In this example, the decrease in value of a unit of the successive denominations between a solar day and a second, are 24 (hours,) 60 (minutes,) and 60 (seconds.) Hence the compound fraction will be 24 of o of 4a, which, multiplied by the given fraction becomes 3 24 60 60 11520 1 1 1 Cancelling, successively, 60 and 24, factors common tu numerator and denominator, we have first Finally, cancelling the factor 4, which is common to the numerator 60, and the denominator 8, we have We have beer particular to give the complete work of cancelling in these examples, by writing down the whole work at the successive stages of operation. In practice, the expression need not be written more than once. With a little practice the pupil will be able to strike out the common factors with accuracy and despatch. Reduce of a pipe of wine to an equivalent fraction of a gill. In this example, the successive denominate values between a pipe and a gill are 2 hogsheads, 63 gallons, 4 quarts, 2 pints and 4 gills; therefore, our compound frac tion is of 3 of 4 of 2 of 4, which, multiplied by the given fraction, becomes of of of 4 of 4 of 4; this becomes, after cancelling like factors, 1 gill. 4. Reduce of a yard to a fraction of a mile. Ans. 100. 5 Reduce of a gill to the fraction of a gallon. Ans. 6. Reduce of a pound to the fraction of a ton. Ans. 3360 7. Reduce of a mile to the fraction of a foot. Ans. 1760 feet. 8. Reduce of of of a yard to the fraction of a Ans. 36960 mile. 9. Reduce of of of a gallon to the fraction of a Ans. 4. gill. 10. Reduce of of a hogshead of wine to the fraction of a gill. Ans. 1792-5971. 11. Reduce of 4 of 4 yards to the fraction of an inch. Ans. 243-344. 12. Reduce of of a farthing to the fraction of a shilling. Ans. 1816. 13. Reduce of an ounce to the fraction of a pound avoirdupois. Ans. 44 14. Reduce of 7 of 1 rod to the fraction of an inch, of a foot, and of a yard. 217212915 inches. Ans. 93 1053 feet. = 231 332 yards. 15. Reduce of of 1 hour to the fraction of a month of 30 days, and to the fraction of a year of 365 days. Ans. { view of a month. 26280 of a year. 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 ob vious that 2 feet 3 inches is the same part of a yard that 27 is of 36, which is 7=2. Hence, we deduce this RULE. Reduce the given quantities to the lowest aenomination 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. 20. 3 What part of a day is 17 minutes 4 seconds? 37 Ans. 4. What part of $700 is $5.30? 6. What part of $3 is 24 cents? Ans. 336. Ans To 7. What part of 10 shillings, 8 pence, is 3 shillings 1 penny? Ans. 37 1278. 12 8. 8. What part of 100 acres is 63 acres, 2 roods, 7 rods of land? Ans. 10167. 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 10. In the United States standard silver coin of one dollar, there are 371 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. 175. 12. The pound Troy contains 5760 grains, the pound Avoirdupois contains 7000 grains. A pound Troy is what part of a pound Avoirdupois ? Ans. 14. cubic inches, What part of Ans. 124. 13. The imperial gallon contains 2771 nearly; the old wine gallon contains 231. 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. Suppose we wish to know the value of of a yard; we know that of a yard equals of 4 of a quarter of a quarter 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 Hence, we deduce this RULE quarter and 2 nails. 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 denom inator; 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 denom inator; 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 ofo of a minute, equals 12 minutes. Ans. 1 quarter, 24 nails. 3. What is the value of of of 1 mile? Ans. 1 furlong, 20 rods. 4. What is the value of ♣ of 1⁄2 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 of 2 days of 24 hours Ans. 9 hours, 36 minutes. 7. What is the value of of of of an hour? Ans. 5 minutes, 37 seconds. |