3. Eight units of the 4th order and four of the 2d. 4. Five units of the 4th order and eight of the 2d. 5. Three units of the 5th order, six of the 4th, four of the 3d, and seven of the 1st. 6. Two units of the 6th order, four of the 5th, nine of the 4th, three of the 3d, and five of the 1st. 7. Three units of the 9th order, eight of the 7th, four of the 6th, six of the 5th, and nine of the 1st. 55. Write and read the following numbers in figures: 1. Twenty-five units in the 2d period, and four hundred ninety-six in the 1st. Ans. 25,496. 2. Four hundred thirty-six units in the 4th period, twelve in the 3d, one hundred in the 2d, and three hundred and one in the 1st. 3. Eighty-one units in the 5th period, two hundred and nineteen in the 4th, and fifty-six in the 2d. 4. Nine hundred and forty units in the seventh period, eighteen in the fifth, and one hundred and three in the 3d. 56. Express the following numbers by figures : 1. Twenty-six thousand twenty-six. 2. Fourteen thousand two hundred eighty. 3. One hundred seventy-six thousand. 5. Seven million thirty-six. 6. Five hundred sixty-three thousand four. 7. One million ninety-six thousand. 8. Ten million ten thousand ten hundred ten. 9. Four hundred eighty-three million eight hundred sixteen thousand one hundred forty-nine. 10. Ninety-nine billion thirty-seven thousand four. 55. Roman Notation employs seven capital letters to express numbers. Thus, Letters. I, V, X, L, C, D, M. Values. 1, 5, 10, 50, 100, 500, 1000. When used alone, each letter has its fixed value. Numbers may be expressed by combining these letters according to the following principles: 1. Repeating a letter repeats its value. Thus, XX represents 20; CCC, 300; DD, 1000. 2. When a letter is placed after one of greater value, its value is to be added to that of the greater. Thus, VI represents 6; XV, 15; LXX, 70; DC, 600. 3. When a letter is placed before one of greater value, its value is taken from that of the greater. Thus, IV represents 4; IX, 9; XL, 40; XC, 90. 4. When a letter of any value is placed between two letters, each of greater value, its value is taken from the sum of the other two. Thus, XIV represents 14; LIX, 59; CXL, 140. 5. A bar or dash placed over a letter increases its value one thousand times. Thus, X represents 10000; XC, 90000; DL, 550000. MDCCCLXXX = 1880, one thousand eight hundred and eighty. 3. Seventy-three. 9. Seven hundred forty. 15. 1069. 10. Nine hundred ninety. 16. 25000. 17. 59300. 4. Sixty-eight. 57. Express by Arabic notation: 1. LXVII. 18. 87040. 6. DCLIII. 11. LIXCCCXLIV. 2. XCLXIV. 7. CXCIX. 3. CXXXV. 8. VDLIX. 4. CCXLIX. ?. DLX 13. MMMMXC. 14. VMDCCXLIX. 5. MXIX. 10. XXXID. 15. MDXXVCDLXXXIX. SYNOPSIS FOR REVIEW. 58. 1. Arithmetic. PRELIMINARY DEFINITIONS. 2. A Unit. 3. A Number. 4. An Integral Number. 5. Unit of a Number. 6. A Concrete Number. 7. An Abstract Number. 8. Like Numbers. 9. Unlike Numbers. 10. A Scale. 11. A Uniform Scale. 12. A Varying Scale. 13. A Decimal Scale. ADDITION ORAL EXERCISES. 59. 1. A man gave 5 dollars for a hat, and 9 dollars for a vest. How many dollars did he pay for both? 2. How many miles are 4 miles and 12 miles? 29 and 5? 24 and 5 ? 21 and 6? 27 and 6? 7 and 19? 7 and 26 ? 3. How many are 6 men and 14 men? 15 and 7? 4. How many are 14 and 5? 5. How many are 15 and 6? 6. How many are 7 and 12? 7. What kind of numbers are 9 pounds and 14 pounds? 8. Can 9 balls and 12 books be added? Why not? 9. Can 7 rods and 10 rods be added? Why? 10. How many are 4, 5, and 7? 5, 7, and 4? 4, 7, and 5? 11. In a shop are 15 men, 8 boys, and 6 girls at work. How many persons are at work in the shop? 12. I gave cents to one boy, 9 to another, and 6 to another. How many cents did I give to all? 13. Add by 2's from 1 to 31. OPERATION.-1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31 Add 14. By 2's from 4 to 50. 15. By 3's from 1 to 43. 16. By 3's from 6 to 51. 17. By 4's from 1 to 53. 18. By 4's from 5 to 45. 19. By 5's from 1 to 61. 20. By 5's from 7 to 82. 21. By 6's from 0 to 72. 22. By 6's from 2 to 80. 23. By 6's from 10 to 88. |
