You are correct. In the addition ( − 9) + ( + 6), the difference of the absolute values is 3, and the number with the larger absolute value is negative, so the result is ( − 3).
Very well, we have the rules for addition:
To add numbers with like signs, find the sum of the absolute values, and attach the common sign. Thus, ( − 7) + ( − 6) = ( − 13), and ( + 7) + ( + 6) = ( + 13).
To add numbers with unlike signs, find the difference of the absolute values, and attach the sign of the number with the larger absolute value. Thus ( − 7) + ( + 6) = ( − 1), and ( + 7) + ( − 6) = ( + 1).
So much for addition. For subtraction, it is only necessary to learn one new rule: In subtraction, you
change the sign of the number being subtracted and then
add the number instead, following the addition rules. Now, if this rule works, it should work for subtraction of one positive number from another. Let’s see if it does. If we have
( + 8) − ( + 5), the rule says to change the sign of the
( + 5) and then add instead of subtract. Thus
change the sign
↓
( + 8) − ( + 5) = ( + 8)
+
( − 5)
↑
add instead of subtract
Now, by the rule for addition of numbers with unlike signs we get
( + 8) + ( − 5) = + 3.
which is correct, isn’t it? since
( + 8) − ( + 5) = 8 − 5 = + 3. All we need to do in subtraction is to change the sign of the number being subtracted, and add that new number.
