CASE VIII. To reduce a fraction of one denomination to the fraction of another, but less, re taining the same value. RULE. Multiply the given numerator by the parts in the denominations between it and that denomination you would reduce it to, for a new numerator, which place over the given denominator: Or, only invert the parts contained in the integer, and make of them a compound fraction as before, then, reduce it to a simple one. EXAMPLES. 1. Reduce of a dollar to the fraction of a cent. 了 By comparing the fraction it will be × 10 x 10 100 4 = =- c. Answer. 175. x I x T 175 7 of 10 of 10; then 2 Reduce of an eagle to the fraction of a mill. 3. Reduce 11 of a dollar to the fraction of a mill. 4. Reduce of a pound to the fraction of a penny. 15000 1 1280 Ans. m. Ans. 1m. Ans. 3d. Ans. d. 5. Reduce of a pound to the fraction of a farthing. Ans. qr. 6. Reduce of a guinea to the fraction of a penny. 7. Reduce of a moidore to the fraction of a shilling 8. Reduce of a lb. Avoirdupois to the fraction of an ounce. 1 28 of a guinea to the fraction of a pound. 7 Ans. s. 12 Ans. 4oz. *9. Reduce 10. Reducer of a lb. Troy to the fraction of a pwt. Ans. "pwt. 11. Reduce of Cwt. to the fraction of a lb. Avoirdupois. Ans. lb CASE IX. To find the value of a fraction in the known parts of the integer, as of coin, weight, measure, &c. RULE.t Multiply the numerator by the parts of the next inferior denomination, and divide the product by the denominator; and if any thing remain, multiply it by the next inferior denomination, and divide by the denominator as before, and so on, as far as necessary; and the quotients placed after one another, in their order, will be the answer required; or, reduce the numerator, as if it were a whole number, to the lowest denomination, and divide the result by the denominator; the quotient will be the number of the lowest denomination, (which must be brought into higher denominations as far as it will go,) and † As the numerator of a fraction may be confidered as a remainder, and the denominator as a divifor: This rule therefore has its reafon m the nature of divifion. the remainder will be a numerator to be placed over the given denominator for a fraction of the lowest denomination. Note. From this rule, in connexion with what has been said of Reduction of Federal Money, it appears, that, annexing to the given numerator as many cyphers, as will fill all the places to the lowest denomination, and dividing the number so formed by the denominator, the quotient will be the answer in the several denominations, and the remainder a numerator to be placed over the given denominator, forming a fraction of the lowest denomination. Ans. 2 qrs. 91b. 10oz. 74dr. 10. What is the value of of a lb. Avoirdupois ? Ans. 12oz. 123dr. 11. What PORTANT COURSE OF STUDY FOR RE TURNED DISABLED SOLDIERS. Letters from Elihu Burritt, Matthew Vassar, Mayor Bowne, George W. Bungay, and other Eminent Gentle men, indorsing the Institution and the Practical and interesting man ner pursued in Teaching, Terms of Tuition, Sketch of City of Poughkeepsie, etc., etc., etc. To reduce any given quantity to the fraction of any greater denomination of the same kind. Reduce the given quantity to the lowest term mentioned, for a numerator; then reduce the integral part to the same term for a denominator; which will be the fraction required. Note. It appears from this rule and what has been said before, that, in Federal Money, where the given quantity contains no fraction of its lowest denomination, the annexing of as many cyphers to 1 of the required denomination, as will extend to the lowest denomination in the given quantity, will form a denominator, which placed under the given quantity used as one number for a numerator, will make the answer, which may be reduced to its lowest terms. Or, if there be a fraction of the lowest denomination, multiply the given whole numbers by its denominator, adding its nnmerator, for a numerator; and let the denominator itself at the left of as many cyphers as were mentioned above be a denominator; the fraction so formed will be the answer; which may be reduced to its lowest terms. EXAMPLES. 1. Reduce 6d. 2c. 5m. to the fraction of a dollar. By the general rule. 6d. 10d. int. pt. This cafe is the reverse of the former, therefore proves it. 2. Reduce. NOTE. If there be a fraction given with the said quantity, it must be farther reduced to the denominative parts thereof, adding thereto the numerator. 2. Reduce 26c. 5 m, to the fraction of a dollar. By the general rule. And, 212=1D. Ans. Ans. as before. Ans. E. 3. Reduce ID. 87c. 5m. to the fraction of an eagle. 29 3 Ans.cwt. 10. Reduce 12oz. 123dr. to the fraction of a lb. Avoirdupois. Ans. lb. 11. Reduce 7oz 4pwt. to the fraction of a lb. Troy. 12. Reduce 4cwt. 2qrs. 12lb. 14oz. 12dr. to the fraction of a ton. Ans.ton. 13. Reduce 2qrs. 23n. to the fraction of a yard. Ans. E. E. 15. Reduce 6fur. 26po. 11ft. to the fraction of a mile. 16. Reduce 16h. 36m. 55s. to the fraction of a day. Ans. m. Ans. day. 17. Reduce 257d. 19h. 45m. 5219s. to the fraction of a Julian year. 18. Reduce 18s. to the fraction of a guinea. 21. Reduce 3r. 17 p. to the fraction of an acre. ADDITION OF VULGAR FRACTIONS.. RULE.* Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different integers to those of the same; and Fractions, before they are reduced to a common denominator, are entirely dif fimilar, and therefore cannot be incorporated with one another; but when they are reduced to a common denominator, and made parts of the fame thing; their fum, or difference, may, then be as properly expreffed by the fum or difference of the numerators, as the fum or difference of any two quantities whatever, by the fum or difference of their individuals; whence the reafon of the rules, both for Addition and Subtraction, is manifeft and all of them to a common denominator; then the sum of the numerators written over the common denominator will be the sun of the fractions required. EXAMPLES. 1. Add 74, of, and 7 together. 15 First. 7, of 3, and 7-7. Then the fractions are 39 , and; therefore, 39x56x 1=2184 15X 5X 1= 75 7x 5X56-1960 4219 5x56x1=280 =1519 together. 6 of 4, of, and 94? 2. Add 4, 9, and of 3. What is the sum of 4, of 3 of 4, and 84 ? 4. What is the sum of 5. Add together E. ΤΟ D. and 1c. Ans. 128. Ans. 7D. 53c. 29m. Ans. 20c. 9m. Ans. . 16 12s. 3 d. of a mile together. Ans. 1100yds. 2ft. 7inches. of a day, of an hour, and of a minute Ans. 2 days, 2 hours, 30 minutes, 45 seconds. SUBTRACTION OF VULGAR FRACTIONS. RULE.* Prepare the fractions as in Addition, and the difference of the numerators, written above the common denominator, will give the difference of the fractions required. EXAMPLES. In fubtracting mixed numbers, when the fractions have a common denominator, and the numerator in the fubtrahend is lefs than that in the minuend, the difference of the whole numbers will be a whole number, and the difference of the numerators a numerator to he placed over the given denominator: this whole number and the fraction thus formed will be the remainder: but, when the numerator in the fubtrahend is greater than that in the minuend, fubtract the numerator in the subtrahend from the common denominator, adding the numerator in the minuend, and carrying 1 to the integer of the fubtrahend. Hence, A fraction is fubtracted from a whole number, by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number." |