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

 Nov 13, 2018
 #1
avatar+539 
+7

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 \(\boxed{1.90}\).

 

cool

 Nov 13, 2018

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