Question:
By what rational number should $\frac{-8}{39}$ be multiplied to obtain $\frac{1}{26} ?$
Solution:
Let the number be $\mathrm{x}$.
Now,
$\mathrm{x} \times \frac{-8}{39}=\frac{1}{26}$
$\Rightarrow \mathrm{x}=\frac{1}{26} \div \frac{-8}{39}$
$\Rightarrow \mathrm{x}=\frac{1}{26} \times \frac{39}{-8}$
$\Rightarrow \mathrm{x}=\frac{39}{-208}$
$\Rightarrow \mathrm{x}=\frac{39 \times-1}{-208 \times-1}$
$\Rightarrow \mathrm{x}=\frac{-39}{208}$
$\Rightarrow \mathrm{x}=\frac{-39 \div 13}{208 \div 13}$
$\Rightarrow \mathrm{x}=\frac{-3}{16}$
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