Question

Answer the following questions.
1. What is the sum of -18 and 12?
2. What is the value of $\left[ 0-\left( -12 \right) \right]$ ?

Answer 1

Hint:We have to perform integer operations in both the questions. In the first question, we have to add -18 and 12. Firstly, we will subtract 12 from 18. Then, we will see which number contains negative signs in -18 and 12. If the largest number contains the negative sign, then we will put a negative sign to the result of step 1. Otherwise, we will leave the result as it is. Now, we will move on to the second question. We will apply inter multiplication on the term $-\left( -12 \right)$ . When a negative sign is multiplied with a negative sign, the result will be positive. We will then apply the result of this operation in the given expression and simplify.

Complete step-by-step solution:
Let us answer each of the given questions.
1. We have to find the sum of -18 and 12. This means that we have to add -18 and 12. We can write this mathematically as
$-18+12...\left( i \right)$
From the above integer addition, we can see that a negative sign appears. So firstly, we have to subtract 12 from 18.
\[\begin{align}
  & \text{ }\text{ }\text{ }18 \\
 & -12 \\
 & \_\_\_\_ \\
 & \text{ }\text{ }\text{ }\text{ }\text{ }6 \\
\end{align}\]
We obtained $18-12=6$ . Now, we have to see whether the negative sign in (i) is on the larger number or smaller number. We can see that the negative sign is on the larger number, 18. Therefore, the result will have a negative sign.
Therefore, $-18+12=-6$ .
Hence, the sum of -18 and 12 is -6.
2. We have to find the value of $\left[ 0-\left( -12 \right) \right]$ . We know that when a negative sign is multiplied by a negative sign, we will get a positive result. Therefore, we can write $-\left( -12 \right)$ in the given expression as
$\Rightarrow \left[ 0+12 \right]$
We know that any number when added with 0 is that number itself.
$\Rightarrow \left[ 0-\left( -12 \right) \right]=12$
Hence, the value of $\left[ 0-\left( -12 \right) \right]$ is 12.

Note: Students must deeply understand integer operations which includes addition, subtraction, multiplication and division. We know that when we add two positive numbers, the result will be positive. When we add two negative numbers, the result will be negative. When we add a positive and a negative number, we will do the subtraction operation and check whether the negative sign is on the larger number. If the largest number contains the negative sign, then we will put a negative sign to the result. When we multiply two positive or negative numbers the result will be positive. When we multiply a positive and negative number, the result will be negative. If we divide a positive number by a negative number or vise-versa, the result is negative. If we divide two negative numbers, the result will be positive.

Integer Sign	Integer Sign	Operation	Answer sign
+	+	Add	+
-	-	Add	-
+	-	Subtract	Largest integer sign
-	+	Subtract	Largest integer sign
+	-	Multiply	-
-	+	Multiply	-
-	-	Multiply	+
+	-	Divide	-
-	+	Divide	-
-	-	Divide	+