Chapter SH, Problem 7SEWI

Solution

To simplify the expression $-8-\left(-12\right)$ .

  $4$

Given:

The expression, $-8-\left(-12\right)$ .

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to simplify the given expression $-8-\left(-12\right)$ , add the reciprocal of the second number with the first number, that is,

  $-8-\left(-12\right)=-8+12$

Now, note that the sign of both numbers is different, so subtract the numbers and keep the sign of larger number with the final result as shown below

  $\begin{array}{c}-8-\left(-12\right)=-8+12\\ =+4\\ =4\end{array}$

Thus, the simplified expression is $4$ .