Well, somewhere along the line we didn’t make ourselves clear. The problem was to add ( − 5) and ( − 8). Now, the rule for adding numbers of like sign is to add the absolute values and attach the common sign to the sum. Here you added the absolute values, all right, but got the wrong sign on the sum.
By the “common sign” of the two numbers we mean the sign that both of the numbers had before adding them together. Here both numbers to be added are negative, so the common sign is -, and the sum should have the - sign.
