Question

How do you find the reciprocal of $4\dfrac{1}{3}$ ?

Answer 1

Hint: In this question, we have to find the reciprocal of a number. Since the number is in the form of a mixed fraction, we first have to change the mixed fraction into an improper fraction, and then we will take the reciprocal of the new fraction. So, we use the improper fraction method. An improper fraction is that fraction in which the numerator is greater than or equal to the denominator. A mixed fraction is a combination of a whole number and a fraction. We start solving this problem by changing the whole number as a sum of 1 and then converting all the 1’s in the form of division. Then, we will take LCM and make further calculations to get an improper function. After that, we flip the numerator and denominator of the new fraction, which is our required solution.

Complete answer:
According to the question, we have to find the reciprocal of a mixed fraction.
The mixed fraction given is $4\dfrac{1}{3}$ --------------- (1)
Now, we first change the mixed fraction into an improper fraction.
Firstly, we will write 4 as a sum of 1, 1, 1, and 1, therefore we get
$\Rightarrow 1+1+1+1+\dfrac{1}{3}$
Now, we know that 1 can also be represented in the division, where both numerator and the denominator are the same, thus in the above equation, we substitute $1=\dfrac{3}{3}$ , we get
$\Rightarrow \dfrac{3}{3}+\dfrac{3}{3}+\dfrac{3}{3}+\dfrac{3}{3}+\dfrac{1}{3}$
Now, we take the LCM of the above equation, we get
$\Rightarrow \dfrac{3+3+3+3+1}{3}$
On further simplification, we get
$\Rightarrow \dfrac{13}{3}$
Therefore, from above we see that we have converted the mixed fraction into an improper fraction.
Now, we take the reciprocal of the improper fraction that is we flip the numerator and the denominator, thus we get
$\Rightarrow \dfrac{3}{13}$ which is our required answer.
Therefore, the reciprocal for the mixed number $4\dfrac{1}{3}$ is $\dfrac{3}{13}$.

Note: Always remember that while converting all the 1’s in the form of division, we take both the numerator and the denominator the same and that number is equal to the fraction part denominator. One of the alternative methods, to solve this problem is that we simply multiply the whole number and the fractional denominator and then add the numerator to the new number, which will become the new numerator. After that flip both the numerator and denominator, which is our required answer.