Answer
$x+\frac{1}{x}=\frac{5}{2}$;
The number is either 2 or $\frac{1}{2}$.
(refer to the step by step part for the complete solution)
Work Step by Step
Let
x =the unknown number
Then
$\frac{1}{x}$ = reciprocal of the unknown number
Thus, the translation of the given sentence as an equation is:
$x+ \frac{1}{x}=\frac{5}{2}$
Solving the equation gives:
$2x(x+\frac{1}{x})=2x(\frac{5}{2})
\\2x^2+2=\frac{10x}{2}
\\2x+2=5x
\\2x^2-5x+2=0$
Factor the trinomial to have:
$(2x-1)(x-2)=0$
Equate each factor to zero then solve each equation to have:
$2x-1=0 \text{ or } x-2=0
\\2x = 1 \text{ or } x=2
\\x = \frac{1}{2} \text{ or } x=2$
Therefore
$\\\frac{1}{x} = \frac{1}{\frac{1}{2}} \text{ or } \frac{1}{2}
\\\frac{1}{x} = 2 \text{ or } \frac{1}{2}$
Therefore the number is either 2 or $\frac{1}{2}$.
