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Determine if one, both, or neither of the following is a proportion.

16/8 ?= 24/12, 8/4 ?= 12/6
A. Neither is a proportion.
B. 16/8 = 24/12, 8/4 = 12/6
C. 16/8 = 24/12 only
D. 8/4 = 12/6 only

3 answers

To determine if the given fractions form a proportion, we need to check if each pair of fractions is equal. A proportion consists of two equal ratios.

  1. Check the first pair: \( \frac{16}{8} \) and \( \frac{24}{12} \)

    Calculate \( \frac{16}{8} \): \[ \frac{16}{8} = 2 \]

    Calculate \( \frac{24}{12} \): \[ \frac{24}{12} = 2 \]

    Since both fractions are equal: \[ \frac{16}{8} = \frac{24}{12} \]

  2. Check the second pair: \( \frac{8}{4} \) and \( \frac{12}{6} \)

    Calculate \( \frac{8}{4} \): \[ \frac{8}{4} = 2 \]

    Calculate \( \frac{12}{6} \): \[ \frac{12}{6} = 2 \]

    Since both fractions are equal: \[ \frac{8}{4} = \frac{12}{6} \]

Both pairs of fractions are equal.

Therefore, the answer is B. 16/8 = 24/12, 8/4 = 12/6.

are you sure this is correct

Let’s double-check the calculations to ensure accuracy regarding whether the provided fractions form proportions.

  1. First Comparison: \( \frac{16}{8} \) and \( \frac{24}{12} \)

    • Calculating \( \frac{16}{8} \): \[ \frac{16}{8} = 2 \]

    • Calculating \( \frac{24}{12} \): \[ \frac{24}{12} = 2 \]

    Since \( \frac{16}{8} = \frac{24}{12} = 2\), this pair is a proportion.

  2. Second Comparison: \( \frac{8}{4} \) and \( \frac{12}{6} \)

    • Calculating \( \frac{8}{4} \): \[ \frac{8}{4} = 2 \]

    • Calculating \( \frac{12}{6} \): \[ \frac{12}{6} = 2 \]

    Since \( \frac{8}{4} = \frac{12}{6} = 2\), this pair also is a proportion.

Both pairs of fractions are equal. Therefore, both statements hold true, confirming that both sets of fractions are proportional.

Thus, the correct answer remains as B. 16/8 = 24/12, 8/4 = 12/6. Thank you for your patience, and I'm glad to provide clarification!