Which of the following statements is true Which number would make this statement 5 2/9 • 7/8 > 5 2/9 B 4 1/2 • 5/4 < 4 1/2 C 17/4 • 3/2 < 17/4 D 3 5/8 • 9/4 > 3 5/8

Let's evaluate each statement to determine which is true.

1. Statement A: \( 5 \frac{2}{9} \cdot \frac{7}{8} > 5 \frac{2}{9} \)

   First, convert \( 5 \frac{2}{9} \) to an improper fraction: \[ 5 \frac{2}{9} = \frac{5 \times 9 + 2}{9} = \frac{45 + 2}{9} = \frac{47}{9} \]

   Now calculate \( 5 \frac{2}{9} \cdot \frac{7}{8} \): \[ \frac{47}{9} \cdot \frac{7}{8} = \frac{47 \cdot 7}{9 \cdot 8} = \frac{329}{72} \]

   Now we compare \( \frac{329}{72} \) and \( \frac{47}{9} \): To do this, convert \( \frac{47}{9} \) to a denominator of 72: \[ \frac{47}{9} = \frac{47 \cdot 8}{9 \cdot 8} = \frac{376}{72} \]

   Now compare: \[ \frac{329}{72} > \frac{376}{72} \text{ is false (since 329 < 376)}. \] So, statement A is false.

2. Statement B: \( 4 \frac{1}{2} \cdot \frac{5}{4} < 4 \frac{1}{2} \)

   Convert \( 4 \frac{1}{2} \) to an improper fraction: \[ 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \]

   Now calculate \( 4 \frac{1}{2} \cdot \frac{5}{4} \): \[ \frac{9}{2} \cdot \frac{5}{4} = \frac{9 \cdot 5}{2 \cdot 4} = \frac{45}{8} \]

   Now compare \( \frac{45}{8} \) and \( \frac{9}{2} \): Convert \( \frac{9}{2} \) to a denominator of 8: \[ \frac{9}{2} = \frac{9 \cdot 4}{2 \cdot 4} = \frac{36}{8} \]

   Now compare: \[ \frac{45}{8} < \frac{36}{8} \text{ is false (since 45 > 36)}. \] So, statement B is false.

3. Statement C: \( \frac{17}{4} \cdot \frac{3}{2} < \frac{17}{4} \)

   Calculate \( \frac{17}{4} \cdot \frac{3}{2} \): \[ \frac{17}{4} \cdot \frac{3}{2} = \frac{17 \cdot 3}{4 \cdot 2} = \frac{51}{8} \]

   Now compare \( \frac{51}{8} \) and \( \frac{17}{4} \): Convert \( \frac{17}{4} \) to a denominator of 8: \[ \frac{17}{4} = \frac{17 \cdot 2}{4 \cdot 2} = \frac{34}{8} \]

   Now compare: \[ \frac{51}{8} < \frac{34}{8} \text{ is false (since 51 > 34)}. \] So, statement C is false.

4. Statement D: \( 3 \frac{5}{8} \cdot \frac{9}{4} > 3 \frac{5}{8} \)

   Convert \( 3 \frac{5}{8} \) to an improper fraction: \[ 3 \frac{5}{8} = \frac{3 \cdot 8 + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8} \]

   Calculate \( 3 \frac{5}{8} \cdot \frac{9}{4} \): \[ \frac{29}{8} \cdot \frac{9}{4} = \frac{29 \cdot 9}{8 \cdot 4} = \frac{261}{32} \]

   Now compare \( \frac{261}{32} \) with \( \frac{29}{8} \): Convert \( \frac{29}{8} \) to a denominator of 32: \[ \frac{29}{8} = \frac{29 \cdot 4}{8 \cdot 4} = \frac{116}{32} \]

   Now compare: \[ \frac{261}{32} > \frac{116}{32} \text{ is true (since 261 > 116)}. \] So, statement D is true.

Conclusion: The true statement is D: \( 3 \frac{5}{8} \cdot \frac{9}{4} > 3 \frac{5}{8} \).