RULE. 1. If the whole number have no assigned denominator, a unity subscribed underneath must be the denominator. 2. If the whole number have an assigned denominator, multiply the whole number by the assigned denominator, and the product will be the numerator to the assigned denomina tor. 3. If the whole number have a fraction annexed, multiply the whole number by the denominator of the fraction, and to the product add the numerator for a new numerator, which place over the denominator. EXAMPLES. (12) Reduce 12, 27, and 176, to fractions. (13) Reduce 27 into a fraction, whose denominator shall be 12. (14) Reduce 43 to an improper fraction. (15) Reduce 164 to an improper fraction. (17) Reduce 1464 to an improper fraction. Case 4. To reduce an improper fraction into its equivalent or proper terms. RULE. Divide the numerator by the denominator: the quotient gives the whole number, and under the remainder (if any) subscribe the denominator. Case 5. To reduce fractions of different denominations to fractions of equal value, that shall have one common denomi nator. RULE. Multiply each numerator, taken separately into all the denominators but its own, and the products will be the new numerators: then multiply all the denominators into one another for a common denominator. I EXAMPLES. (22) Reduce ,, and fo to a common denominator. (23) Reduce,,, and of, to a common denominator. (24) Reduce, 춤, 즉, 중, and 중, to a common denominator. (25) Reduce,,, and of 3, to a common denominator. Case 6. To reduce fractions of one denomination to another, retaining the same value. RULE. 1. If the fraction given is to be brought from a less to a greater denomination, multiply the denominator by the parts contained in the several denominations between it and that you would reduce it to, for a new denominator; which, placed under the given numerator, will give the new fraction, which reduce to its lowest terms. 2. If the fraction given is to be brought from a greater to a less denomination, then multiply the numerator in the same manner as you did before the denominator, and place over the given denominator, and it will give the new fraction, which also reduce to its lowest terms. EXAMPLES. (26) Reduce of a shilling to the fraction of a guinea. 344 (30) Reduce ᅮ of a guinea to the fraction of a farthing. (31) Reduce of a dwt. to the fraction of a lb. Troy. (32) Reduce of a cwt. to the fraction of a lb. avoirdu pois. (33) Reduce of a drachm to the fraction of a cwt. (37) Reduce head. 7 of a gallon of wine to the fraction of a hogs of a hhd. of ale to the fraction of a pint. (39) Reduce of a chaldron to the fraction of a bushel. (38) Reduce (40) Reduce (42) Reduce (41) Reduce of a gallon to the fraction of a chaldron. of a week to the fraction of a second. 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 of a moidore to its proper quantity. (44) Reduce 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 of a £.? (48) Reduce of a lb. Troy to its proper quantity. (40) What is the value of f of a cwt.? (50) Reduce of a ton to its proper quantity. (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? (55) Reduce of a barrel of beer to its proper quantity. (56) Reduce 줄 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. 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 a unit of the integer for a denominator, then reduce the fraction to its lowest terms. EXAMPLES. (59) Reduce 6s. 84d. to the fraction of a pound. (60) Reduce 44d. to the fraction of a shilling. (61) Reduce 21. 17s. 75d. 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 drs. to the fraction of a cwt. (65) Reduce 10 cwt. 18 lb. 1oz. to the fraction of a ton. (66) Reduce 34 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) 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. 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. Σ ΧΧΧΙΧ. 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 numerators 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,, and together. (2) Add,,,, and together. (3) Add of, and, together. (4) Add of, to of . (5) Add, and, 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 annex their sum to the sum of the integers. EXAMPLES. (6) Add 4 and 17 together. (7) Add 7, 94, and 6, together. (8) Add 8, 9, 10, 11号, 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. (10) Add of a lb. Troy to of a shilling. of an oz. (11) Add of a cwt. to of a lb. (12) Add of a yard, to of an ell English. (13) To of a mile, add of a yard. (14) Add of a chaldron, to of a peck. (15) To of a week, add & of a month. (16) Add (17) Add of an hour, to of a week. of 121.+431+ of of a L.+ of of a shilling, into one sum. |