The pupil will perceive, that this method does not express the fractions in so low terms as the other; although they both have the same value. From the above illustrations, we deduce the following RULE. Find the least common multiple of all the denominators by Case VI., and it will be the denominator required. Divide the common multiple by each of the denominators, and multiply the quotients by the respective numerators of the fractions and their products will be the numerators required. Or, multiply each numerator into all the denominators except its own for a new numerator; and all the denominators into each other for a common denominator. Let the following questions be performed by the second method. 16. Reduce, and to fractions having a common denominator. 96 105 120 120 120. Ans. 80 630 630 630. 572 616 Ans. 546 Ans. 364 192 4836 624 624 024. 2295 2295 2295. 540 26316 2295 2295, 2295. Ans. 2, 3, 42, 42 21 28 24 336 Ans., 9, 396. 176 252 2013 8 Ans. 24, 36 816 48, 48, 48, 48. To reduce fractions of a lower denomination to a higher. 1. What part of a pound is of a penny? Now as pence are twelfths of a shilling and shillings are twentieths of a pound, it is evident, that the operation should be performed by Case V. of compound fractions; Thus, XX1920-843 Ans. From the above illustration, we see the propriety of the following RULE. Let the given fraction be reduced to a compound one by comparing it with all the denominations between the one given, and the one to which it is required to reduce it; then reduce this compound fraction to a simple one. 2. Reduce of a farthing to the fraction of a pound. 3. Reduce of a grain troy to the fraction of a pound. 4. Reduce of a scruple to the fraction of a pound. 5. Reduce of an ounce to the fraction of a hundred weight. 6. Reduce of a pound to the fraction of a ton. 7. Reduce of an inch to the fraction of an ell English. 8. Reduce of an inch to the fraction of a mile. 9. Reduce of a barleycorn to the fraction of a league. 10. Reduce of an inch to the fraction of an acre. 11. Reduce of a quart to the fraction of a tun, wine measure. 12. Reduce of a pint to the fraction of a bushel. 13. Reduce of a minute to the fraction of a year, (3651 10 days.) CASE IX. To reduce fractions of a higher denomination to a lower. 1. What part of a penny is of a pound? As questions of this kind are the reverse of those in the last Case, it is evident they must be performed by multiplying the numerator, which is the same as dividing the fraction. Thus, XXY-340-34-3 Ans. Hence the propriety of the following RULE. Let the given numerator be multiplied by all the denominations between it and the one to which it is to be reduced; then place the product over this denominator and reduce the fraction to its lowest terms. 2. Reduce 1200 of a pound to the fraction of a farthing. 3. Reduce of a pound troy to the fraction of a grain. 4. Reduce of a pound apothecaries' weight to the 9600 fraction of a scruple. 5. Reduce of a cwt. to the fraction of an ounce. 9856 6. Reduce of a ton to the fraction of a pound. 8960 7. Reduce of an ell English to the fraction of an inch. 8. Reduce 1100 of a mile to the fraction of an inch. 9. Reduce 1140480 of a league to the fraction of a barley corn. 10. Reduce 25090566 of an acre to the fraction of an inch. of a tun of wine measure to the fraction 11. Reduce To find the value of a fraction in the known parts of the integer. 1. What is the value of of a £.? By Case IX. 60d. 608. £.=X00-5s.; and X 5d. God.=5&d.; and X=20=1&qr. Ans. 5s. 5d. låqr. This question may be analyzed thus: - If 1£. is 20s., of a £. is of 20s. -5s.; and if 1s. is 12d., of a shilling of 12d. 5d.; and if 1d. is 4qr., of a penny is of 1qr. answer as before. is 4qr. = From these illustrations, we derive the following RULE. Multiply the numerator by the next lower denomination of the integer, and divide the product by the denominator; if anything remain, multiply it by the next less denomination, and divide as before, and so continue as far as may be required; and the several quotients will be the answer. 11. What is the value of g of a furlong? Ans. 35rd. 9ft. 2in. Ans. 2R. 6rd. 4yd. 5ft. 127in. 12. What is the value of of an acre? 13. What is the value of of a rod? Ans. 144ft. 19 in. 14. What is the value of of a cord? Ans. 9ft. 1462in. 15. What is the value of of a hhd. of wine? Ans. 6gall. 2qt. 1pt. Ogi. 16. What is the value of of a hhd. of beer? Ans. 42gal. 17. What is the value of of a year (365 days)? Ans. 174d. 16h. 26m. 5 sec. 18. What is the value of 73å of a dollar? 42 Ans. $7.74. CASE XI. To reduce any mixed quantity of weights, measures, &c. to the fraction of the integer. 1. What part of a shilling is 1d.? Is 2d.? Is 3d.? Is 4d.? 2. What part of a pound is 2s.? 3s.? 4s.? 5s.? 6s.? 9s.? 3. What part of a furlong is 3rd.? 4rd.? 5rd.? 8rd.? 9rd.? 4. What part of a hogshead is 5gal.? 8gal.? 10gal.? 5. What part of a foot is 2 inches? 3in.? 4in.? 5in.? 8in.? 6. What part of a £. is 5s. 5d. 1qr.? Reduce the given number to the lowest denomination it contains for a numerator; and then reduce the integers to the same denomination, for the denominator of the fraction required. Ans. 7. Reduce 3d. to the fraction of a shilling. Ans. . 9. Reduce 2qr. 15lb. 4oz. 5 dr. to the fraction of a cwt. Ans.. 10 What part of a pound are 7oz. 17dr.? Ans.. |