Six times the reciprocal of a number equals 3 times the reciprocal of 9. Find the number. The number is square

Let the number be \( x \).<br /><br />The reciprocal of \( x \) is \( \frac{1}{x} \).<br /><br />According to the problem, six times the reciprocal of the number equals three times the reciprocal of 9. We can write this as:<br /><br />\[ 6 \times \frac{1}{x} = 3 \times \frac{1}{9} \]<br /><br />Simplifying the right side:<br /><br />\[ 6 \times \frac{1}{x} = \frac{3}{9} \]<br /><br />\[ 6 \times \frac{1}{x} = \frac{1}{3} \]<br /><br />Now, solve for \( x \):<br /><br />Multiply both sides by \( x \) to eliminate the fraction on the left:<br /><br />\[ 6 = \frac{x}{3} \]<br /><br />Multiply both sides by 3 to solve for \( x \):<br /><br />\[ 18 = x \]<br /><br />Thus, the number is \( \boxed{18} \).