Solve Fraction Division: Calculate 1/9 ÷ 1/3 Step-by-Step

To solve the division of the fractions $\frac{1}{9}$ and $\frac{1}{3}$, we'll employ the method of "invert and multiply":

• Step 1: Identify the reciprocal of the divisor. The divisor is $\frac{1}{3}$, and its reciprocal is $\frac{3}{1}$.
• Step 2: Convert the division into a multiplication. Therefore, $\frac{1}{9} \div \frac{1}{3}$ becomes $\frac{1}{9} \times \frac{3}{1}$.
• Step 3: Carry out the multiplication of the two fractions.
  $\frac{1}{9} \times \frac{3}{1} = \frac{1 \times 3}{9 \times 1} = \frac{3}{9}$.
• Step 4: Simplify the resulting fraction.
  $\frac{3}{9}$ simplifies to $\frac{1}{3}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

Therefore, the solution to the problem $\frac{1}{9} \div \frac{1}{3}$ is $\frac{1}{3}$.