Divide. Write the quotient in lowest terms. \( \frac{5}{8} \div 1 \frac{1}{3}=\square \)

To divide \( \frac{5}{8} \) by \( 1 \frac{1}{3} \), we first convert the mixed number to an improper fraction. This gives us \( 1 \frac{1}{3} = \frac{4}{3} \). Next, we use the rule that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we rewrite the expression as: \[ \frac{5}{8} \div \frac{4}{3} = \frac{5}{8} \times \frac{3}{4} \] Now, we multiply the numerators and the denominators: \[ \frac{5 \times 3}{8 \times 4} = \frac{15}{32} \] The final answer is \( \frac{15}{32} \), which is in its lowest terms.