In a base-6 number system, what is the product of '12' and '3'?

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Question: In a base-6 number system, what is the product of \'12\' and \'3\'?

Options:

Correct Answer: 42

Solution:

\'12\' in base-6 is 1*6 + 2 = 8. \'3\' is 3. Their product is 8*3 = 24, which is \'42\' in base-6.

In a base-6 number system, what is the product of '12' and '3'?

In a base-6 number system, what is the product of '12' and '3'?

Step 1: Understand that '12' in base-6 means 1 group of 6 and 2 units.
Step 2: Calculate the value of '12' in base-10: 1*6 + 2 = 6 + 2 = 8.
Step 3: Recognize that '3' in base-6 is the same as '3' in base-10.
Step 4: Multiply the two values in base-10: 8 (from '12') * 3 = 24.
Step 5: Convert the product (24) back to base-6.
Step 6: To convert 24 to base-6, divide 24 by 6. The quotient is 4 and the remainder is 0.
Step 7: Divide the quotient (4) by 6. The quotient is 0 and the remainder is 4.
Step 8: Read the remainders from last to first. The base-6 representation of 24 is '40'.

Base Conversion – Understanding how to convert numbers from one base to another, specifically from base-6 to decimal.
Multiplication in Different Bases – Performing multiplication after converting numbers to a common base (decimal in this case).
Base Representation – Converting the final product back into the original base (base-6) for the final answer.