Question

Multiply:

$\frac{8}{35}\times \frac{21}{-32}$

Answer 1

We know, $\mathrm{Product}\mathrm{of}\mathrm{two}\mathrm{rational}\mathrm{numbers}=\frac{\mathrm{Product}\mathrm{of}\mathrm{their}\mathrm{numerators}}{\mathrm{Product}\mathrm{of}\mathrm{their}\mathrm{denominators}}$

So, $\frac{8}{35}\times \frac{21}{-32}$

$$\begin{gathered} =\frac{8\times 21}{35\times (-32)} \\ =\frac{8\times {\displaystyle \stackrel{3}{\cancel{21}}}}{{\displaystyle \underset{5}{\cancel{35}}}\times (-32)} \\ =\frac{\cancel{8}\times {\displaystyle 3}}{{\displaystyle 5\times (-\underset{4}{\cancel{32}})}} \\ =\frac{3}{5\times (-4)} \\ =-\left(\frac{3}{20}\right) \end{gathered}$$

Hence, $\frac{8}{35}\times \frac{21}{-32}=-\left(\frac{3}{20}\right)$.