Add and subtract octal numbers 369 and 715.

Adding and subtracting octal numbers is similar to the process used in decimal numbers, but instead of carrying or borrowing from multiples of 10, we do so from multiples of 8, because octal is a base-8 number system.

Adding Octal Numbers: 369 + 715

Step 1: Write the numbers one under the other, aligning the digits according to their place values.

  369
+ 715
------

Step 2: Add the digits in each column, starting from the rightmost column. If the sum is equal to or greater than 8, carry over to the next column.

  369
+ 715
------
 (1)4  (since 6 + 5 = 11, which is 8 + 3, so we write down 3 and carry over 1)

Step 3: Add the next column along with the carried over value.

  369
+ 715
------
 1(1)0  (since 1 (carried) + 6 + 1 = 8, which is 10 in octal, so we write down 0 and carry over 1)

Step 4: Repeat the process for the remaining columns.

  369
+ 715
------
11(1)4  (since 1 (carried) + 3 + 7 = 11, which is 8 + 3, so we write down 3 and carry over 1)

Step 5: If there is a carryover after the last column, write it down as the leftmost digit.

  369
+ 715
------
1304  (since 1 (carried) + 0 = 1)

So, the sum of 369 and 715 in octal is 1304.

Subtracting Octal Numbers: 369 - 715

Step 1: Write the numbers one under the other, aligning the digits according to their place values.

  369
- 715
------

Step 2: Subtract the digits in each column, starting from the rightmost column. If the digit on the top is smaller than the digit on the bottom, borrow from the next column.

  369
- 715
------
   (7)4  (since 9 - 5 = 4, no borrowing needed)

Step 3: Move to the next column. Since 6 is less than 1, we need to borrow from the next column.

  369
- 715
------
 (6)54  (borrowing from the '3' makes it '2', and the '6' becomes '16' in octal; 16 - 1 = 15 in octal)

Step 4: Continue to the next column. We've already borrowed from this column, so it's now a '2'.

  369
- 715
------
(1)654  (since we cannot subtract 7 from 2, we would need to borrow from an additional place value, which we don't have, indicating that the result will be negative)

Since we can't borrow from a higher place value (as there isn't one), this indicates that 369 is smaller than 715, and the result will be negative. To find the positive difference, we'll subtract 369 from 715 and then indicate the result as negative.

  715
- 369
------

Starting from the rightmost column:

  715
- 369
------
   (6)6  (since 15 (after borrowing 1 from the next column, making it 7) - 9 = 6 in octal)

Next column:

  715
- 369
------
  (7)26  (since 7 (after borrowing 1 from the next column, making it 6) - 6 = 1 in octal)

Last column:

  715
- 369
------
  326  (since 6 - 3 = 3 in octal)

So, the difference between 369 and 715 in octal is -326 (since 369 is less than 715).

In summary:

Operation	Result
369 + 715	1304
369 - 715	-326