determine if one both or neither of the following is a proportion 16/8=24/12, 8/4=12/6

given
8/4=12/6 only
16/8=24/12 only
neither is a proportion
16/8=24/12, 8/4=12/6

1 answer

To determine if the given fractions are proportions, we can simplify each fraction and check if they are equal.

  1. First, let's check the first pair: \( \frac{16}{8} \) and \( \frac{24}{12} \).

    \[ \frac{16}{8} = 2 \quad \text{and} \quad \frac{24}{12} = 2 \]

    Since both simplify to 2, we conclude that \( \frac{16}{8} = \frac{24}{12} \), so this pair is a proportion.

  2. Now, let's check the second pair: \( \frac{8}{4} \) and \( \frac{12}{6} \).

    \[ \frac{8}{4} = 2 \quad \text{and} \quad \frac{12}{6} = 2 \]

    Since both simplify to 2, we conclude that \( \frac{8}{4} = \frac{12}{6} \), so this pair is also a proportion.

Based on the analysis, both pairs are proportions. Therefore, the correct conclusion from the choices provided is:

16/8=24/12, 8/4=12/6.