Question

Simplify:

(i) $\frac{3}{20}\times \frac{4}{5}$
(ii) $\frac{-7}{30}\times \frac{5}{14}$
(iii) $\frac{5}{-18}\times \frac{-9}{20}$
(iv) $\frac{-9}{8}\times \frac{-16}{3}$
(v) $-32\times \frac{-7}{36}$
(vi) $\frac{16}{-21}\times \frac{-14}{5}$

Answer 1

$\begin{array}{l}\left(i\right)\\ \frac{3}{\sout{2}{\sout{0}}_5}\times \frac{{\sout{4}}^1}{5}\\ =\frac{3\times 1}{5\times 5}\\ =\frac{3}{25}\\ \\ \left(ii\right)\\ \frac{-{\sout{7}}^1}{\sout{3}{\sout{0}}_6}\times \frac{{\sout{5}}^1}{\sout{1}{\sout{4}}_2}\\ =\frac{-1\times 1}{6\times 2}\\ =\frac{-1}{12}\\ \\ \left(iii\right)\\ \frac{{\sout{5}}^1}{-\sout{1}{\sout{8}}_2}\times \frac{-{\sout{9}}^1}{\sout{2}{\sout{0}}_4}\\ =\frac{1\times (-1)}{-2\times 4}\\ =\frac{-1}{-8}=\frac{1}{8}\\ \\ \left(iv\right)\\ \frac{-{\sout{9}}^3}{{\sout{8}}_1}\times \frac{-\sout{1}{\sout{6}}^2}{{\sout{3}}_1}\\ =(-3)\times (-2)\\ =6\\ \\ \left(v\right)\\ \frac{-32}{1}\times \frac{-7}{36}\\ =\frac{-\sout{3}{\sout{2}}^8\times (-7)}{1\times \sout{3}{\sout{6}}_9}\\ =\frac{-8\times (-7)}{9}\\ =\frac{56}{9}\\ \\ \\ \text{(vi)}\\ \text{We need a positive denominator.}\\ \therefore \frac{16}{-21}\times \frac{-1}{-1}=\frac{-16}{21}\\ \mathrm{Now},\frac{-16}{\sout{2}{\sout{1}}_3}\times \frac{-\sout{1}{\sout{4}}^2}{5}\\ \\ =\frac{(-16)\times (-2)}{3\times 5}\\ =\frac{32}{15}\end{array}$