The reciprocals of five and a number add up to eight-elevenths.

 Nov 13, 2018

The reciprocal of \(5\) is \(\frac{1}{5}\).


The reciprocal of a number, let's say \(x\), is \(\frac{1}{x}\).


(I'm assuming both are reciprocals because you said reciprocals.)


\(\frac{1}{5} + \frac{1}{x} = \frac{8}{11}\).


We need to put this under a common denominator, our smallest one being \(55\).


\(\frac{11}{55} + \frac{1}{x} = \frac{40}{55}\).


\(\frac{1}{x} = \frac{29}{55}\).


Cross multiplying, we get 


\(29x = 55\).


\(x = 55 \div 29\).


\(x = 1.89655...\)


You can round this to any digit needed, but I'm going to round it to the hundredths, making our answer \(\boxed{1.90}\).



 Nov 13, 2018

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