when any of the parts are not an exact multiple of the divisor: 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 251. 12s. 3d. divided by 9, will be the same as 181. 144s. 99d. divided by 9, which is equal to 21. 16s. 11d. as by the rule; and the method of carrying from one denomination to another is exactly the same. EXAMPLES OF MONEY. 1. Divide 2251. 2s. 4d. by 2. 2)2251. 2s. 4d. 1121. 115. 2d. the quotient. If the divisor exceed 12, divide continually by its com ponent parts, as in simple division. EXAMPLES. 1. What is cheese per cwt, if 16cwt, cost 301. 18s. 8d.? 2. If 20cwt. of tobacco comes to 1201, Ios. what iş that per cwt. ? 3. Divide 571. 3s. 7d. by 35. 4. Divide 851. 6s. by 72. 5. Divide 311. 2s. 10d. by 99. Ans. 61. 6d. Ans. 11. 125. 8d. Ans. 11. 3s. 8-d. Ans. 6s. 3-d. Ans. 3s. 4-d. 6. At 181. 18s. per cwt, how much per lb. ? CASE II, If the divisor cannot be produced by the multiplication of small numbers, divide it after the manner of long division. EXAMPLES. 1. Divide 231b. 7oz. 6dwt. 12gr. by 7. Ans. 3lb. 4oz. gdwt. 12gr. 2. Divide 131b. 1oz. 2dr. Iogr. by 12. Ans. Ilb. 1oz. 2sc. Iogr. 3. Divide 106Icwt. 2qrs. by 28. Ans. 37cwt. 3qrs. 18lb. 4. Divide 375mls. 2 fur. 7pls. 2yds. 1ft. 2in. by 39. Ans. gmls. 4fur. 39pls. 2ft. 8in. 5. Divide 571yds. 2qrs. Inl. by 47. Ans. 12yds. 2nls. 6. Divide 120L. 2qrs. ibu. 2pe. by 74. Ans. 1L. 6qrs. ibu. 3pe. 7. Divide 120mo. 2w. 3d. 5h. 20' by 111. Ans. Imo. 2d. 10h. 12. DUODECIMALS. DUODECIMALS. DUODECIMALS are so called because they decrease by twelves, from the place of feet toward the right hand. Inches are sometimes called primes, and are marked thus'; the next division, after inches, is called parts, or seconds, and is marked thus " ; the next is thirds, and marked thus ; and so on. Duodecimals are commonly used by workmen and artificers in casting up the contents of their work. MULTIPLICATION of DUODECIMALS ; or, CROSS MULTIPLICATION. RULE. 1. Under the multiplicand write the same names or denominations of the multiplier; that is, feet under feet, inches under inches, parts under parts, &c. 2. Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write each result under its respective term, observing to carry an unit for every 12, from each lower denomination to its next superior. 3. In the same manner multiply every term in the multiplicand by the inches in the multiplier, and set the result of each term one place removed to the right of those in the multiplicand. 4. Proceed in like manner with the seconds and all the rest of the denominations, if there be any more; and the sum of all the lines will be the product required. Or |