Question

Multiply the following rational numbers.

(i) $\frac{3}{11}\times \frac{2}{5}$

(ii) $\frac{12}{5}\times \frac{4}{15}$

(iii) $\frac{\left(-8\right)}{9}\times \frac{3}{4}$

(iv) $\frac{0}{6}\times \frac{3}{4}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{3}{11}\times \frac{2}{5} \\ =\frac{3\times 2}{11\times 5} \\ =\frac{6}{55} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{ii}\right)\frac{12}{5}\times \frac{4}{15} \\ =\frac{12\times 4}{5\times 15} \\ =\frac{48}{75} \\ =\frac{48÷3}{75÷3}\left(\mathrm{Since},\mathrm{HCF}\mathrm{of}48\mathrm{and}75\mathrm{is}3\right) \\ =\frac{16}{25} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iii}\right)\frac{\left(-8\right)}{9}\times \frac{3}{4} \\ =\frac{\left(-8\right)\times 3}{9\times 4} \\ =\frac{-24}{36} \\ =\frac{-24÷12}{36÷12}\left(\mathrm{Since},\mathrm{HCF}\mathrm{of}24\mathrm{and}36\mathrm{is}12\right) \\ =-\frac{2}{3} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iv}\right)\frac{0}{6}\times \frac{3}{4} \\ =\frac{0\times 3}{6\times 4} \\ =\frac{0}{24} \\ =0 \end{gathered}$$