Determine if one, both, or neither of the following is a proportion. 16/8=?24/12 , 84=?12/6

To determine if the given expressions represent proportions, we need to check if the two ratios involved are equal.

1. The first expression: \( \frac{16}{8} = ? \frac{24}{12} \)

First, we evaluate the left side: \[ \frac{16}{8} = 2 \]

Now we evaluate the right side: \[ \frac{24}{12} = 2 \]

Since both sides equal 2, the first expression is a proportion.

2. The second expression: \( 84 = ? \frac{12}{6} \)

We need to find the value of \( ? \) first. Start by evaluating \( \frac{12}{6} \): \[ \frac{12}{6} = 2 \]

Now, we have the equation: \[ 84 = ? \cdot 2 \]

To find \( ? \), we can solve for it: \[ ? = \frac{84}{2} = 42 \]

Next, we check if this can be written as a proportion: If we treat it as \( 84 : ? = ? : 6 \) (which would be \( \frac{84}{42} \) to \( \frac{42}{6} \)), we evaluate: \[ \frac{84}{42} = 2 \quad \text{and} \quad \frac{42}{6} = 7 \]

These two values are not equal, so the second expression does not represent a proportion.

Conclusion:

• The first expression \( \frac{16}{8} = \frac{24}{12} \) is a proportion.
• The second expression \( 84 = ? \frac{12}{6} \) is not a proportion.

Thus, the answer is: Only the first is a proportion.