Question

Fill in the blanks: The sum of two negative integers is always a ______integer.

Answer 1

Hint: We start solving the problem by assuming variables for representing two negative numbers. We then perform the addition operation between those two assumed variables. We then make use of the facts that the sum of two positive integers is also a positive integer and the negative of a positive integer is negative to get the required answer.

Complete step by step answer:
According to the problem, we need to fill the given blank: The sum of two negative integers is always a ______integer.
Let us assume the negative integers be $-p$ and $-q$, where $p$ and $q$ are positive integers.
Now, let us find the sum of the integers $-p$ and $-q$.
$\Rightarrow -p+\left( -q \right)=-p-q$.
$\Rightarrow -p+\left( -q \right)=-\left( p+q \right)$.
We know that the sum of two positive integers is also a positive integer, so we get $\left( p+q \right)$ as a positive integer.
We know that the negative of a positive integer is negative, so we get $-\left( p+q \right)$ as a negative integer.
So, we have found the sum of two negative integers as a negative integer.
$\therefore $ We need to fill the blank with negative.

Note:
 We should not confuse sign convention while solving this type of problem. We can also two negative numbers as an example to prove the obtained answer as shown below:
Let us consider the two negative numbers –2, –5. Let us add these two numbers.
So, we have sum as $-2+\left( -5 \right)=-2-5$.
$\Rightarrow -2+\left( -5 \right)=-\left( 2+5 \right)$.
$\Rightarrow -2+\left( -5 \right)=-7$, which is also a negative integer. Similarly, we can expect the problems to find the result of the product of two negative numbers.