Question

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

Answer 1

Hint: In this question, we are given a mixed fraction and we have to find its reciprocal. To do so, we will convert the mixed fraction into an improper fraction. We switch the positions of the numerator and the denominator with each other to find the reciprocal of a fraction, that is, at the place of the denominator we write the numerator and at the place of the numerator we write the denominator. For example, let a fraction be \[\dfrac{x}{y}\] then the reciprocal of this fraction is $\dfrac{y}{x}$ .

Complete step by step answer:
Now, we will find the solution of the question,
$3\dfrac{3}{4}$ can be written in the improper fraction form as –
$3\dfrac{3}{4} = \dfrac{{15}}{4}$
Now the reciprocal of this fraction is equal to $\dfrac{4}{{15}}$ .
This fraction cannot be simplified further as the numerator and the denominator don’t have any common factor.
Hence, the reciprocal of $3\dfrac{3}{4}$ is equal to $\dfrac{4}{{15}}$ .

Note: A fraction is of three types namely, proper fraction, improper fraction and mixed fraction. When a whole number is written with a proper fraction, we get a mixed fraction. The improper fractions are expressed in a simpler way with the help of mixed fractions. So they can be converted into each other easily. We multiply the denominator of the proper fraction with the whole number and then add the result obtained with the numerator, the number obtained is now written as the numerator and the denominator remains the same for converting a mixed fraction into an improper fraction.