Question

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

Answer 1

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.**