Solve the Fraction Division: Finding the Missing Number in 1/3 : x = 3/8

To solve this problem, we need to determine the missing value in the division:

$\frac{1}{3} :\_{\text{ —}} = \frac{3}{8}$.

Let's follow these steps:

• Step 1: Identify the given division problem as: $\frac{1}{3} \div x = \frac{3}{8}$.
• Step 2: Rearrange to find $x$, giving us $x = \frac{1}{3} \div \frac{3}{8}$.
• Step 3: Use the reciprocal method of dividing fractions: $x = \frac{1}{3} \times \frac{8}{3}$.
• Step 4: Multiply the numerators and the denominators: $\frac{1 \times 8}{3 \times 3} = \frac{8}{9}$.

Therefore, the missing number is $\frac{8}{9}$.