128. 1. If to of a person's age, 1, 1, 1, and of his age is added, the sum will be 1 year less than his age, how old is he? 2. There were two equal sums of money on interest, one for 2 years at 3 per cent., and the other for 1 year at 4 per cent. the interest on both sums was $1.20; what was the interest on each? What was the value of each sum? 3. Suppose a cistern has one pipe which will fill it in 4 hours, and another which will empty it in 3 hours; if the cistern is full, and the water is allowed to run freely through both pipes, in what time will the cistern be emptied? 4. A's hat and coat together cost $15; his hat and vest together cost $13; his vest and coat together cost $18; what was the cost of each article? 5. A and B can do a piece of work in 5 days: B and C can do it in 6 days, and A and C can do it in 10 days; in what time can all do it together? In what time can each do it alone? 6. A boy had a certain number of apples: if he had sold them at the rate of 2 for 1 cent, he would have lost 2 cents; by selling them at the rate of 3 for 2 cents, he gained 7 cents; how many apples had he? 7. A man went to market with a certain number of pigs the first day he sold of them, the next day he sold 6 pigs more than of the remainder, after which he had 4 pigs left; how many had he at first? 8. When the value of gold coin is 50 per cent. higher than paper money, how many whole dollars in gold can I get for a 10-dollar bill, and how much paper currency besides? WRITTEN ARITHMETIC. EXPRESSING NUMBERS. 1. 1. All numbers are expressed by using, singly or in combination, the figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. 2. To express any number of units, from one to nine, a single figure is used; thus, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. 2, 3, 4, 5, 6, 7, 1, 8, g. 3. A collection of ten units is called one ten, or a unit of the second order; two such collections, two tens; three such collections, three tens, etc. To express any number of tens, from one to nine, the same figures are again used, but they are now placed at the left of another figure, as follows: 1 ten is (expressed Phase), 10; 1 ten with 1 unit is (expressed), 11; 2 tens are 66 3 tens are 66 etc. 20; 2 tens with 9 units are etc. 66 29; 4. A collection of ten tens is called one hundred, or a unit of the third order; two such collections, two hundred, etc. To express any number of hundreds, from one to nine, the same figures are again used, but now they are placed at the left of two other figures; as follows: 1 hundred is expressed thus, 100; 2 hundred, 200; 5 hundred, 500; 1 hundred with 1 ten and 1 unit is expressed thus, 111; 2 hundreds with no tens and 4 units are 9 hundreds with 9 tens and 9 units are 66 204; 66 999; 5. A collection of ten hundreds is called one thousand, or a unit of the fourth order; two such collections, two thousand, etc. (150) To express any number of thousands, from one to nine, the same figures are again used, but they are now placed at the left of three other figures; as follows: 1 thousand is expressed thus, 1 thousand with 1 hundred, 1 ten and 1 unit, is expres'd 1111; From the above, we see that numbers, from single units to thousands, are expressed by a scale of tens. All numbers are expressed by the same scale; thus, 10 units (1st order) 10 tens 10 hundreds 10 thousands 10 ten thousands etc. = 1 ten (2d order). 10 hundred thousands = 1 million. etc. From the above, we see that a unit of the second order equals 10 units of the first order; that a unit of the third order equals 10 units of the second order; and generally, that a unit of any order equals 10 units of the next lower order. When whole numbers are expressed by figures, the units' figure occupies the first place at the right, the tens, the second place, the hundreds, the third place, the thousands, the fourth place, etc.; thus, — sands. ∞ 7th. Millions. 3d. Hundreds. c2d. Tens. 8 9 7 8 2 3 2 Number. 232 is read two hundred thirty-two. 8,230 is read eight thousand, two hundred thirty. 78,032 is read seventy-eight thousand, thirty-two. 970,200 is read nine hundred seventy thousand, two hundred. 8,970,000 is read eight million, nine hundred seventy thousand. 2. 1. In what place should a figure be written to represent units? to represent tens? hundreds? 2. Write 2 so that it shall represent tens; so that it shall represent hundreds. 3. How many units are there in 1 ten? in 3 tens? in 1 hundred? 4. How many tens in 20 units? in 60 units? How many tens and units in 15? in 25? in 42? 5. Express in figures, six; forty-six; thirty. Read the following numbers: — 25. Where should a figure be written to represent thou Read the following numbers: sands? Express in figures, 34. Four thousand. 35. Four thousand, one hundred. 36. Three thousand, four hundred seven. 37. Five thousand, two hundred sixteen. 38. Seven thousand, thirty-six. 39. Eight thousand, two. 40. Where should a figure be written to represent ten thousands? Express in figures, 49. One hundred six. 50. Seventeen thousand, eight hundred. 51. Three thousand, forty-five. 52. Seventy thousand, seventy. 53. Four thousand, four. 54. Where should a figure be written to represent hun、 dred thousands? Read the following numbers: 55. 183. 57. 36,075. | 59. 365,000. 61. 932,001. 56. 1,702. 58. 82,101. 60. 800,000. 62. 700,110. Express in figures,— 63. One hundred sixty thousand. 64. Fifty-five thousand, seven hundred sixty-two. 65. One hundred six thousand, forty. 66. Three hundred seventy-five thousand, eight hundred. 67. Four hundred thousand, four. 68. Where should a figure be written to represent millions? Read the following numbers: Express in figures, 78. Eighteen thousand. 79. Eight million, one hundred eighty-five. 80. One hundred eighty-five thousand. 81. Two million, two hundred thousand. 82. Fifty-eight thousand, six. 83. Write 5 so that it shall represent tens; so that it shall represent hundreds; thousands; ten thousands. 84. Write 17 so that it shall represent tens; hundreds. Ans. 17 tens = 170; 17 hundreds = 1700. 85. Write 45 so that it shall represent tens; hundreds; thousands. The number of units of the different orders of a number are sometimes called its terms. Thus, in the number 235, the terms are hundreds, 3 tens, and 5 units. 86. Name the terms of the number 768. |