III. This was to reduce both fractions to like units. IV. The numerators only were used in the division. VI. This could have been done by inverting the divisor and multiplying the dividend by it. SUGGESTION. The quotient is not changed if both dividend and divisor are multiplied by the same number. Hence both dividend and divisor were multiplied by 4, the least common denominator of the fractions, in order to get numbers free of fractions. - 45. (a of d) ÷ (b of c). NOTE. This table may be used if more abstract drill is desired. Each exercise above furnishes 10 examples, making 450 in all. Practical Problems 1. A merchant bought 750 lb. of sugar at 41 a pound and sold it at 4 a pound. What was his profit ? 2. If a dealer and sells it at 131 buys 6500 lb. of cotton at 11 a pound a pound, how much does he make? Find the 3. A farmer cut three crops of alfalfa from his field in one season, as follows: 9 T., 83 T., and 61 T. total yield for the season. 4. How many baskets, each containing bu. of pears, can a dealer fill from a barrel containing 21 bu. ? 5. How many -lb. boxes of candy can be filled from a box containing 12 lb.? 6. On the remnant counter Marie found a piece of cloth containing yd., marked 494. How much did it cost per yard? 7. At the rate in Problem 6, at what price should a remnant containing 23 yd. be marked? 8. A remnant containing 5ğ yd. is marked 90¢. Which is cheaper, and how much, to buy the remnant or to buy the same amount of goods from the regular counter at 20¢ per yard? 9. If it takes yd. of ribbon to make the school colors for one pupil, how many yards will it take for 36 pupils? How many can be made from a bolt containing 121 yd. ? 10. If a boy makes the 100-yd. dash in 11 sec., what is his speed per second? 11. Four boys in a relay race ran as follows: the first 93 sec., the second 8 sec., the third 10 sec., the fourth 9 sec. How long did it take to complete the race? 12. A drainage ditch 120 yd. long is to have a fall of in. per yard. Find the total fall of the ditch. 13. John gathered a bushel of walnuts and sold 20 qt. What fraction of the bushel did he sell? Express it in lowest terms. 14. A man had a farm containing 160 A. He sold 60 A. of it. What fraction of the farm did he sell? Express it in lowest terms. 15. A farmer had a herd of 240 sheep. He sold 180 of them. What fraction of the herd did he sell? Express in lowest terms. 16. From Chicago to Omaha is 492 mi., and from Chicago to Denver is 1062 mi. What fraction of the distance from Chicago to Denver is the distance from Chicago to Omaha? Express in lowest terms. 17. If you pay 35¢ for 6 pencils, how much is that for each ? 18. Mary needs yd. of ruching for each sleeve of a dress and yd. for the neck. How much does she need altogether? 19. Mr. King cut 4 T. of hay from one field, 3g T. from another, and 5 T. from another. How many tons did he cut in all? 20. Rain fell to a depth of 2 day, and 11⁄2 in. the next day. three days. in. one day, 15 in. the next Find the total rainfall for the 21. The average rainfall in Indiana for a period of 36 yr. was 41 in. per year. If, during one year, the rainfall was only 36 in., this was how much less than the average ? 22. During the same period the average rainfall in New Mexico was 144 in. per year. How much more was the annual rainfall in Indiana than in New Mexico? 23. The least rainfall was in Arizona, where the average was only 3 in. per year. The annual rainfall in Indiana was how many times as much as that in Arizona? 24. The state having the greatest average rainfall per year was Alabama, where the average was 62 in. The annual rainfall of Alabama was how many times that of Arizona? 25. Ice cutters who were storing ice in the winter found that the ice was 12 in. thick at night and the next morning 155 in. thick. How much did it freeze during the night? 26. John kept a record of his growth in height from the time that he was 9 yr. old until he was 12 yr. old. During the tenth year he grew 25 in., during the eleventh 11 in., and during the twelfth in. Find his growth during the three years. 27. If I nail two boards together, one in. and the other 1 in. thick, how long a nail will it take to just reach through them? 28. By how much does the thickness of a 1-in. board exceed the length of a 7-in. screw? 29. From a barrel containing 31 gal. of vinegar a merchant sold on the different days of one week the following amounts: 34 gal., 41 gal., 31 gal., 41 gal., 2 gal., and 10 gal. How much remained in the barrel? 30. The record for the 100-yd. dash in a recent year was 9 sec. If you could run it in 14 sec., your time would be how much more than the record? 31. What does it cost to mail a package of newspapers weighing 12 oz., at 1 per ounce ? 32. If Harry grew 13 in. during a year, find how much he grew, on the average, per month. 33. How many pieces of ribbon each yd. long can be cut from a piece of ribbon 74 yd. long? 34. A grocer bought 2400 lb. of sugar at 49 per pound and sold it at 5 per pound. Find his profit. |