Determine if 2.5/10 =? 12/48 or 2.5 2 =? 12/24 is a proportion.(1 point)

Responses

2.5/10 = 12/48

2.5/2 = 12/24

Neither is a proportion.

Both are proportions.

1 answer

To determine if these ratios are proportions, we need to check if the two fractions in each statement are equal:

  1. For the first statement:

    \[ \frac{2.5}{10} \quad \text{and} \quad \frac{12}{48} \]

    To simplify \( \frac{2.5}{10} \): \[ \frac{2.5 \div 2.5}{10 \div 2.5} = \frac{1}{4} \]

    To simplify \( \frac{12}{48} \): \[ \frac{12 \div 12}{48 \div 12} = \frac{1}{4} \]

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

    So, \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.

  2. For the second statement:

    \[ \frac{2.5}{2} \quad \text{and} \quad \frac{12}{24} \]

    To simplify \( \frac{2.5}{2} \): \[ \frac{2.5 \div 2.5}{2 \div 2.5} = \frac{1}{0.8} = 1.25 \]

    To simplify \( \frac{12}{24} \): \[ \frac{12 \div 12}{24 \div 12} = \frac{1}{2} \]

    Since \( 1.25 \neq 0.5 \), we have: \[ \frac{2.5}{2} \neq \frac{12}{24} \]

    Thus, \( \frac{2.5}{2} = \frac{12}{24} \) is not a proportion.

Based on this, we can conclude:

Responses:

  • \( 2.5/10 = 12/48 \) is a proportion.
  • \( 2.5/2 \neq 12/24 \) is not a proportion.

Therefore, the correct answer is:

Only the first statement is a proportion.