Tell whether the sum is always, sometimes, or never negative.

The sum of a negative integer and a positive integer.

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.

Draw the number line and locate the first integer (– 9), then move 11(2^nd integer) units to the right from the location of – 9. The answer will be the point you end on.

Evaluate: – 9 + 11 = + 2

Consider, the statement provided in the question,

The sum of negative integers and positive integers

The sum of negative integer and a positive integer is sometimes negative and sometime positive.

If the absolute value of negative integer is greater than positive integer then there sum is negative and if the absolute value of negative integer is less than positive then there sum is positive. This is shown below:

Suppose the negative and positive integers be $-3$ and $5$ respectively. Then there sum is $-3+5=2$

In the above example it can be observed that the absolute value of negative integer is less than positive integers and hence the sum is positive.

Now, suppose the negative and positive integers be $-8$ and $3$ respectively. Then there sum is $-8+3=-5$

In the above example it can be observed that the absolute value of positive integer is less than negative integers and hence the sum is negative.

From the entire above example it can be observed that if the absolute value of negative integer is greater than positive integers and hence the sum is negative or if the sum of a negative integer and a positive integer is sometime negative.

Thus, the sum of negative integer and a positive integer is sometime negative.