PROBLEMS-FRACTIONS 109 1. Which is the greater, the quotient of 1÷or 2 ÷ 1? 10. In Exercise 6, 3÷= 3 × ; in Exercise 7, 6 ÷ =6X. Write the corresponding relations for Exercises 8 and 9. In a similar way find the quotients: II. 8÷5. 12. 9 ÷ 12. 15. 95. 16. 5. 19. 3÷. 20. 64. Simplify the results by canceling : 13. 18÷. 14. 11÷. 17. 7. 18. 8÷g. 21. 7. 22. 7÷8. 22. 23. If one garment requires yd. of cloth, how many such garments can be cut from 12 yd.? 24. A real estate owner divided 6 acres of land into lots of of an acre each; how many lots did he have? 25. A bootblack used of a box of blacking to each pair of shoes; how many pairs did he black with 6 boxes? 26. A cook used lb. of sugar for each cake; how many cakes could she make with 10 lb. of sugar? 27. A baker used & lb. of flour to a loaf of bread; how many loaves could he make from a barrel of flour? (1 barrel of flour weighs 196 lb.) 110 FRACTIONS-DIVISION 1. Find from the diagram the quotient of 1÷; also of ÷ 1. 2. Which is the greater; 1 or 1÷1? How many times as great? Show by diagram that: 3. The quotient of is of that of 1÷ᄒ. 4. The quotient of÷is 5. The quotient of÷is of that of 1. of that of 1. 6. Find from the diagram the quotient of 3; also that of ÷ 1. 7. Which is the greater, 3 or ÷? How many times as great? Show by diagram that: 21. In dividing one fraction by another, by what may the dividend be multiplied? In this way find the quotients; simplify the results by canceling: GENERAL REVIEW Summary 1. If two fractions have the same number for denominators and unequal numerators, which fraction is the larger? 2. If two fractions have the same number for numerators and unequal denominators, which fraction is the larger? 3. If the numerator of a fraction is multiplied by a certain number, how is the value of the fraction changed? 4. What is the effect on the value of a fraction, if both numerator and denominator are multiplied or divided by the same number? 5. The value of a fraction may be divided by a number by dividing the numerator by that number. Explain why this is true. 6. The value of a fraction may be divided by a number by multiplying the denominator by that number. Explain why this is true. 7. How is an integer multiplied by 10? By 100? 9. How is a decimal divided by 10? By 100? 10. How is any number multiplied by 5 in the shortest way? II. Write a mixed number. Explain how to change it to an improper fraction. 12. What is meant by canceling? Illustrate by an example. 13. How is the work of division of fractions tested? 14. What is of 100? What is of 100? of 100? 15. Name some important parts of 100. What part of 100 is 871? 16. Illustrate what is meant by reducing a fraction to its lowest terms. 112 Written. PROBLEMS-GENERAL REVIEW 1. Find the area of each of the following triangles: 2. 6,000 lb. of small egg coal at $7 a ton; 4,000 lb. of large egg coal at $6.75 per ton; 2,000 lb. cannel at $7.25 per ton; carrying in, 25¢ per ton. 3. 7 lb. mixed nuts at 15¢ per pound; 2 doz. oranges at 18¢ a dozen; 2 gal. of vinegar at 44 per quart; 1 gal. of maple sirup at 24¢ per quart. Divide. No quotient need be expressed beyond 3 decimal places: PROBLEMS-GENERAL REVIEW 113 1. How many pickets 21 in. wide, set 41 in. apart, will be required to make a fence 90 ft. long? What is the cost of the pickets at 134 apiece? = 2. Taking 14 cu. ft. 1 bu., how many bushels are there in a bin 8 ft. long, 41 ft. wide, 3 ft. 4 in. deep? 3. If the pressure of the atmosphere is 14.7 lb. per square inch, what is the pressure on the top of a table 1 yd. long and yd. wide? 4. A man bought a lot for $6,000, the price being 621¢ per square foot; how many square feet did it contain? 5. The frontage was 60 ft.; how deep was the lot? What was the price per front foot? 6. If a glass of soda-water costs a druggist 2g4, how much does he make in selling 380 glasses at 5¢ each? 7. A border 3 feet wide is painted on a floor 24 ft. long, 21 ft. wide; what are the dimensions of the unpainted part? Of the border? What part of the whole floor is painted? 8. A gas burner consumed 550 cu. ft. of gas in 80 hours at a cost of 66 cents, what is the cost of 1 hour's light? What is the cost for 4 burners used 30 nights, 4 hours each night? 9. If 500 sheep are fed 10,500 pounds of hay in 7 days, how much hay are 500 sheep fed in one day? How much is 1 sheep fed in a day? How much are 800 sheep fed in 16 days? 10. A contractor had agreed to finish a building costing $300,000 by a certain date, and, if not finished, he was to pay a fine of a certain amount for each day. The building was finished 12 days after time and his fine was $240. What was his fine per day? II. According to Exercise 10 what was the daily fine per thousand dollars? At the same rate, what would have been the daily fine on a building worth $75,000? |