Question

Which of the following statements is correct?
Statement-1: When a positive integer and a negative integer are added, we always get a negative integer.
Statement-2: When two negative integers are added, we get a positive number.
(a). Only Statement-1
(b). Only Statement-2
(c). Both Statement-1 and Statement-2
(d). Neither Statement-1 nor Statement-2

Answer 1

Hint: First, we should know the concept of adding two negative numbers and one positive and one negative number together. For example: $\left( -a \right)+\left( -a \right)=-2a$ for both integers to be negative number and for one positive and one negative i.e. $\left( -a \right)+\left( b \right)=b-a$ provided number is greater than a so, there will be plus sign in the answer. Similarly, vice-versa for number a to be greater than b, so sign will be minus in final answer.

Complete step-by-step answer:

Here, we have to find whether statement-1 or statement-2 is correct, or both are correct or not.
So, we will first check the Statement-1 given as: When a positive integer and a negative integer are added, we always get a negative integer.
So, for this let’s take two numbers, one positive and one negative. We take suppose 7 and $-10$ and adding these two numbers, we get
$\Rightarrow 7+\left( -10 \right)=-10+7=-3$
Here, we should also know that $\left( + \right)\times \left( - \right)=\left( - \right)$ . So, we got our answer $-3$ because here comparing 7 and 10, 10 is greater so, the sign corresponding to 10 will be there in answer. So, there is a minus sign in answer.
Now checking another number i.e. 7 and $-5$ . Adding these numbers, we get
$\Rightarrow 7+\left( -5 \right)=7-5=2$
Here, we can see that 7 is greater as compared to 5 so, in the answer positive sign is there in answer.
If taking same number with different sign, we get as:
$\Rightarrow 7+\left( -7 \right)=7-7=0$
0 is neither positive nor negative digit.
So, in statement-1 it is told that we always get a negative answer which is not true by seeing above two examples.
Now, we will check Statement-2 given as: When two negative integers are added, we get a positive number.
Taking 2 negative numbers, suppose $-7,-5$ .On adding this, we get as:
$\Rightarrow \left( -7 \right)+\left( -5 \right)=-7-5=-12$
So, adding two negative numbers we will get an answer in negative numbers only.
We can also solve by taking minus sign common i.e.,
$\Rightarrow \left( -7 \right)+\left( -5 \right)=-7-5=-\left( 7+5 \right)=-12$ Which will be also negative.
So, according to statement-2 by adding two negative numbers we don’t get positive numbers. So, it is not true.
Hence, option (d) is correct.

Note: Remember that in this addition of two numbers is asked so, the rule of signs i.e. $\left( + \right)\times \left( - \right)=\left( - \right)$ is applicable for multiplication also . Don’t mix up with multiplication rule i.e. $\left( - \right)\times \left( - \right)=\left( + \right)$ with the addition rule $\left( - \right)+\left( - \right)=\left( - \right)$ . Here, generally students made up ending mistakes. So, be careful while using this formula. Also, in this type of questions always take 2 or 3 examples for checking whether it satisfies the statement or not and select the correct answer.