Question

Simplify each of the following and express the result as a rational number in standard form:
(i) $\frac{-16}{21}\times \frac{14}{5}$

(ii) $\frac{7}{6}\times \frac{-3}{28}$

(iii) $\frac{-19}{36}\times 16$

(iv) $\frac{-13}{9}\times \frac{27}{-26}$

(v) $\frac{-9}{16}\times \frac{-64}{-27}$

(vi) $\frac{-50}{7}\times \frac{14}{3}$

(vii) $\frac{-11}{9}\times \frac{-81}{-88}$

(viii) $\frac{-5}{9}\times \frac{72}{-25}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{-16}{21}\times \frac{14}{5}=\frac{-2\times 2\times 2\times 2}{3\times 7}\times \frac{2\times 7}{5}=\frac{-32}{15} \\ \left(\mathrm{ii}\right)\frac{7}{6}\times \frac{-3}{28}=\frac{7}{2\times 3}\times \frac{-3}{2\times 2\times 7}=\frac{-1}{8} \\ \left(\mathrm{iii}\right)\frac{-19}{36}\times 16=\frac{-19}{2\times 2\times 3\times 3}\times 2\times 2\times 2\times 2=\frac{-76}{9} \\ \left(\mathrm{iv}\right)\frac{-13}{9}\times \frac{27}{-26}=\frac{-13}{3\times 3}\times \frac{3\times 3\times 3}{-2\times 13}=\frac{3}{2} \\ \left(\mathrm{v}\right)\frac{-9}{16}\times \frac{-64}{-27}=\frac{-9}{16}\times \frac{-4\times 16}{-3\times 9}=\frac{-4}{3} \\ \left(\mathrm{vi}\right)\frac{-50}{7}\times \frac{14}{3}=\frac{-50}{7}\times \frac{2\times 7}{3}=\frac{-100}{3} \\ \left(\mathrm{vii}\right)\frac{-11}{9}\times \frac{-81}{-88}=\frac{-11}{9}\times \frac{-9\times 9}{-8\times 11}=\frac{-9}{8} \\ \left(\mathrm{viii}\right)\frac{-5}{9}\times \frac{72}{-25}=\frac{-5}{9}\times \frac{8\times 9}{-5\times 5}=\frac{8}{5} \end{gathered}$$