221 ft. +2 35/24 ft. (0 ft. 12 294 +8 35/302 (8 in. 280 22 1 rd. 1 yd. 8 in. Ans. 3's of 42 rd. 7 rd. 1 yd.; remainder, 7 yd., 22 24 ft. of 24 33 294 in.; add 8 in. 302 in. 833 in. NOTE. ft. 0 ft. 315 of 302 When both dividend and divisor are compound, reduce them to the same denomination, and divide. The quotient will be abstract. 3. Divide 169 bu. 3 pk. 5 qt. by 7. 4. If a man travelled 607 mi. 169 rd. 11 ft. 6 in. in 10 days, what average distance did he travel in 1 day? 5. If one gross of spools weighs 44 lb. 9 oz., how much will one dozen weigh? 6. If one bottle holds 1 pt. 3 gi., how many dozen bottles will be required to hold 65 gal. 2 qt. 1 pt. ? 7. A man has 451 A. 138 sq. rd. 29 sq. yd. of land, which he wishes to divide equally among his six children. How much land will each child receive? 8. If 12 persons share equally in the contents of a bin containing 20 bu. 2 pk. 4 qt. of apples, what is the share of each? 9. If the entire area of 24 equal fields is 242 A. 20 sq. rd. 15 sq. yd., what is the size of each field? 10. A man walked 50 mi. 71 rd. 2 yd. in 15 hours. What was his rate per hour? 11. If it takes a man 12 hr. 35 min. 15 sec. to walk 45 miles, what is the average time taken for each mile? (Divide by the factors of 45.) 12. When $12 will buy 11 gal. 2 qt. 1 pt. of maple sirup, how much will $1 buy? 13. A man travelled 100 miles in 9 hours. the average rate per hour? What was 14. If a horse eats 12 qt. of oats per day, how long will 10 bu. 1 pk. 4 qt. last him? 15. If a package weighs 4 cwt. 15 lb., how many such packages will it take to weigh 3 T. 2 cwt. 25 lb. ? 16. A man had 5 acres of land which he divided into 12 equal parts. How much land did each part contain? 17. Divide 102 T. 15 cwt. 27 lb. 9 oz. by 8. 18. Divide 16 bu. 3 pk. 6 qt. by 2 bu. 1 pk. 19. I have 84 lb. 14 oz. of salt which I wish to put into packages of 2 lb. 6 oz. each. How many packages will there be? 20. If a horse eats 1 pk. 2 qt. of oats a day, how many days will 16 bu. 3 pk. 6 qt. last him? 21. How many sacks, each containing 2 bu. 3 pk. 2 qt., will be needed to hold 165 bu. 2 pk. of meal? 22. 16 cwt. 75 lb. 9 each containing 93 lb. oz. of butter are to be put into jars How many jars will be needed? To multiply or divide a compound number by a fraction. NOTE. To multiply by a fraction, multiply by the numerator, and divide the product by the denominator. To divide by a fraction, multiply by the denominator, and divide the product by the numerator. 23. How much is of 16 hr. 17 min. 14 sec.? 24. How much is of 303 53 19 8 gr.? 25. Divide 120 cd. 50 cd. ft. 34 cu. in. by 3. 26. How many times is 98 lb. 3 oz. ? contained in 840 T. 15 cwt. 27. A man sold 4 bu. 3 pk. 2 qt. of potatoes, which was of what he raised; how much did he raise ? 28. A butcher sells 120 tons, 9 cwt. 75 lb. of beef every month. How much does he sell in of a month? 29. If 6 bottles hold 5 gal. 2 qt. of milk, how much milk will 3 such bottles hold? 30. A field contains 10 acres 12 sq. rd. of land, which is the size of the whole farm. Find the size of the farm. 31. A railroad track extends 144 miles, 40 rd. 3 yd. How far has a train of cars gone which has travelled this distance? of 32. If a pipe discharges 25 gal. 3 qt. 1 pt. of water in 1 hr., how much will it discharge in 53 hr., if the water flows with the same velocity? NOTE. When the multiplier or divisor is a mixed number, reduce to an improper fraction, and proceed as above. 33. Divide 8 lb. 11 oz. 15 pwt. 18 gr. by 2. 34. If a railroad train runs 60 mi. 35 rd. 16 ft. in one hour, how far will it run in 12 hr. at the same rate of speed? 35. Divide 14 bu. 3 pk. 6 qt. 1 pt. by 7. 36. Divide 5 yr. 1 mo. 1 wk. 1 da. 1 hr. 1 min. 1 sec. by 3%. MISCELLANEOUS PROBLEMS. 161. 1. Name two numbers which multiplied together make 14. 2. Write three sets of factors for 24. 3. Find the prime factors of 2205. 5. How many yards of silk, 24 inches wide, will it take to line a skirt containing six yards of cloth 28 inches wide? 6. Find the least common multiple of 2, 3, 4, 5, 6, 7, 8, 9. 7. Find the greatest common divisor of 285, 465. 8. Find the smallest number that will exactly contain 9, 15, 18, 20. 9. Find the length of the longest stick that will exactly measure the sides of a room 216 yd. by 111 yd. 10. What is the smallest sum of money with which you can buy pears at 75¢ a basket, peaches at 90g, and grapes at 50%, using the same amount of money for each kind? 11. How many times is 1 contained in ? 144 12. How many times is contained in 1? 13. A man bought a horse for $240, which is of what he sold it for. What did it sell for? 14. A man bought a horse for $240, and sold it for of what he paid for it. What did it sell for? 15. A pole stands in the mud, in the water, and the remaining 10 feet are above the water. How long is the pole? 16. A man owns 4 farms containing 365, 375, 2843. and 254 acres respectively. How many acres in all? 17. The man owning the above farms sells A 234 acres, and B 366 acres. How many acres has he left ? 60 18. What is the value of 38 × 1 × 3 × 14 × 31% × 1% X 12 X X 13 X 1. 19. Find the least common multiple of 273, 462, 1785, and 399. 20. A man owns a farm containing 400 acres. He sells of the farm, and divides the remainder among his six children. How many acres does each child receive? 21. Find the sum of 3 bu. 6 pk. 2 qt. 1 pt., 3 pk. 1 qt. 1 pt., 7 bu. 3 pk., 4 bu. 7 qt. 1 pt., and 19 bu. 2 pk. 2 qt. 1 pt. 22. Find the sum of 4 lb. 6 oz. 21 pwt. 9 gr., 5 oz. 11 gr., 3 lb. 9 oz. 18 pwt., 11 oz. 17 pwt. 5 gr., 16 lb. 4 oz. 11 pwt., 18 lb. 17 gr., 21 lb. 15 pwt. 11 gr., 23 lb. 10 oz. 21 pwt. 23 gr. 23. What part of a mile is 214 rd. 2 yd. 2 ft. 3 in. ? 24. Reduce 1 pk. 4 qt. 13 pt. to the fraction of a bushel. 25. What is the quotient of 184 bales, 4 bundles, 1 ream, 13 quires, 20 sheets, divided by ? 26. A farm is 60 ch. 25 1. long. How many rods long is it? 27. A surveyor measured my farm, and found that it is 80 ch. long and 60 ch. broad. How many acres does it contain? 28. In 133128 in. how many miles? 29. How many times will a wheel 12 ft. 3 in. in circumference turn round in going 15 mi. 20 rd. 12 ft. 2 in.? 30. How many steel rails 30 ft. long are needed in the construction of 7 mi. 305 rd. 7 ft. 6 in. of double-track railroad? |