How do you solve the math problem 41base6 - 22 base6?

Answer 1

Here are two different ways to approach this problem. They are both equally valid.

1. Convert each number to base 10, subtract, and then convert the answer back to base 6.

a. Convert each number to base 10.

41base6 = (4 * 6) + 1 = 25

22base6 = (2 * 6) + 2 = 14

b. Subtract.

25 - 14 = 11

c. Convert the answer to base 6.

11 / 6 = 1 remainder 5 = 15base6

2. Do the subtraction operation in base 6.

Do the subtraction one digit at a time, starting from the right just like in base 10. When you try to subtract the "2" in 22 from the "1" in 41, you have a problem because 2 > 1. Just like subtracting in base 10, you have to "borrow" from the 4. If you were in base 10, you'd borrow 10, making the 1 into 11; however, in base 6, you borrow 6, making the 1 into 1+6 = 7. Thus you have 7-2 = 5 for the right hand digit.

Now when you subtract the left hand digit, remember that you have borrowed from the 4, so now it's 3. Thus the right hand digit in the answer is 3-2 = 1.

Put it together and you have 41base6 - 22base6 = 15base6.