How can you tell the sign of the sum
of a positive and negative integer without doing
any calculations?

SUM:
If the numbers are the same sign, the sum will be the same sign as the numbers.
If they are different signs, the sum will be the same sign as the number with the largest size.

DIFFERENCE:
If the numbers are of different signs, the difference will be the same sign as the first number.
If the numbers are of the same sign, the difference will be the same sign as the numbers if the first number has the larger size, and the opposite sign to the numbers if the second number has the larger size.