What is 18*56 in base 12, assuming 18 and 56 are base 10?
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We need to find 18 times 56 in base 12, where both numbers are given in base 10.
First, we'll calculate the product in base 10, then convert the result to base 12.
Let's start by multiplying 18 times 56, which equals 1008 in base 10.
Now we convert 1008 from base 10 to base 12. We divide repeatedly by 12 and collect remainders.
First, 1008 divided by 12 equals 84 with remainder 0.
Next, 84 divided by 12 equals 7 with remainder 0.
Finally, 7 divided by 12 equals 0 with remainder 7.
Reading the remainders from bottom to top gives us 700 in base 12.
Let's verify our answer. To check that 700 in base 12 equals 1008 in base 10,
we expand it: 7 times 12 squared plus 0 times 12 plus 0 times 1.
This gives us 7 times 144, which equals 1008. Perfect!
Therefore, 18 times 56 in base 12 is 700.
Base 12 is a positional number system that uses twelve digits: 0 through 9, plus A for ten and B for eleven.
Each position represents a power of 12, from right to left: ones, twelves, and 144s.
In our answer 700 base 12, we have 7 in the 144s place, giving us exactly 1008 in base 10.
This demonstrates how different number bases can represent the same quantity.
To summarize our solution: We calculated 18 times 56 equals 1008 in base 10.
Then we converted to base 12 by repeatedly dividing by 12 and collecting remainders.
The division gave us remainders 0, 0, and 7, which read bottom to top gives 700 in base 12.
We verified this by converting back: 7 times 144 equals 1008.
Therefore, 18 times 56 in base 12 is 700.