Question

Find the reciprocal of \[2\dfrac{1}{3}\].
A) $\dfrac{7}{3}$
B) $ - \dfrac{7}{3}$
C) $ - \dfrac{3}{7}$
D) $\dfrac{3}{7}$

Answer 1

Hint: We will first convert the given mixed fraction into an improper fraction and the just change the numerator to the denominator and denominator to numerator to get the required inverse.

Complete step by step answer:
We are given the number: \[2\dfrac{1}{3}\].
We know that if we have a mixed fraction \[a\dfrac{b}{c}\], then it can be converted into fraction as follows:-
\[ \Rightarrow a\dfrac{b}{c} = \dfrac{{c \times a + b}}{c}\].
Therefore, we can write \[2\dfrac{1}{3}\] as \[\dfrac{{3 \times 2 + 1}}{3}\].
On simplifying it, we will then get
\[ \Rightarrow 2\dfrac{1}{3} = \dfrac{7}{3}\]
Now, we know that, if we need reciprocal of any fraction, we just replace the numerator by denominator and the denominator by the numerator.
Here, the numerator is $7$, and the denominator $3$. So, we will now change it to the numerator being $3$ and the denominator being $7$.
Hence, the reciprocal of \[\dfrac{7}{3}\] is \[\dfrac{3}{7}\].
Therefore, the reciprocal of \[2\dfrac{1}{3}\] is \[\dfrac{3}{7}\].

Hence, the correct option is (D).

Note:
The students must note that there is one more way to find the reciprocal of a fraction.
Since, we had \[2\dfrac{1}{3} = \dfrac{7}{3}\], let us assume that it has the reciprocal $x$.
We know that the product of a number and its reciprocal is always equal to one. (Number should not be equal to 0)
Therefore, \[\dfrac{7}{3} \times x = 1\].
We can write it as: \[\dfrac{{7x}}{3} = 1\].
Taking the 3 from division in LHS to multiplication in RHS, we will get
\[ \Rightarrow 7x = 3\]
Taking the 7 from multiplication in LHS to division in RHS, we will get
\[ \Rightarrow x = \dfrac{3}{7}\].
Did you notice that we said: Number should not be equal to 0? Let us understand why we used that.
If the number is equal to 0, we can write it as $\dfrac{0}{1}$. Therefore, its reciprocal will be $\dfrac{1}{0}$ which is undefined.
Therefore, we cannot find the reciprocal of 0 and similarly, 0 cannot be reciprocal of any number as well.