Ask a New Question
Menu

Determine if 2.2510=?940 , 2.510=?9040 , or 2.2512=?9040 is a proportion.(1 point) Responses 2.2510=940 Start Fraction 2.25 over 10 End Fraction equals Start Fraction 9 over 40 End Fraction 2.2512=9040 Start Fraction 2.25 over 12 End Fraction equals Start Fraction 90 over 40 End Fraction 2.510=9040 Start Fraction 2.5 over 10 End Fraction equals Start Fraction 90 over 40 End Fraction None of these sets of ratios is a proportion.

1 answer

To determine if the given ratios form a proportion, we need to check if the cross-products of the fractions are equal.

The set of ratios can be written as follows:

  1. \( \frac{2.25}{10} = \frac{9}{40} \)
  2. \( \frac{2.25}{12} = \frac{90}{40} \)
  3. \( \frac{2.5}{10} = \frac{90}{40} \)

We will check each one:

For the first ratio:

  1. \( \frac{2.25}{10} = \frac{9}{40} \)

Cross-multiplying:

\( 2.25 \times 40 = 90 \)

\( 10 \times 9 = 90 \)

Since \( 90 = 90 \), the first set of ratios is a proportion.

For the second ratio:

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

Cross-multiplying:

\( 2.25 \times 40 = 90 \)

\( 12 \times 90 = 1080 \)

Since \( 90 \neq 1080 \), the second set of ratios is not a proportion.

For the third ratio:

  1. \( \frac{2.5}{10} = \frac{90}{40} \)

Cross-multiplying:

\( 2.5 \times 40 = 100 \)

\( 10 \times 90 = 900 \)

Since \( 100 \neq 900 \), the third set of ratios is not a proportion.

Conclusion

Only the first set of ratios is a proportion: \( \frac{2.25}{10} = \frac{9}{40} \).