Question

Determine if one, both, or neither of the following is a proportion. 168=?2412
, 84=?126
(1 point)
Responses

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

16/8=24/12
only

Neither is a proportion.

8/4=12/6
only

Answer 1

To determine if the given statements form proportions, we need to check if the ratios are equivalent.

1. **168 = ? 2412**:
We can express this as a fraction:
\[
\frac{168}{2412}
\]
To check if it simplifies, we can find the GCD (greatest common divisor) of 168 and 2412, but we can start with a simpler method for checking proportions. Instead, we will calculate:
- Dividing both sides by 84:
\[
\frac{168}{84} = 2 \quad \text{and} \quad \frac{2412}{84} = 28.71428571 \quad (\text{approx.})
\]
Since \(2 \neq 28.714\), this is not a proportion.

2. **84 = ? 126**:
\[
\frac{84}{126}
\]
We simplify it:
- Dividing both sides by 42:
\[
\frac{84}{42} = 2 \quad \text{and} \quad \frac{126}{42} = 3
\]
Since \(2 \neq 3\), this is also not a proportion.

Now let’s check both provided fractional forms:
- **First fractional form provided: \( \frac{16}{8} = \frac{24}{12}\)**:
- \( \frac{16}{8} = 2 \)
- \( \frac{24}{12} = 2 \)
- Since both sides equal \(2\), **this is a proportion**.

- **Second fractional form provided: \( \frac{8}{4} = \frac{12}{6}\)**:
- \( \frac{8}{4} = 2 \)
- \( \frac{12}{6} = 2 \)
- Since both sides equal \(2\), **this is also a proportion**.

Thus, both the fractional forms are proportions. Therefore, the final determination is:

**Both are proportions.**