Question

The simplification of $7\frac{1}{2}-[2\frac{1}{4}÷\{1\frac{1}{4}-\frac{1}{2}(1\frac{1}{2}-\frac{1}{3}-\frac{1}{6})\}]$ yields.

• A. $\frac{2}{9}$
• B. $4$ $\frac{1}{2}$
• C. $9$ $\frac{1}{2}$
• D. $1$ $\frac{77}{228}$$

Answer 1

The correct option is B $4$ $\frac{1}{2}$

Accordung to question:

$\begin{array}{c}7\frac{1}{2}-\left[2\frac{1}{4}÷\left\{1\frac{1}{4}-\frac{1}{2}\left(1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]\\ \Rightarrow \frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)\right\}\right]\\ \Rightarrow \frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{9-2-1}{6}\right)\right\}\right]\\ \Rightarrow \frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\right\}\right]\\ \Rightarrow \frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5-2}{4}\right\}\right]\\ \Rightarrow \frac{15}{2}-\left[\frac{9}{4}÷\frac{3}{4}\right]\\ \Rightarrow \frac{15}{2}-3=\frac{15-6}{2}=\frac{9}{2}=4\frac{1}{2}\\ wefindaftersimplification:4\frac{1}{2}\\ so,thatwecansaythecorrectoptionisB.\end{array}$