Question

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\frac{0.23\left(7\right)+\frac{43}{450}}{0.5\left(61\right)-\frac{113}{495}}$

Answer 1

fisrtly change the mixed infinite fraction into common fraction so

$.23\left(7\right)$

can be written in coomon fraction as $\frac{214}{900}=\frac{107}{450}$

$0.5\left(61\right)$ can b written as common fraction is $\frac{556}{900}$

now solve the given expression $\frac{\frac{107}{450}+\frac{43}{450}}{\frac{556}{900}-\frac{113}{495}}$

$\frac{\frac{107+43}{450}}{\frac{556\times 11-113\times 20}{9900}}$

$\frac{\frac{150}{450}}{\frac{6116-2260}{9900}}$

$\frac{150}{450}\times \frac{9900}{3856}$

$\frac{3300}{3856}$ answer