VIII. To reduce fractions of a lower denomination to a higher. 1. Reduce % of a farthing to the fraction of a pound, OPERATION. X qr. ==jd. This question may be anI5 x . = gs. alyzed thus ; since 4 far25 X dgs. = to £. things make a penny, there will be as many pence as farthings ; therefore 4 of $ of a farthing is = 5 of a penny. Again, as 12 pence make a shilling, there will be iz as many shillings as pence, therefore iz of į of a penny is idg of a shilling. As 20 shillings make a pound, there will be zo as many pounds as shillings, therefore ab of Tds of a shilling is zico of a pound. Q. e. d. The operation of this question may be abridged thus : one I the given fraction be reduced to a compound one by com; ng it with all the denoininations between the given the one to which it is required to reduce it ; then reduce fis compound fraction to a simple one. 2. Reduce 4 of a grain Troy to the fraction of a pound. 4 X 1 X 1 X 1 1 Ans. 7 X 24 X 20 X 12 10080 3. What part of an ounce is iof a scruple ? 8 X1 X1 1 Ans. 10 X 8 X 8 80 4. What part of a ton is of an ounce ? 4 X1 X1 X1 X 1 1 Ans. 5 X 16 X 28 X 4 X 20 44800 = 5. What part of a mile is g of a rod ? 8 X1 X1 1 Ans. 9 X 40 X 8 360 6. What part of 3 acres is g of a square foot ? 4 X 1 1 X 1 X1 X 1 1 Ans. 9 X 2724 X 40 X 4 X 3 294030 7. What part of 3hhds. is of a quart? 4 X1 X1 X1 1 Ans. 7 X4 X 63 X 3 1323 8. What part of 3 yards square, are 3 square yards ? Ans. š. 9. What part of of a solid foot is & of a foot solid ? Ans. IX. To reduce fractions of a higher denomination to a lower. 1. Reduce Tibo of a pound to the fraction of a farthing. Ans. We explain this question in the following manner. As shillings are twen1200 X 4 = tffo = 7hs. tieths of a pound, there 70 X *=*= d. will be 20 times as many 395 X*= }qr. Ans. parts of a shilling in Tato of a pound, as there are parts of a pound; therefore tapo of a pound is equal to Too of 20 = Teo=of a shilling. And as pence are twelfths of shillings, there will be twelve times as many parts of a penny in 7 of a shilling, as there are parts of a shilling ; therefore o of a shilling is equal to to of <= %= of a penny. Again, as farthings are fourths of a penny, there will be 4 times as many parts of a farthing in 35 of a penny, as there are parts of a penny ; therefore set of a penny are equal to 35 of 4 = 3 of a farthing. Q. e. d. The operation of this question may be facilitated by the following manner. TIVO X X X = 196 = $tqr. Ans. OPERATION. OPERATION. Hence 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. What part of a grain is geto of a pound Troy? 640 X 42 X X = 5748 = Ans. 3. Reduce Takto of a furlong to the fraction of a foot. 1325 X 4 X 16 = = 1 Ans. 4. What part of a square foot is G8080 of an acre ? 58050 X 4 X 4 X 272 =48848 = Ans. 5. What part of a peck is of a bushel ? 6. What part of a pound is ado of a cwt. ? Ans. 6. Ans. the X. To find the value of a fraction in the known parts of the integer. RULE. Multiply the numerator by the next lower denomination of the integer, and divide the product by the denominator; if any thing remains, 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. 1. What is the value of 3t of a pound? Ans. 5s. 10d. OPERATION d. 7 24) 7 0 0 0 5 10 2. What is the value of f af a cwt. ? Ans. 3qr. 3lb. loz. 12fdr. H* 9)7 0 0 0 0 0 3 3 1 124 3. What is the value of 7 of a yard? Ans. 3qr. Ofna. OPERATION. 7 9)7 0 0 4. What 0 3 0 Ans. IR. 28p. 155ft. 827in. 7)3 0 0 0 0 0 1 28 155 824 5. What is the value of g of a mile ? Ans, 1fur. 31rd. ift. 10in. 0 1 31 1 10 6. What is the value of it of an ell English ? Ans. Iqr. I fina. 7. What is the value of 4 of a hogshead of wine ? Ans. 18gal. Oqt. Opt. 8. What is the value of It of a year r? Ans. 232da. 10h. 21m. 49 4 sec. XI. To reduce any mixed quantity of weights, measures, &c. to the fractions of the integer. 1. What part of a pound is 3s. 6. ? OPERATION. To perform this question, 38. 6d. = 42d. we reduce the 3s. 6d. to pence, 20s. = 240d. = to Ans. it being the lowest denomina tion in the question, and we make them the numerator of the fraction. We then reduce the one pound to pence, and make them the denom-, inator of the fraction. This fraction we reduce to its lowest terms, and we have the answer required ; wherefore the following RULE. Reduce the given number to the lowest denomination it contains for a numerator, and reduce the integers to the same denomination, for the denominator of the fraction required. 2. Reduce 4s. 8d. to the fraction of a pound. OPERATION. = Ans. 3. What part of a ton is 4cwt. 3qr. 121b. ? OPERATION. 4cwt. 3qr. 121b. = 5441b. 20cwt. = 17 Ans. = 22401b. 4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ? 5. What part of 2A. 2R. 32p. is 3R. 24p. ? |