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Math Help - Multiplying Bases

  1. #1
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    Multiplying Bases

    I don't understand how to multiply bases.

    Ex. 342 base 7
    X 3 base 7

    I understand that you can only use numbers 0,1,2,3,4,5,6 but I just have no idea what else to do. I don't get how to convert it to base 10.
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  2. #2
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    Quote Originally Posted by Avitus View Post
    I don't understand how to multiply bases.

    Ex. 342 base 7
    X 3 base 7

    I understand that you can only use numbers 0,1,2,3,4,5,6 but I just have no idea what else to do. I don't get how to convert it to base 10.
    It is exactly like multiplying in base ten, just remember where your arithmetic lives

    3_7 \cdot 2_7=6_7

    Now the next one is just a bit harder

    3_7 \cdot 4_7=15_7 why is this true?

    Remember that multiplication is just repeated addition i.e

    4_7+4_7=11_7 i.e we have 1 seven and one left over

    11_7+4_7=15_7

    And for the last one we have

    3_7\cdot 3_7=12_7


    Now when you multiply just use these compuations and don't forget to carry to the next column.

    Also remember what base seven really means is

    342_7=3\cdot 7^2+4\cdot 7^1+2\cdot 7^0

    This is just like base 10 i.e

    342=3\cdot 10^2+4\cdot 10^1+2\cdot 10^0

    I hope this helps.
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