Exploring Math in Base -5: Addition & Multiplication Tables

In summary, the addition tables would look the same, and the multiplication would be the same as well.
  • #1
1+1=1
93
0
i am curious as to how this would look. i wonder how the addition tables would look in base -5? would the multiplication look the same?

here is what i know so far:

addition multiplication
0 1 2 3 4 0 0 0 0 0
1 2 3 4 10 0 1 2 3 4
2 3 4 10 11 0 2 4 11 13
3 4 10 11 12 0 3 11 14 22
4 10 11 12 13 0 4 13 22 31

i know this, but where are the negative signs at??
 
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  • #2
Negative bases

Interesting concept, here's some links to info on negative bases:
http://mathforum.org/library/drmath/view/55710.html
http://www.maa.org/devlin/devlinfeb.html
One thing the articles point out is that no sign is necessary,
instead negative and positive numbers differ in their number
of digits.
 
Last edited by a moderator:
  • #3
these negative bases are quite interesting, although are they reallly used all that much? i know that everyone I've talked to is basically saying "no." however, almost anyone could make up their own number system, but no one else could understand it.
 
  • #4
In Alice in Wonderland, when Alice has fallen down the rabbit hole, she wonders if she's swapped places with someone called Mabel. To discover her true identity, she recites the 4 times table:

"But if I'm not the same, the next question is, 'Who in the world am I?' Ah, that's the great puzzle!... and I'm sure I can't be Mabel, for I know all sorts of things, and she, oh! she knows such a very little!... I'll try all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is -- oh dear! I shall never get to twenty at that rate!"

Figure out why this is true !
 
  • #5
this definitely has something to do with numbers that are NOT base 10. other than that, i'll have to sleep on it. :wink:
 

1. What is base -5 and how does it differ from traditional base 10?

Base -5 is a number system that uses a negative base instead of a positive one like in traditional base 10. This means that instead of each place value being a power of 10, it is a power of -5. For example, in base -5, the ones place represents -5^0, the fives place represents -5^1, and so on.

2. How do you add numbers in base -5?

To add numbers in base -5, you follow the same process as traditional addition, but you have to account for the negative base. So, for example, in base -5, 4 + 3 would be written as 4 + 3 = 12. This is because in base -5, the digit "1" represents -5, and the digit "2" represents -10. Therefore, the sum of 4 and 3 in base -5 is 12, or -10 in base 10.

3. Can negative numbers be represented in base -5?

Yes, negative numbers can be represented in base -5. In fact, the negative numbers in base -5 are represented by using the negative sign "-" followed by the positive number in the same base. For example, in base -5, -3 would be written as -3 = -13. This is because the digit "1" represents -5, and the digit "3" represents -15, which combined give us -3 in base -5.

4. How does multiplication work in base -5?

Multiplication in base -5 follows the same principle as traditional multiplication, but you have to account for the negative base. For example, in base -5, 4 x 3 would be written as 4 x 3 = 11. This is because in base -5, the digit "1" represents -5, and the digit "1" represents -5, which when multiplied together give us -25, or 11 in base -5.

5. Can you convert numbers from base -5 to base 10?

Yes, numbers in base -5 can be converted to base 10. To do so, you can use the same process as converting numbers from any other base to base 10. You multiply each digit by its corresponding place value, then add all the results together. For example, in base -5, the number 23 would be converted to base 10 as follows: 23 = (2 x (-5)^1) + (3 x (-5)^0) = (-10) + 3 = -7.

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