How many 50. From a piece of cloth containing 1001 yards, were sold 20 yards, 28 yards, and 314 yards, respectively. How many yards remained ? 51. A fisherman caught 3 fish. The first weighed 1 pound, the second s pound, and the third 14 pounds. How much did the 3 fish weigh ? 52. A real estate agent bought 161 acres of land; he sold 21 acres to one man, and 57 acres to another. acres had he remaining ? 53. The sum of two fractions is J, and one of the fractions is . What is the other? 54. Robert had $64 and his father gave him $54. How much had he then ? 55. The McJunkin dairy sold milk as follows: Monday 65gallons, Tuesday 602 gallons, Wednesday 714 gallons, Thursday 69 gallons, Friday 677 gallons, and Saturday 901 gallons. What were the total sales for the week? 56. A salesman traveled in 4 days as follows : Monday 1227 miles, Tuesday 1874 miles, Wednesday 93} miles, and Thursday 207 miles. How many miles did he travel in all? 57. A grocery bill is as follows: flour $24, oranges $ }, lettuce $1, celery #2%, sugar $1, dried peaches $1, canned tomatoes $, and preserves $. What is the amount of the bill ? 58. If a boat will carry safely 800 pounds, how many pounds of provisions can be carried when three men whose weights are, respectively, 1654 pounds, 1824 pounds, and 208 pounds, are in the boat ? 59. If a merchant's collections in 4 days are $128, $1923, $2802, and $1644, what is his average collection per day? MULTIPLICATION OF FRACTIONS Multiplying a fraction by an integer. 1. 4 x 4 days means 4 days are taken 4 times as an addend; thus, 4 days + 4 days + 4 days + 4 days = 16 days. By multiplication 4 x 4 days = 16 days. Explain in the same way what 4 * $ 1 means. Multiplication is a short form of addition. 2. In the problem 8 x } days = f days = 24 days, what term of the fraction is multiplied by 8? What is 8 x days? 8 x rods? 10 x { pounds ? 3. In 8 x 1 hour do we increase or decrease the number of fractional units? Do we change the size of the fractional units ? Observe, then, that a fraction can be multiplied by an integer by multiplying the numerator of the fraction by the integer. 4. 5x 1 hour = 1 hour. What term of the fraction divided by 5 changes the fraction to ? 5. Compare to and j in number of fractional units. In size of the fractional units. Is 1, 5 times it in size ? 6. In 5 x 10 = 1, what change is made in the number of fractional units? in the size of the fractional units ? Observe, then, that a fraction can also be multiplied by an integer by dividing the denominator of the fraction by the integer. Give products: 7. 15. 12 x 8. 6 x 18 7 x 9. 15 x 15 17. 9 x 11 10. 11 x 14. 10 x 11 18. 10 x 8 X 24 11. 5 x 12. 16. 9 x4 13. 8x Written Work = 1. Multiply it by 3. 8 x 1 1 3 x Since multiplying the numerator of a 12 12 4 fraction by an integer multiplies the 4 fraction by the integer, 3 x Is = in, or . A fraction is multiplied by an integer by multiplying the numerator or by dividing the denominator of the fraction by the integer. NOTE. — Shorten the work, when possible, by cancellation. 8. 13 x 18 19. 33 x 132 56 135 Multiply: 13. 15 x 18. 27 x bi 14. 10 x 1 5. 45 x 10. 12 x 17 15. 21 x 25 20. 45 x 6. 18 x 40 11. 11 x 2 16. 36 x 21. 36 x 14 22. At $per dozen, find the cost of 12 dozen oranges. 23. Find the cost of 230 histories at $ each. 24. Find the cost of 250 readers at $io each. 25. Find the cost of 36 yards of carpet at $ per yard. 26. Find the cost of digging a ditch 125 rods long at $zo per rod. 27. Multiply 2 by 12. 2 12 First we multiply the fraction and then the 9=12 x integer by the multiplier. Then we add the re24 sults. 33 28. 33. Find the value of: 9 x 21 7 x 81 38. 27 x 1256 29. 12 x 33 34. 10 272 39. 19 x 87 30. 18 x 5 35. 16 x 912 40. 26 x 539 31. 22 x 43 36. 24 x 84 41. 36 x 7} 32. 21 x 24 37. 32 x 713 42. 42 x 812 43. At $3% a day, how much will a man earn in 26 days ? 44. Find the cost of 18 tons of hay at $154 per ton. 45. Find the cost of 48 suits for boys at $4 each. 46. Find the cost of 18 dozen spoons at $72 a dozen. 47. Find the cost of 10 pairs of shoes at $2a pair. 48. A gardener sold 275 crates of strawberries averaging $24, 168 crates of blackberries averaging $14, 200 crates of raspberries averaging $21. How much did he receive for them ? 49. A laborer earns $27 per day and his son earns $13 per day. Find their total earnings for 310 days. 50. A New York State apple grower sold 320 barrels of apples at $14 per barrel; 200 barrels at $24 per barrel; and 372 barrels at $1% per barrel. Find the amount received for them. 51. Find the cost of labor and material for fencing a farm 100 rods long and 60 rods wide, at $1; per rod. 52. A street-car conductor averages 10 hours per day for 30 days. Find his monthly wages at 221& per hour. 53. An automobile party travels 1352 miles Monday, 1764 miles Tuesday, 1936 miles Wednesday, 96} miles Thursday, and 18531 miles Friday. If the cost of the trip is 1116 per mile, find the total cost. 54. If a department store buys 300 boys' suits at $54 and retails them at $7.98, what is the gain? 55. One newsboy averages 23 per day for 320 days, another averages 3645€ per day for 300 days, and a third 394¢ per day for 297 days. Find their total earnings. 56. James walks 17 miles to school each morning. How many miles does he walk to and from school if he attends 160 days in the term ? 57. How much will 8 pounds of pork cost @ 11¢? 58. A father bought 5 pairs of skates for his children. If they cost $27 per pair, how much did the five pairs cost ? 59. A track-laying gang lay 4g miles of track in a week. How many miles can they lay in 12 weeks ? 60. A grocer bought 3 tubs of butter weighing, respectively, 27 pounds, 31 pounds, and 24 pounds at 111 cents a pound. How much did all cost ? 61. His average price realized on the sale of this butter was 172 cents per pound. How much did he make on the transaction ? 62. When lead is worth $5% per hundred pounds, how much will 1800 pounds cost? 63. If creamery butter is worth 27 cents a pound and country butter 24} cents a pound, how much will 20 pounds of the former and 25 pounds of the latter cost ? 64. In one day the receipts of coffee at New York were 30,250 bags. Each bag contained 135 pounds. How much was it worth at 6} cents per pound ? 65. When pig iron is worth $16% per ton, how much will 42 tons cost ? 66. When raisins are worth 64 cents a pound, how much will 50 pounds cost ? HAM. INT. ARITH. -11 |