Question:
By what rational number should we multiply $\frac{-15}{56}$ to get $\frac{-5}{7} ?$
Solution:
Let the number be $\mathrm{x}$.
Now,
$\mathrm{x} \times \frac{-15}{56}=\frac{-5}{7}$
$\Rightarrow \mathrm{x}=\frac{-5}{7} \div \frac{-15}{56}$
$\Rightarrow \mathrm{x}=\frac{-5}{7} \times \frac{56}{-15}$
$\Rightarrow \mathrm{x}=\frac{280}{105}$
$\Rightarrow \mathrm{x}=\frac{280 \div 5}{105 \div 5}$
$\Rightarrow \mathrm{x}=\frac{56}{21}$
$\Rightarrow \mathrm{x}=\frac{56 \div 7}{21 \div 7}$
$\Rightarrow \mathrm{x}=\frac{8}{3}$