Question

What is the reciprocal of $6\dfrac{2}{7}$?

Answer 1

Hint: The fraction which is represented in the form $a\dfrac{b}{c}$ is called mixed fraction. To convert a mixed fraction into improper fraction we follow the following method $\dfrac{a\times c+b}{c}$ .
The reciprocal of a number $x$ is given by $\dfrac{1}{x}$. Thus, it means that the product of the number and its reciprocal gives the value $x\times \dfrac{1}{x}=1$.
The inverse of a fraction $\dfrac{a}{b}$ is given by inverting the fraction upside-down i.e. the reciprocal of the fraction is $\dfrac{b}{a}$ .

Complete step by step answer:
Given,
$6\dfrac{2}{7}$ …(1)
To find the reciprocal of the given number.
First, we will convert the mixed fraction into improper fraction we will get:
$\dfrac{6\times 7+2}{7}=\dfrac{44}{7}$ …(2)
Now we convert the improper fraction into reciprocal by inverting the number upside down then from equation (2) we get,
$\dfrac{7}{44}$

Thus, the reciprocal of the number $6\dfrac{2}{7}$ is $\dfrac{7}{44}$

Note: There is another method to find the reciprocal of the number the first step would be the same that is converting the mixed fraction into improper fraction.
Then we can use the result that the product of a number and its reciprocal is always 1.
Therefore, the improper fraction obtained is $\dfrac{44}{7}$ and now let us assume that its reciprocal is $r$. Therefore, we can write:
$\begin{align}
  & r\times \dfrac{44}{7}=1 \\
 & r=1\times \dfrac{7}{44} \\
 & r=\dfrac{7}{44} \\
\end{align}$
Hence the reciprocal of the number obtained by this method is the same as that obtained above.
The common mistake is that we can make mistakes while converting the mixed fraction into improper fraction i.e we have to multiply the number in the denominator to the central number and add it to the number in the numerator.