divide in the indicated base

3 212
5 / 5

To divide in a specific base (in this case, base 5), you can follow these steps:

Step 1: Set up the division problem.

Write down the dividend (which is the number you want to divide) on the top left, and write the divisor (the number you are dividing by) on the bottom left.

3
-------
5

Step 2: Find the largest multiple of the divisor that is less than or equal to the first digit of the dividend.

In this case, the first digit of the dividend is 2. Therefore, we need to find the largest multiple of 5 that is less than or equal to 2.

The largest multiple of 5 that is less than or equal to 2 in base 5 is 0. So, we write down 0 on top of the line and subtract 0 from 2.

3
-------
5
-0

Now, bring down the next digit from the dividend (which is 1) and write it next to the result of the subtraction.

3
-------
5
-0
21

Step 3: Repeat steps 2 and 3 until you have used all the digits in the dividend.

Now, we need to find the largest multiple of 5 that is less than or equal to 21 (the number we obtained from our previous step).

The largest multiple of 5 that is less than or equal to 21 in base 5 is 4. Write down 4 on top of the line and subtract 20 (the result of multiplying 5 by 4) from 21.

3
-------
5
-0
21
-20

The result is 1. Bring down the next digit, which is 2, and write it next to the result of the subtraction.

3
-------
5
-0
21
-20
2

Step 4: Repeat steps 2 and 3 until you have used all the digits in the dividend.

Now, we need to find the largest multiple of 5 that is less than or equal to 12 (the number we obtained from our previous step).

The largest multiple of 5 that is less than or equal to 12 in base 5 is 2. Write down 2 on top of the line and subtract 10 (the result of multiplying 5 by 2) from 12.

3
-------
5
-0
21
-20
2
-10

The result is 2. Bring down the next digit, which is 2, and write it next to the result of the subtraction.

3
-------
5
-0
21
-20
2
-10
22

Step 5: If there are no more digits to bring down, the division is complete. The quotient is the numbers written on top of the line, and any remaining digits are the remainder.

In this case, we have no more digits to bring down. Therefore, the quotient is 302 (the numbers written on top of the line), and the remainder is 2 (the remaining digit).

So, the division is complete and the result is:

3
-------
5
-0
21
-20
2
-10
22
______
Quotient: 302
Remainder: 2