EXAMPLES. 1. If in Birmingham, England, 150 million pens are manufactured annually, how many great gross will they make per year? Ans. 86805 great gross 6 gross 8 dozen. 8 2. In 100000 sheets of paper, how many bales are there? Ans. 20 bales 4 bundles 6 quires 16 sheets. 3. What is the age of a man 4 score and 10 years old ? 4. How many printed pages, 2 pages to each leaf, will there be in an octavo book, having 8 fully printed sheets ? Ans. 128 pages. 5. How large a book will ten 32mo sheets make, if every page is printed ? Ans. 640 pages. PROMISCUOUS EXAMPLES IN REDUCTION. 1. How many suits of clothes, each containing 6 yd. can be cut from 3304 yards of cloth ? Ans. 49. 2. A man bought a gold chain, weighing 1 oz. 15 pwt., at seven dimes a pennyweight. What did it cost? Ans. $ 24.50. 3. If a human heart beats 72 times a minute, how many times will it beat in a day? 4. A man bought 1 T. 11 cwt. 12 lb. of hay, at 14 cents a pound. What did it cost? Ans. $ 38.90. 5. What will be the cost of a load of oats weighing 1456 pounds, at 37} cents per bushel ? Ans. $ 17.0625. 6. If one bushel of wheat will make 45 pounds of flour, how many barrels will 1000 bushels make ? Ans. 229 bbl. 116 lb. 7. A load of wheat weighing 2430 pounds is worth how much, at $ 1.20 a bushel ? Ans. $ 48.60. 8. I paid $ 12.50 for a barrel of beef. How much was that per pound ? Ans. 64.cents. links are 9. How many steres of wood are there in a pile 4 meters long, 5 meters wide, and 6 meters high ? 10. In 10 mi. 7 ch. 4 rd. 20 l., how many there? Ans. 80820 links. 11. What is the value of a city lot, 25 ft. wide and 100 ft. long, if every square inch is worth 1 cent? Ans. $ 3600. 12. How many cords of wood can be piled in a shed 50 ft. long, 25 ft. wide, and 10 ft. high ? Ans. 97 Cd. 5 cd. ft. 4 cu. ft. 13. Reduce 25 hektoliters to liters. Ans. 2500 1. 14. A cistern 10 ft. square and 10 ft. deep, will hold how many hogsheads of water? Ans. 118 hhd. 4644 gal. 15. A bin 8 ft. long, 5 ft. wide, and 41 ft. high, will hold how many bushels of grain ? Ans. 144 14 bu. 16. How many grains (troy) are there in 10 grams? 17. How many seconds less are there in every autumn than in either spring or summer ? Ans. 86400 sec. 18. If a person could travel at the rate of a second of distance in a second of time, how much time would he require to travel round the earth? Ans. 15 days. 19. A printer calls for 4 reams 10 quires and 10 sheets of paper to print a book. How many sheets does he call for ? Ans. 2170 sheets. 20. How many bushels are there in 5 hektoliters ? Ans. 14.18+ bu. 21. How many times will a wheel, 16 ft. 6 in. in circumference, turn round in running 42 miles ? 22. How many days, working 10 hours a day, will it require for a person to count $10000, at the rate of 1 cent each second ? Ans. 27 da. 7 h. 46 min. 40 sec. 23. A town, 6 miles long and 41 miles wide, is equal to how many farms of 80 acres each ? Ans. 216. 24. At $ 21.75 per rod, what will be the cost of grading 10 mi. 176 rd. of road? Ans. $ 73428. a REDUCTION OF DENOMINATE FRACTIONS. EXAMPLES. 211. To reduce a denominate fraction from a greater to a less unit. bu. 1. Reduce of a bushel to the fraction of a pint. OPERATION. pt. SOLUTION. To reduce bushels to pints, we must multiply by 4, 8, and 2, the numbers in the scale. Since the given number is a fraction of a bushel, we indicate the process as in multiplication of fractions, and after canceling, we obtain . RULE.-Multiply the fraction of the higher denomination by the numbers in the scale successively, between the given and the required denominations. 1. Cancellation may be applied wherever practicable. 2. For reduction in the metric system, we reduce the fraction to a decimal and then proceed as in whole numbers by moving the decimal point. 2. Reduce of a £ to the fraction of a penny. Ans. d. 3. Reduce 1400 of a week to the fraction of a minute. 4. What part of a gill is Ans.min. of a hogshead? Ans. † gi. of an ounce troy? Ans. gr. 6. Reduce 100booo of a mile to the fraction of an Ans. 198 in. 3125 inch. 7. Reduce of of 2 pounds to the fraction of an ounce troy. Ans. oz. 8. Reduce of a hogshead to the fraction of a Ans. pt. pint. 212. To reduce a denominate fraction from a less to a greater unit. 1. Reduce of a pint to the fraction of a bushel. RULE. SOLUTION. To reduce pints to bushels, we must divide by 2, 8, and 4, the numbers of the scale. Since the given number of pints is a fraction, we indicate the process, as in division of fractions, and canceling, we obtain . · Divide the fraction of the lower denomination by the numbers in the scale, successively, between the given and the required denomination. The operation may frequently be shortened by cancellation. 2. What part of a rod is of a foot? Ans. rd. 3. What part of a pound is of a dram? Ans. 1 lb. 4. Reduce of a cent to the fraction of an eagle. Ans. 2000 E. Ans. 1540 mi. 5. A hand is of a foot. What fraction of a mile is that? 6. Reduce of 2 pwt. to the fraction of a pound. Ans. 2 lb. 7. How much less is of a pint than of a hogs head? Ans. 18 hhd. 8. of an inch is what fraction of a mile? Ans. 100 mi. 9. of an ounce troy is of what fraction of 2 pounds? 10. of an ounce is of what fraction of 2 pounds troy? 213. To reduce a denominate fraction to integers of lower denominations. 1. What is the value of of a hogshead? OPERATION. § hhd. × 63 = 315 gal. = 393 gal. gal. x 412 qt. 14 qt.; qt. x 2 = pt. = 1 pt. = Ans. 39 gal. 1 qt. 1 pt. SOLUTION. % hhd. = § of 63 gal., or 39 gal.; and gal. = 3 of 4 qt., or 1 qt.; and qt. of 2 pt., or 1 pt. = RULE.-I. Multiply the fraction by that number in the scale which will reduce it to the next lower denomination, and if the result is an improper fraction, reduce it to a whole or mixed number. II. Proceed with the fractional part, if any, as before, until reduced to the denominations required. III. The units of the several denominations, arranged in their order, will be the required result. 2. Reduce of a month to lower denominations. Ans. 3. What is the value of Ans. 8s. 6d. 3 far. 4. What is the value of 2 of a bushel? 5. Reduce of 15 cwt. to its equivalent value. 6. Reduce of of a pound avoirdupois to integers. Ans. 42 oz. 7. What is the value of of an acre? Ans. 133 P. 8. Reduce 18 of a day to its value in integers. 9. What is the value of 10. What is the value of Ans. 16 h. 36 min. 555 sec. of a pound troy? 7 of 51⁄2 tons ? Ans. 4 T. 5 cwt. 555 lb. Ans. 1 A. 60 P. 11. What is the value of of 33 acres? |