Find the product of 235base6 and 14base6
( 2*6^2 + 3*6^1 + 5*6^0) (1*6^1 + 4*6^0)
(72 + 18 + 5)(10)
950
Oh, you want me to do math in base 6? I'm sorry, I'm more of a clown than a mathematician. But I can give it a try!
235base6 multiplied by 14base6 is... let me think... well, 5 times 4 is 20base6, which is equivalent to 34 in base 10.
Now, we multiply 2 (tens place) by 4 (ones place), which is 8base6, equivalent to 14 in base 10.
Finally, we have to multiply 3 (hundreds place) by 4 (ones place), which is 12base6, equivalent to 22 in base 10.
So, when we add all these up, we get 224base6, which is equivalent to 134 in base 10. Voilà!
To multiply numbers in different bases, we can convert the numbers to base 10, perform the multiplication, and then convert the result back to the desired base.
To convert 235base6 to base 10, we can use the place value system:
2 * 6^2 + 3 * 6^1 + 5 * 6^0 = 2 * 36 + 3 * 6 + 5 * 1 = 72 + 18 + 5 = 95base10
To convert 14base6 to base 10:
1 * 6^1 + 4 * 6^0 = 1 * 6 + 4 * 1 = 6 + 4 = 10base10
Now, we multiply the two base 10 numbers:
95 * 10 = 950
Finally, we convert the result back to base 6:
950base10 = 2354base6
Therefore, the product of 235base6 and 14base6 is 2354base6.
To find the product of two numbers in base 6, you can follow the same procedure as you would for multiplying numbers in base 10. Here's how you can find the product of 235 base 6 and 14 base 6:
Step 1: Write down the two numbers:
235 base 6
x 14 base 6
Step 2: Multiply the rightmost digit of the second number (in this case, 4) by each digit of the first number:
235 base 6
x 4 base 6
-------------
1410 base 6
Step 3: Multiply the second rightmost digit of the second number (in this case, 1) by each digit of the first number, but shifted one place to the left:
235 base 6
x 1 base 6
-------------
235 base 6
Step 4: Add the results from steps 2 and 3:
1410 base 6
+ 235 base 6
-------------
1645 base 6
So, the product of 235 base 6 and 14 base 6 is equal to 1645 base 6.