Question

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

The sum of two negative integers.

Short answer

The sum of two negative integers is always negative.

Step-by-step solution

Step 1. Rules for sum of two negative integers

Just add the absolute value of each number together, put a negative sign in front of your answer.

Step 2. Adding two negative integers using a number line

When you add two negative integers together, the sum is always a negative number since you are moving further down (to the left) of the number line.

Take a look at the expression(−7) + (−3).

First, let’s draw a number line and start at −7.

Next, add −3 to −7. This is essentially the same as subtracting 3 from −7.

Step 3. Tell whether the sum of two negative integers is always, sometimes, or never negative. 

Consider, the statement provided in the question: The sum of two negative integers.

The sum of two negative integers is always negative and is less than both the integers.

Suppose the two negative integers be $-2$and $-3$, and there sum is:

$-2 - 3=- (2+3) = - 5$

From the above example it can be observed that the sum of two negative integers is negative.

Thus, the sum of two negative integers is always negative.