(37) Reduce Hogshead. (38) Reduce (39) Reduce of a Gallon of Wine to the Fraction of a of a Hhd. of Ale to the Fraction of a Pint. of a Chaldron to the Fraction of a Bushel. (40 Reduce of a Gallon to the Fraction of Chaldron. (41) Reducer of a Week to the Fraction of a Second. (42) Reduce of a Minute to the Fraction of a Day. 10 Τ 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 remains, 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. 1106 EXAMPLES. (43) Reduce of a Moidore to its proper Quantity. (44) Reduce of a Guinea to its proper Quantity. 72 (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 of a £.? (48) Reduce of a lb. Troy to its proper Quantity. (49) What is the Value of of a cwt? (50) Reduce of a Ton to its proper Quantity. 124 51 What is the Value of of a Mile? (52) Reduce of an Ell English to its proper Quantity. (53) Reduce of an Acre to its proper Quantity. (54) What is the Value of of a Hhd. of Wine? 732 (55) Reduce of a Barrel of Beer to its proper Quantity. (56) Reduce of a Chaldron of Coals to its proper Quan tity. (57) What is the Value of of a Month? (58) Reduce of a Day to its proper Quantity. Case 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 an Unit of the Integer for a Denominator, then reduce the Fraction to its lowest Terms. EXAMPLES. (59) Reduce 6s 8d. to the Fraction of a Pound. (60) Reduce 44d. to the Fraction a Shilling. (61) Reduce 2/ 17s 7 d. to the Fraction of a Three-PoundTwelve. (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 drs. to the Fraction of a cwt. (65) Reduce 10 cwt. 18lb. 1 oz. to the Fraction of a Ton. (66) Reduce 34 qrs. to the Fraction of an Ell English. (67) Reduce 2 ft. 6 in. to the Fraction of a Yard. (68) Reduce 4 fur. 32 p. to the Fraction of a Mile. (69) Reduce 3 r. 2 p. to the Fraction of an Acre. (70) Reduce 42 gal. of Wine to the Fraction of a Hhd. (71) Reduce 28 gal. of Beer to the Fraction of a Barrel./ (72) Reduce 14 bu. 2p. to the Fraction of a Chaldron. (73) Keduce 1 w. 3 d. 12 h. to the Fraction of a Month. (74) Reduce 243 d. 8h. 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 Deno minators. RULE. 1. Reduce the given Fractions to a common Denominator, by Case V. in Reduction. 2. Add all the Numerators together for a new Numerator, under which subscribe the common Denominator. And, if it. is an improper Fraction, reduce it to its proper Terms (by Case IV.) and you have the Sum of all the Fractions. (2) Add 4, 3, 4, 4, and together. (3) Add of, and, together. (4) Add 3 of, to I of 4. (5) Add 1, 3, 4, and of, into one Sum. 49 Case 2. To add mixed Numbers. RULE. Reduce the Fractions to a common Denominator, and add them together, as before directed and annex their Sum to the Sum of the Integers. EXAMPLES. (6) Add 44 and 17 together. (7) Add 73, 94, and 6, together. (8) Add 8, 9, 10, 114, and 125 into one Sum.' Case 3. When the given Fractions are of several 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 0% of a . to of a Shilling. 460 (10) Add of a lb. Troy to of an oz. (11) Add & of a cwt. to of a lb. (12) Add of a Yard, to of an Ell English. (14 Add & of a Chaldron, to of a Peck. (17) Add of 121. + 431.+of of a £. + of of a Shilling into one Sum. 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 11. (2) From 2 take. I (3) From 4 take T (4) From of take 3. (5) From of take of 4. (6) From 10 take 6. (7) From 17 take 169. (8) From 12 take of of 4. (9) From of a Shilling take of a Penny. (10) From of a cwt. take of an oz. (1) From of a Yard take 3 of an Inch. (12) From of a Chaldron take of a Peck. (13) From of a Day take of an Hour. XLI. MULTIPLICATION of VULGAR FRAC TIONS. RULE. I. 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. 1. PREPARE the Fractions as before directed in Multiplation. hiply the Numerator of the Dividend into the Denotes or of the dividing Fraction for a new Numerator, and multiply the other Numerator and Denominator together for a new Denominator; or inyert the Divisor, and then proceed as in the last Rule. THERE are two Methods to perform this Rule: the second of which is the most expeditious, and easiest. RULE. 1. Prepare the Fractions, if required, as directed in Multiplication; then proceed as in Sect. 12,-Or, |
