Question

In the following exercise, simplify each expressions.

(a) $13-7$

(b) role="math" localid="1644741992011" $-13-\left(-7\right)$

(c) $-13-7$

(d)$13-\left(-7\right)$

Short answer

Part (a) The simplified value is 6.

Part (b) The simplified value is $-6$.

Part (c) The simplified value is $-20$.

Part (d) The simplified value is 20.

Step-by-step solution

Part (a) Step 1. Concept Used. 

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Part (a) Step 2. Calculation. 

Add the opposite of 7 to 13.

$\begin{array}{rcl}13-7& =& 13+\left(-7\right)\\ & =& 6\end{array}$

Part (b) Step 1. Concept Used. 

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Part (b) Step 2. Calculation.

Add the opposite of 13 with the opposite of the opposite of 7.

$\begin{array}{rcl}-13-\left(-7\right)& =& -13+7\\ & =& -6\end{array}$

Part (c) Step 1. Concept Used. 

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Part (c) Step 2. Calculation.

Add the opposite of 7 with the opposite of 13.

$-13-7=-20$

Part (d) Step 1. Concept Used.

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Part (d) Step 2. Calculation. 

Add 13 with the opposite of the opposite of 7.

$\begin{array}{rcl}13-\left(-7\right)& =& 13+7\\ & =& 20\end{array}$