8. 83 of 4 ac. 3 po. of 1 sq. mile + 13 of 3 r. 20 sq. yds. 9. (5 of 11) of 35° 36′ 25′′; (27%÷ 14 of 13) of 30°. of 1 lb. Troy + of 1 lb. Troy -3% of 1 lb. Avoirdupois (=7000 grains). 5 of 3 guineas 10. 11. of # of £1. 3s. 10d,; & of 1 ton + 2 of 3 qrs. — 11⁄2 of 7 cwt. 12. 2 of 15 h. 10′ 13′′ of 1 day, 12 h. 11′ 12′′. To Reduce a given Quantity to the Fraction of any other given Quantity of the same kind. 29. RULE.-Reduce both the given quantities to the same denomination, and the fraction required will have the number of units in the first quantity as numerator, and that of the second quantity as denominator. Ex. 1.-Reduce 3s. 8d. to the fraction of £1. NOTE.-It is always best to keep the denominations to which the given quantities are reduced as high as possible. Ex. 2.--Reduce of a moidore to the fraction of 21 guineas. of a moidore = (4 × 27)s., and 2 guineas = (2 × 21)s. × 27 2 × 21 × 27 1X27×2 5X21X7 Ex. 3.-Reduce 3 cwt. 23 qrs. to the fraction of 4 cwt. 141 qrs., and 4 cwt. 2 qrs. 4 lbs. = 4 cwt. 24 qrs. = 18+ qrs. Ex. IX. Reduce 1. 1s. 8d. to the fraction of £1; 7d. to the fraction of 10s. 2. 2s. 4d. to the fraction of 10s. 8d.; 1s. 74d. to the fraction of 3s. 44d. 3. 3 qrs. 15 lbs. to the fraction of 1 ton; 2 stones 10 oz. to the fraction of 3 cwt. 4. 3 lbs. avoirdupois to troy weight; 10 lbs. 3 oz. 4 dwt. troy to avoirdupois. 5. 3 quires, 10 sheets to the fraction of 2 3 ft. 8 in. to the fraction of 3 yards. reams, 3 quires; 6. 30° 3′ 12′′ to the fraction of a right angle (= 90°); 57° 16' 21" to the fraction of two right angles. 11. What fraction of his original income has a person left after paying a tax of 4d. in the £? 12. A garden roller is 2 ft. 6 in. wide, and it is rolled at the rate of 1 mile in 20 minutes: find in what fraction of a day a man will roll of an acre. To Find the Value of a Decimal of a Concrete Quantity. 30. RULE.-Multiply the given decimal by the number of units in the concrete quantity when expressed in terms of one denomination, and the integral part of the result will be the number of units of this denomination. Then multiply the decimal part of this denomination by the number of units connecting it with the next lower and the integral part will be units of this latter denomination, and so on, Ex. 1.-Find the value of ·325 of £3. 10s. = £3. 10s. 70s.; proceeding then according to rule, we have: Ex. 2.-Find the value of 546875 of 3 tons. 1. £375; £98125; £815625. 2. 416 of £3; 428571 of 6s. 5d.; 8.571428 of 3s. 0ąd. 3. 625 of 1 ton; 046875 of 3 tons; 4:39 of 1 cwt. 53 lbs. 4. 1.6671875 acres; 3475 rood; 076923 of 5 acres, 6 poles. 5. 2083 of 1 ream; 4583 quire; 383 of 3 reams, 12 sheets. 6. 3078125 pipe; 490625 tun; 37125 bushel. 7. Express in grains 142857 of 4 lbs. avoirdupois, and express the result in troy weight. 8. Express 10 oz. 3 dwt. 14 grs. as the decimal of 1 lb. avoirdupois. 9. What is the sum of 6 of 1 guinea, 083 of 1 crown, and 037 of £1. Os. 3d. To Reduce from one Denomination to the Decimal of another Denomination of the same kind. 31. RULE.-Bring the given quantity to the fraction of the proposed denomination, and reduce this fraction to a decimal, Ex. 1.-Reduce 3s. 3d. to the decimal of 8s. 1d. 5 X 13 and the fraction Hence 4 is the decimal required. Ex. 2.-Reduce 3 qrs. 21 lbs. to the decimal of 2 cwt. 3 qrs. 3 qrs. 21 lbs. and the fraction 185 15 X 7 44 X 7 Hence 3409 is the decimal required. 11. Ex. 3.-Reduce 18s. 81d. to the decimal of £1. •934375 934375 is the decimal required. The farthing is first reduced to the decimal of a penny, and the 8d. prefixed; then 8.25d. are reduced to the decimal of a shilling, and the 18s. prefixed; lastly, 18-6875s. are reduced to the decimal of £1. Ex. 4.-Reduce 3 qrs. 21 lbs. to the decimal of 1 ton. 21 3. 1. 12s. 6d., 10s. 7 d., 11s. 1d., 18s. 62d., each to the decimal of £1. 2. 13s. 0ąd., 10s. 84d., 9s. 6d., each to the decimal of 15s. 51d. 3. 7s. 8d. to the decimal of a guinea; and 3s, 24d, to the decimal of a moidore, |