Question

Divide:
(i) $\frac{3}{8}\mathrm{by}\frac{5}{9}$
(ii) $3\frac{1}{4}\mathrm{by}\frac{2}{3}$
(iii) $\frac{7}{8}\mathrm{by}4\frac{1}{2}$
(iv) $6\frac{1}{4}\mathrm{by}2\frac{3}{5}$

Answer 1

(i)
$$\begin{gathered} \frac{3}{8}÷\frac{5}{9}=\frac{3}{8}\times \frac{9}{5} \\ \Rightarrow \frac{3\times 9}{8\times 5}\iff \frac{27}{40} \end{gathered}$$

(ii)
$$\begin{gathered} 3\frac{1}{4}÷\frac{2}{3}=\frac{(3\times 4)+1}{4}\times \frac{3}{2} \\ \Rightarrow \frac{13}{4}\times \frac{3}{2}\iff \frac{39}{8}=4\frac{7}{8} \end{gathered}$$

(iii)
$$\begin{gathered} \frac{7}{8}÷4\frac{1}{2}=\frac{7}{8}÷\frac{(4\times 2)+1}{2} \\ \Rightarrow \frac{7}{\cancel{8^4}}\times \frac{\cancel{2}}{9} \\ \Rightarrow \frac{7}{4}\times \frac{1}{9}\iff \frac{7}{36} \end{gathered}$$
(iv)
$$\begin{gathered} 6\frac{1}{4}÷2\frac{3}{5}=\frac{(6\times 4)+1}{4}÷\frac{(2\times 5)+3}{5} \\ \Rightarrow \frac{25}{4}÷\frac{13}{5}=\frac{25}{4}\times \frac{5}{13} \\ \Rightarrow \frac{125}{52}=2\frac{21}{52} \end{gathered}$$