A proportion is an equation that states that two ratios are equal. To determine if either of the options is a proportion, we can check if the two fractions on either side of the equation are equivalent.
Let's evaluate both options:
Option 1: \( \frac{4}{5} = \frac{20}{25} \)
To check if these two fractions are equivalent, we can simplify \( \frac{20}{25} \):
- \( \frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5} \)
Since both fractions are equal (\( \frac{4}{5} = \frac{4}{5} \)), Option 1 is a proportion.
Option 2: \( \frac{4}{5} = \frac{16}{30} \)
To check if these two fractions are equivalent, simplify \( \frac{16}{30} \):
- \( \frac{16}{30} = \frac{16 \div 2}{30 \div 2} = \frac{8}{15} \)
Now, we compare \( \frac{4}{5} \) and \( \frac{8}{15} \). To do this, we can cross-multiply:
- \( 4 \times 15 = 60 \)
- \( 5 \times 8 = 40 \)
Since \( 60 \neq 40 \), the fractions are not equal (\( \frac{4}{5} \neq \frac{8}{15} \)), so Option 2 is not a proportion.
Therefore, the correct answer is Option 1: 4/5 = 20/25 is a proportion.