Question

The sum of two negative integers is always,
A) $ 0 $
B) Negative
C) $ - 1 $
D) Positive.

Answer 1

Hint: We are given the question in which we have to find the sum of two negative integers. First we will take for a simple example any two negative integers and see the result upon performing the operation of addition upon them and then we will select the relevant option given in the question.

Complete step-by-step solution:
We will first take two sample integers as the question asks us to take the negative integers we take,
 $ - 4 $ and $ - 5 $ ,
These are the two integers upon which we will operate upon, the operation given is the addition,Here by using the sign rule we can solve it as $( - ) \times ( + ) = ( - )$
 $ - 4 + ( - 5) = - 4 - 5 $
Which upon solving gives the values as
 $ - 4 - 5 = - 9 $
The answer is thus $ - 9 $ ,
The option A is $ 0 $ which will be incorrect,
The option $ B $ is the number is negative which is the correct option,
Other options $ C $ and $ D$ are also incorrect as the number $ - 9 $ is not $ - 1 $ or positive. Hence the option $ B $ is correct. The option will remain same for any other integers which are negative as well.

Thus our correct answer is option $ B $ .

Note: When adding two integers which are of different signs or of same sign.
The following sign table will help,
$
  ( - ) \times ( + ) = ( - ) \\
  ( + ) \times ( + ) = ( + ) \\
  ( - ) \times ( - ) = ( + ) \\
 $
These given signage table will only tell us the operation to perform whether we have to perform addition or subtraction to the two numbers, the sign of the resultant number is independent of this table . It will be decided by the sign of the number which is largest by magnitude in the operation.