Question

By what rational number should $\frac{-8}{39}$ be multiplies to obtain $\frac{1}{26}$ ?

Answer 1

Let $x$ be the required multiplied number.

then

$\frac{-8}{39}\times x=\frac{1}{26}$

$\Rightarrow x=\frac{1}{26}÷\frac{-8}{39}$

$\Rightarrow x=\frac{1}{26}\times \frac{39}{-8}$

$\Rightarrow x=\frac{39}{-208}$

$\Rightarrow x=\frac{39÷13}{-208÷13}$

$\Rightarrow x=\frac{3}{-16}$

Therefore $\frac{-8}{39}\times x=\frac{1}{26}$ is required rational number.

Verification:

$\frac{-8}{39}\times \frac{3}{-16}=\frac{-1}{13}\times \frac{1}{-2}=\frac{1}{26}$

Hence, verified.