21. Reduce, 31, 34 and 34. 22. Reduce 3, 13, 27 and 36. 23. Reduce, 4, 3, 25 and 27• 24. Reduce, 15 and 17. NOTE 2. - The first clause of Rule 2 is omitted by many authors, but its necessity is apparent from Ex. 25. Reduce, and to equivalent fractions having the least common denominator. Disregarding the first clause of the rule, we find 72 to be the least common multiple of the denominators, and the fractions, §, and, reduce to, and 3; but, regarding the first clause, we have §, and which have a common denominator less than 72. 12 NOTE 3. 36 2 , and 9 12, 12 and 12, Ans., and . - In this and the following cases, each fraction should, if necessary, be reduced to a simple form before applying the rule. 34 31. Reduce of and to a common denominator. 5층 34 = 51 24 ÷ 4 = 159; but 7 and 191814 and 1884, Ans. and 53 to fractions having a common denomi 7 CASE 10. ། 134. As 1 penny is equal to 4 farthings, so any fraction of a penny is 4 times as great a fraction of a farthing; e. g. d. #qr., d. #qr., etc. Hence, = To reduce a fraction of a higher denomination to one of a lower, RULE. Multiply the fraction by such numbers as are necessary to reduce the given to the required denomination. Ex. 1. Reduces. to the fraction of a farthing. s. (=d. X 12) = 3d. (= fqr. X 4) = 28qr., Ans.; or, 3. Reduce of a rod to the fraction of a barleycorn. 4. Reduce of a pound Troy to the fraction of a grain. Ans. 336. 5. Reduce of a pound Apothecaries' weight to the fraction 9. Reduce yd. to the fraction of an inch, cubic measure. 10. Reduce 11. Reduce sign to the fraction of a second. sq. m. to the fraction of an inch. 12. Reduce 1m. to the fraction of a link. 13. Reduce 114400wk. to the fraction of a second. 14. Reduce acres to the fraction of a square yard. 15. Reduce 2 yd. of cloth to the fraction of an inch. 16. Reduce circ. to the fraction of a second. CASE 11. 135. In 15 barleycorns there is only of 15 inches, so in of a barleycorn there is only of of an inch; in & of a peck there is but of of a bushel, etc. Hence, To reduce a fraction of a lower to a fraction of a higher denomination, RULE.-Divide the given fraction by such numbers as are required to reduce the given to the required denomination. Ex. 1. Reduce 28qr. to the fraction of a shilling. 28qr. (28d. 4) = 3d. (= fs. 12)=6s., Ans.; or, 28 7 3 X 4 X 12 ÷ = 368., Ans. as before. 2. Reduce 448oodr. to the fraction of a ton. 44800 2800 175 7 3 × 16 × 16 × 25 × 4 × 20 7 = tons, Ans. 240 3. Reduce 1982b. c. to the fraction of a rod. 4. Reduce 336gr. to the fraction of a pound Troy weight. Ans. 5. Reduce 336gr. to the fraction of a pound Apothecaries' weight. 6. Reduce 1282sec. to the fraction of a day. 7. Reduce 32pt. to the fraction of a bushel. 8. Reduce gills to the fraction of a gallon. 9. Reduce 31404c. in. to the fraction of a yard. 10. Reduce 1440sec. to the fraction of a sign. 11. Reduce 12043468800sq. in. to the fraction of a mile. 12. Reduce 153000 links to the fraction of a mile. 13. Reduce sec. to the fraction of a week. 14. Reduce 3872yds. to the fraction of an acre. 15. Reduce in. to the fraction of a yard. 16. Reduce 432092sec. to the fraction of a circumference. To reduce a fraction of a higher denomination to whole numbers of lower denominations, . RULE.-Reduce the given fraction to a fraction of the next lower denomination by Case 10; then, if the fraction is improper, reduce it to a whole or mixed number by Case 6. If the result is a mixed number, reduce the fractional part of it to the next lower denomination, as before, and so proceed as far as desirable. NOTE.-If, at any time, the reduced fraction is proper, there will be no whole number of that denomination. Ex. 1. Reduce of a shilling to pence and farthings? 11s. (d. 12)=d. 5d., and Jd. (=qr. 4)=2 qr. .. 11s. 5d. +2qr., Ans. = 2. Reduce of a furlong to rods, yards, etc. again, hyd. (= ¿ft. × 3) = 3ft. = 14ft.; and, finally, ft. (= in. × 12) = 6 in. ; ..fur. 9rd. Oyd. 1ft. 6in., Ans. 3. What is the value of of an acre; Ans. 2r. 5rd. 10yd. Oft. 108in. 4. What is the value of of a pound Troy? 5 5. What is the value of of a pound, Apothecaries' weight? lb., Avoirdupois, to ounces and drams. 6. Reduce 7. Reduce 8. Reduce 9. Reduce 10. Reduce 11. Reduce 7 of a mile to furlongs, chains, etc. of a cord to cord feet, cubic feet, etc. of a yard to quarters, nails, etc. of a gallon to quarts, pints, etc. bush. to pecks, quarts, etc. 12. Reduce of a Julian year to lunar months, etc. 13. Reduce circ. to signs, degrees, etc. 14. Reduce 15. Reduce 24 of a league to miles, furlongs, etc. of a ton to cubic feet and inches. 16. Reduce of a civil year (365 days) to days, etc. 17. Reduce 2878lb. to ounces, drams, scruples, etc. 18. Reduce circ. to signs, degrees, etc. 77 CASE 13. 137. 3 farthings are the same as of a penny; again, 6d. = 25qr., and 1s. = 48 qr.; .. 6d. and 1qr. +1qr. Hence, = To reduce whole numbers of lower denominations to the fraction of a higher denomination, RULE 1.-Reduce the given quantity to the lowest denomination it contains, for a numerator; and reduce a unit of the higher denomination to the same denomination as the numerator, for a denominator. Ex. 1. Reduce 5d. and 2qr. to the fraction of a shilling. 5d.2qr.22qr., and 1s. = 48qr.; .. 5d.2qr.338.148., Ans. 2. Reduce 9 rods, 1 foot and 6 inches to the fraction of a fur |