How can you perform arithmetic operations like addition, subtraction, etc. on numbers in other bases?

Well, I hate to tell you this, but unless you can train yourself to memorize math facts in other bases (and really, who wants to remember that 4_sixteen + 7_sixteen is B_sixteen, and A_sixteen x 4_sixteen is 28_sixteen, and all of the other math facts for base sixteen - plus the math facts for all the other bases!) the best option is to convert your numbers into base ten, perform the operation, and then convert them back.

EXAMPLE
Calculate the value of 23_fifteen + 11_fifteen. Write your answer in base fifteen.

2 x 15 + 3 = 33
1 x 15 + 1 = 16

33 + 16 = 49

Convert 49 (base ten) back into base fifteen using the process described in the previous page, and you find that the result is 34_fifteen.

EXAMPLE
Calculate the value of 132_twelve - 1020_three

Here it looks like the second number is larger than the first one (it has more digits) but in reality, it is not, because its place value is such a small number (three).

1 x 12² + 3 x 12 +2 = 182
1 x 3³ + 0 x 3² + 2 x 3 + 0 = 33

182 - 33 = 149

Since we haven't been asked to give the answer in a particular base, we will leave it as a base ten number.