SCHOOL ARITHMETIC REVIEW OF FUNDAMENTAL PROCESSES NOTATION AND NUMERATION A unit is a single thing; as one, one cent, one inch, one dollar. A number is a unit or a collection of units. Notation is a method of writing numbers by means of symbols. Numeration is a method of naming or reading numbers represented by symbols. The Arabic notation by the figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 is the system in common use. The Roman notation, used for certain purposes, employs seven capital letters, I, V, X, L, C, D, and M for the representation of numbers. ARABIC SYSTEM For convenience in reading large numbers, in the Arabic system, the figures are generally separated by commas into groups of three figures each, called periods. The first period, counting from the right, is units; the second, thousands ; the third, millions; the fourth, billions ; the fifth, trillions; etc. The following table shows the arrangement of these periods, and the three orders of figures in each period: The number in the table is read, 101 trillion, 345 billion, 642 million, 1 thousand, 346. Write : 1. 246 billion, 25 million, 161 thousand, 104. 2. 20 billion, 2 million, 12 thousand, 8. 3. 14 billion, 36 million, 1 thousand, 109. 4. 300 billion, 304 million, 100 thousand, 40. 5. 16 billion, 9 million, 70 thousand, 700. 6. 900 billion, 26 million, 18 thousand, 9. 7. 7 billion, 46 million, 900 thousand, 90. 8. 74 billion, 7 million, 46 thousand, 809. Point off and read : 9. 700102 . 16. 5050504 23. 60414 10. 6067004 12126012 102365 8011100 18. 87649101 25. 14763487 12. 90314607 19. 104706950 26. 243540038 13. 910723586 20. 1202436414 27. 2452603467 14. 837421012 21. 3183456109 28. 8703005020 15. 987654321 22. 7891234560 29. 6010100100 17. 24. ROMAN SYSTEM I V. X L C D M 1 5 10 50 100 500 1000 The other numbers are represented by combinations thus: I. When a letter is followed by the same letter or by one of less value, the values of the letters are to be added: Thus, XX represents 20; XI represents 11. II. When a letter is followed by one of greater value, the value of the smaller is to be subtracted from that of the greater. Thus, IV represents 4; IX represents 9. III. When a letter is placed between two letters of greater value, the value of the smaller is to be subtracted from the sum of the other two. Thus, XIV represents 14; XIX represents 19. A bar placed over a letter multiplies its value by 1000. Thus, V represents 5000. The following table further illustrates the system. XC, 90 DCCC, 800 C, 100 CM, 900 L, 50 CD, 400 MCM, 1900 VI, 6 XIV, 14 LX, 60 D, 500 V, 5000 VII, 7 XV, 15 LXX, 70 DC, 600 M, 1,000,000 Read: 1. XLIII CDXLIX MDII MCDXCII 2. XCIX MCMVIII MDLXXVI. MDCCCLXI 3. . Express in Roman notation: 41, 63, 84, 99, 107, 218, 572, 735, 996, 1907, 1564, 1616, 1000, 260,000, ADDITION Addition is the process of uniting two or more numbers to form one number. The addends are the numbers to be added. The sign +, called plus, indicates addition; and the sign = indicates equality. Like numbers are numbers that express the same units, as 3 pounds and 5 pounds, or 3 and 5. Unlike numbers are numbers that express different units, as 7 days and 3 yards. Only like numbers can be added. 1. Add the numbers that you wrote in examples 1-8, p. 8. Add the following. Drill until each example can be added in 1 minute or less. In adding, group numbers into convenient combinations : 5. 6. 6720 2954 3783 1751 5068 2091) 4604 3261 5427 7173 7504 8675 ) 7259 5050 7891 5009 8795 6985) 8753 7406 5030 4287 6474 3745 ) 6758 2834 6793 5783 2758 5268 20 4326 6498 7406 7205 6471 7777 6734 5065 5872 4987 2050 5989 7583 8439 3458 6034 6579 7481 3586 9823 7295 2985 2068 5479) 2734 7984 8376 3046 6579 4725 2030 2794 1154 2068 3074) 6050 5984 6384 3683 5547 0 7438 3749 6589 4594 4280 6875) 5006 5308 7405 5181 5683 3014) 2899 1234 9826 3001 7219 7256) 3333 5678 5432 9050 9005 2. 3. 4. 5608 149 SUBTRACTION Subtraction is the process of finding the difference between two numbers, or of taking one number from another. The minuend is the number from which we subtract. The general method of subtraction has already been learned. The following methods are also convenient : 1. Take 378 from 653. I. By adding (the method used in making change). 653 What number added to 8 will make 13? (5.) Carry 1. 378 What number added to 8 will make 15? (7.) Carry 1. 275 What number added to 4 will make 6? (2.) II. By subtracting from 10. 5 – 3 = 2. The steps in the general method of subtraction are borrow, add, subtract. In this, they are borrow, subtract, add. |