Question

Reciprocal of \[\dfrac{7}{5}\] is
A) \[1\dfrac{2}{5}\]
B) \[\dfrac{5}{7}\]
C) \[5\dfrac{2}{3}\]
D) \[\dfrac{12}{5}\]

Answer 1

Hint:
We are given an improper fraction whose reciprocal we have to find. We know that reciprocal of any number is the exchange of the numerator and denominator with each other and that is reciprocal of \[x=\dfrac{1}{x}\] when nothing is there in the denominator then it’s \[1\] there.

Complete step by step solution:
Given that,
A fraction \[\dfrac{7}{5}\]
Reciprocal of fraction \[=?\]
Since we know that reciprocal of function is the exchange of numerator and denominator with each other in any fraction. Means after reciprocal the new numerator will be the denominator of previous and denominator will be the numerator of previous fraction.
Let assume a fraction \[\dfrac{a}{b}\]
Then it’s reciprocal will be \[\dfrac{b}{a}\]
Now comparing this with given question,
We get \[a=7\] and \[b=5\]
Now the reciprocal is \[\dfrac{b}{a}\]
\[\Rightarrow \dfrac{5}{7}\]
Thus, we have calculated the reciprocal of the given fraction and that is \[\dfrac{5}{7}\]

Hence, option (b) is correct.

Note:
When we have to calculate the reciprocal of any fraction like proper, improper or mixed fraction just exchange the numerator and denominator with each other in fraction. When the fraction is mixed note that first we need to convert that is proper or improper then simply exchange. Also note that if a fraction is lesser than one then after reciprocal its value will be greater than one also the proper fraction converted into improper and vice versa.