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Math Help - Base 5 Division

  1. #1
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    Base 5 Division

    I am stuck on a base five division problem.

    I have to divide 4 base five into 134 base five.

    I have the first part which is 2 which gives me 8 and then that gives me 13. I'm then left with 4 and 4 can't be divided by base 5 because base five is larger than 4. I'm stuck. Can someone please help.

    Thanks
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  2. #2
    Super Member Bacterius's Avatar
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    What do you mean by "dividing by base 5". Base 5 means there are only 4 possibly used digits : 0, 1, 2, 3 and 4. So you can get 32, 44, 10, but you cannot get 5, nor can you get 77 or 19. See what I mean ? You don't divide a number by a base, this is totally different sort of stuff.

    So, do you mean that you want to divide 134 by 4, knowing you are only working on base 5 ? Or do you want to convert 4 and 134 (they are in base 10 then) into base 5 ?
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  3. #3
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    I don't have to covert the number (they're already in base ten). I have to divide 4 base five by 134 base five. Is there a "pencil icon" so that I can write it out?
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  4. #4
    Super Member Bacterius's Avatar
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    Quote Originally Posted by albinuta View Post
    I don't have to covert the number (they're already in base ten). I have to divide 4 base five by 134 base five. Is there a "pencil icon" so that I can write it out?
    Uhm ... what do you mean ? You say they are already in base 10, but then you say they are in base 5. What base are they in, and what base should they be in ?
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  5. #5
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    the question reads: 4five divided 134five

    I know that if I times 2 by 4 it gives me 8 and the eight converted to base five is 1 with a remainder of three which leaves me with the 4 of the 134. I don't know what to do with that 4. If I multiply the 4 by 1 it gives me just a 4 and that cant be coverted into base five. But the 4 can be multiplied by 1 which would give me 4.

    Would my final answer be 21five?

    Is there a writing tool so that I can write out the actual problem? I don't see a pencil icon anywhere.
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  6. #6
    Super Member Bacterius's Avatar
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    Quote Originally Posted by albinuta View Post
    I know that if I times 2 by 4 it gives me 8 and the eight converted to base five is 1 with a remainder of three [...]
    I think you are confusing bases with modular arithmetic.

    Bases : 8 (base 10) converted to base 5 gives 13 (the first numbers in base 5 are : 0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31 ...)
    Modular arithmetic : 8 \equiv 3 (mod 5) (which means that the remainder of the division of 8 by 5 is 3)

    To write out the actual problem, you can either try to use LaTeX symbols (painful to write), or you can open Paint and roughly scribble your problem, then upload and paste the image on a new comment ?
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  7. #7
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    Quote Originally Posted by albinuta View Post
    I am stuck on a base five division problem.

    I have to divide 4 base five into 134 base five.

    I have the first part which is 2 which gives me 8 and then that gives me 13. I'm then left with 4 and 4 can't be divided by base 5 because base five is larger than 4. I'm stuck. Can someone please help.

    Thanks
    i don't know if this what you mean. 4(base5) / 134(base5) = 0.0211402114...(base5)
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  8. #8
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    4(base5) / 134(base5) ?

    Quote Originally Posted by albinuta View Post
    I am stuck on a base five division problem.

    I have to divide 4 base five into 134 base five.

    I have the first part which is 2 which gives me 8 and then that gives me 13. I'm then left with 4 and 4 can't be divided by base 5 because base five is larger than 4. I'm stuck. Can someone please help.

    Thanks
    i don't know if this what you mean. 4(base5) / 134(base5) = 0.0211402114...(base5)
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  9. #9
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    You could try the basis representation theorem, that all numbers, say, of base 5, can be written like this: a_0 + a_15^1 + a_25^2 + \cdot\cdot\cdot + a_n5^n
    and numbers of base 4 can be written like this: a_0 + a_14^1 + a_24^2 + \cdot\cdot\cdot + a_n4^n

    see where you can get from there...

    Hope I helped!
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