A motor racing circuit has length \( 5 \frac{5}{6} \) miles. A straight section of the circuit has length \( 1 \frac{1}{4} \) miles. What fraction of the circuit is the straight section? Give your answer in its simplest form.

To find what fraction of the circuit is the straight section, we first convert the mixed numbers into improper fractions. The length of the circuit, \( 5 \frac{5}{6} \), can be converted as follows: \[ 5 \frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{30 + 5}{6} = \frac{35}{6} \] Next, we convert the straight section's length, \( 1 \frac{1}{4} \): \[ 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} \] Now, we calculate the fraction of the circuit that corresponds to the straight section: \[ \text{Fraction} = \frac{\text{Straight section}}{\text{Circuit length}} = \frac{\frac{5}{4}}{\frac{35}{6}} \] To divide by a fraction, we multiply by its reciprocal: \[ \frac{5}{4} \times \frac{6}{35} = \frac{5 \times 6}{4 \times 35} = \frac{30}{140} \] Next, we simplify the fraction \( \frac{30}{140} \): Both the numerator and the denominator can be divided by 10: \[ \frac{30 \div 10}{140 \div 10} = \frac{3}{14} \] Thus, the straight section of the circuit is \( \frac{3}{14} \) of the total length of the circuit.