What will be the reciprocal of the product of the reciprocals of \(\frac{5}{3}\) and \(\frac{27}{40}\) ?

Given:

Numbers: \(\frac{5}{3}\) and \(\frac{27}{40}\)

Formula used:

The reciprocal of a number is \(\frac{1}{\text{number}}\).

The product of reciprocals is the reciprocal of their product.

Calculations:

Reciprocal of \(\frac{5}{3}\) is \(\frac{3}{5}\),

Reciprocal of \(\frac{27}{40}\) is \(\frac{40}{27}\).

⇒ Product of reciprocals = \(\frac{3}{5} \times \frac{40}{27}\)

⇒ \(\frac{3 \times 40}{5 \times 27} = \frac{120}{135} = \frac{8}{9}\)

Reciprocal of product = \(\frac{9}{8}\)

∴ The answer is \(\frac{9}{8}\).