RULE. Find the equivalent value of each denomination separately, (as in the previous examples,) beginning with the highest, and their sum (the sum of these equivalents) will be the ANSWER. EXAMPLES. 1. Reduce 8£. 17s. 6d. 3far. to farthings. Thus: 8£. 8 times 960far. to 7 680 farthings 17s. 6d. = 6 times 3far. are 66 Hence, 8£. 17s. 6d. 3far. = 2. Reduce 56lbs. 7ozs. 12dwts. 18 grains, to grains. 56lbs. 56 times 5760grs.=to 3 2 2 560 grains. 7 times 480grs.=to 3360 12 times 24grs. to Thus: 7ozs. 12dwts. 18grs. are =to 288 Hence, 56lbs. 7ozs. 12dwts. 18grs.= 326226 grs. 3. Reduce 7Ts. 9cwts.* 3qrs. 23lbs. 14ozs. to drams. Ans. 258048 4. In 7s. 53s. 63s. 29s. 15 grains, how many grains? 7 times 5760grs.to 4 0 3 20 grains. 7bs. 256=to 5888 16 to 224 Hence, 4299744 drs. Ans. * Should be pronounced Hundreds weight when there are more than ONE. 43135 grains. Ans. 5. In 25bus. 3pks. 7qts. 1pt., how many gills? 25bus. 25 times 256 gills.to 6 4 00 gills. 3 times 64 gills. to 192 Thus: 3pks. 7qts. 7 times 1pt. = 1 time 8 gills.=to Hence, 25bus. 3pks. 7qts. 1pt.= 6. In 9 tuns, 1pi. 1hhd. 28gals. 2qts. 9Ts. 66 56 66 6652 gills. Ans. = 9 times 8064 gills 1pt., how many gills? to 7 2 5 7 6 gills. 7. In 5cirs. 20degs. 8 miles, 3 furlongs, 30 poles, 4 yds., inches? Thus: how many 5cirs. 5 times 1585267200ins. to 7 9 2 6 3 3 6 0 0 0 ins. Hence, 5cirs. 20degs. 8miles, 3 furlongs, 30 poles, 4 yards, 8. In 7 ells E., 8 yards, 10 ells F., 12 ells H., 3ers. 2 nails, how many inches? 7es.E. 8yds. 10es.F. 12es.H. 3qrs. 2nas.= 9. In 12 revolutions, 20 signs, 15 degrees, 45 minutes, 57 seconds, how many seconds? Thus: 12 revs. 12 times 1296000" to 1 5 5 5 2000 seconds. 10. In 50 years, 9 months, 3 weeks, 5 days, 20 hours, how many seconds? 50 years Thus : 50 times 31557600sec. to 1577880000 secs. In the preceding examples, we make the number representing each denomination of the quantity to be reduced, the multiplier, and the equivalent value of a UNIT of the mutliplier, gives the multiplicand, on the PRINCIPLE, that Two is twice one, and also twice the equivalent of ONE. To explain this, we will go through the process of reducing 4£. 8s. 10d. 3qrs. to farthings; thus, first, if 1£=960 farthings, then 4£s. will 4 times 960 farthings to 3840 farthings; second, if 1 shilling 48 farthings, then 8 shillings will 8 times 48 farthings to 384 farthings; third, if 1 penny = 4 farthings, then 10 pence will = 10 times 4 farthings to 40 farthings; and, lastly, 3840 far. +384far. +40far+3 farthings are to 3267 farthings. ANSWER. = = On the same principle, the pupil may furnish the answer to the following QUESTIONS FOR EXERCISE. 1. Reduce 6£. 7s. 8d. to pence. In 9£. 10s. 7d. 3qrs., how many farthings? Reduce 78£. 6s. 8d. to pence. 2. In 8lbs. 6ozs. 10dwts., how many penny weights? how many grains? Reduce 48lbs. 9ozs. 17dwts. 19grs. to grains. 3. In 9Ts. 12cwts. 3qrs. 20lbs. 8ozs., how many ounces? how many drams? In 27Ts. 19cwts. 25lbs, how many pounds? 4. 12 s. 83s. 53s., how many scruples? how many grains? In 16 s. 93s. 29s. 18 grains, how many grains? 5. Reduce 12bus. 3pks. 7qts. 1pt. to gills? In 327 bus. 1pk. 3qts. 2gills, how many gills? 6. Reduce 8 Tuns, 3hhds. 1 tierce, to gallons-in those gallons, how many quarts? pints? gills? In 20 puncheons of wine, how many tierces? 7. In 8 circles, how many miles? how many yards? In 7 degrees, 4 leagues, 16 miles, 3 furlongs, 6 poles, how many yards? how many feet? how many inches? 8. In 9sq. ms. 5As. 20sq. pls., how many square feet? how many square inches? 9. In 25 cubic yards, how many cubic inches? In 26 cords, 98 cubic feet, how many cubic feet-in those feet, how many cubic inches? 10. In 7 Tons of round timber, how many cubic feet? how many cubic inches? 11. Reduce 46yds. 3qrs. 3nas. to nails, and these nails to inches. In 25es. H. 2 qrs., how many nails? how many inches? In 17es. Fl. 1qr. 1na., how many nails? 12. Reduce 56s. 25°, 48', 57", to seconds. In 560revs. 8s. 20°, 36', 45", how many seconds? 13. In 25ys. 250das. 20hs. 48 ms., how many minutes? how many seconds? Reduce 9mos. 3wks. 5das. to hoursin those hours, how many minutes? When a lower denomination, is to be reduced to an equivalent value in a higher one, the plainest method is that already given on pages 139 and 140, observing to reduce the fraction (when any occurs,) to an equivalent value in the next lower denomination, the integers of which are retained, and the fraction (if any,) should be reduced to the next lower deno mination, as before, and so on till no fraction remains, as in the following. RULE. First. MULTIPLY the equivalent value of a UNIT, of the quantity to be reduced, in the highest denomination required by the question, by the quantity itself, and reduce the PRODUCT to a mixed number, retaining the INTEGER; then, Second. MULTIPLY the number which shows how many of the next lower denomination, are necessary to make a unit in the denomination last found, by the fraction of that denomination, and reduce the PRODUCT, (retaining the integers, (if any,) and multiplying by the fraction,) as before, this repeated till no fraction remains, and the several denominations, arranged in order, will give the DENOMINATE NUMBER sought, or the ANSWER. EXAMPLES. 1. Reduce 584620 farthings to an equivalent denominate number. 960 48 = 248 12 1 Thus, 1 farthing £. Now, first, if 1 far.=} of a £., then 584620 farthings will =584620 times of a £. 980 = to 584620 of a £. to 29231 of a £. to 608£., and 4 of a £. Second, if 1=20s., then 4 of a £. will =47 of 20s. to 240 of a s. to 235 of a shilling to 19 shillings, and of a shilling. Third, if 1s. = 12d., then will = of 12d. 12 to of a d. = to 7 pence. Hence, 584620 farthings, reduced to an equivalent denominate number, equals 608£. 19s. 7d., ANSWER, which has been found in exact accordance with the provisions of the Rule. of a s., 2. Reduce 63450 grains of silver, to an equivalent denominate number 4 of 12ozs. = to 1 Third, if 1 oz. = 20dwts., then 20dwts. = tog of a dwt. = to 1 of an oz. oz. will ounce of an of a dwt. = of a dwt. Fourth, if 1dwt = 24grs., then I of 3dwts., and 3 of a dwt. will |