To determine which option is a proportion, we need to check if the ratios on either side are equivalent.
A. \( \frac{4}{5} = \frac{20}{25} \)
To check if this is true, we can simplify \( \frac{20}{25} \):
\[ \frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5} \]
So, \( \frac{4}{5} = \frac{20}{25} \) is true.
B. \( \frac{4}{5} = \frac{16}{30} \)
Now let's simplify \( \frac{16}{30} \):
\[ \frac{16}{30} = \frac{16 \div 2}{30 \div 2} = \frac{8}{15} \]
Now we compare \( \frac{4}{5} \) and \( \frac{8}{15} \):
Cross-multiplying to check for equivalence: \( 4 \times 15 = 60 \) and \( 5 \times 8 = 40 \)
Since \( 60 \neq 40 \), \( \frac{4}{5} \) is not equal to \( \frac{16}{30} \).
Therefore, Option 1 (A) \( \frac{4}{5} = \frac{20}{25} \) is a proportion.