Question

Simplify:
(i) $\frac{12}{25}\times \frac{15}{28}\times \frac{35}{36}$
(ii) $\frac{10}{27}\times \frac{39}{56}\times \frac{28}{65}$
(iii) $2\frac{2}{17}\times 7\frac{2}{9}\times 1\frac{33}{52}$

Answer 1

(i)
$$\begin{gathered} \frac{12}{25}\times \frac{15}{28}\times \frac{35}{36}\iff \frac{\cancel{12}\times {\cancel{15}}^3\times {\cancel{35}}^5}{{\cancel{25}}^5\times {\cancel{28}}^4\times {\cancel{36}}^3} \\ \Rightarrow \frac{\cancel{3}\times \cancel{5}}{\cancel{5}\times 4\times \cancel{3}}\iff \frac{1}{4} \end{gathered}$$

(ii)
$$\begin{gathered} \frac{10}{27}\times \frac{39}{56}\times \frac{28}{65}\iff \frac{\cancel{10}\times {\cancel{39}}^{{\cancel{3}}^1}\times \cancel{28}}{{\cancel{27}}^9\times {\cancel{56}}^{\cancel{2}}\times {\cancel{65}}^{\cancel{5}}} \\ \Rightarrow \frac{1}{9} \end{gathered}$$
(iii)
$$\begin{gathered} 2\frac{2}{17}\times 7\frac{2}{9}\times 1\frac{33}{52}\iff \frac{(2\times 17)+2}{17}\times \frac{(7\times 9)+2}{9}\times \frac{(52\times 1)+33}{52} \\ \iff \frac{\cancel{{36}^{\cancel{4}}}\times {\cancel{65}}^5\times {\cancel{85}}^5}{\cancel{17}\times \cancel{9}\times {\cancel{52}}^{\cancel{4}}} \\ \Rightarrow \frac{25}{1} \end{gathered}$$