Determine if 2.25/10 =? 9/40

, 2.5/10 =? 90/40
, or 2.25/12 =? 90/40
is a proportion.(1 point)
Responses

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

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

2.5/10 = 90/40

1 answer

To determine if the ratios form a proportion, we need to check if the cross-products are equal for each pair of fractions. A proportion is established if \( \frac{a}{b} = \frac{c}{d} \), which implies that \( a \cdot d = b \cdot c \).

Let's analyze each case:

  1. For \( \frac{2.25}{10} \) and \( \frac{9}{40} \):

    • Cross-multiplying gives: \[ 2.25 \cdot 40 \quad \text{and} \quad 10 \cdot 9 \]
    • Calculate: \[ 2.25 \cdot 40 = 90 \] \[ 10 \cdot 9 = 90 \]
    • Since \( 90 = 90 \), this is a proportion.
  2. For \( \frac{2.5}{10} \) and \( \frac{90}{40} \):

    • Cross-multiplying gives: \[ 2.5 \cdot 40 \quad \text{and} \quad 10 \cdot 90 \]
    • Calculate: \[ 2.5 \cdot 40 = 100 \] \[ 10 \cdot 90 = 900 \]
    • Since \( 100 \neq 900 \), this is not a proportion.
  3. For \( \frac{2.25}{12} \) and \( \frac{90}{40} \):

    • Cross-multiplying gives: \[ 2.25 \cdot 40 \quad \text{and} \quad 12 \cdot 90 \]
    • Calculate: \[ 2.25 \cdot 40 = 90 \] \[ 12 \cdot 90 = 1080 \]
    • Since \( 90 \neq 1080 \), this is not a proportion.

Summary:

  • Proportion found: \( \frac{2.25}{10} = \frac{9}{40} \)
  • Not proportions: \( \frac{2.5}{10} = \frac{90}{40} \), \( \frac{2.25}{12} = \frac{90}{40} \)

Final answer: None of these sets of ratios is a proportion, except for the first one. However, since the question was whether any of the sets are a proportion, the solution is:

2.25/10 = 9/40 is a proportion.