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Determine if 2.5/10 ?= 12/48 or 2.5/2 ?= 12/24 is a proportion.

A. Both are proportions.
B. 2.5/2 = 12/24
C. Neither is a proportion.
D. 2.5/10 = 12/48

3 answers

To determine if the fractions are proportions, we need to find out if the two fractions on each side of the equation are equal.

First, we will simplify both fractions:

  1. For 2.5/10 and 12/48:

    • \( \frac{2.5}{10} \) simplifies to \( \frac{1}{4} \) because \( 2.5 \div 2.5 = 1 \) and \( 10 \div 2.5 = 4 \).

    • \( \frac{12}{48} \) simplifies to \( \frac{1}{4} \) because \( 12 \div 12 = 1 \) and \( 48 \div 12 = 4 \).

    Since both simplify to \( \frac{1}{4} \), we have: \[ \frac{2.5}{10} = \frac{12}{48} \]

  2. For 2.5/2 and 12/24:

    • \( \frac{2.5}{2} \) simplifies to \( \frac{2.5 \div 2.5}{2 \div 2.5} = \frac{1}{0.8} = \frac{5}{4} \).
    • \( \frac{12}{24} \) simplifies to \( \frac{1}{2} \).

    Since \( \frac{5}{4} \neq \frac{1}{2} \), we have: \[ \frac{2.5}{2} \neq \frac{12}{24} \]

From the analysis:

  • The first set \( \frac{2.5}{10} \) and \( \frac{12}{48} \) is a proportion.
  • The second set \( \frac{2.5}{2} \) and \( \frac{12}{24} \) is not a proportion.

Thus, the correct answer is:

A. Both are proportions. (This is incorrect.)

The correct conclusion would actually be:

D. 2.5/10 = 12/48.

are you sure this is correct

Let’s clarify the evaluation and ensure the conclusions are correct by checking each comparison step-by-step.

Comparing the first set: \( \frac{2.5}{10} \) and \( \frac{12}{48} \)

  1. Simplifying \( \frac{2.5}{10} \): \[ \frac{2.5}{10} = \frac{2.5 \div 2.5}{10 \div 2.5} = \frac{1}{4} \]

  2. Simplifying \( \frac{12}{48} \): \[ \frac{12}{48} = \frac{12 \div 12}{48 \div 12} = \frac{1}{4} \]

Since both \( \frac{2.5}{10} \) and \( \frac{12}{48} \) simplify to \( \frac{1}{4} \), we conclude: \[ \frac{2.5}{10} = \frac{12}{48} \] Thus, this is a proportion.

Comparing the second set: \( \frac{2.5}{2} \) and \( \frac{12}{24} \)

  1. Simplifying \( \frac{2.5}{2} \): \[ \frac{2.5}{2} = 1.25 \quad \text{(or we can express it as } \frac{5}{4} \text{)} \]

  2. Simplifying \( \frac{12}{24} \): \[ \frac{12}{24} = \frac{1}{2} \]

Since \( 1.25 \) or \( \frac{5}{4} \) is not equal to \( \frac{1}{2} \): \[ \frac{2.5}{2} \neq \frac{12}{24} \] Thus, this is not a proportion.

Conclusion

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

Therefore, the correct answer would be D. 2.5/10 = 12/48 as they form a proportion, and the other comparison does not.

Thanks for your patience, and I apologize for the confusion in my previous response.