Question

Solve.

(i) $\frac{5}{12}+\frac{7}{16}$ (ii) $3\frac{2}{5}-2\frac{1}{4}$ (iii) $\frac{12}{5}\times \frac{\left(-10\right)}{3}$ (iv) $4\frac{3}{8}÷\frac{25}{18}$

Answer 1

(i)
$$\begin{gathered} \frac{5}{12}+\frac{7}{16}=\frac{5\times 4}{12\times 4}+\frac{7\times 3}{16\times 3} \\ =\frac{20}{48}+\frac{21}{48} \\ =\frac{20+21}{48} \\ =\frac{41}{48} \end{gathered}$$
(ii)
$$\begin{gathered} 3\frac{2}{5}-2\frac{1}{4}=\frac{17}{5}-\frac{9}{4} \\ =\frac{17\times 4}{5\times 4}-\frac{9\times 5}{4\times 5} \\ =\frac{68}{20}-\frac{45}{20} \end{gathered}$$
$$\begin{gathered} =\frac{68-45}{20} \\ =\frac{23}{20} \end{gathered}$$
(iii)
$$\begin{gathered} \frac{12}{5}\times \frac{\left(-10\right)}{3}=\frac{4\cancel{12}\times \left(\cancel{-10}\right)\left(-2\right)}{\cancel{5}\times \cancel{3}} \\ =4\times \left(-2\right) \\ =-8 \end{gathered}$$
(iv)
$$\begin{gathered} 4\frac{3}{8}÷\frac{25}{18}=\frac{\cancel{735}}{4\cancel{8}}\times \frac{9\cancel{18}}{5\cancel{25}} \\ =\frac{7\times 9}{4\times 5} \\ =\frac{63}{20} \end{gathered}$$