How can you tell whether the sum of – 71 and 43 is positive or negative without actually finding the sum?

Rule: The sum of any integer and its opposite is equal to zero.

Explanation: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

To add two numbers with the same sign, first add the two numbers ignoring the sign and then put their common sign before the answer.

To add two numbers with the opposite sign, ignore their signs and subtract the smaller number from the bigger number. Then put the sign of the bigger number before the answer.

To add two integers, we need the signs of those two integers.

Rule: If they are with the opposite sign (one is positive and other is negative), subtract the smaller number from the bigger number ignoring the sign, then put the sign of bigger number before the answer.

Here the bigger number 71 is negative, so according to the rule answer is negative.