Question

Solve the following:
$32-(-18)$

Answer 1

Hint: In this question we are given an equation whose value we have to find and for this first we will learn definition of integers and then we will learn rules of addition and multiplication of integers along with an example then we will use these basic rules of multiplication and addition of integers to solve our given equation.

Complete step by step answer:
Integers:
Integers consist of all negative numbers, positive numbers, and zero.
As we know there are four basic operations in mathematics that are:
a) Addition
b) Subtraction
c) Multiplication
d) Division
In integers if we want to add or subtract two numbers then there is a rule to perform these operations.
If we add both positive numbers then we will do basic addition.
Like if we want to add $8$ and $6$
Then we will simply do addition
$\begin{align}
  & 8+6 \\
 & \Rightarrow 14 \\
\end{align}$
$\therefore 14$ Is our required answer.
If we add two numbers and one number is positive and other number is negative then resultant operation will be of subtraction and sign of answer is of a number whose value is bigger irrespective of its sign
Example:
Solve $-12+15$
$\begin{align}
  & -12+15 \\
 & \Rightarrow 3 \\
\end{align}$
$\therefore 3$ Is our required answer.
In this example one number is negative and other number is positive
So we have done subtraction and the sign of the answer is the same as the sign of a bigger value number irrespective of its sign as $15$ is greater than $12$ .
If both the numbers are negative numbers then the resultant operation will be of addition and sign will be negative
Example:
Add:$-12+(-8)$
$\begin{align}
  & -12+(-8) \\
 & \Rightarrow -20 \\
\end{align}$
$\therefore -20$ Is our required answer.
Now we will learn the rules of multiplication in integers.
If we multiply two numbers and both the numbers are positive then the sign of the answer will also be positive.
Example:
$8\times 5=40$
If we multiply two numbers in which one is positive and other is negative then the sign of the answer will also be negative.
Example:
$12\times (-5)=-60$
If we multiply two numbers and both the numbers are negative then the sign of the answer will be positive.
Example:
$(-4)\times (-5)=20$
Now we will proceed to our question.
Our given equation is
 $32-(-18)$
First we will try to simplify it
As we know product of two negative signs will give us positive sign
So our equation becomes
$32+18$
Now this become a simple addition problem
$\begin{align}
  & 32+18 \\
 & \Rightarrow 50 \\
\end{align}$
$\therefore 50$ Is our required answer.

Note:
 In integers there are two important terms which are additive identity and multiplicative identity. $0$is called additive identity which means if we add or subtract any number from $0$ then we will get the number itself and $1$ is called multiplicative identity which means if we multiply or divide any number from $1$ then we will get the number itself.