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Math Help - Bases

  1. #1
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    Bases

    i PLEASE NEED HELP WITH 4010 base five minus 1234 base 5!! please and thank you I know that the numbers add to more than five so they need to be different
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  2. #2
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    Re: Bases

    I'd just use the usual method taught in schools, 'borrowing', but it's a little difficult to illustrate on here.

    Instead you could use 'equal addition' as follows.

    4010-1234

    adding 1 to both numbers

    =4011-1240

    adding 10 to both numbers

    =4021-1300

    adding 200 to both numbers

    =4221-2000

    =2221

    It's rather less efficient though.
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  3. #3
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    Re: Bases

    is this base five then? and would I use the same method for all bases? thank you so much for your quick response
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  4. #4
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    Re: Bases

    Well, you said it was base 5...?

    I wouldn't use the method I posted. I'd use 'borrowing'. Yes it works for any base.
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  5. #5
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    Re: Bases

    Hello, cathyharris4!

    Have you never ever done a subtraction in other bases?


    4010_5 - 1234_5

    \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 4 & 0 & 1 & 0 \\ - & 1 & 2 & 3 & 4 \\ \hline  \end{array}


    In C4, we can't subtract 4 from 0, so we "borrow" from C3.

    \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 4 & 0 & ^0\rlap{/}1\; & ^10\; \\ - & 1 & 2 & 3 & 4 \\ \hline  \end{array}


    The "1" we borrowed represents "5", so we have:

    \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 4 & 0 & 0 & 5 \\ - & 1 & 2 & 3 & 4 \\ \hline  \end{array}


    Subtract in C4 and we have:

    \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 4 & 0 & 0 & 5 \\ - & 1 & 2 & 3 & 4 \\ \hline &&&&1 \end{array}


    In C3, we can't subtract 3 from 0, so we "borrow" from C2.
    But C2 has "0"; we can't borrow.

    So we must borrow from C1.

    \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & ^3\rlap{/}4\;\; & ^10\;\; & 0 & 5 \\ - & 1 & 2 & 3 & 4 \\ \hline &&&&1 \end{array} \quad\Rightarrow\quad \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 3 & 5 & 0 & 5 \\ - & 1 & 2 & 3 & 4 \\ \hline &&&&1 \end{array}


    Now we can borrow from C2:

    \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 3 & ^4\rlap{/}5\;\; & ^10\;\; & 5 \\ - & 1 & 2 & 3 & 4 \\ \hline &&&&1 \end{array} \quad\Rightarrow\quad \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 3 & 4 & 5 & 5 \\ - & 1 & 2 & 3 & 4 \\ \hline &&&&1 \end{array}


    And we can complete the subtraction:

    \begin{array}{ccccc}  & ^{C1} & ^{C2} & ^{C3} & ^{C4} \\ & 3 & 4 & 5 & 5 \\ - & 1 & 2 & 3 & 4 \\ \hline &2&2&2&1 \end{array}

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