High School

Which statement is true about the product of the mixed number one and eleven twelfths and 14,649?

A. It is less than 1 because the mixed number one and eleven twelfths is a fraction less than 1.

B. It is greater than the fraction one twelfth of 14,649 because the mixed number one and eleven twelfths has a denominator of 12.

C. It is greater than 11 times 14,649 because the mixed number one and eleven twelfths has a numerator of 11.

D. It is greater than 14,649 because the mixed number one and eleven twelfths is a fraction greater than 1.

Answer :

Final answer:

It is greater than 14,649 because the mixed number one and eleven twelfths is a fraction greater than 1. The correct answer is option D).

Explanation:

The true statement D) It is greater than 14,649 because the mixed number one and eleven twelfths is a fraction greater than 1. To support this, let's analyze the mixed number: One and eleven twelfths is composed of a whole (1) plus a fraction (11/12) that is less than 1, but when combined, they form a quantity greater than 1. Here's a step-by-step explanation:

  1. Convert the mixed number to an improper fraction: 1 11/12 = (12/12 + 11/12) = 23/12.
  2. Notice that 23/12 is greater than 1 because the numerator is larger than the denominator.
  3. Any number greater than 1, when multiplied by another positive number, will result in a product larger than the original number. Therefore, 23/12 * 14,649 will be greater than 14,649.

Therefore, the correct answer is option D).

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