Solve for X in the Equation: 1/3x = 9

Great question! Multiplying by 3 and dividing by $\frac{1}{3}$ are exactly the same operation! Dividing by a fraction means multiplying by its reciprocal, so it's often easier to just multiply by 3.

You'd multiply both sides by $\frac{3}{2}$ (the reciprocal of $\frac{2}{3}$). The reciprocal flips the numerator and denominator, so always use the reciprocal to eliminate fractional coefficients!

Not directly! Cross multiplication works when you have $\frac{a}{b} = \frac{c}{d}$. Here you have $\frac{1}{3}x = 9$, which isn't two fractions set equal. Multiplying by the reciprocal is the right method here.

The reciprocal of any fraction $\frac{a}{b}$ is $\frac{b}{a}$. When you multiply them together, you always get 1: $\frac{1}{3} \times 3 = 1$. That's how you eliminate the coefficient!

Double-check your arithmetic! For this problem, $3 \times 9 = 27$ exactly. If you're getting decimals, you might have made an error in multiplication or used the wrong reciprocal.