40. How many cents will 16 bushels of potatoes cost, at 2 dimes a bushel LESSON VIII. REMARK.-A fraction may be multiplied, by multiplying the numerator (as you have already observed), or by dividing the denominator. 1. How many are 5 times? SOLUTION.-5 times are 35, or 31. REMARK.-In accordance with the above remark we have SOLUTION.-5 times are 1, or 31. 18. How many times 12 are 9 times 19. How many times 8 are 11 times 20. How many times 100 are 25 times 21. How many times 20 are 35 times 22. 5 times is 4 times Mary's age; what is her age? MULTIPLICATION &C., OF FRACTIONS. 23. 13 times 77 equals of the number of dollars a certain wagon cost. Required the cost of the wagon. 25 24. 25 times equals of the number of men Gen. Santa Anna had at the battle of Buena Vista. How many men had he? 25. 6 times 2 is of the number of men he had wounded. How many men were wounded? 26. 7 times 569 is of the number of men he had killed. How many were killed? 27. 4 times 450 is of the number of men Gen. Taylor had. How many had he? 28. 9 times is of the number of men he had killed. How many were killed? 29. 8 times 1 is of how many times 3? 30. 4 times 2 is of how many times 5? 31. A laborer worked 12 months, at the rate of $103 a month; how much did his year's wages amount to? 32. If 2 quarts of wine cost 48 cents, what will 1 gill cost? 33. How much ought I to pay for 3 oranges, at of a cent a piece? 34. If a certain piece of work can be performed in 96 hours, how many days will be required to perform it by working 6 hours a day? 35. If 1 man can dig a ditch in 15 days, how long will it take 5 men to dig it? 36. If a certain quantity of provision serve a family of 4 persons 16 days, how long would it last a family of 8 persons? 37. If 8 men can perform a certain piece of work in 56 days, in how many days can 112 men do the same? 38. If 3 men can plow 18 acres in 6 days, in how many days could 9 men do the same? 39. 4 men can mow a certain field in 6 days, in how many days can 5 men perform the same work? 40. A man bought 6 barrels of cider, at $3 a barrel; how many boxes of butter, at $4 a box, will it take to pay for it? 41. A merchant bought 6 yards of cloth and sold it for $20 which was of what it cost; what did it cost a yard? 42. Bought 36 yards of cloth, and sold of it for $25, which was of what it cost; how much would I have gained by selling the whole at the same rate! 43. 7 men in of a day can earn $10, how long would it take 1 man to earn the same? 44. James is 33 years of age, which is of the age of Henry; and Henry is 9 times as old as George. What is the age of Henry, and of George respectively? 45. of 36 is 3 times of what number? 46. of 32 is of three times what number? 48. 47. of 60 is of 40 is of twice what number? of as many dollars as Mr. B's horse cost; what was the cost of his horse? 49. A person, being asked his age, said, that was of ten times his age. 50. Morgan is 20 years of the age of his brother. age? of 80 What was his age? old, and of his age is What was his brother's 1. How many thirds are there in 3 ? SOLUTION.-In 1 there are 3 thirds, and in 3 there are 3 times 3 thirds, which are. The following solution is preferred to the above. SOLUTION.-In 1 there are 3 thirds, therefore, 3 times the number of whole ones, equal the number of thirds. 3 times 3 are 9. Therefore, in 3 there are f 2. How many fourths are there in 3 ? 3. How many halves are there in 6? in 5? in 4? in 6? in 4? in 5.? in 3 in 6? ? 4. How many fifths are there in 4 5. How many fifths are there in 7? 6. How many sixths are there in 4 7. How many sevenths are there in 2? 8. How many eighths are there in 7 9. How many fifteenths are there in 2? 10. How many tenths are there in 4 in 6? in 7? 11. How many fourths are there in 3 and 4 ? 12. How many thirds are there in 4 and 13. How many thirds are there in 3 and 14. How many halves are there in 8 and } ? 15. Reduce 63 to an improper fraction. 16. Reduce 93 to an improper fraction. 17. Reduce 7 to an improper fraction. 18. Reduce 53 to an improper fraction. 19. Reduce 43 to an improper fraction. 20. Among how many men, can 5 wheat be distributed, provided each receives bushel? bushels of of a 21. Among how many boys, can 73 oranges be divided, provided each receives of an orange? 183 22. 8 and are how many times & ? SOLUTION.—8 and equal . is contained in 74 37 times. 23. 9g are how many times? 35. 5 times 63 are how many times ? 36. 8 times 83 are how many times ? 37. 6 times 24 are how many times? 38. A boy distributed 93 apples equally among his companions, giving to each of an apple; how many companions had he? 39. Homer distributed $12 equally among some poor women, giving to each $13; how many women were there? 40. Mary gave of a pie to each of her 9 visitors; how many pies did it take? 41. Bought 8 yards of cloth, at $5 a yard; how many yards of silk, worth $1 a yard will it take to pay for it? 42. Bought 9 yards of cloth, worth $14 a yard, and paid for it with raisins, at $13 a box; how many boxes did it take? 43. How many bushels of turnips, at $3 a bushel, can be bought for 8 bushels of apples, at $3 a bushel ? 44. How many apples, at of a cent each, can be bought for 6 oranges, at 2 cents a piece? 45. How many yards of cloth, at $4 a yard, can be bought for 10 boxes of butter, at $52 a box? 46. How many geese, at $7 cach, can be bought for 14 ducks, at $3 a piece? 47. How many boxes of cheese, worth $23 a box, may be had for 17 boxes of butter, at $1 a box? 48. How many barrels of flour, worth $53 a barrel, may be had for 17 bunches of cotton, at $11 a bunch? 49. How many sheep, at $11 a head, may be had for 8 calves, at $3 each? 50. How many quarts of alcohol, at of a cent a pint, may be had for 12 quarts of molasses, at 4 cents a quart? 51. Mary and Jane together picked 5 times 2 quarts of strawberries and shared them equally with their companions; how many companions had each, provided each received 1 quarts? |