To TEACHERS.-Numerous questions should be asked on each Table, similar to the following: 1. How many pints in 1 quart? in 2? in 3? in 47 in 5? in 6? in 7? in 9? in 10? 2. How many quarts in 1 peck? in 2? in 3? in 4? in 5? in 6? in 7? in 8? in 9? in 10? 3. How many pecks in 1 bushel? in 2? in 3? in 4? in 5? in 6? in 7? in 8? in 9? in 10? 4. How many quarts in 2 pints? in 5? in 6? in 8? in 9? in 11? in 12? in 13? in 14? 5. How many pecks in 8 quarts? in 16? in 24? in 35? in 40? in 49? in 56? in 65? 6. How many bushels in 4 pecks ? in 12? in 20? in 11? in 15? in 27? in 32? in 39? ART. 79. THE PRECEDING EXAMPLES SHOW, THAT To reduce quarts to pints, multiply the number of quarts by the number of pints in a quart. To reduce pecks to quarts, multiply the number of pecks by the number of quarts in a peck. To reduce bushels to pecks, multiply the number of bushels by the number of pecks in a bushel. Hence, REDUCTION DESCENDING is performed by Multiplication: the multiplier being that number of the lower order or denomination, which makes a UNIT of the next higher. ART. 80. To reduce pints to quarts, divide the pints by the number of pints in a quart. To reduce quarts to pecks, divide the quarts by the number of quarts in a peck. To reduce pe to bushels, divide the pecks by the number of pecks in a bushel. Hence, REDUCTION ASCENDING is performed by Division: the divisor being that number of the lower order or denomination, which makes a UNIT of the next higher. REVIEW.-78. For what is Dry Measure used? Repeat the Table. What is the standard unit of Dry Measure? 7. Reduce 3 bushels to pints. SOLUTION. To reduce bushels to pecks, multiply by 4, because there are 4 pecks in a bushel. To reduce pecks to quarts, multiply by 8, because there are 8 quarts in a peck, or 8 times as many quarts as pecks. To reduce quarts to pints, multiply by 2, because there are 2 pints in a quart. 8. Reduce 192 pints to bushels. SOLUTION.--To reduce pints to quarts, divide by 2, because there are 2 pints in a quart. To reduce quarts to pecks, divide by 8, because there are 8 quarts in a peek. To reduce pecks to bushels, divide by 4, because there are 4 peeks in a bushel. OPERATION. 2) 192 Pints. 8)96=qt. 4)12 pk. 3=bu. The two preceding examples show that Reduction Descending and Ascending prove each other. 9. Reduce 7 bushels, 3 pecks, 4 quarts, 1 pint, to pints, SOLUTION. In solving this example, multiply the bushels by 4, which make 28 pecks; to these add the 3 pecks. Then, multiply the pecks (31) by 8, and add the 4 quarts; multiply the quarts (252) by 2, and add the 1 pint. REVIEW.-78. NOTE 1. What other denominations of Dry Measure? What does the quarter contain? For what is it used? What does the chaldron contain? For what is it used? NOTE 2. How many pounds in a bushel of wheat? How many in other grains? 79. How are quarts reduced to pints? Pecks to quarts? Bushels to pecks? How is reduction descending performed? What the multiplier? 80. How are pints reduced to quarts? Quarts to pecks? Pecks to bushels ? How is reduction ascending performed? What is the divisor? The remainder is always of the same denomination as the dividend, Art. 38. Hence, ART. 81. GENERAL RULES. TO REDUCE FROM A HIGHER TO A LOWER ORDER, Rule. Multiply the highest denomination given, by that num ber of the next lower, which makes a unit of the higher; add to the product the number, if any, of the lower denomination. Proceed in like manner with the result thus obtained, till the whole is reduced to the required denomination. TO REDUCE FROM A LOWER TO A HIGHER ORDER, Rule.-Divide the given quantity by that number of its own denomination which makes a unit of the next higher. Proceed in like manner with the quotient thus obtained, till the whole is reduced to the required denomination. The last quotient, with the several remainders, if any, annexed, will be the answer. PROOF.-Reverse the operation: that is, reduce the answer back to the denomination from which it was derived. If this result is the same as the quantity given, the work is correct. REVIEW.-81. What is the general rule for reducing from a higher to a lower order? From a lower to a higher? What the method of proof? 17. / 16. Reduce 4 bu. 2 pk. 1 qt. to pints. 7 bu. 3 pk. 7 qt. 1 pt. to pt. Ans. 290 pt. Ans. 511 pt. 19. 384 pt. to bushels. Ans. 6 bu. ART. 82. TROY OR MINT WEIGHT Is used in weighing gold, silver, jewels, liquors, &c. NOTE.-The standard unit of weight in the United States, is the Trog pound, containing 5760 grains. For interesting historical and other information with respect to coins, see "Ray's Higher Arithmetic." TEACHERS should ask questions on each Table, as on Dry Measure. 1. Reduce 13 lb. 11 oz. 16 pwt. 14 gr. to grains. · REVIEW.-82. For what is Troy Weight used? Repeat the Table NOTE. What is the standard unit of weight in the United States? 5. 14 lb. 11 oz. 19 pwt. 23 gr. to gr. Ans. 86399 gr. 6. 8 lb. 9 oz. 13 pwt. 17 gr. to gr. 7. 171 gr. to pennyweights. 8. 505 gr. to ounces. Ans. 50729 gr. Ans. 7 pwt. 3 gr. Ans. 1 oz. 1 pwt. 1gr. 9. 12530 gr. to pounds. Ans. 2 lb. 2 oz. 2 pwt. 2 gr. 805 pwt. to pounds. Ans. 3 lb, 4 oz. 5 pwt. 10. 11. 25591 gr. to pounds. Ans. 4 lb. 5 oz. 6 pwt. 7 gr. ART. 83. APOTHECARIES WEIGHT Is used by Apothecaries in compounding medicines. The grain, ounce, and pound, in Apothecaries and Troy weight, are the same but the ounce is differently divided. Questions should be asked on the Table, as before. 1. Reduce 3 lb to grains. 2. 4 lb 53 2 gr. to grains. 3. 7b 29 to scruples. 4. 7 lb 23 19 to grains. 5. 673 to pounds. 6. 4313 to pounds. 7. 9750 to pounds. 8. 6321 gr. to pounds. 9. 30941 gr. to pounds. 10. 29239 gr. to pounds. Ans. 17280 gr. Ans. 23342 gr. Ans. 2018 0. Ans. 41300 Ans. 5 lb 73. gr. Ans. 4th 53 73. Ans. 3b 43 53. Ans. 1tb 13 13 10 1 gr. Ans. 5b 43 33 29 1 gr. . Ans. 5 lb 73 19 gr. REVIEW.-83. For what is Apothecaries Weight used? Repeat the Table. What is said of the grain, ounce, and pound, of Apothecaries and Troy weight? What is differently divided? |