Question

Simplify:
(i) $\frac{3}{10}÷\frac{10}{3}$
(ii) $4\frac{3}{5}÷\frac{4}{5}$
(iii) $5\frac{4}{7}÷1\frac{3}{10}$
(iv) $4÷2\frac{2}{5}$

Answer 1

(i)
$$\begin{gathered} \frac{3}{10}÷\frac{10}{3}=\frac{3}{10}\times \frac{3}{10}\iff \frac{3\times 3}{10\times 10} \\ \Rightarrow \frac{9}{100} \end{gathered}$$
(ii)
$$\begin{gathered} 4\frac{3}{5}÷\frac{4}{5}=\frac{(4\times 5)+3}{5}÷\frac{4}{5} \\ \Rightarrow 4\frac{3}{5}÷\frac{4}{5}=\frac{23}{5}÷\frac{4}{5}\iff \frac{23}{5}\times \frac{5}{4} \\ \Rightarrow \frac{23}{4}=5\frac{3}{4} \end{gathered}$$

(iii)
$$\begin{gathered} 5\frac{4}{7}÷1\frac{3}{10}=\frac{(5\times 7)+4}{7}÷\frac{(1\times 10)+3}{10} \\ \Rightarrow 5\frac{4}{7}÷1\frac{3}{10}=\frac{39}{7}÷\frac{13}{10}\iff \frac{\cancel{{39}^3}}{7}\times \frac{10}{\cancel{13}} \\ \Rightarrow \frac{30}{7}=4\frac{2}{7} \end{gathered}$$

(iv)
$$\begin{gathered} 4÷2\frac{2}{5}=\frac{4}{1}÷\frac{(2\times 5)+2}{5}\iff \frac{\cancel{4}}{1}\times \frac{5}{\cancel{{12}^3}} \\ \Rightarrow \frac{5}{3}=1\frac{2}{3} \end{gathered}$$