OPERATION. Second Method. 3 x 6 x 8 144 numerator for 14. × 4 x 6 168 numerator for = 160 168 = 192. 4 x 6 x8 = 192 common denominator. NOTE. It will be perceived, that this method does not express the fractions in so low terms as the other. From the above illustration we deduce the following RULE. Let compound fractions be reduced to simple fractions, mixed numbers to improper fractions, and whole numbers to improper fractions, by writing a unit under them; then find the least common multiple of all the denominators by the last rule, 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; anu tors into each other for a common denomio. 2. Reduce and to a common denominator, 3. Reduce,, and . 4. Reduce 4,, and . 5. Reduce,, and . 6. Change, T2, §, and 1. 7. Change,, %, and 7. 8. Change,,, and . 'nomina 9. Reduce, o, and 72. 3 8 28, 11. Reduce, 1, 8, 1, 7, and . Ans. 1,1,2, 11, 21, 14. 6 12. Change,,,,, and 24 24 16 24 9 6 . Ans. 36, 38, 36, 36, 3 Ans. 38, 36, 31. Ans. 341, 244, 34, TI VIII. To reduce fractions of a lower denomination to a higher. 1. Reduce of a farthing to the fraction of a pound. Στοσ 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 of a shilling. As 20 shillings make a pound, there will be as many pounds as shillings, therefore of Tg of a shilling is of a pound. Q. e. d. The operation of this question may be abridged thus: comp RULE. he given fraction be reduced to a compound one by it with all the denominations between the given ong the one to which it is required to reduce it; then reduce is compound fraction to a simple one. 2. Reduce of a grain Troy to the fraction of a pound. 4 X 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 Ans. 80 ? 1 44800 4 Ans. 4 X 1 X 1 X1X 1 5 X 16 X 28 X 4 X 20 5. What part of a mile is of a rod ? = Ans. 9 X 272 X 40 X 4 X 3 294030 7. What part of 3hhds. is of a quart? 8. What part of 3 yards square, are 3 square yards? Ans. 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 o of a pound to the fraction of a farthing. Ans. We explain this question in the following manner. OPERATION. = 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 Too of a pound is equal to T of 20=480 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 7% 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 4 = of a farthing. Q. e. d. = 5 6 35 35 = The operation of this question may be facilitated by the following manner. OPERATION. 960 1400 TH00 X 20 X 12 × 1 = √2%= tqr. Ans. 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 ʊ of a pound Troy ? 8640 X 12 X 20 X 248788 Ans. 3. Reduce T30 of a furlong to the fraction of a foot. 161: 1320 X 40 X 16 = 6880 = 1 Ans. 4. What part of a square foot is 300 of an acre ? BROS X X 40 X 2721 = 18888 = 5. What part of a peck is of a bushel? 6. What part of a pound is zoo of a cwt. ? Ans. 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. |