14. Find the value of § of 10. Reduce the mixed number to an improper fraction. SUGGESTION. Reducing the mixed numbers to improper fractions, regarding the integer 6 as f, and canceling, we find the product to be 75, or 183. tons of 28. A California vineyard of 114 acres yielded 4 grapes per acre. Find the total yield. How far did it 29. During a recent balloon contest, a balloon remained in the air 353 hours and traveled 333 miles per hour. travel? 30. If an electric plow travels 3531 feet per minute, how far will it travel in 12 minutes? 31. The Simplon tunnel between Switzerland and Italy is 124 miles long. If of its length is in Italian territory, how many miles of the tunnel are in each country? 32. Find the value of cocoa at $1 per pound obtained from of an acre of cacao trees, planted 408 trees to the acre, if 11 pounds of marketable cocoa are obtained per tree. DIVISION 181. Division of fractions by integers. 1. If of a cantaloupe is divided equally among 5 girls, what part of the cantaloupe will each receive? ÷ 5 =? In dividing by 5, which term of the fraction is divided? 2. Multiply the denominator of 5 by 5 and express the result in its lowest terms. Compare your answer with ÷ 5. + 3. In what two ways, then, may be divided by 5? 4. Which of these two ways should you use to divide by 2? by 2? by 3? by 3? 0 182. A fraction may be divided by an integer by dividing the numerator or by multiplying the denominator by the integer. The first method should be used whenever the numerator exactly contains the divisor. 13. Divide 4 by 2; by 2; 42 by 2. 14. It is not so easy to divide 33 by 2 as to divide 43 by 2. How many thirds are there in 33? Then 33 ÷ 2 = ? 23. If it is 16 feet around a square, how long is each side? 24. A boy sawed a board 131 feet long into 3 pieces to make 3 shelves for a cupboard. How long was each shelf? 25. Three boys weighed 2103 lb. Find their average weight. 26. A man did of a piece of work in 6 days. What part of the work did he do in 1 day? 27. A fly wheel made 12 revolutions in 5 seconds. How many revolutions per second did it make? 28. Four cars contained 1681 tons of coal. weight of coal per car. Find the average 29. A retail meat dealer used 33 tons of ice in his refrigerators in 5 days. Find the daily consumption of ice. 30. A boy earned $33 in 9 days. What part of a dollar did he earn per day? WRITTEN EXERCISES 184. 1. Divide 14 by 7; divide by 2; divide 15 by 6. Thus 4 is contained in 3231, 80 times with 31, or, undivided; } ÷ 4 = }· The entire quotient, then, is 807. Find their rate per hour. Paris and Calais in 3 hours. 42. If 381 ounces of gold were extracted from 68 tons of ore, what was the amount of gold per ton of ore? 43. From 50,000 pounds of cod 683 gallons of cod-liver oil were obtained. Find the yield of oil per 1000 pounds of fish. 44. It cost $71⁄2 to store 30 cases of eggs in Philadelphia. Find the storage rate per case. 45. It cost $2061 to dig a reservoir. If 330 cubic yards of clay were removed, what was the expense per cubic yard? 46. If 1 of this clay was carted away at a cost of $1 per cubic yard and sold for $1123, how much was gained per cubic yard over not selling it at all? 188 87 185. Division of integers by fractions. 1. Divide 40 by 8; by 4; by 2; by 1. When the divisor is halved, how is the quotient affected? 2. Since 1 is contained 40 times in 40, how many times is of 1 contained in 40? 1 How does multiplying the divisor by 2 affect the quotient? 5. Divide 20 by, then by 2 times . What part of 20÷ 3 is 20 ÷ 3? Since 20+ 3 x 20, 20÷ = == of 3 × 20= of 20. 6. Divide 8 by . By what number must you divide this result to find the value of 8÷? 186. An integer may be divided by a fraction by multiplying the integer by the denominator of the fraction and dividing the product by the numerator. 13. Robert paid $2 for phonograph records. If the cost of each was $4, how many did he purchase? 14. If it costs $ to store one ton of goods, how many tons can be stored for $4 for the same length of time? 15. If a laborer on a sugar-cane plantation earns $ & per day, in how many days will he earn $6? |