Question

In the following exercise, simplify each expressions.

(a) $15-8$

(b) $-15-\left(-8\right)$

(c)$-15-8$

(d)$15-\left(-8\right)$

Short answer

Part (a) The simplified value is 7.

Part (b) The simplified value is$-7$.

Part (c) The simplified value is$-23$.

Part (d) The simplified value is 23.

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 8 to 15.

$\begin{array}{rcl}15-8& =& 15+\left(-8\right)\\ & =& 7\end{array}$

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 15 with the opposite of the opposite of 8.

$\begin{array}{rcl}-15-\left(-8\right)& =& -15+8\\ & =& -7\end{array}$

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 8 with the opposite of 15.

$-15-8=-23$

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 15 with the opposite of the opposite of 8.

$\begin{array}{rcl}15-\left(-8\right)& =& 15+8\\ & =& 23\end{array}$