To determine if the given statements are proportions, we need to check if the cross products of the two fractions in each equation are equal.
- For the first equation \( 2.510 = 1248 \):
This can be rewritten as \( \frac{2.5}{10} = \frac{12}{48} \).
Calculating the cross products:
- Left side: \( 2.5 \times 48 = 120 \)
- Right side: \( 10 \times 12 = 120 \)
Since both cross products are equal (120 = 120), the equation \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
- For the second equation \( 2.52 = 1224 \):
This can be rewritten as \( \frac{2.5}{2} = \frac{12}{24} \).
Calculating the cross products:
- Left side: \( 2.5 \times 24 = 60 \)
- Right side: \( 2 \times 12 = 24 \)
Since the cross products are not equal (60 ≠ 24), the equation \( \frac{2.5}{2} = \frac{12}{24} \) is not a proportion.
Conclusion:
- The first equation \( 2.510 = 1248 \) is a proportion.
- The second equation \( 2.52 = 1224 \) is not a proportion.
So the correct response is: "One is a proportion and the other is not." However, this option was not provided in your list, so the closest answer consistent with the given options indicates that "both are proportions" is incorrect, and "neither is a proportion" is also incorrect. The first is a proportion while the second is not.