4. Reduce .742cwt. to quarters, etc. Ans. 2qr. 24lb. 3oz. 3.2dr. 5. Reduce .9625bu. to pecks, etc. Ans. 4da. 19hr. 30min. 7. Change £.89 to shillings, etc. Ans. £8 15s. 8d. 1.6far. 10. What is the value of 15.9375cwt.? Ans. 15cwt. 3qr. 18lb. 12oz. CASE V. ART. 197. To reduce a fraction of a LOWER denomination to another of a HIGHER denomination. Ex. 1. Reduce & of a gallon to the fraction of a hogshead. Analysis. This question is just the same as if we had asked, “What part of a hogshead is § of a gallon?" Since 63 gallons=1hhd., then 1 gallon is of 1 hogshead; and of a gallon is as much = 54 of a hogshead; and of a gallon will be 5 times as much of a hogshead. = 554 2. What part of a mile is of a yard? Ans. hhd. Analysis. Reducing 1 mile to yards, we have 1760 yards. Then 1 yard is 176 of a mile; and of a yard is as much = = 150 of a mile; and of a mile will be 7 times as much 15940 of a mile. Ans. 150mi. The above example might have been exhibited under the form of a series of Equations, thus: EXAMPLES. 3 Reduce & of a pint to the fraction of a bushel. 4. What part of a shilling is of a farthing? Ans.bu. Ans. 8. 5. What part of a pound, Troy, is of a dwt.? Ans. 14lb. Ans. 172gda. of a pound? Ans. 7750T. 6. What part of a day is § of a minute? 7. What fraction of a ton is 8. What fraction of a pound sterling is of a penny? Ans. £to 9. What part of an acre is of a square yard? CASE VI. Ans. A. ART. 198. To reduce a fraction of a HIGHER denomina tion to another of a LOWER denomination. Ex. 1. Reduce 19ʊ of a mile to the fraction of a yard. Analysis. This question is the same as to ask, “What part of a yard is of a mile?" Reducing 1 mile to yards, we have 1760 yards. Then ' of a mile is the same as 1980 of 1760 yards 1780yd. = 8yd. Ans. gyd. 2. Reduce 1728 of a pound sterling to the fraction of a penny. = but Analysis. Reducing 1 pound to pence we have 240 pence Then 1728 of a pound is the same as 172 of 240 pence; (728 of 240 pence is 240 of a penny, and 172 1728 nuch = 1688 of a penny £1 = 35 of a penny. OPERATION. = 240d. £1728 = 14208d. 1680d. =ffd. is 7 times as Ans. d. EXAMPLES. 3. Reduce of a bushel to the fraction of a pint. Ans. pt. 4. Reduce of a hogshead to the fraction of a quart. Ans. qt. 5 Reduce of a pound, Troy, to the fraction of a dwt. Ans. dwt. 6. Reduce of a yard to the fraction of an inch. Ans. in 7. Reduce of an acre to the fraction of a sq. rd. Ans. 5 sq. rd. 8. Reduce of a day to the fraction of a minute. Ans. min. 9. Reduce of a shilling to the fraction of a farthing. Ans. far. ADDITION OF DENOMINATE FRACTIONS. ART. 199. Ex. 1. What is the sum of 3 of a pound, Troy, of an ounce and of a pennyweight? Analysis. In their present shape we cannot add them. We may, however, reduce them to integral quantities of lower denominations, and then add them. By CASE III., of a pound is equal to 9oz. 6dwt. 16gr., † of an ounce is 6dwt. 16gr., and of a pennyweight is 21 grains. Hence, the question is reduced simply to finding the sum of 9oz. 6dwt. 16gr., 6dwt. 16gr, and 21 grains. The process may be exhibited thus: 2. What is the sum of .3675 of a day, .875 of an hour and .45 of a minute? Analysis. By CASE IV. (Art. 196), .3675da. may be reduced to 8hr. 49min. 12sec., .875hr. may be changed to 52min. 30sec., and .45min. to 27sec., after which the several quantities may be added according to the Rule for Compound Addition. The whole process may be thus shown: 7. Add £.3125 .5625s. and .75d. Ans. 6s. 10d. 2far. 3. Add .375hhd. .4375gal. and .875qt. Ans. 24gal. 1qt. Opt. 1gi. JUBTRACTION OF DENOMINATE FRACTIONS. ART. 200. The preliminary operations required in the Subtaction of Denominate Fractions are precisely the same with those required in the Addition of those fractions. We first reduce the fractions to whole numbers of lower denominations, and then subtract as in Compound Subtraction. ARTICLE 201. The sun in his apparent daily course from east to west passes over 360° of longitude in a day, or 24 hours; then, in 1 hour, he passes over 4 of 360°,360° = When the sun is directly over the meridian of any given place, it is noon at that place, and to all places east of this the time is past noon, and to those west of it it is before noon, |