2. Reduce to a fraction of the same value, whose numerator shall be 1. Ans. . 3. Reduce 48 to a fraction of the same value, whose numerator shall be 6. Ans.. 4. Reduce to a fraction of the same value, whose numerator shall be 75. Ans. Too 75 CASE X. To reduce a mixed fraction to a single one. RULE 1. When the numerator is the integral part. (1) Multiply the numerator of the fraction by the denominator of its fractional part, and to the product add (or take in) the numerator of its fractional part, for a numerator. (2) Multiply the denominator of the fraction, by the denominator of its fractional part, for a denominator. RULE 2. When the denominator is the integral part, then, (1) Multiply it by the denominator of its fractional part, and to the product add (or take in) the numerator of its fractional part for a denominator. (2) Multiply the numerator of the fraction by the denominator of its fractional part for a numerator. CASE XI. To find the proper quantity of a fraction in the known parts of an integer. RULE. Multiply the numerator by the known common parts of the integer, and divide the product by the denominator. EXAMPLES. 1. Reduce ofa pound (money) to its proper quantity. 2. Reduce 49 of a shilling, to its proper quantity. 18 43)216(5d. Ans. 215 1 3. Reduce of a pound Troy, to its proper quantity Ans. 9 ounces. 4. Reduce of a ton to its proper quantity. Ans. 15 cwt. 5. Reduce of £5 9, to its proper quantity. 6. Reduce 7. Reduce £59 6 7)32 14 £4 13 5 Ans. of an Ell English, to its proper quantity. Ans. 1 yard. of a tun of wine to its proper quantity. Ans. 1 hogshead, 49 gallons. 8. Reduce of 24 hours, to its proper quantity. Ans. 12h. 55 m. 23 seconds, T quantity. 10. Reduce 9. Reduce of a pound Avoirdupois, to its proper Ans. 8oz. 14dr. 3. of a mile, to its proper quantity. Ans. 4fu. 22po. 4yds. 2ft. lin. 2bc. 4. of a barrel of beer to its proper quan、 Ans. 31 gallons. 11. Reduce tity. 12. Reduce of a chaldron of coals, to its proper tity. tity. quantity. Ans. 13 bushels. 13. Reduce of 10C. 1qr. 121b. to its proper quan. Ans. 8C. 1qr. 25lb. loz. 7 dr. 14. Reduce of a yard of cloth, to its proper quan. Ans. 3qrs. 2na. of a hogshead Ans. 12 gals. of a barrel of Ans. 6 gals. of an acre of 15. What is the proper quantity of of beer? 16. What is the proper quantity of ale ? 7 Ans. 1 rood, 30 rods. 17. What is the proper quantity of land? 18. What is the proper quantity of Troy? 19. Reduce of a dollar to its proper of a pound Ans. 9oz. quantity. Ans. 60 cents. 20. What is the proper quantity of of 180 dollars. Ans. $140. CASE XII. To reduce any given quantity to the fraction of any greater denomination of the same kind. RULE 1. Reduce the given quantity to the lowest term mentioned, for a numerator. 2. Reduce the integral part to the same term, for a denominator. NOTE 1. If there be a fraction given with the said quantity, add it to the numerator of the fraction required. NOTE 2. This case and Case XI. prove each other. EXAMPLES. 1. Reduce 13s. 4d. to the fraction of a pound (money.) 13 4 12 160 1 20 20 12 240 Ans. 140. 2. Reduce 54 pence, to the fraction of a shilling. 43 213 216 Ans. 18=43. 3. Reduce 9 ounces Troy, to the traction of a pound. Ans. 4. Reduce 15. cwt. to the fraction of a ton. Ans. 5. Reduce £4 13 54 to the fraction of £59. 5.9 4 13 54 6. Reduce 1 yard to the fraction of an Ell English. Ans.. 7. Reduce 1 hogshead, 49 gallons, to the fraction of a ton. Ans.. 8. Reduce 12 h. 55 m. 23 sec. to the fraction of a natural day. Ans. .9. Reduce 8oz. 14drs., to the fraction of a pound, Avoirdupois. Ans. Ans. 4. 10. Reduce 4 fu. 22 po. 4 yds. 2 f. 1 in. 2 bc., to the fraction of a mile. 11. Reduce 31 gallons of beer to the fraction of a barrel. Ans. . 12. Reduce 13 bushels of coals to the fraction of a chaldron. 13. Reduce 8C. 1qr. 25lb. 1oz. 7 of 10C. 1qr. 12lb. 14. Reduce 3 qrs. 2 na. of cloth, yard. Ans. dr. to the fraction Ans.. to the fraction of a Ans.. 15. Reduce 12 gallons of beer to the hogshead? 16. Reduce 6 gallons of ale to the barrel. 17. Reduce 1 rood, 30 rods of land, to the fraction of an acre. Ans. T 18. Reduce 9 ounces Troy, to the fraction of a pound. Ans. 108 19. Reduce 60 cents to the fraction of a dollar. 20. Reduce 140 dollars to the fraction of 180 dollars. Ans. 140 180 14 ADDITION OF VULGAR FRACTIONS. Reduce the fractions (given to be added together) to their lowest terms by Case I. If they are of different denominations, reduce them to a common denominator by Case II. Add all the numerators together, for a new numerator, under which write the common denominator. NOTE. This rule may be proved by subtraction, when only two fractions are given to be added. |