Question

What is the reciprocal of $${\displaystyle \frac{5}{8}}$$?

Answer 1

Hint: We are asked to find the reciprocal of $${\displaystyle \frac{5}{8}}$$. In order to find the reciprocal of $${\displaystyle \frac{5}{8}}$$ we have to interchange the numerator to the denominator and denominator to the numerator. Then the reciprocal of any fraction can be obtained.

Complete step-by-step answer:
Let us know more about reciprocal of fraction. In simple words, swapping the numerator and denominator gives us the reciprocal of a fraction. If we multiply the original fraction with its reciprocal, we get $$1$$ as the result. If the reciprocal of a mixed fraction is to be found, then we have to convert it into an improper fraction at first and then find its reciprocal. While finding the reciprocal, if a number does not have a denominator, then consider one as its denominator and on swapping we get one in the numerator. The reciprocal of a fraction is applicable when two fractions are to be divided. The divisor fraction would be converted into reciprocal and then multiplied
The general form of a fraction and its reciprocal is $${\displaystyle \frac{a}{b}}={\displaystyle \frac{b}{a}}$$.
Now let us find out the reciprocal of the given fraction$${\displaystyle \frac{5}{8}}$$.
Applying the rule of reciprocal, we get $${\displaystyle \frac{8}{5}}$$ as the reciprocal of $${\displaystyle \frac{5}{8}}$$.
$$\therefore$$ The reciprocal of $${\displaystyle \frac{5}{8}}$$ is $${\displaystyle \frac{8}{5}}$$.

Note: The reciprocal of a proper fraction would be an improper fraction and the reciprocal of improper fraction would give us a proper fraction. The product of a fraction and its reciprocal is always one.