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Math Help - Base three division

  1. #1
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    Base three division

    I need help with division in base three;
    Find the quotient for 222(base three) / 22(base three)
    it would be helpful if you can explain step by step

    I also need help with subtraction in different bases beside base 10. For example 21(base four) - 13(base four)
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  2. #2
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    Re: Base three division

    Hey JojoZ.

    Do you want to convert to base 10 and do it that way or do it natively in base 3?
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  3. #3
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    Re: Base three division

    can you show me in both ways
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  4. #4
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    Re: Base three division

    In base 10 we convert both by using

    2*3^2 + 2*3^1 + 2*3^0 = 18 + 6 + 2 = 26 in Base 10
    2*3^1 + 2*3^0 = 6 + 2 = 8.

    26/8 = 3 remainder 2 Which gives a quotient of 3 and in base 3 that is 10_(base3)

    To do it in base 3 natively we use the long division algorithm

    222
    )-------
    22

    22 goes into 222 10 times (remember 10 is 3 not 10 in base 10)
    22*10 = 220
    222-220 = 2

    So 222_(base 3) = 22_(base3) * 10_(base3) + 2_(base3).
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  5. #5
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    Re: Base three division

    okay this starting to make sense, can you teach me subtraction as well?
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  6. #6
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    Re: Base three division

    Give me some example numbers to work with.
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  7. #7
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    Re: Base three division

    21(base four) - 13(base four)
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  8. #8
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    Re: Base three division

    21-13 (Base four).

    1 is less than 3 so we cross out 2 replace with 1 and we get 11-3=2. Then we do 1-1 (remember we crossed out 1 in 2nd digit) = 0 so 21-13 = 2(base4).

    Confirming in base 10, we get 21 = 2*4^1 + 1*4^0 = 9 and 13 = 1*4^1 + 3*4^0 = 7 and 9-7 = 2 as expected.
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  9. #9
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    Re: Base three division

    why is 11-3=2?
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  10. #10
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    Re: Base three division

    Its in base 4, not base 10.
    Thanks from JojoZ
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  11. #11
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    Re: Base three division

    oh i get it now. Thanks so much for the help XD
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