II. TO CONVERT NUMBERS FROM A LOWER TO A HIGHER DENOMINATION. RULE.-1. Divide the given denomination by the number of times that it is contained in one of the next higher denomination, the sum is thus converted to the denomination immediately above it: thus, to convert 345 farthings into pence, divide by 4, the number of farthings in a penny, and the answer is 86 pence, and 1 farthing over. 2. If the conversion is to be carried further, divide the new denomination by the number of times that it is contained in one of the denomination above it: thus, to convert 86 pence into shillings, divide by 12, the number of pence in a shilling, and the answer is 7s. and 2 pence over; and so on, dividing each denomination in succession, till the sum has been converted to its highest required denomination. The remainders at each stage of the division are of the same denomination as the number from which they arise, and must be marked as such in the answer; thus, in the above example, the answer is 7 shillings, 2 pence, 1 farthing, or, 7s. 24d. Example 1.-In 3840 farthings, how many pounds? 4)3840 farthings. 12)960 pence. The farthings are first converted into pence, by dividing the number by 4, because there are four farthings in one penny: to convert pence into shillings, divide by 12, since twelve pence are one shilling and to convert shillings into pounds, divide by 20, as twenty shillings are one pound. Example 2.-Reduce 5863 farthings to pounds. The number of farthings, or pence, or shillings, 4)5863 farthings. to be brought to a higher denomination, is not 12)1465, always an exact number of that denomination; there may be a remainder after each division, and here, in bringing the farthings to pence, there is a remainder of 3-that is, of 3 farthings; again, in bringing the pence to shillings, 1 remains that is, I penny: and in bringing the shillings to pounds, there is a remainder of 2 shillings; we find thus that 5863 farthings make £6, 2s. 1ąd. All questions of reduction of money, weights, measures, &c., whether from a higher to a lower, or from a lower to a higher denomination, are wrought by these two rules of Reduction. Exercises in Reduction of Money. " 6. Reduce £73, 12s. 6d. to sixpences, Ans. 7. In 257 crowns, how many shillings? 8. In 324 guineas, how many pence? 9. In 836 pence, how many shillings? 10. In 9568 farthings, how many pounds? 11. Reduce 875 shillings to crowns, 12. In 83765 farthings, how many guineas? 13. Reduce to farthings, £17, 13s. 41d. " £63, 13s. 113d. £302, 5s. 94d. halfpence, £34, 14s. 7d. " " 15 tons. 300 cuts. 1200 grs. 28 9600 2400 33600 lbs. 201600 33600 Ans. 537600 oz. This is reduction from a higher to a lower denomination, and is done by multiplying. The tons are first to be reduced to hundredweights, and are multiplied by 20, because there are 20 cwts. in one ton; the cwts. are then brought to quarters by multiplying by 4; the quarters to pounds by multiplying by 28; and, lastly, the pounds to ounces, by multiplying by 16. We find, therefore, that in 15 tons there are 300 cwts., or 1200 qrs., or 33600 lbs., or 537600 ounces. Example 2.-Reduce 7 tons 8 cwt. 2 qrs. 15 lbs. to pounds. Example 3.-Convert 54659 lbs. to tons. This is reduction from a lower to a higher denomination, and is done, by dividing. The pounds are divided by 28, to bring them to quarters, since there are 28 lbs. in one quarter; the answer is 1952 quarters, and 3 lbs. over. The quarters are now divided by 4, to bring them to cwts.; the answer is 488 cwts., and no remainder. The cwts. are now divided by 20, to make tons, and the answer is 24 tons, and 8 cwts. over. We find, thus, that in 54659 lbs. there are 24 tons 8 cwts. 0 qrs. 3 lbs. Exercises in Avoirdupois Weight. 1. In 8 tons 7 cwt., how many lbs. ? 2. In 3 cwts. 2 qrs. 13 lbs., how many ounces? 3. Reduce 7865 lbs. to tons. Ans. 18704 lbs. " 6480 oz. Ans. 3 tons 10 cwts. 0 qrs. 25 lbs. 6. 735 tons 12 cwts. 3 qrs. to lbs. Ans. 1647828 lbs. 7. Bought 15 chests of tea, which weighed each 13 cwts. 2 qrs. 17 lbs. How many lbs. were there in the 15 chests? Ans. 22935 lbs. 8. In a hogshead of sugar, weighing 13 cwts. 2 qrs. 17 lbs., how many lbs. ? Ans. 1529 lbs. 9. How many lbs. are there in 8375 ounces? Ans. 523 lbs. 7 oz. 10. The quantity of tea used in Great Britain is reckoned at about 36 millions of lbs. every year; how many tons is that? Ans. 16071 tons 8 cwts. 2 qrs. 8 lbs. Ans. 39536 lbs. 76123 ounces to cwts., Ans. 42 cwts. 1 qr. 25 lbs. 11 oz. 11. Convert 17 tons 13 cwts. of sugar to lbs. 12. Troy Weight. Example 1.-Reduce 3 lbs. 5 oz. 14 dwts. 16 grs. to grains. Example 2.-Reduce 20032 grains to lbs. Grains 20 This is just the reverse operation of 24) 20032 (834. 16 the former, and is done by division. 192 12)41.14 The grains are divided by 24, to bring them to dwts., and the result is 834 dwts. 83 lbs. 3.5. 14. 16 and 16 grains. The dwts, divided by 20, 72 112 96 16 gives 41 oz. 14 dwts. Finally, the oz. divided by 12, gives 3 lbs. 5 oz.; to this annex the other remainders, and the answer is 3 lbs. 5 oz. 14 dwts. 16 grs. Exercises in Troy Weight. 1. In 4 lbs. 7 oz. of gold, how many ounces? Ans. 7 oz. 16 dwts. 21 grs. 3. In 7 lbs., how many ounces, pennyweights, and grains? Ans. 84 oz., or 1680 dwts., or 40320 grs. 4. Reduce 84627 grains to lbs. Ans. 14 lbs. 8 oz. 6 dwts. 3 grs. 8 oz. 13 dwts. to grains, Ans. 4152 grains. 5. 6. 1 dozen silver table-spoons weighs 976 pennyweights, how many pounds do they weigh? Ans. 4 lbs. O oz. 16 dwts. 76 yards 2 feet 7 inches to inches, 4. In 847365 yards, how many miles? Ans. 1880 perches. " 2767 inches. Ans. 2134 yds. 2 ft. 6 in. 481 miles 805 yds. 14 miles 380 yds. 1 ft. how many yards? Ans. 153864 yards. 6. In 87 miles 3 furlongs 15 perches 2 yards, 3. In 56 yards 2 qrs. 3 nails, how many nails? 4. In 7463 nails, how many yards? Ans. 13376 nails. Ans. 466 yds. 1 qr. 3 nails. 5. In 367 English ells, how many yards? 6. In 534 yards, how many ells English? Square Measure. " 427 ells 1 qr. 1. Reduce 276 acres 3 ro. 17 per. to yards, Ans. 13399844 sqr. yds. 4785694 square inches to square yards, Ans. 3692 yds. 5 feet 142 inches. 4. In a field containing 67654 square yards, how many acres? Ans. 13 acres 3 roods 36 per. 15 yds. 5. In a room 25 feet long by 18 feet broad, how many square yards? Ans. 50 square yards. Cubic Measure. 1. In 1259712 cubic inches, how many cubic yards? Ans. 27 yds. 2. In 235 cubic yards, how many cubic inches? Ans. 10905160 inches. 3. In 2280 cubic feet, how many tons of shipping? Ans. 57 tons. 4. How many solid yards in 391256 solid inches? Ans. 8 yds. 10 ft. 728 in. Liquid Measure of Capacity. 1. Reduce 875 gallons to pints, 187564 gills to gallons, 2. " Ans. 7000 pints. Ans. 5861 galls. 1 quart 1 pint. 3. In 76854 pints, how many gallons? 4. In 6 hogsheads, how many quarts? . Grain Measure, or Dry Measure of Capacity. 1. Reduce 56 quarters 5 bushels to pecks, Ans. 1812 pecks. 7684 pecks to quarters, 3. In 79 quarters 3 bushels pecks 1 gall., Ans. 240 qrs. 1 bush. how many gallons? Ans. 5085 gallons. " 20736 pecks. 4. In 648 quarters of wheat, how many pecks? Time. 1. Reduce 26 days 7 hours to minutes, 2. Ans. 37860 min. " 447300 sec. 5 days 4 hours 15 minutes to seconds, 3. In 876543 days, how many years? Ans. 2401 years 178 days. 4. In 17 weeks 3 days 7 hours, how many hours? Ans. 2935 ho. 5. How many hours has a boy lived who is 9 years and 15 weeks old? Ans. 81144 hours. 1. How many pounds in 78543 fourpences? "1 58604 lbs. Ans. 148 lbs. 10 oz. 6 dwts. 4. In 23 miles 2 fur. 219 yds., how many feet? 5. How many yards in 78325 nails of cloth ? 6. In 73926 inches, how many miles ? Ans. 4895 yds. 1 qr. 1 nl. Ans. 1 m. 1 fur. 73 yds. 1 ft. 6 in. 7. How many poles in 76 acres 1 rood 39 poles of land? Ans. 12239 poles. S. In 56 gallons 3 pints of water, how many gills? Ans. 1804 gs. 9. How many pecks in 208 quarters 3 bushels of wheat? Ans. 6668 pecks, 10. If a steamer sail 240 nautical miles in 24 hours, how many imperial miles is that per hour? |