To determine if these ratios are proportions, we need to check if the two fractions in each statement are equal:
-
For the first statement:
\[ \frac{2.5}{10} \quad \text{and} \quad \frac{12}{48} \]
To simplify \( \frac{2.5}{10} \): \[ \frac{2.5 \div 2.5}{10 \div 2.5} = \frac{1}{4} \]
To simplify \( \frac{12}{48} \): \[ \frac{12 \div 12}{48 \div 12} = \frac{1}{4} \]
Since both fractions simplify to \( \frac{1}{4} \), we have: \[ \frac{2.5}{10} = \frac{12}{48} \]
So, \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
-
For the second statement:
\[ \frac{2.5}{2} \quad \text{and} \quad \frac{12}{24} \]
To simplify \( \frac{2.5}{2} \): \[ \frac{2.5 \div 2.5}{2 \div 2.5} = \frac{1}{0.8} = 1.25 \]
To simplify \( \frac{12}{24} \): \[ \frac{12 \div 12}{24 \div 12} = \frac{1}{2} \]
Since \( 1.25 \neq 0.5 \), we have: \[ \frac{2.5}{2} \neq \frac{12}{24} \]
Thus, \( \frac{2.5}{2} = \frac{12}{24} \) is not a proportion.
Based on this, we can conclude:
Responses:
- \( 2.5/10 = 12/48 \) is a proportion.
- \( 2.5/2 \neq 12/24 \) is not a proportion.
Therefore, the correct answer is:
Only the first statement is a proportion.