90. To find what fractional part one quantity is of another of the same kind, but of different denominations. Suppose we wish to know what part of 1 yard, 2 feet 3 inches is. We reduce 1 yard to inches, which gives 1 yard 36 inches we also reduce 2 feet 3 inches to inches, which gives 2 feet 3 inches=27 inches. Now, it is obvious that 2 feet 3 inches is the same part of a yard that 27 is of 36, which is Hence, we deduce this RULE. Reduce the given quantities to the lowest denomination mentioned in either. Then take the number which expresses the quantity of which the other is to be the fractional part, for a denominator, and the other number for a numerator, and the fraction thus formed will denote the fractional part sought. EXAMPLES. 1. What part of £3 4s. 1d. is 2s. 6d. ? . In this example, the quantities, when reduced, become £3 4s. 1d. 769d.; and 2s. 6d. 30d.; therefore, is the fractional part which 2s. 6d. is of £3 4s. 1d. 2. What part of 3 miles, 40 rods, is 27 feet 9 inches? Ans. 200 3 What part of a day is 17 minutes 4 seconds? . Ans. 4. What part of $700 is $5.30? Ans. 336 Ans To 6. What part of $3 is 24 cents? 7. What part of 10 shillings, 8 pence, is 3 shillings penny? Ans. 3. 8. What part of 100 acres is 63 acres, 2 roods, 7 rods of land? Ans. 19167. 9. In the Eagle there are 232 grains of pure gold, and 12 grains of silver, and the same quantity of copper. The silver and copper is each what part, by weight, of the gold? And the silver and copper together is what part of the gold? Silver and copper are each Ans. of the gold. Silver and copper together are of the gold. 10. In the United States standard silver coin of one dollar, there are 3714 grains of pure silver, and 414 grains of copper. What fractional part is the copper of the silver? Ans.. 11. The silver in standard gold coin is what part of the silver in the same value of standard silver coin? Ans. T 12. The pound Troy contains 5760 grains, the pound Avoirdupois contains 7000 grains. A pound Troy is what part of a pound Avoirdupois? 13. The imperial gallon contains 277 nearly; the old wine gallon contains 231. Ans. 14. cubic inches, What part of Ans. 12. the imperial gallon is the old wine gallon? 14. The solar year is 365 days, 5 hours, 48 minutes, 48 seconds. By what part of a day does this exceed 365 days? Ans. 188. 91. To reduce a fraction of any given denomination to whole denominate numbers. of a Suppose we wish to know the value of 3 of a yard; we know that of a yard equals of 4 of a quarter quarer 1 quarter+ of a quarter. The of a quarter may be considered as a remainder. Again, of a quarter equals of 4 of a nail-2 nails. Therefore, of a yard equals 1 quarter and 2 nails. Hence, we deduce this RULE. Multiply the numerator by the number expressing how many of the next lower denomination make one of the denom ination of the fraction, and divide the product by the denominator; multiply the remainder, if any, by the number expressing how many of the next lower denomination make one of that remainder, and again divide the product by the denominator; continue this process until there is no remainder, or until we reach the lowest denominate value. The successive quotients will form the whole denominate numbers required. EXAMPLES. 1. What is the value of of an hour? In this example, of an hour equal of of a minute, equals 12 minutes. Ans. 1 quarter, 2o nails. 3. What is the value of of 3 of 1 mile? Ans. 1 furlong, 20 rods. 4. What is the value of of 5 of 1 cwt.? 5. What is the value of Ans. 2 miles, 6. What is the value of each? Ans. 1 quarter, 12 pounds. of 14 miles, 6 furlongs? 3 furlongs, 26 rods, 11 feet. of 2 of 2 days of 24 hours Ans. 9 hours, 36 minutes. 7. What is the value of of 7 of of an hour? Ans. 5 minutes, 37 seconds. 8 What is the value of 198 of a solar day? Ans. 5h. 48m. 48sec. 9. What is the value of 1 of a pound Avoirdupois ? 10. What is the value of 11. What is the value of Ans. 13oz. 214 dr. of a bushel? Ans. 34 quarts. of a year of 365 days? Ans. 30 days. 12. What is the value of of 4 of of an acre? Ans. 25 rods. ADDITION OF DENOMINATE FRACTIONS. 92. So long as fractions are of different denominate values, they cannot be added, any more than integers can of different denominate values. Hence, before seeking to add, it is necessary to reduce them to the same denomination, then, to a common denominator, and apply the rule under ART. 43. What is the Rule for the Addition of Denominate Fractions? 1. Add EXAMPLES. of a shilling to of a pound. I. of a shilling equals of of a pound=1b。 of a pound, which added to of a pound of a pound, gives of a pound for the sum. II. of a pound of 20 of a shilling 5 shillings, which, added to of a shilling, gives 5=26 of a shilling for the sum. If our work is right, these two results ought to be of the same value, that is, of a pound must equal 5 shillings. We know that 3 of a pound=43 of 2o of a shilling= 26 of a shilling. 2. Add of a yard, § of a foot, and ✯ of a mile. These fractions, before adding, might be reduced to fractions of a yard, or of a foot, or of a mile, or of any of the denominate values of Long Measure. But a better way would be to reduce each to its integral denominate value, by Rule under ART. 91. of a mile of † of a furlong=3 furlongs. Therefore, the sum is 3 furlongs, 1 foot, 10 inches. 3. Add of a week, of a day, ‡ of an hour. of a week of 7 of a day=34 days=3 days+ of of an hour 3 days, 12 hours. of a day of 24 hour-4 hours. of an hour of o of a minute=15 minutes. Hence, the sum is 3 days, 16 hours, 15 minutes. 4. Add of a year, of a week, of a day, together. Ans. 75da. 2hr. 5. What is the sum of of a cwt., of a qr., of a lb.? Ans. 2qr. 9lb. 9oz. 5 dr. 6. What is the sum of of a bushel, a quart? 7. What is the sum of of a yard, and 8. What is the sum of of a week, of an hour? of a peck, † of Ans. 56gt. of a foot? Ans. 73 inches. of a day, and 9. What is the sum off of a bushel, + of a quart? of a peck, and Ans. 3pk. Oqt. Opt. |