A proportion is defined as an equation that states that two ratios are equal. To determine which option is a proportion, we can simplify both sides of the equations and see if they are equivalent.
Option 1: \( \frac{5}{6} = \frac{15}{18} \)
To check if this is true, we simplify \( \frac{15}{18} \):
\( \frac{15 \div 3}{18 \div 3} = \frac{5}{6} \)
Since both sides equal \( \frac{5}{6} \), Option 1 is a valid proportion.
Option 2: \( \frac{5}{6} = \frac{20}{18} \)
Now let's simplify \( \frac{20}{18} \):
\( \frac{20 \div 2}{18 \div 2} = \frac{10}{9} \)
Since \( \frac{5}{6} \) does not equal \( \frac{10}{9} \), Option 2 is not a valid proportion.
Therefore, Option 1 is a proportion.