Chapter 1.8, Problem 38E

To determine

To find : Whether the sum is always, sometimes, or never negative.

Answer to Problem 38E

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

Explanation of Solution

Given information :

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 negative integer is greater than positive integers and hence the sum is negative.

From the above examples it can be observed that the sum of a negative integer and a positive integer is sometime negative.

Hence,

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