CASE 11. Q. How do you find the proper quantity of a fraction in the known parts of an integer? A. Multiply the numerator by the common parts of the Integer, and divide by the denominator. EXAMPLES. 1 Reduce of a pound sterling to its proper quantity. Facit 13s 4d. 2 Reduce of a shil. to its proper quantity. Facit 5d.. 3 Reduce of 51 9s to its proper quantity. Facit 4l 13s 5d. . 4 Reduce 12 of a lb. troy to its proper quantity. Facit 9 oz. 5 Reduce of a ton weight to its proper quantity. Faeit 3C. Oqr. 81b. 9oz. 13dr. 44. 6 Reduce of a lb. of Avoirdupois to its proper quantity. Facit 80z. 14dr.. 7 Reduce of 10C 1qr. 12lb to its proper quantity. Facit &C 1qr 25lb loz. 7dr.. 8 Reduce of a mile to its proper quantity. Faeit 4 fur. 125 yards 2 feet, 1 in. 2 b. c. 4. 9 Reduce of a yard to its proper quantity. Facit 2 feet, 8in. 1 b. c. 43. 10 Reduce of an Ell English to its proper quantity. Facit 1 yard. of an Acre to its proper quantity. Facit 11 Reduce rood, 30 perches. of a ton of wine to its proper quantity. 12 Redace Facit 1 hhd. 49 gallons. 13 Reduce Facit 31 gals.. of a barrel of Beer to its proper quantity. 14 Reduce of a chaldron of coals to its proper quantity. Facit 13 bush. . 15 Reduce of a quarter of corn to its proper quantity. Facit 2 bush. i peck.. 16 Reduce of a day natural to its proper quantity. Facit 2 hours 55 min. 23 sec. 7. 17. Reduce of a month to its proper quantity. Facit 3 weeks, 1 day, 9 hours, 36 min. 18 What is the proper quantity of of yd. of cloth? Aus. 3 qrs. 2 na. 19 What is the proper quantity of 3 of a hhd. of beer? Ans. 12 gals., 20 What is the proper quantity of of a barrel of Ale? Ans. 6 gals. CASE 12. Q. How do you reduce any given quantity to the fraction of any greater denomination of the same kind? A. 1. Reduce the given quantity to the lowest term mentioned for a numerator. 2. Reduce the integral part of the same term for a denominator, and that will be the fraction required. Note 1. If there be a fraction given with the said quantity, let it be put to the numerator of the fraction required. 2. Cases 11 and 12 prove each other, EXAMPLES. 1. Reduce 13s 4d to the fraction of a pound sterling. Facit 1. 16 24 43 2. Reduce 5d to the fraction of a skilling. Facit §. 3. What part of 51 9s is 41 13s 5d ? Answer . 4. Reduce 9 oz. troy to the fract. of a lb. Facit 3lb. 5. Reduce 3C. 0qr 8lb 9 oz 13dr 43. to the fraction of a ton. Facit ton. 6. Reduce 8 oz 14dr to the fraction of a lb. avoirdupois. Facit lb. 7. What part of 10C. 1qr 12 lb. is 8C 1qr 25 lb 1 oz 7dr ? Answer, å 8. Reduce 4fur 125yds 2feet lin 2bc to the faction of a mile. Facit mile. 9. Reduce 2ft 8in 1bc to the fraction of a yard. eit yard. Fa 10. Reduce 1 yard to the fraction of an ell. Facit ell. 11. Reduce 1 rood, 36 poles to the fraction of an acre. Facit acre. 12. Reduce 1hhd 49 gals of wine to the fraction of a tun. Facit tun. 13. Reduce 31 gallons of beer to the fraction of a barrel. Facit barrel. 14. Reduce 13 bushels of coals to the fraction of a chaldron. Facit chaldron. 15. Reduce 2 bushels, i peck, of corn to the fraction of a quarter. Facit quarter. 16. Reduce 12hrs 55min 23sec to the fraction of a day natural. Facit day. 17. Reduce 3 weeks, 1d 9hrs 36mins to the fraction of a month. Facit month. 18. Reduce 3qrs 2na to the fraction of a yard. Fa. 7 yd. 19. Reduce 12 gallons of beer to the fraction of a bhd. Facit 20. Reduce 6 gallons of ale to the fraction of a barrel. Facit barrel. 21. Reduce 13 hours, 30 minutes, to the fraction of a day. Facit 10 Q. 1440 OF ADDITION OF VULGAR FRACTIONS. How are Vulgar Fractions added together? A. 1. Reduce the given fraction to a common denominator. 2. Add all the numerators together for a new numerator; under which subscribe the common denominator. Note. This rule is proved by Subtraction, when two fractions only are given. EXAMPLES. 1 Add and together. Facit 18 68 2 Add and and together. Facit 26§ 7 Add 124 and 34 and 44 together. Facit 20 22 224 8 Add 67 of 8 and of and 7 together. Fa. 131 Note. In order to find the following facits, the fractions given must be reduced to their proper quantities by case 11 in Reduction, and then add as in addition of whole numbers. 9 Add of a pound to of a shilling. Facit 18s 3d. 10 Add of a penny to of a pound. Fa. 28 4d 1qr. 11 Add of a pound troy to, of an ounce. Facit 6 oz 17 Add of a week, 4 of a day, and 1⁄2 of an hour together. Facit 2 days 14 hours 18 Add of a yard, of a foot, and of of a mile together. Facit 1540 yards, 2 feet, 9 inches. OF SUBTRACTION OF VULGAR FRACTIONS. "How are Vulgar Fractions subtracted? A. 1. Reduce the given fractions to a common De-Bominator. 2 Subtract the lesser Numerator from the greater, and place that difference over the common Denominator. 3 Wren the lower fraction is greater than the upper, subtract the numerator of the lower fraction from the denominator, and to that difference add the upper numerator, carrying to the units place of the lower whole number. Note. This Rule is proved by Addition. 6 From 700' Facit 8i 1. Facit 95 %. of 76 take of 21. 110 7 From 71 Facit 9 ༡ 12. take of of. Facit 18. take 17. Facit 70 23. 8 From 14 take of 19. Facit 172. Note. In order to find the following Facits, the Fractions given must be reduced to their proper quantities by Case 11, in reduction, and then subtracted, as in Subtraction of whole Numbers. 9 From of a pound take 3 of a shilling Facit 9s 3d. 10 From of a shilling take of a penny. Facit 5d 4. 11 From of an oz. take 7 of a dwt. Facit 11 dwts. 3 grs. 12 12 From of a Cwt. take of a pound. Facit 1 qr. 27 lb. 6 oz. 10 dr. 8 13 From of a league take 2 furlongs, 16 poles. 17 of a mile. Facit 1 mile 14 From 1 ell take of a qr. Facit 1 yard, Oqr. Ina.. 15 From of a hhd. of beer take 1 gal. Facit 12 gal. 16 From of a chaldron take 3 of a bushel. Facit 17 bushels, 1 peck. 17 From 7 weeks take 9 days. Facit 5 weeks, 4 days, 7 hours, 12 minutes. 18 From 4 days, 7 hours take 1 day, 9 hours, T. Facit 2 days, 22 hours 4. OF MULTIPLICATION OF VULGAR FRACTIONS. Q. How are Vulgar Fractions multiplied? A. 1 Prepare the given Numbers (if need be) by the rules of Reduction. 2 Multiply all the given numerators for a new numerator, and all the denominators for a new denominator. Note. When any Number, either whole or mixt, is multiplied by a Fraction, the Product is always less than the Multiplicand, in the same Proportion as the multiplying Fraction is less than 1 or an Unit. OF DIVISION OF VULGAR FRACTIONS. Q. How are Vulgar Fractions divided? A. 1. Prepare the Numbers given (if need be) by the Rules of Reduction. 2. Multiply the Denominator of the Divisor into the Numerator of the Dividend, for a new Numerator; and the Numerator of the Divisor into the Denominator of the Dividend, for a new denominator. Note. 1. When the dividend is greater than the Divisor, the Quetient will be greater than the Dividend: But when the Dividend is less than the Divisor, then the Quotient will be less than the Dividend, and in the same Proportion as an unit is greater or less than the dividend Fraction. 2. Multiplication and Division prove each other. 1 Divide 17 21 2 Divide 13 Facit 13. by 3 19 3 Divide i by Facit 127 137 Facit 38 5 Divide by Facit 6 Divide 4 by 궁 Facit 4 7 Divide 99 by 108 Facit 1 by of 2 Facit 7 9 Divide of by of Facit 10 Divide by of Facit 112 11 Divide by of 4 Facit 2 20 12 Divide of by 4 Facit 32 |