Question

Carry out the following divisions.
(i) $\frac{2}{3}÷\frac{1}{4}$

(ii) $\frac{{\displaystyle 5}}{{\displaystyle 9}}÷\frac{{\displaystyle 3}}{{\displaystyle 2}}$

(iii) $\frac{{\displaystyle 3}}{{\displaystyle 7}}÷\frac{{\displaystyle 5}}{{\displaystyle 11}}$

(iv) $\frac{{\displaystyle 11}}{{\displaystyle 12}}÷\frac{{\displaystyle 4}}{{\displaystyle 7}}$

Answer 1

(i)
$$\begin{gathered} \frac{2}{3}÷\frac{1}{4}=\frac{2}{3}\times \frac{4}{1} \\ =\frac{2\times 4}{3\times 1} \\ =\frac{8}{3} \end{gathered}$$

(ii)
$$\begin{gathered} \frac{{\displaystyle 5}}{{\displaystyle 9}}÷\frac{{\displaystyle 3}}{{\displaystyle 2}}=\frac{{\displaystyle 5}}{{\displaystyle 9}}\times \frac{{\displaystyle 2}}{{\displaystyle 3}} \\ =\frac{{\displaystyle 5\times 2}}{{\displaystyle 9\times 3}} \\ =\frac{{\displaystyle 10}}{{\displaystyle 27}} \end{gathered}$$

(iii)
$$\begin{gathered} \frac{{\displaystyle 3}}{{\displaystyle 7}}÷\frac{{\displaystyle 5}}{{\displaystyle 11}}=\frac{{\displaystyle 3}}{{\displaystyle 7}}\times \frac{{\displaystyle 11}}{{\displaystyle 5}} \\ =\frac{{\displaystyle 3\times 11}}{{\displaystyle 7\times 5}} \\ =\frac{33}{35} \end{gathered}$$

(iv)
$$\begin{gathered} \frac{{\displaystyle 11}}{{\displaystyle 12}}÷\frac{{\displaystyle 4}}{{\displaystyle 7}}=\frac{{\displaystyle 11}}{{\displaystyle 12}}\times \frac{{\displaystyle 7}}{{\displaystyle 4}} \\ =\frac{{\displaystyle 11\times 7}}{{\displaystyle 12\times 4}} \\ =\frac{{\displaystyle 77}}{{\displaystyle 48}} \end{gathered}$$