1. ## Base three division

I need help with division in base three;
Find the quotient for 222(base three) / 22(base three)
it would be helpful if you can explain step by step

I also need help with subtraction in different bases beside base 10. For example 21(base four) - 13(base four)

2. ## Re: Base three division

Hey JojoZ.

Do you want to convert to base 10 and do it that way or do it natively in base 3?

3. ## Re: Base three division

can you show me in both ways

4. ## Re: Base three division

In base 10 we convert both by using

2*3^2 + 2*3^1 + 2*3^0 = 18 + 6 + 2 = 26 in Base 10
2*3^1 + 2*3^0 = 6 + 2 = 8.

26/8 = 3 remainder 2 Which gives a quotient of 3 and in base 3 that is 10_(base3)

To do it in base 3 natively we use the long division algorithm

222
)-------
22

22 goes into 222 10 times (remember 10 is 3 not 10 in base 10)
22*10 = 220
222-220 = 2

So 222_(base 3) = 22_(base3) * 10_(base3) + 2_(base3).

5. ## Re: Base three division

okay this starting to make sense, can you teach me subtraction as well?

6. ## Re: Base three division

Give me some example numbers to work with.

7. ## Re: Base three division

21(base four) - 13(base four)

8. ## Re: Base three division

21-13 (Base four).

1 is less than 3 so we cross out 2 replace with 1 and we get 11-3=2. Then we do 1-1 (remember we crossed out 1 in 2nd digit) = 0 so 21-13 = 2(base4).

Confirming in base 10, we get 21 = 2*4^1 + 1*4^0 = 9 and 13 = 1*4^1 + 3*4^0 = 7 and 9-7 = 2 as expected.

9. ## Re: Base three division

why is 11-3=2?

10. ## Re: Base three division

Its in base 4, not base 10.

11. ## Re: Base three division

oh i get it now. Thanks so much for the help XD