Question

Question:-

$What \: \: should \: \: ( \frac{5}{7} ) ^{ - 2} \: \: be \: \: multilied \: \: by \: \: to \: \: get \: \: ( \frac{15}{28} )^{ - 1}$
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Answer 1

Solution :-

let x be the required number.

$( \frac{5}{7} )^{ - 2} \times x = ( \frac{15}{28} )^{ - 1} \\ \\ \implies \: ( \frac{7}{5})^{2} \times x = \frac{28}{15} \\ \\ \implies \: x = \frac{28}{15} \times ( \frac{5}{7})^{2} \\ \\ \implies \: x = \frac{28}{15} \times \frac{5}{7} \times \frac{5}{7} = \frac{20}{21} .$

The required number is 20/21.

Answer 2

Solution :-

Let x be the required number.

$\therefore (\frac{5}{7})^{-2} \times x = (\frac{15}{28})^{-1}$

$\implies (\frac{7}{5})^2 \times x = \frac{28}{15}$

$\implies \frac{49}{25} \times x = \frac{28}{15}$

$\implies x = \frac{28}{15} \times \frac{25}{49}$

$\implies x = \frac{\cancel{28}}{\cancel{15}} \times \frac{\cancel{25}}{\cancel{49}}$

$\implies x = \frac{20}{21}$

Therefore, the required number is 20/21.