Question

Evaluate: $\left(iii\right)(\frac{11}{-9}\times \frac{21}{44})+\left(\frac{-5}{9}\right)\times \left(\frac{63}{-100}\right)$

Answer 1

Simplifying each term

Given,
$(\frac{11}{-9}\times \frac{21}{44})$

$\therefore \frac{11}{-9}\times \frac{21}{44}$

$=-\frac{11\times 3\times 7}{3\times 3\times 4\times 11}$

$=-\frac{7}{12}$

and $\left(\frac{-5}{9}\right)\times \left(\frac{63}{-100}\right)$

$\therefore \frac{-5}{9}\times \frac{63}{-100}$

$=\frac{5\times 63}{9\times 100}$

$=\frac{5\times 9\times 7}{9\times 20\times 5}$

$=\frac{7}{20}$

Evaluating the given expression

Given $(\frac{11}{-9}\times \frac{21}{44})+\left(\frac{-5}{9}\right)\times \left(\frac{63}{-100}\right)$

$=-\frac{7}{12}+\frac{7}{20}$

$=\frac{-7\times 5}{12\times 5}+\frac{7\times 3}{20\times 3}$

[$\because LCM$ of $12$ and $20=60$]

$=\frac{-35}{60}+\frac{21}{60}=\frac{-35+21}{60}$

$=\frac{-14}{60}$

$=-\frac{7}{30}$

Hence, the required answer is $-\frac{7}{30}$.