1 / 48

Understanding Base Systems and Arithmetic Operations in Different Numerical Bases

This resource explores various base systems, including Roman numerals and bases 5, 6, 7, and 2. It provides exercises on converting between bases, performing addition and subtraction in non-decimal systems, and manipulating numeric representations with units, strips, and mats. It covers algorithms for multiplication and division, highlighting their applications with real-world examples. The content encourages a hands-on approach with homework problems focused on mastering operations across different bases, enhancing numerical fluency and problem-solving skills.

hayden-sellers
Télécharger la présentation

Understanding Base Systems and Arithmetic Operations in Different Numerical Bases

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. Numerations Systems 336 would be written as

  2. Roman Numerals I V X L C D M 1 5 10 50 100 500 1000 M D CCC L V I IV = 4 IX = 9 XL = 40 CD = 400 CM= M CM L IX =

  3. Base 10 • Sticks in Bundles • Unifix Cubes • Units, Strips, Mats • Base Ten Blocks

  4. Homework Pg 159 # 1,2,13,14,16,17,18,26-29

  5. Different Base Systems Base Five Digits used 0,1,2,3,4 Decimal Value of Positions 54 = 625 53 = 125 52 = 25 51 = 5 50 = 1 1 3 2 4 2Five 625 + 3 x 125 + 2 x 25 + 4 x 5 + 2 x 1 = 625 + 375 + 50 + 20 + 2 = 1072

  6. Base 6 Base 6 Digits used 0,1,2,3,4,5 Decimal Value of Position 64 = 1296 63 = 216 62 = 36 61 = 6 60 = 1 1 2 3 5 2six =

  7. Base Seven Base 7 Digits used 0,1,2,3,4,5,6 Decimal Value of Position 74 = 2401 73 = 343 72 = 49 71 = 7 70 = 1 1 2 3 5 2seven =

  8. Base 2 Base 2 Digits used 0,1 Decimal Value of Position 25 = 32 24 = 16 23 = 8 22 = 4 21 = 2 20 = 1 1 0 1 1 0 1two =

  9. Convert to Base 10 notation 413 five 2004 five 100 five 214 seven 213 six 415 eight 2E4twelve 1TEtwelve

  10. Homework Pg 165 # 1,5,9,10,11,13

  11. Addition Algorithm • Making exchanges with Units, Strips, Mats • 15 units, 11 strips, and 2 mats. What exchanges must be made in order to represent the same number but with the smallest number of pieces? • Pg 166

  12. Units, Strips, Mats Adding 1 mats, 3 strips, and 5 units + 2 mats, 4 strips, and 3 units 3 mats, 7 strips, and 8 units

  13. Add 3 mats, 5 strips, 7 units + 2 mats, 7 strips, 4 units 5 mats, 12 strips, 11 units Exchange 5 mats, 13 strips, 1 unit Exchange 6 mats, 3 strips, 1 unit

  14. Use Mats, strips, and Units • 457 + 265 =

  15. Subtraction Algorithm • 9 – 5 = • 9 take away 5 =

  16. 3 mats, 7 strips, 5 units - 2 mats, 4 strips, 3 units 1 mat, 3 strips, 2 units

  17. 375 – 189 • =

  18. 375 – 18936 (15) – 189

  19. 375 – 18936 (15) – 189 • =

  20. 375 – 18936 (15) – 1892(100) + 16(10) + 15(1)

  21. 375 – 1892(100) + 16(10) + 15(1) – 189=186

  22. 324- 156 100s 10s 1s 3 2 4 - 1 5 6 3 1 14 - 1 5 6 2 11 14 - 1 5 6 1 6 8 Exchange

  23. 3 hours 24 minutes 54 seconds + 2 hours 47 minutes 38 seconds 6 hours 12 minutes 32 seconds 7 hours 46 minutes 29 seconds - 3 hours 27 minutes 52 seconds 4 hours 18 minutes 37 seconds

  24. Adding & Subtracting in Other Bases 143 five +234 five

  25. 25s 5s 1s 1 4 3 five + 2 3 4 five 3 12 12 five 4 3 2 five

  26. Add 231 five 434 five 144 five 243 five 430 five 1232 five

  27. Subtract 231 five 434 five 144 five 243 five 32 five 141 five

  28. What Base ? 231 344 534 +414 +143 +245 1200 1042 1112 1020 572 - 203- 144 312 427

  29. HomeworkPg 181 #1a,3,5,6,7,21,33-36,

  30. Multiplying Whole Numbers 9 times 3 = 3+3+3+3+3+3+3+3+3 2 groups of 10 and 7 ones = 27

  31. Multiplying Whole Numbers 9 times 3 = 3+3+3+3+3+3+3+3+3 • Use Sticks in Bundles • Unifix Cubes • Units, Strips, Mats • Base Ten Blocks

  32. Multiplying Whole Numbers 3 times 213 = 213+213+213 • Use Sticks in Bundles • Unifix Cubes • Units, Strips, Mats • Base Ten Blocks

  33. Multiplying Whole Numbers 4 times 243 = 243+243+243 • Use Sticks in Bundles • Unifix Cubes • Units, Strips, Mats • Base Ten Blocks

  34. 15 x 324 324 15 20 100 1500 40 200 3000 4860 5 x 4 5 x 20 5 x 300 10 x 4 10 x 20 10 x 300

  35. Final Algorithm 1 2 324 x 15 1620 324 4860

  36. Sum = 4860

  37. 324 x 15

  38. 463 x 34

  39. 527 x 43

  40. DivisionA ÷ B A/B B  A • Meaning of Division: • How many groups? • How many in each group?

  41. How many groups? • A ÷ B • 8 ÷ 2 • 8 objects are divided into groups with 2 objects in each group. • “How many Groups?”

  42. How many in each group? • A ÷ B • 8 ÷ 2 • How many objects are in each group when 8 objects are divided into 2 groups.

  43. Division Algorithms • Standard Method • Scaffold Method • Repeated Subtraction

  44. Homework • Pg 192 # 1a,7,10,11,13,14,17,35-38 • Pg 183 #21,22,23a,d,e, • Finish Wkst.

  45. Mental Arithmetic & Properties • 35 + 7+ 15 (Comm.) • 8+3+4+6+7+12+4+3+6+3 (add to 10s) • 25 x 8 • 4 x 99

  46. Rounding Numbers • Determine to which position your are rounding • If the digit immediately to the right of this position is 5 or more, add 1 to the digit in the position to which you are rounding. Otherwise leave the digit unchanged. • Replace with 0s all digits to the right of the position to which you are rounding, up to the decimal point.

  47. Homework • Pg 206 # 1,2,4,5,28 – 31 • Review Packet on Web

More Related