Question

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

Neither is a proportion.
Neither is a proportion.

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

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

84=126 only

Answer 1

To determine if each equation represents a proportion, we need to set up a comparison of fractions and see if they are equivalent (proportional).

1. **First equation:** \( 168 = ? 2412 \)

To find the missing value (let's call it \( x \)), we can set up the proportion:

\[
\frac{168}{x} = \frac{1}{2412}
\]

Cross multiplying gives us:

\[
168 \cdot 2412 = 1 \cdot x
\]

Which means:

\[
x = 168 \cdot 2412
\]

This does not seem to provide a simple fraction comparison as \( 168 \) is not equal to \( 2412 \) directly.

2. **Second equation:** \( 84 = ? 126 \)

Again, let's find the missing value \( y \):

\[
\frac{84}{y} = \frac{1}{126}
\]

Cross multiplying gives us:

\[
84 \cdot 126 = 1 \cdot y
\]

So:

\[
y = 84 \cdot 126
\]

This also does not lead to determining a direct proportionality.

To check if each pair is proportional, we can take the fractions:

For the first equation, using whole numbers:

\[
\frac{168}{2412}
\]

For the second equation:

\[
\frac{84}{126}
\]

Now simplify both fractions:

1. \(\frac{84}{126} = \frac{2}{3}\) (after dividing both by 42).
2. For \(\frac{168}{2412}\), \(2412 = 168 \times 14.375\), which is not a clean fraction simple like \(\frac{2}{3}\).

Hence:

- **168 and 2412** do not provide a clean proportion.
- **84 and 126** simplify down to a simple fraction.

Thus:

**Conclusion**: **Only 84 = 126 is a proportion.**

Therefore, the correct response is: **"84=?126 only."**