1 / 34

Section 4.2

Section 4.2. Place Value System. Objectives:. Understand and use the Babylonian System. Understand and use the Hindu-Arabic Expanded Notation with addition and subtraction. Use the Galley Method for multiplication. Use Napier’s Rods for multiplication. Key Terms:.

maude
Download Presentation

Section 4.2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Section 4.2 Place Value System

  2. Objectives: • Understand and use the Babylonian System. • Understand and use the Hindu-Arabic Expanded Notation with addition and subtraction. • Use the Galley Method for multiplication. • Use Napier’s Rods for multiplication.

  3. Key Terms: • Place Value System – the placement of the symbols in a numeral determines the value of the symbols, also called a positional system. • NOTE: In order to have a true place value system, you must have a symbol for zero.

  4. Babylonian Number System • The Babylonians developed an early example of a place value system. • This system was based on powers of 60, called a sexagesimal system. • There are only 2 symbols in the Babylonian system: • Represents 1 - • Represents 10 -

  5. For Example: • The number 23 can be written as: ,however, for larger numbers, they used several symbols separated by spaces, and multiplied the value of these groups, of symbols, by increasing powers of 60.

  6. Example 1: • Convert to Hindu-Arabic

  7. Example 2: • Convert to Hindu-Arabic

  8. Example 3: • Convert to Hindu-Arabic

  9. Example 4: 7,717 • Convert to Babylonian • In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

  10. Example 5: 7,573 • Convert to Babylonian • In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

  11. Example 6: 128,485 • Convert to Babylonian • In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

  12. Section 4.2 Assignment I • Class work: • TB pg. 216/1 – 16 All • Remember you must write the problem and show ALL work to receive credit for this assignment. • NO work, NO grade!

  13. Hindu-Arabic Numeration System Place Value • Based on Powers of 10. • Writing numbers in expanded notation. • 6,582 = (6x103)+(5x102)+(8x101)+(2x100)

  14. Example 7: 5,389 • Write the number using expanded notation.

  15. Example 8: 31,157 • Write the number using expanded notation.

  16. Example 9: 2,100,405 • Write the number using expanded notation.

  17. Section 4.2 Continued Addition and Subtraction using the Hindu-Arabic Expanded Notation

  18. Example 10: 4,625 + 814 • Add/Subtract using Expanded Notation

  19. Example 11: 5,264 + 583 • Add/Subtract using Expanded Notation

  20. Example 12: 728 – 243 • Add/Subtract using Expanded Notation

  21. Example 13: 4,317 – 2,561 • Add/Subtract using Expanded Notation

  22. Section 4.2 Assignment II • Class work: • TB pg. 216/33 – 40 All • Remember you must write the problem and show ALL work to receive credit for this assignment. • NO work, NO grade!

  23. Galley Method: 685 x 49 • Begin by constructing a rectangle.

  24. Galley Method: 685 x 49 • Divide into triangles called a galley.

  25. Galley Method: 685 x 49 • Compute partial products in each box

  26. Galley Method: 685 x 49 • Add numbers along the diagonals.

  27. Example 14: 7 x 364 • Multiply using the Galley Method.

  28. Example 15: 22 x 867 • Multiply using the Galley Method.

  29. Example 16: 239 x 456 • Multiply using the Galley Method.

  30. Napier’s Rods/Bones • Developed by John Napier in the 16th Century, for doing multiplication. • TB pg. 215 The Napier's rods consist of strips of wood, metal or heavy cardboardand are three dimensional.

  31. Example 17: 8 x 346 • Using Napier’s Rods

  32. Example 18: 21 x 768 • Using Napier’s Rods

  33. Example 19: 241 x 365 • Using Napier’s Rods

  34. Section 4.2 Assignment III • Class work: • TB pg. 216/41 – 52 All • Remember you must write the problem and show ALL work to receive credit for this assignment. • NO work, NO grade!

More Related