Write the ratio \( 2 \frac{1}{7} \) to \( 3 \frac{4}{7} \) as a simplified fraction.

To find the ratio \( 2 \frac{1}{7} \) to \( 3 \frac{4}{7} \), we first convert both mixed numbers into improper fractions. For \( 2 \frac{1}{7} \): \[ 2 \frac{1}{7} = 2 \times 7 + 1 = 14 + 1 = 15 \quad \text{so} \quad 2 \frac{1}{7} = \frac{15}{7} \] For \( 3 \frac{4}{7} \): \[ 3 \frac{4}{7} = 3 \times 7 + 4 = 21 + 4 = 25 \quad \text{so} \quad 3 \frac{4}{7} = \frac{25}{7} \] Now we can write the ratio of \( 2 \frac{1}{7} \) to \( 3 \frac{4}{7} \): \[ \frac{15/7}{25/7} \] This simplifies to: \[ \frac{15}{25} \] Now we can simplify \( \frac{15}{25} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 5: \[ \frac{15 \div 5}{25 \div 5} = \frac{3}{5} \] Thus, the simplified fraction representing the ratio \( 2 \frac{1}{7} \) to \( 3 \frac{4}{7} \) is: \[ \frac{3}{5} \]