(37) Reduce il of a gallon of wine to the fraction of a hogs head. (38) Reduce of a hhd. of ale to the fraction of a pint. (39) Reduce the of a chaldron to the fraction of a bushel. (46) Reduce of a gallon to the fraction of a chaldron. (41) Reduce of a week to the fraction of a second. (42) Reduce ti of a minute to the fraction of a day. Case 7. To find the proper quantity or value of a fraction in money, weights, measures, &c. RULE. Multiply the numerator of the given fraction by the parts contained in the integer to which it belongs; then divide that product by the denominator; and, if any thing remain, reduce it to the next denomination less, and divide again by the denominator; thus proceed to the least denomination, and the quotients placed in their order will be the answer. EXAMPLES (43) Reduce 107 of a moidore to its proper quantity. (44) Reduce iz of a guinea to its proper quantity. (45) Reduce of a shilling to its proper quantity. (46) Reduce of a three-pound-twelve to its proper quantity. (47) What is the value of ļof a £.? (48) Reduce 477 of a Ib. Troy to its proper quantity. (40) What is the value of of a cwt. ? (50) Reduce 12 of a ton to its proper quantity: (51) What is the value of of a mile? (52) Reduce of an eli English to its proper quantity. (53) Reduçe į of an acre to its proper quantity. (54) What is the value of ' of a hhd. of wine? (55) Reduce of a barrel of beer to its proper quantity. 156) Reduce of a chaldron of coals to its proper quantity. (57) What is the value of } of a month ? (58) Reduce { of a day to its proper quantity. Cuse 8. To reduce money, weights, or measures, into fractions. RULE. Reduce the given quantity to the lowest name mentioned, for a numerator; under which put the number of those parts contained in a unit of the integer for a denominator, then reduce the fraction to its lowest ternis. cwt. EXAMPLES. (59) Reduce 6s. 8{d. to the fraction of a pound. (60) Reduce 4 d. to the fraction of a shilling. (61) Reduce 21. 175. 7{d. to the fraction of a three-pound twelve. (62) Reduce 8s. 2d. to the fraction of a guinea. (63) Reduce 6 oz. 17 dwts. 21 grs. to the fraction of a lb. Troy. (64) Reduce 3 qrs. 3 lb. 1 oz. 125 (1rs. to the fraction of a (65) Reduce 10 cwt. 18 lb. l ' oz. to the fraction of a ton. (66) Reduce 3į qrs. to the fraction of an ell English. (67) Reduce 2 f. 6 in. to the fraction of a yard. (68) Reduce 4 fur. 32 p. to the fraction of a mile. (69) Rednce 3 r. 2 p. to the fraction of an acre. (70) Reduce 42 gal. of wine to the fraction of a bhd. (71) Reduce 28 gal. of beer to the fraction of a barrel, (72) Reduce 14 bu. 2 p. to the fraction of a chaldron. (73) Reduce 1 w. 3 d. 12 h. to the fraction of a month. (74) Reduce 243 d. 8 h. to the fraction of a year, allowing 365 days to the year. XXXIX. ADDITION of VULGAR FRACTIONS. Case 1. To add fractions together having different denominators. RULE. 1. Reduce the given fractions to a common denominator by Case V. in Reduction. 2. Add all the nunierators together for a new numerator, under which subscribe the common denominator. And, if it be an improper fraction, reduce it to its proper terms by Case IV. and you have the sum of all the fractions. H EXAMPLES. (1) Add , I, and together. (2) Add {, 5, $,$, and together. (3) Aud of , and , together. (4) Add of , to of: (5) Add i, j, . and ļ, of , into one sum. Case 2. To add mixed numbers. RULE. Reduce the fractions to a common denominator, and add them together, as before directed, and amnex their sum to the sum of the integers. EXAMPLES (6) Add 44 and 17 together. 7) Add 7, 94, and 6%, together. (8) Add 87, 93, 104, 11g, and 125, into one sum. Case 3. When the given fractions are of sereral denominations. RULE. Reduce them to one denomination, by Case VIII. then add them together as before directed; or you may reduce them to their proper quantities, by Case IX. and add them together. EXAMPLES. (9) Add zit of a £. to s of a shilling. (10) Aild of a lb. Troy to šof an oz. (11) Ald of a cwt. to ļof a lb. (12) Adid of a yard, toof an ell English. (13) To z of a mile, add of a yard. (14) Adil of a chaldron, to ļof a peck. (15) To $ of a week, add of a month. (10) Add i of an hour, to of a week. (17) Add į of 121.+431.+} of % of a £.+} of of a shilling, into one surn. XL. SUBTRACTION of VULGAR FRACTIONS. RULE. 1. PREPARE the fractions as before directed in Addition. 2. Subtract one numerator from the other, and their difference will be a new numerator, under which subscribe the common denominator. EXAMPLES (1) It is required to subtract from it. (2) From 12 take the (3) From # take yr (4) From of s take ž. (5) From of to take of (6) From 10take 6. (7) From 1741 take 16%. (8) From 12 take of į of . (9) From ź of a shilling take of a penny. (10) From į of a cwt. take of an oz. (11) From of a yard take of an inch. (12) From of a chaldron take of a peck. (13) From šof a day take of an hour. XLI. MULTIPLICATION of VULGAR FRACTIONS. RULE. 1. REDUCE compound fractions to simple ones, per Case II. ; bring mixed numbers into improper fractions, per Case III. 2. Multiply the numerators together for a new numerator; and the new denominators for a new denominator; or, if the fractions will cancel, do it as in Case II. EXAMPLES. (1) Mul. á hy ta. (6) Mul. 1 of H by 6. (2) Mul. 12 by 6. (7) Mul. ß of by of į of (3) Mul. 17} by ž. 14. (4) Mul. 2 by 1 of g. (8) Mul. 3} by \, and this (5) Mul. 12 by } of 12. product again by of XLII. DIVISION of VULGAR FRACTIONS. RULE. 1. PREPARE the fractions as before directed in multiplication. 2. Multiply the numerator of the dividend into the denominator of the dividing fraction for a new numerator, and multiply.the other numerator and denominator together for a new denominator; or invert the divisor, and then proceed as in the last rule. EXAMPLES. (1) Divide by (7) Divide 96 by 146. (8) Divide 14} by of 12. (9) Divide 1427 by 12. (10) Divides of 6 by 1 of of H. XLIII. THE RULE of THREE DIRECT, In VULGAR FRACTIONS. THERE are two methods to perform this rule: the second of which is the easiest and most expeditious. RULE. 1. Prepare the fractions, if required, as directed in multiplication; then proceed as in Sect. 12.-Or, |