Question

The reciprocal of 4 plus the reciprocal of 5 is the reciprocal of what number?

Answer 1

Hint: In order to solve this question first we reciprocate two numbers and then we use plus sign in between them and then we equate that number to a variable and take LCM in denominator and solve that expression and then we again reciprocate the answer to get the final answer because we know that reciprocal of reciprocal is the same number.

Complete step-by-step answer:
We have given two numbers that are 4 and 5.
We will reciprocate both the numbers and add them.
Reciprocal of the numbers are \[\dfrac{1}{4}\] and \[\dfrac{1}{5}\].
Now we add them and equate this to a variable.
\[x = \dfrac{1}{4} + \dfrac{1}{5}\]
Now on taking LCM in denominator-
\[x = \dfrac{{4 + 5}}{{20}}\]
On further solving
\[x = \dfrac{9}{{20}}\]
The number obtained is the reciprocal of 4 plus the reciprocal of 5.
We have asked which number is theirs whose reciprocal answer is obtained.
Now we reciprocate the last equation:
After reciprocating the answer is \[\dfrac{9}{{20}}\]
So the actual number is \[\dfrac{{20}}{9}\].
Final answer:
The final answer is reciprocal of \[\dfrac{{20}}{9}\].

Note: In order to solve this question, you must have a good knowledge of the number system. We must be able to understand the language of the question and try to express it in the form of mathematical expression and then calculate the answer. Students often make mistakes in reciprocating and taking the LCM on the denominator they add directly nominator with numerator and denominator with denominator. And forget to reciprocate at last.