LESSON XXVIII. 1. If a melon costs 8 cents, what will 1 fourth of a melon cost? 2. At $5 a yard, what will 1 fifth of a yard cost? 3. At $6 a ton, what will 7 sixths of a ton cost? 4. At $12 a barrel, what will 1 barrel and 1 sixth of a barrel of flour cost? 5. When a man is working for $15 a week, how much does he earn in 2 weeks and 1 fifth of a week? ANALYSIS. If in 1 week a man earn $15, in 2 weeks he will earn 2 times $15, which are $30, and in 1 fifth of a week he will earn 1 fifth of $15, which is $3; $3 added to $30 make $33. Therefore, in 2 weeks and 1 fifth of a week, at the rate of $15 a week, a man will earn $33. 6. At 16 cents a pound, what cost 3 pounds and 3 fourths of a pound of sugar? 7. At $8 a cord, what cost 4 cords and 3 fourths of a cord of wood? 8. At 6 dimes a bushel, what cost 10 bushels and 2 thirds of a bushel of corn? 9. A teacher, being asked how many scholars he had, replied that the smallest number that ever had been present was 18, which was just 3 ninths of his whole number; how many had he? 10. Sold a horse for $150, which was 5 thirds of what he cost; what did he cost? 11. I have $4, which is 1 fifth of what I divided among 10 men; how much did each receive? 12. William has 63 cents in his pocket, which is 9 fifths of what he has in his money-box; how much has he in his money-box? 13. A boy, being asked how many chickens he had, answered that his largest brood contained 20, which was 4 fifths of the whole number, and the whole number was 5 times as many as he had in the smallest brood; how many had he, and how many were there in the smallest brood? 14. A farmer had 42 sheep, and sold 5 sevenths of them to 5 of his neighbors, each receiving an equal number; how many did each receive? 15. I had 24 cherries, but have divided 5 sixths of them equally among 10 children; how many does each receive? 16. A gentleman had 36 pears, and gave 1 sixth of them to Frank, and divided the remainder equally among his 5 brothers; how many did Frank receive more than each of his brothers? 17. At 10 cents a pound, what cost 20 pounds and 3 tenths of a pound of raisins? 18. At 18 cents a pound, what cost 8 pounds and 5 ninths of a pound of butter? 19. Henry gave $5 for a vest, which was just 1 half of 4 times as much as he gave for a hat; how much did he give for the hat? 20. What cost 5 barrels of flour, if 1 tenth of a barrel cost 9 dimes? 21. John has 20 cents, which is 4 fifths of 5 times as many as Joseph has; how many has Joseph ? 22. Emma is 12 years old, and 7 sixths of her age is just 7 eighths of her sister's age; what is her sister's age? 23. A pier of a certain bridge stands 10 feet in the water, which is 2 fifths of the height of the pier lacking 5 feet; what is the height of the pier ? 24. Bought 4 pounds and 3 fourths of a pound of rice at 8 cents a pound, and paid for it with berries at 5 cents a quart; how many quarts did it take? 25. Bought a watch for $ 40, and a chain for $5 more than 2 fifths the cost of the watch; what did both cost? 26. Sold a hogshead of molasses for $ 36, which was 9 eighths of what it cost; what did it cost? 27. A farmer has 6 cows, and 2 thirds of the number of cows is equal to 1 fourth of the number of his sheep; how many sheep has he? 66 28. Four boys wished their father to divide 50 cents equally among them. No," said he; "but I will give you 4 fifths of it, and 1 half of the remaining fifth to the one that will tell how to divide it" how much would the one who could tell receive? 29. If 6 pounds of sugar cost 96 cents, what cost 5 eighths of a pound? 30. A man, wishing to draw the water from a well containing 120 gallons, found that while he could draw out 12 gallons in a minute, 2 thirds as many gallons would run in during the same time; how long would it take him to exhaust the well? 31. Bought 9 yards of broadcloth for $ 36, which was 4 fifths of its real value; what was its real value per yard? 32. James, in reciting, had given in one day 8 imperfect answers, and 3 fourths of the imperfect answers were just 2 thirds of the number of perfect answers; how many perfect answers had he given ? 33. In a small basket there are 12 pears, and 2 thirds of these are 2 sixths of the number in a large basket; if the whole be divided equally among 4 boys, how many will each receive? 34. If 10 copies of a book cost $12, what will 5 copies cost? (See Appendix, Les. XVIII. Ex. 25.) 35. When 8 cents will buy 12 apples, how many apples will 2 cents buy? 36. If 9 hats cost $24, how many hats can be bought for $8? 37. If 13 pounds of veal cost 91 cents, what part of 42 cents will 2 pounds cost? 38. Bought a horse for 120 dollars, and sold him at 1 sixth more than he cost; for how much was he sold? 39. James has 48 apples, and his brother has 3 fourths as many; how many has his brother? 40. Bought a horse for $160, and a wagon for $5 more than 3 fourths the cost of the horse; what was the cost of the wagon? 41. When 35 cents will buy a pound of butter, how many cents will buy 3 sevenths of a pound? 5 sevenths of a pound? 42. A boy at recitation having answered 4 questions wrong, found the number to be just 2 sevenths of all the questions asked; how many were asked? 43. If a piece of land is worth $75, how many times $5 is 1 fifth of it worth? 44. Edward has 48 walnuts, and Alfred has 5 eighths as many; how many has Alfred? 45. What cost 3 tenths of a ton of hay, at 7 dimes a hundred-weight? 46. William earns 63 cents a day, and John 10 ninths as many and 5 cents more; how many cents does John earn? 47. What cost 2 ninths of a hogshead of molasses, at 10 cents a quart? 48. What cost 5 twelfths of a gross of writing books, at 10 cents a book? 49. If 2 thirds of a pound of sugar cost 8 cents. what will 3 fourths of a pound cost? 50. Robert, having $60 to spend, paid 1 twelfth of it for a hat, 2 fifths for a suit of clothes, and 3 tenths for tuition; how much had he left? 51. Frank had 2 bags filled with nuts, and his brother wished to buy 1 of the bags. "William," said Frank, "I have 9 quarts in the smaller bag, and 2 thirds of that number is just 1 half the number of quarts in the larger bag; and if you will tell me the number of quarts in the larger bag, I will give them to you; how many were there in both bags ? 52. A certain school is divided into three classes: in the first class there are 54 pupils, which are 9 tenths of the number in the second class, and the number in the second class is equal to 6 fifths of 2 times the number in the third class; how many are there in each of the classes? LESSON XXIX. Such expressions as one half, one third, two thirds, &c., may be represented by figures, thus: The figure or figures above the short horizontal line are called the numerator of the fraction, and the figure or figures below the line are called the denominator. The denominator shows into how many equal parts a unit has been divided, and the numerator shows how many of these equal parts have been taken. The numerator and denominator are called the terms of the fraction. When the numerator is less than the denominator, the fraction is called a proper fraction; when the numerator is equal to or larger than the denominator, the fraction is called an improper fraction. A fraction with a whole number is called a mixed number. |