Chapter 8, Problem 1CRE

To determine

Simplified form of the given expression $\frac{8-4\cdot 2^2+15÷5}{\left|-3+7\right|}$ .

Answer to Problem 1CRE

Solution:

The simplified form of the given expression is $-\frac{5}{4}$ .

Explanation of Solution

Given:

The expression $\frac{8-4\cdot 2^2+15÷5}{\left|-3+7\right|}$.

Formula used:

PEMDAS:This rule tells us the sequence in which mathematical operations should be performed. So, the sequence is parenthesis, exponents, multiplication, division, addition, subtraction.

Calculation:

  $\begin{array}{l}\frac{8-4\cdot 2^2+15÷5}{\left|-3+7\right|}\\ =\frac{8-4\cdot 2^2+3}{\left|-3+7\right|}\left[\begin{array}{l}\text{Performing division as according to PEMDAS, }\\ \text{division is having precedence over subtraction and addition}\end{array}\right]\\ =\frac{8-4\cdot 4+3}{\left|-3+7\right|}\\ =\frac{8-16+3}{4}\left[\begin{array}{l}\text{Performing multiplication as according to PEMDAS, }\\ \text{multiplication is having precedence over subtraction}\end{array}\right]\\ =-\frac{5}{4}\end{array}$

Conclusion:

  $\frac{8-4\cdot 2^2+15÷5}{\left|-3+7\right|}=-\frac{5}{4}$ .