Determine if one, both, or neither of the following is a proportion. 168=?2412

Question

, 84=?126
(1 point)
Responses

Neither is a proportion.
Neither is a proportion.

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

84=126
only

Answer 1

To determine if either of the given equations is a proportion, we need to express each equation as a fraction and then check if the cross products are equal.

1. For the first equation, $168=2412$:

   • This can be expressed as $\frac{168}{1}=\frac{2412}{1}$.
   • Clearly, both sides are not equal, thus it is not a proportion.

2. For the second equation, $84=126$:

   • This can be expressed as $\frac{84}{1}=\frac{126}{1}$.
   • Again, both sides are not equal, thus it is also not a proportion.

Now, examining the ratios:

• The ratio $\frac{16}{8}$ simplifies to $2$.

• The ratio $\frac{24}{12}$ simplifies to $2$ as well.

• Hence, $\frac{16}{8}=\frac{24}{12}$ is indeed a proportion.

• The ratio $\frac{8}{4}$ simplifies to $2$.

• The ratio $\frac{12}{6}$ simplifies to $2$ as well.

• Hence, $\frac{8}{4}=\frac{12}{6}$ is also a proportion.

Thus, we conclude that:

• $168=2412$ is not a proportion, and $84=126$ is not a proportion.
• The fractions $\frac{16}{8}=\frac{24}{12}$ and $\frac{8}{4}=\frac{12}{6}$ are proportions.

Final Answer: Neither is a proportion.