Question

detrmine if 2.5/10=12/48 or 2.5/2=12/24 is a proportion

2.5/2=12/24
2.5/10=12/48
both are proportions
neither is a proportion

Answer 1

To determine if the given ratios are proportional, we check if the cross-products are equal.

1. For the proportion \( \frac{2.5}{2} = \frac{12}{24} \):
- Cross-multiply:
\[
2.5 \times 24 = 60
\]
\[
2 \times 12 = 24
\]
Since \( 60 \neq 24 \), this means \( \frac{2.5}{2} \neq \frac{12}{24} \).

2. For the proportion \( \frac{2.5}{10} = \frac{12}{48} \):
- Cross-multiply:
\[
2.5 \times 48 = 120
\]
\[
10 \times 12 = 120
\]
Here, \( 120 = 120 \), which means \( \frac{2.5}{10} = \frac{12}{48} \).

Based on this assessment:
- \( \frac{2.5}{2} = \frac{12}{24} \) is **not a proportion**.
- \( \frac{2.5}{10} = \frac{12}{48} \) **is a proportion**.

So the final answer is that **one of them is a proportion (specifically \( \frac{2.5}{10} = \frac{12}{48} \)), and the other is not**. If the options provided are only "both are proportions" or "neither is a proportion," it would indicate the only valid choice is that **neither of the pairs are proportions**.