Determine if 2.5/10=^? 12/48 or 2.5/2=?12/24 is a proportion.(1 point)

Question

Responses

Both are proportions.
Both are proportions.

2.5/2=12/24
Start Fraction 2.5 over 2 End Fraction equals Start Fraction 12 over 24 End Fraction

2.5/10=12/48
Start Fraction 2.5 over 10 End Fraction equals Start Fraction 12 over 48 End Fraction

Neither is a proportion.
Neither is a proportion.

Answer 1

To determine if the given fractions form proportions, we need to check if the cross products are equal for each pair of fractions.

1. For \( \frac{2.5}{10} \) and \( \frac{12}{48} \):

   • Cross-multiplying gives us: \[ 2.5 \times 48 \quad \text{and} \quad 10 \times 12 \] Calculating these: \[ 2.5 \times 48 = 120 \quad \text{and} \quad 10 \times 12 = 120 \] Since both products are equal, \( \frac{2.5}{10} = \frac{12}{48} \), so they form a proportion.

2. For \( \frac{2.5}{2} \) and \( \frac{12}{24} \):

   • Cross-multiplying gives us: \[ 2.5 \times 24 \quad \text{and} \quad 2 \times 12 \] Calculating these: \[ 2.5 \times 24 = 60 \quad \text{and} \quad 2 \times 12 = 24 \] Since the products are not equal, \( \frac{2.5}{2} \neq \frac{12}{24} \), so they do not form a proportion.

In conclusion:

• \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
• \( \frac{2.5}{2} \neq \frac{12}{24} \) is not a proportion.

Therefore, the correct response is: 2.5/10=12/48 (proportion). 2.5/2≠12/24 (not a proportion).