Multiply in the indicated base
12
x 5
4
5
_________________
To multiply numbers in a specific base, follow these steps:
1. Write down the multiplicand (the number being multiplied) and the multiplier (the number you are multiplying by) side by side, aligning the rightmost digits.
In this case, the multiplicand is 12 and the multiplier is 5.
2. Multiply each digit of the multiplicand by each digit of the multiplier, just like you would in decimal multiplication. Start with the rightmost digit of the multiplier.
- Multiply 5 (the rightmost digit of the multiplier) by each digit of the multiplicand:
5 multiplied by 2 (the rightmost digit of the multiplicand) = 10.
5 multiplied by 1 (the leftmost digit of the multiplicand) = 5.
3. Write down the products under each column, starting from the rightmost column. If there are multiple products in a column, align them so the rightmost digit of each product lines up with the corresponding digit in the column above it.
- Write down 0 (the rightmost digit of the product 10) under the rightmost column.
- Write down 1 (the leftmost digit of the product 10) in the next column to the left.
- Write down 5 (the product of 5 and 1) under the leftmost column.
12
x 5
4
5
_________________
0
+ 1
+ 5
_________________
4. Add up the numbers in each column, starting from the rightmost column, just like you would in decimal addition.
- In the rightmost column, there is only a single digit, so no carrying needs to be done. Write down 0 in the answer.
- In the next column to the left, the sum of 1 and 0 is 1. Write down 1 in the answer.
- In the leftmost column, there is only a single digit, so no carrying needs to be done. Write down 5 in the answer.
The final result is 15.
Therefore, in the base indicated by the number 4, 12 multiplied by 5 is equal to 15.