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

Great question! Multiplying by 3 is actually the same thing as dividing by $\frac{1}{3}$. When you divide by a fraction, you multiply by its reciprocal. Since the reciprocal of $\frac{1}{3}$ is 3, we multiply by 3!

You'd multiply both sides by $\frac{3}{2}$ (the reciprocal of $\frac{2}{3}$). Always flip the coefficient fraction to get the reciprocal, then multiply both sides by it.

Look for the greatest common factor of 3 and 9, which is 3. Divide both the numerator and denominator by 3: $\frac{3 \div 3}{9 \div 3} = \frac{1}{3}$

Not directly! Cross-multiplication works when you have $\frac{a}{b} = \frac{c}{d}$. Here we have $\frac{1}{3}x = \frac{1}{9}$, which isn't two separate fractions. Stick with multiplying by the reciprocal method.

Sometimes that happens! You can leave your answer as a fraction (like $\frac{1}{3}$) or convert to decimal (0.333...). Fractions are often more exact, so they're usually preferred in algebra.