Determine if 2.25/10=?9/40, 2.510=?90/40, or 2.25/12=?90/40 is a proportion.(1 point)

Question

Responses

2.2512=9040
Start Fraction 2.25 over 12 End Fraction equals Start Fraction 90 over 40 End Fraction

None of these sets of ratios is a proportion.
None of these sets of ratios is a proportion.

2.510=9040
Start Fraction 2.5 over 10 End Fraction equals Start Fraction 90 over 40 End Fraction

2.2510=940

Answer 1

To determine if the given sets of ratios are proportions, we can check if the cross products of the fractions are equal. A proportion states that \( \frac{a}{b} = \frac{c}{d} \) if and only if \( a \cdot d = b \cdot c \).

Let's evaluate each option:

1. For \( \frac{2.25}{12} = \frac{90}{40} \):

   • Cross products: \( 2.25 \times 40 \) and \( 12 \times 90 \)
   • \( 2.25 \times 40 = 90 \) (since \( 2.25 \times 40 = 90 \))
   • \( 12 \times 90 = 1080 \)
   • Since \( 90 \neq 1080 \), this is not a proportion.

2. For \( \frac{2.5}{10} = \frac{90}{40} \):

   • Cross products: \( 2.5 \times 40 \) and \( 10 \times 90 \)
   • \( 2.5 \times 40 = 100 \)
   • \( 10 \times 90 = 900 \)
   • Since \( 100 \neq 900 \), this is not a proportion.

3. For \( \frac{2.25}{10} = \frac{90}{40} \):

   • Cross products: \( 2.25 \times 40 \) and \( 10 \times 90 \)
   • \( 2.25 \times 40 = 90 \) (since \( 2.25 \times 40 = 90 \))
   • \( 10 \times 90 = 900 \)
   • Since \( 90 \neq 900 \), this is not a proportion.

Since none of the sets of ratios are equal based on their cross products, we conclude that:

None of these sets of ratios is a proportion.