VIII. To reduce fractions of a lower denomination to a higher. 1. Reduce of a farthing to the fraction of a pound. Στο Ans. This question may be analyzed thus; since 4 farthings make a penny, there will be as many pence as of a farthing is of a farthings; therefore of penny. Again, as 12 pence make a shilling, there will be as many shillings as pence, therefore of of a penny is Tog of a shilling. As 20 shillings make a pound, there will be as many pounds as shillings, therefore of Tug of a shilling is of a pound. Q. e. d. The operation of this question may be abridged thus: Let the given fraction be reduced to a compound one by comparing it with all the denominations between the given one and the one to which it is required to reduce it; then reduce this compound fraction to a simple one. 2. Reduce of a grain Troy to the fraction of a pound. 4 X I X 1 X 1 7 X 24 X 20 X 12 1 Ans. 10080 3. What part of an ounce is of a scruple? 4. What part of a ton is of an ounce ? 4 X 1 X 1 X1 X 1 1 Ans. 8. What part of 3 yards square, are 3 square yards? Ans. 9. What part of of a solid foot is of a yard solid? Ans. . IX. To reduce fractions of a higher denomination to a lower. 1. Reduce Too of a pound to the fraction of a farthing. Ans.. We explain this question in the following manner. As shillings are twentieths of a pound, there will be 20 times as many parts of a shilling in Too of a pound, as there are parts of a pound; therefore of a pound is equal to Too of 20=1280 of a shilling. And as pence are twelfths of shillings, there will be twelve times as many parts of a penny in of a shilling, as there are parts of a shilling; therefore of a shilling is equal to 70 of 12=48=of a penny. Again, as farthings are fourths of a penny, there will be 4 times as many parts of a farthing in of a penny, as there are parts of a penny; therefore of a penny are equal to 3 of = 品 of a farthing. Q. e. d. 35 The operation of this question may be facilitated by the following manner. 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 go of a pound Troy? 8640 X 12 X 20 X 24 = 8788 Ans. 3. Reduce T20 of a furlong to the fraction of a foot. 660 1320 X 40 X 162=Ans. 4. What part of a square foot is 5805ʊ of an acre ? 55050 X 4 X 40 X 2724-48888 = & Ans. 5. What part of a peck is of a bushel? 6. What part of a pound is zoo of a cwt. ? Ans.. Ans.. 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 of a pound? Ans. 5s. 10d. 7. What is the value of 8. What is the value of of a hogshead of wine? of a year? Ans. 232da. 10h. 21m. 49 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. 6d. ? OPERATION. 3s. 6d. 42d. 20s. =240d. To perform this question, we reduce the 3s. 6d. to pence, Ans. it being the lowest denomination in the question, and we make them the numerator.of the fraction. We then reduce the one pound to pence, and make them the denominator 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. 3. What part of a ton is 4twt. 3qr. 12lb. ? OPERATION. 4cwt. 3qr. 12lb. = 544lb. 20cwt. = Ans. =2240lb. 4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ? 5. What part of 2A. 2R. 32p. is 3R. 24p.? |