Question

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

168=2412
only
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction only

168=2412
, 84=126
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction , Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction

Neither is a proportion.
Neither is a proportion.

84=126
only

Answer 1

To determine if either of the given statements is a proportion, we need to check if the ratios are equivalent.

1. For the first statement: \( 168 = 2412 \).
- Simplifying this as a fraction gives us \( \frac{168}{x} = \frac{24}{12} \).
- We can simplify \( \frac{24}{12} \) to \( 2 \). So we check \( \frac{168}{x} = 2 \).
- This means \( 168 = 2x \). Dividing both sides by 2 yields \( x = 84 \).
- Therefore, \( 168 \) does not equal \( 2412 \), but it could be equated if we solve for \( x \).

2. For the second statement: \( 84 = 126 \).
- If we check \( \frac{84}{x} = \frac{12}{6} \).
- Simplifying \( \frac{12}{6} \) yields \( 2 \). Thus, \( \frac{84}{x} = 2 \).
- This gives \( 84 = 2x \), or \( x = 42 \). Therefore \( 84 \) does not equal \( 126 \).

Checking if they create proportions:
- For \( 168 : 2412 \approx 1 : 14.5 \) and \( 84 : 126 \approx 1 : 1.5 \).

The two statements do not equal each other and are therefore not proportions.

Based on the analysis of the provided options, the correct response is:
**Neither is a proportion.**