By what rational number should we multiply

Question:

By what rational number should we multiply $\frac{-15}{56}$ to get $\frac{-5}{7} ?$

Solution:

Let the number be $\mathrm{x}$.

Now,

$\mathrm{x} \times \frac{-15}{56}=\frac{-5}{7}$

$\Rightarrow \mathrm{x}=\frac{-5}{7} \div \frac{-15}{56}$

$\Rightarrow \mathrm{x}=\frac{-5}{7} \times \frac{56}{-15}$

$\Rightarrow \mathrm{x}=\frac{280}{105}$

$\Rightarrow \mathrm{x}=\frac{280 \div 5}{105 \div 5}$

$\Rightarrow \mathrm{x}=\frac{56}{21}$

$\Rightarrow \mathrm{x}=\frac{56 \div 7}{21 \div 7}$

$\Rightarrow \mathrm{x}=\frac{8}{3}$

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