jmc

Let $x$ be the number. Converting the words in the problem into an equation gives us $3+\frac{1}{x}=\frac{7}{x}$. Subtracting $\frac{1}{x}$ from both sides gives $3=\frac{6}{x}$. Multiplying both sides of this equation by $x$ gives $3x=6$, and dividing both sides of this equation by 3 gives $x=\boxed{2}$.