Grapes (1) Flour (6) Apples and pears in bas- Baled hay (D) kets (2) Plows, set up (2) Apples and pears in sacks Plows, not set up (4) or barrels (6) Grain in bulk (D) Power cutter, set up (1) Power cutter, not set up (3) The freight rate between two cities per 100 lbs. being : 1st class $1.03, 2d 92 cts., 3d 79 cts., 4th 65 cts., 5th 54 cts., 6th 43 cts., A 33 cts., B 39 cts., D 33 cts., E 54 cts., H 66 cts. Solve the following problems: 49. What will be the freight on a shipment of bicycles, weight 200 lbs., set up? Not set up? In a shipment of bicycles weighing 500 lbs., what is the saving in freight if they be not set up? 50. How much cheaper is it to ship 1500 lbs. of new furniture not set up than to ship it set up? 51. How much cheaper is it to ship 1500 lbs. of old household furniture, value limited to $5 per hundred pounds in case of loss, than to ship the same weight of new furniture set up? Than to ship the same weight of new furniture not set up? 52. What is the cost of shipping one car-load (20,000 lbs.) of old furniture? How many pounds of the same goods shipped by the hundred will it take to cost the same for freight? 53. What is the difference in freight cost between 200 lbs. of empty barrels and the same weight of trunks of baggage? 54. What is the difference in cost of freight on a ton (2000 lbs.) of canned vegetables and the same weight not canned? 55. What is the difference in cost between a car-load (24,000 lbs.) of canned vegetables and the same weight sent in two separate shipments, i.e., by the hundredweight? 56. What is the difference in freight cost between 1900 lbs. of apples in baskets and the same weight in barrels ? 57. Which costs the most, the freight on 1700 lbs. of flour or on 1700 lbs. of wheat? The express charge between the points for which freight rates were given above is 25 cts. for less than 1 lb., 35 cts. from 1 to 2 lbs., 45 cts. from 2 to 3 lbs., 55 cts. from 3 to 4 lbs., 60 cts. from 4 to 5 lbs., 70 cts. from 5 to 7 lbs., 75 cts. from 7 to 10 lbs., 85 cts. from 10 to 15 lbs., $1.00 from 15 to 20 lbs., $1.10 from 20 to 25 lbs., $1.15 from 25 to 50 lbs., $2.30 from 50 to 100 lbs., and $2.30 per hundred for weights greater than 100 lbs. 58. What will be the difference of cost for a 200-lb. trunk shipped by express and by freight? 59. What will be the difference between freight and express charges on 300 lbs. of apples? 60. Which will be the cheaper way to ship a suit of clothes weighing, when boxed, 11 lbs.? How much cheaper? 61. Pupils may add problems concerning produce shipped to or from their nearest freight and express offices. DIVISORS AND MULTIPLES 85. Name two factors of 18, 25, 32, 81, 120. Name three factors of 18, 30, 45, 50, 66. Name a factor common to 12 and 36. If 3 is taken as one of the factors of 18, what is the other factor? How is the second factor found? The process of separating a number into its factors is called Factoring. 86. An exact Divisor of a number is a factor of that number. 87. A factor or a divisor that is common to two or more numbers is called a Common Divisor. 88. Name all the factors or exact divisors of 3, 7, 19. A number that has no factors or divisors except itself and 1 is called a Prime Number, e.g., 7, 11, 19, are prime numbers. 89. Factors that are prime numbers are called Prime Factors. 90. A number not a prime number is called a Composite Number. 91. Which of the following numbers are exactly divisible by 2 or have 2 as a factor: 2, 4, 6, 9, 11, 13, 14, 15, 16, 17, 21, 22, 27, 30? 92. Every number which contains the factor 2 is called an Even Number. 93. Numbers that are not divisible by 2 are called Odd Numbers. 94. Numbers that have no common factors are said to be prime to each other. EXERCISE 45.- WRITTEN 1. Write a list of all prime numbers below 100. 2. Write a list of all odd numbers below 100. 3. Write all the exact divisors of all the numbers from 1 to 50. 4. Separate the following into prime factors: 4, 5, 7, 8, 10, 12, 13, 14, 16, 18, 21, 24, 25, 30, 34, 36. 5. Separate the prime, composite, even, and odd numbers in the following, and give reasons for your answers: 1, 6, 7, 10, 11, 12, 14, 19, 21, 24, 26, 27, 32, 33. 6. Write a list of the numbers from 2 to 50 that contain 2 as a factor. What do you note regarding the units' figure of each number? 7. Write a list of the numbers from 5 to 100 that contain 5 as a factor. What do you note regarding the units' figure in each case? 8. Write a list of the numbers from 3 to 60 which contain 3 as a factor. What do you note regarding the sum of the figures or digits of each number? 9. Write a list of the numbers from 9 to 90 that contain 9 as a factor, and find whether 9 is exactly contained in the sum of the digits of each of these numbers. 95. A number is divisible: by 2 if the units' figure is 2, 4, 6, 8, or 0; by 3 if the sum of its digits is divisible by 3; by 4 if the number represented by the two right-hand figures is so divisible; by 5 if the units' figure is 5 or 0; by 8 if the number represented by the three right-hand figures is so divisible; by 9 if the sum of its digits is so divisible. 96. Find the prime factors of 720. 5)720 2)144 2) 72 2) 36 2) 18 3) 9 3 According to divisibility test 5 is a factor. 2 is a second, third, fourth, and fifth factor, 3 is the last factor. Hence, the prime factors of 720 are 5, 2, 2, 2, 2, 3, and 3. |