computation in other bases: multiplication

1. computation in other bases: multiplication Pamela Leutwyler

2. base 10 example Examine the familiar base 10 algorithm. Multiplication in other bases works the same way.

5. ones times ones = ones 6x4 = 24

6. ones times ones = ones 6x4 = 24 Each set of 10 “ones” is replaced by 1 “ten”

7. ones times ones = ones 6x4 = 24 2 Put down 4 and carry 2 Each set of 10 “ones” is replaced by 1 “ten”

8. 2

9. ones timestens =tens 4x2 = 8 2

10. ones timestens =tens 4x2 = 8 2 plus the 2 carried from the last step puts ten pebbles In the tens pile

11. ones timestens =tens 4x2 = 8 2 Each set of 10 “tens” is replaced by 1 “hundred”

12. ones timestens =tens 4x2 = 8 2 Each set of 10 “tens” is replaced by 1 “hundred”

13. ones timestens =tens 4x2 = 8 2 1 Put down 0 and carry one Each set of 10 “tens” is replaced by 1 “hundred”

14. ones timestens =tens 4x2 = 8 2 1 Put down 0 and carry one Each set of 10 “tens” is replaced by 1 “hundred”

17. tens times ones =tens 3x6 = 18

18. tens times ones =tens 3x6 = 18 Each set of 10 “tens” is replaced by 1 “hundred”

19. tens times ones =tens 3x6 = 18 1 Put down 8 and carry one Each set of 10 “tens” is replaced by 1 “hundred”

20. 1

21. tens timestens =hundreds 3x2 = 6 1

22. tens timestens =hundreds 3x2 = 6 1 plus the 1 carried from the last step

23. tens timestens =hundreds 3x2 = 6 1 plus the 1 carried from the last step Put down 7

24. tens timestens =hundreds 3x2 = 6 1 plus the 1 carried from the last step Put down 7

26. Add

27. base 5 example

30. 3 x 4

31. 2 3 x 4

32. 2 Put down 2 and carry 2 3 x 4

33. 2

34. 2 3 x 2

35. 2 3 x 2

36. 2 3 x 2

37. 2

38. 2 1 Put down 3 and carry 1

39. 2 1

42. 1 x4

43. 1 x 2 fives times fives = twenty fives

44. Add in the base 5

47. 1

48. 1

49. 1

50. another example This time we will not bother with the pebble board. As you work the familiar algorithm, it helps if you think in the base ten and then switch to the base 5.