Add and subtract octal numbers 369 and 173.

Adding and subtracting octal numbers is similar to adding and subtracting decimal numbers, but instead of carrying or borrowing from a multiple of 10, you carry or borrow from a multiple of 8, since octal is a base-8 number system.

Adding Octal Numbers: 369 + 173

Let's start by adding the two octal numbers, 369 and 173. We'll add the numbers column by column, starting from the rightmost digit.

  3 6 9
+ 1 7 3
-------

Step 1: Add the rightmost digits (units place).

  9 (octal) + 3 (octal) = 12 (octal)

Since 12 in octal is greater than 7 (the highest single digit in octal), we need to carry over. In octal, 12 is equivalent to 1 group of 8 and 4 leftover (since 12 - 8 = 4).

  Carry: 1
  Sum: 4

Step 2: Add the next set of digits (eights place) along with the carry from the previous operation.

  6 (octal) + 7 (octal) + 1 (carry) = 16 (octal)

Again, 16 in octal is greater than 7, so we carry over. In octal, 16 is equivalent to 2 groups of 8 and 0 leftover (since 16 - 2*8 = 0).

  Carry: 2
  Sum: 0

Step 3: Add the leftmost digits (sixty-fours place) along with the carry from the previous operation.

  3 (octal) + 1 (octal) + 2 (carry) = 6 (octal)

There is no need to carry over since 6 is less than 8.

  Carry: 0
  Sum: 6

Now, let's put it all together:

    1 2 (carries)
  3 6 9
+ 1 7 3
-------
  6 0 4

The sum of 369 and 173 in octal is 604.

Subtracting Octal Numbers: 369 - 173

Now, let's subtract the two octal numbers, 369 and 173. We'll subtract the numbers column by column, starting from the rightmost digit.

  3 6 9
- 1 7 3
-------

Step 1: Subtract the rightmost digits (units place).

  9 (octal) - 3 (octal) = 6 (octal)

No borrowing is needed since 9 is greater than 3.

  Borrow: 0
  Difference: 6

Step 2: Subtract the next set of digits (eights place). Since 6 is less than 7, we need to borrow from the next column.

  16 (octal, after borrowing) - 7 (octal) = 7 (octal)

We borrowed 1 group of 8 (which is 10 in octal), so the 6 became 16 in octal.

  Borrow: 1
  Difference: 7

Step 3: Subtract the leftmost digits (sixty-fours place) along with the borrow from the previous operation.

  2 (octal, after borrowing) - 1 (octal) = 1 (octal)

We borrowed 1 group of 8 from the 3, so it became 2 in octal.

  Borrow: 1
  Difference: 1

Now, let's put it all together:

  Borrow: 1 1 0
  3 6 9
- 1 7 3
-------
  1 7 6

The difference of 369 and 173 in octal is 176.

Summary Table

Operation	Octal Numbers	Process	Result
Addition	369 + 173	Column-wise addition with carrying over from multiples of 8	604 (octal)
Subtraction	369 - 173	Column-wise subtraction with borrowing from multiples of 8	176 (octal)

In conclusion, when adding or subtracting octal numbers, it's important to remember that you carry or borrow in multiples of 8, not 10 as in the decimal system.