Question

How do you find the reciprocal of $\dfrac{6}{7}$?

Answer 1

Hint: To find the reciprocal of a number, we have to divide that particular number by unity, that is by \[1\], then the resultant number which can be whole number or in a fractional form, will be the required reciprocal number of that particular given number.

Complete answer:
The given number, of which we have to find the reciprocal form $ = \dfrac{6}{7}$
Now, as we know to find the reciprocal form of a number, we have to do its division by unity or \[1\]. So let us divide $\dfrac{6}{7}$ by \[1\], we will get,
$ = \dfrac{1}{{\dfrac{6}{7}}}$
We can also write $\dfrac{1}{{\dfrac{6}{7}}}$, with the help of division sign, as follows
$ = 1 \div \dfrac{6}{7}$
Now, we know that if we reciprocate $\dfrac{6}{7}$ , that is to $\dfrac{7}{6}$ then the division sign between \[1\] and $\dfrac{6}{7}$ will be replaced by or you can say will be converted into multiplication sign, that is we can rewrite the above line as
$ = 1 \times \dfrac{7}{6}$
As you can see, on reciprocating the number $\dfrac{6}{7}$ into the number $\dfrac{7}{6}$, a multiplication sign replaced the division sign between \[1\] and $\dfrac{6}{7}$, so now we will do a simple multiplication between \[1\] and $\dfrac{7}{6}$, then we will get the desired result, let us do the multiplication
$
   = 1 \times \dfrac{7}{6} \\
   = \dfrac{7}{6} \\
 $
So we have got our required result, the reciprocal of $\dfrac{6}{7}$ which comes out to be $\dfrac{7}{6}$.

Note: Finding reciprocal of a proper fraction is very simple, we just have to turn the given number upside down. Let us take a general example of $\dfrac{a}{b}$ , where $a$ and $b$ belongs to whole number, it is a proper fraction, so it’s reciprocal can be written as $\dfrac{b}{a}$ , see how simple it is.
Also, if a number is multiplied by its reciprocal then the result $ = 1$