How to Add and Multiply in Base 12

In the previous post, I explained some basics about base 12 counting. Since you’re back, clearly you’re a glutton for punishment (or your Algebra book is requiring you to do this).

Either way, here’s how to add in base 12:

And how to multiply:

I cheated a little here here, because to me this is the easiest way. If you need an example or two to do it “right,” post it in the comments and I’ll do a few for you.

A big thanks goes out to Kellie for the question.

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10 Responses to How to Add and Multiply in Base 12

    • Ellen, there are probably multiple ways of multiplying in base 12, it depends on who you are as to how complex or simple each are. In my experience with students over the years, personal preference is a bigger determining factor than a textbook or teacher ever can be.

      Can you explain a little bit more on which way you like it shown?

    • Sorry for the delay, tanasha.

      EE = 11(12) + 11(1) = 132

      2E = 2(12) + 11(1) = 35

      So EE + 2E = _____

      132 + 35 = 167 (base 10)

      167 = 1(144) + 1(12) + 11(1) = 11E (base 12)

      Thus EE + 2E = 11E (base 12)

    • If you’re translating 178, then yes…

      175 = 1(144) + 2(12) + 10(1) = 12T (base 12)

      (btw, thanks for stopping by to ask, Tanasha!)

  1. I don’t have to do this for colege or anything like that, but I am seriously interested in base 12 counting system, and I would be happy if you made a video on the ‘real’ way to multiply with base 12.

    • Technically it goes

      0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, …

      But A and B are just arbitrary – the first couple of letters in the alphabet. The T and E stand for ten and eleven, which might help as you think about this.

  2. Can you explain how solve this because im really having problems.

    5ETT x 3 = 15E86 but I always get 17E86

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