Write the following in Arabic numerals: 37. Four hundred sixty-four thousand one hundred fifty-two. 38. Thirty-five thousand sixty-nine. 39. Seventeen hundred eighty-five. 40. Ninety-four hundred sixty-two. 41. Five million thirty-two thousand three hundred eighty. 42. Fifty-four million six thousand eight. 43. Two hundred thirty million sixteen thousand seventy. 44. Eight hundred thirty-six thousand two hundred ninety-one. 45. Three hundred two thousand six hundred fifteen. 46. Seventy-seven hundred ninety-eight. 47. Six hundred twenty-nine thousand two hundred forty-five. 48. Seven million two hundred thousand one hundred ninety-six. 49. Seventy-six million six thousand seventy-one. 50. One hundred thousand eighty-six. 51. Two hundred seventeen million seventy-five thousand eight hundred four. 52. Twelve million six thousand forty-seven. 53. One million eight hundred forty thousand. HISTORICAL NOTES 8. Origin of the Arabic Numerals. -The Arabians learned the system of numerals which now bears their name from the Hindoos and brought it with them to Europe when they invaded Spain about 1100 years ago. After that it spread very slowly, and it was not until 400 years later that it became known even to the scholars of Europe outside of Spain. But by the time Columbus discovered America, the Arabic System had almost entirely displaced the old Roman System for commercial purposes in southern Europe. In England it gained firm hold somewhat later. 9. Comparison of the Arabic and Roman Systems. To appreciate the superiority of the Arabic over the Roman numerals one may write two large numbers in Roman numerals and try to multiply them. The operations of addition and subtraction were not even performed by using numerals, but by means of an instrument called the abacus. 10. The Abacus. - This consists of a frame with rods, on each of which are ten beads. Each bead on the lowest rod represents one. Each bead on the next rod represents ten, each bead on the third rod represents one hundred, and so on. Numbers are expressed by pushing beads to the right of the frame. The arrangement of the beads in the figure represents the number 8324. By means of the abacus numbers can be added and subtracted very rapidly. It is said that by using it an expert Japanese computer can add numbers as rapidly as they can be read to him. 11. Early Methods of Multiplication and Division. - Multiplication and division are not performed very easily on the abacus. As late as the year 944, a distinguished European mathematician multiplied 400 by 5 by adding. The same mathematician divided 6152 by 15 by finding all the multiples of 15 up to 6000. That is, he wrote the numbers. 30, 45, 60, 75, 90, 105, and so on up to 6000. In this way he found that 15 is contained 400 times in 6000. way that 15 is contained 10 times in 150. 15 is contained 410 times in 6152 with a Then he found in the same From this he concluded that remainder 2. CHAPTER II ADDITION 12. Use of Addition in Business. In business addition is the most generally used of the fundamental processes, and considerable skill in adding is absolutely essential for any one who is to become a competent accountant or business man. It is also of great use to every citizen in his daily life. 13. Definition of Addition. Addition is the process of taking two or more numbers together to form one number. The numbers to be added 14. Addends, Sum, Sign of Addition. are called addends, and the result is called the sum. The sign of addition, +, is called plus. Numbers to be added are usually arranged in a column. Accuracy in addition depends partly upon attention to the proper writing of the figures. They should be made of uniform size, uniformly spaced, and legible. Figures of the same order should stand in a straight column. For the practical accountant it is important to be able to dictate numbers understandingly and also to be able to write them down from dictation in proper form to be added. But it is still more important to be able to copy figures accurately, since this is part of the accountant's daily work. EXERCISES From dictation write the following sets of numbers in columns ready for adding. Also copy them: 1. 47 607, 304 783, 2364 189, 402 683, 50 763 457, 37 126 872. 2. 269 478, 9 251 260, 849, 200 458, 752 645, 9 654, 212, 78 769. 3. 75 254, 9287 484, 20 953 787, 548 175, 25 658 214, 174 195, 25 310, 378 061, 19756 480, 900 465 628. 4. 122 759, 984 561, 67 458, 200 045, 17 479, 452 890, 17 284, 348 765, 427 859, 24 856. ORAL EXERCISES Give the sums below very rapidly. Note that in 7 + 8 and 57 +8 we have the same combination of figures of the first order. 59 4 24 54 7 47 5 5 Beginning with 4 count to 95 by 7's, that is, say 4, 11, 18, ... Count from 8 to 98 by 9's, also from 6 to 94 by 8's. Count from 5 to 97 by 4's, also from 6 to 94 by 11's. |