hich statement is correct about the product of ​323​ and ​109​?

Question

Responses

Because 109 is greater than 1, the product of 323 and ​109​ is less than ​323​.
Because 10 over 9 is greater than 1, the product of 3 and 2 over 3 and ​ 10 over 9 ​ is less than ​ 3 and 2 over 3 ​.

Because 109 is less than 1, the product of 323 and ​109​ is greater than ​323​.
Because 10 over 9 is less than 1, the product of 3 and 2 over 3 and ​ 10 over 9 ​ is greater than ​ 3 and 2 over 3 ​.

Because 109 is greater than 1, the product of 323 and ​109​ is greater than ​323​.
Because 10 over 9 is greater than 1, the product of 3 and 2 over 3 and ​ 10 over 9 ​ is greater than ​ 3 and 2 over 3 ​.

Because 109 is less than 1, the product of 323 and ​109​ is less than ​323​.

Answer 1

To evaluate the statements about the products in question, let's analyze both examples.

1. About the product of \(323\) and \(109\):

   • \(109\) is greater than \(1\).
   • Therefore, the product of \(323\) and \(109\) is indeed greater than \(323\).

2. About the second product, which involves \(3\) and \(2/3\) (or \(3 \frac{2}{3}\)) and \(10/9\):

   • First, we compute \(3 \frac{2}{3}\) which is equivalent to \(11/3\).
   • And since \(10/9\) is greater than \(1\), \( \frac{11}{3} \times \frac{10}{9} \) will be greater than \( \frac{11}{3} \).

Based on this analysis, the correct statement is:

Because 109 is greater than 1, the product of 323 and 109 is greater than 323. Because 10 over 9 is greater than 1, the product of 3 and 2 over 3 and 10 over 9 is greater than 3 and 2 over 3.