" 4. In £5, 16s. 7., how many farthings? Ans. 5596 far 5. In £18 how many pence? 6. In £23, 9s., how many shillings? 7. In 17s. 2d. 3 far., how many farthings? 8. Reduce 5 lbs. 6 oz. Troy weight, to grains. 9. Reduce 13 lbs. Troy, to ounces. Ans. 31680 grs. 10. Reduce 4 lbs. 3 oz. Troy, to penny weights. 11. Reduce 15 oz. 6 pwts. 4 grs. Troy, to grains. 12. In 2 cwt. 3 qrs. 7 lbs. 4 oz. 3 drams, avoirdupois weight, how many drams? Ans. 72259 drams. 13. In 13 lbs. 4 oz. avoirdupois, how many ounces? 14. In 2 qrs. 17 lbs. avoirdupois, how many pounds! 15. In 6 lbs. 12 oz. avoirdupois, how many drams? 16. In 12 cwt. 1 qr. 6 lbs. avoir., how many ounces? 17. In 16 miles, how many rods? 18. In 28 rods and 2 feet, how many inches? 19. In 19 fur. 4 rods and 2 yds., how many feet? 20. In 25 leagues and 2 m., how many rods? 21. Reduce 14 yards cloth measure to quarters. 22. Reduce 21 yards 2 quarters to nails. 23. Reduce 17 yards 3 quarters 2 nails, to nails. 24. How many quarts in 23 gallons, wine meagare ? 25. How many gills in 30 gallons and 2 quarts? 26. How many gills in 63 gallons? 27. How many quarts in 41 hogsheads? 29. How many pints in 3 pecks and 2 quarts? REDUCING LOWER DENOMINATIONS TO HIGHER. 125. Ex. 1. Reduce 1920 farthings to pounds. Suggestion. First reduce the given farthings (1920) to pence, the next higher denomination, by dividing them by 4, because 4 far. make 1d. Next reduce the pence (480) to shillings, by dividing them by 12, because 12d. make 1s. Finally, re Operation. duce the shillings (40) to pounds, by dividing them by 20, because 20s. make £1. The answer is £2. That is, 1920 far. are equal to £2. Operation. 4)1075 far. 2. In 1075 farthings, how many pounds? Suggestion. In dividing the given farthings by 4, there is a remainder of 3 far., which should be placed on the right. In dividing the pence (268) by 12, 12)268d. 3 far. over, there is a remainder of 4d., which Ans. £1, 2s. 4d. 3 far. should also be placed on the right. In dividing the shillings (22) by 20, the quotient is £1 and 2s. over. The last quotient with the several remainders is the answer. That is, 1075 far. are equal to £1, 2s. 4d. 3 far. OBS. In the last two examples, it is required to reduce lower denominations to higher, as farthings to pence, pence to shillings, &c. The operation is exactly the reverse of that in Reduction Descending. 126. The process of reducing lower denominations to higher is usually called Reduction Ascending. It consists in successive divisions, and may with propriety be called Reduction by Division. QUEST.-125. Ex. 1. How are farthings reduced to pence? Why divide by 4? How reduce pence to shillings? Why? How shillings to pounds? Why? 126. What is reducing compound numbers to higher denominations usually called? Which of the fundamental rules is employed in Reduction Ascending ? 127. From the preceding illustrations we derive the following RULE FOR REDUCTION ASCENDING. Divide the given denomination by that number which it takes of this denomination to make ONE of the next higher. Proceed in this manner with each successive denomination, till you come to the one required. The last quotient, with the several remainders, will be the answer sought. 128. PROOF.-Reverse the operation; that is, reduce back the answer to the original denominations, and if the result correspond with the numbers given, the work is right. OBS. Each remainder is of the same denomination as the dividend from which it arose. (Art. 51, Obs. 2.) EXAMPLES. 3. In 429 feet, how many rods? Suggestion.-We first reduce the feet to yards, then reduce the yards to rods by dividing them by 5. (Art. 86.) Or, we may divide the given feet by 161, the number of feet in a rod, and the quotient will be the answer. We first reduce the rods back to yards, (Art. 84,) then reduce the yards to feet. The result is 429 feet, which is the same as the given number of feet. Or, we may multiply the 26 by 161, and the product will be 429. 4. Reduce 256 pence to pounds. Ans. £1, 1s. 4d. 5. Reduce 324 pence to shillings. QUEST.-127, What is the rule for reduction ascending? 128, How is reduction proved? Obs. Of what denomination is each remainder ? 6. Reduce 960 farthings to shillings. 8. In 265 ounces Troy weight, how many pounds? 9. In 728 pwts., how many pounds Troy? 10. In 548 grains, how many ounces Troy? 11. In 638 oz. avoirdupois weight, how many pounds? 12. In 736 lbs. avoirdupois, how many quarters? 13. In 1675 oz. avoirdupois, how many hundred weight? 14. In 1000 drams avoirdupois, how many pounds? 15. In 4000 lbs. avoirdupois, how many ons? 16. How many yards in 865 inches ? 17. How many rods in 1000 feet? 18. How many miles in 2560 rods? 19. How many miles in 3261 yards? 20. How many leagues in 2365 rods? EXAMPLES IN REDUCTION ASCENDING AND DESCENDING. 129. In solving the following examples, the pupil must first consider whether the question requires higher denominations to be reduced to lower, or lower denominations to higher. Having settled this point, he ill find no difficulty in applying the proper rule. FEDERAL MONEY. (ART. 88.) 1. In 3 dollars and 16 cents, how many cents? 3. In 245 cents, how many dollars? 10. In 61 dolls., 12 cts., and 3 mills, how many mills? STERLING MONEY. (ART. 90.) 11. Reduce £17, 16s. to shillings. 16. Reduce 2880 farthings to shillings. TROY WEIGHT. (ART. 91.) .19. In 7 lbs., how many ounces? 20. In 9 lbs. 2 oz., how many pennyweights? 21. In 165 oz., how many pounds? 22. In 840 grains, how many ounces? 23. In 3 lbs. 5 oz. 2 pwts. 7 grs., how many grains? 24. In 6860 grains, how many pounds? AVOIRDUPOIS WEIGHT. (ART. 92.) 25. In 200 oz., how many pounds? APOTHECARIES' WEIGHT. (ART. 9J.) 31. Reduce 45 pounds to ounces. LONG MEASURE. (ART. 94) |