Question

Add and subtract the equations given below.
(i). m-n, m+n
(ii). mn+5-2, mn+3

Answer 1

Hint: We will use the basic properties of addition and subtraction of integers. We will add and subtract both the terms to get the final result.

Complete step-by-step answer:
It is given in the question that we have to add and subtract the given terms, firstly we have (m-n) and (m+n) and then in the second part of question we have (mn+5-2) and (mn+3). Here, to add and subtract the given terms, we will use basic rules of addition. For example,
1. Addition/subtraction of two positive integers gives a positive integer as \[\left( + \right)+\left( + \right)=\left( + \right)\] or\[\left( + \right)-\left( + \right)=\left( + \right)\].
2. Addition of two negative integers gives a negative integer as \[\left( - \right)+\left( - \right)=\left( - \right)\]
3. When we have a positive and a negative integer, we have to find the difference between them and then consider the sign of the highest integer.
The properties of multiplication of integers is as below,
\[\begin{array}{*{35}{l}}
+\times +\text{ }=\text{ }+ \\
+\times -\text{ }=\text{ }- \\
-\times +\text{ }=\text{ }- \\
-\times -\text{ }=\text{ }+ \\
\end{array}\]
Let us solve the first part of question i.e., addition and subtraction of (m-n) and (m+n), we get
= (m-n) + (m+n)
=m-n+m+n
Cancelling the similar terms, we get
= 2m
Thus, addition of (m-n)+(m+n) is 2m.
Now, we will subtract (m-n) and (m+n), we get
= (m-n) – (m+n)
=m-n-m-n
Cancelling the similar terms, we get
=-2n
Thus, subtraction of (m-n) - (m+n) = -2n
Now, let us solve the second part of the question i.e., addition and subtraction of (mn+5-2) and (mn+3).
= (mn+5-2) + (mn+3)
= (mn+3) + (mn+3)
= mn+3+mn+3
= 2mn+6
Thus, the addition of (mn+5-2) and (mn+3), we get 2mn+6.
Now, we will subtract (mn+5-2) and (mn+3), we get
= (mn+5-2) - (mn+3)
= (mn+3) - (mn+3)
= mn+3-mn-3
= 0
Cancelling the similar terms, we get 0.
Thus, subtraction of (mn+5-2) and (mn+3) is 0.

Note: We just have to perform basic addition and subtraction for given terms. But, many times we will make mistakes even in adding and subtracting. So, be conscious while adding and subtracting the terms and use basic rules of adding and subtracting integers.