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# help

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

Nov 13, 2018

#1
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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