Question

Simplify the algebraic expression $\frac{\mathrm{x}}{2}÷(2\frac{2}{3}\mathrm{x}÷1\frac{5}{8}\mathrm{x})$ in its simplest form :

Answer 1

To simplify : $\frac{\mathrm{x}}{2}÷(2\frac{2}{3}\mathrm{x}÷1\frac{5}{8}\mathrm{x})$

$\frac{\mathrm{x}}{2}÷(2\frac{2}{3}\mathrm{x}÷1\frac{5}{8}\mathrm{x})=\frac{\mathrm{x}}{2}÷(\frac{8}{3}\mathrm{x}÷\frac{13}{8}\mathrm{x})$ (By BODMAS rule solving bracket terms first)

$=\frac{\mathrm{x}}{2}÷(\frac{8}{3}\mathrm{x}\times \frac{8}{13x})$ (Reciprocal of the divisor is taken when multiplication replaces division)

$=\frac{\mathrm{x}}{2}÷\left(\frac{64}{39}\right)$

$=\frac{\mathrm{x}}{2}\times \frac{39}{64}$ (Reciprocal of the divisor is taken when multiplication replaces division)

$=\frac{39x}{128}$

Thus, $\frac{\mathrm{x}}{2}÷(2\frac{2}{3}\mathrm{x}÷1\frac{5}{8}\mathrm{x})$$=\frac{39x}{128}$ Answer