To evaluate each statement, we can simplify the expressions and compare the results.
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\( \frac{2}{5} \cdot \frac{11}{3} < \frac{2}{5} \):
- Calculate \( \frac{2}{5} \cdot \frac{11}{3} = \frac{2 \cdot 11}{5 \cdot 3} = \frac{22}{15} \).
- Compare \( \frac{22}{15} \) with \( \frac{2}{5} \).
- Convert \( \frac{2}{5} \) to a fraction with a denominator of 15: \( \frac{2}{5} = \frac{6}{15} \).
- Thus, \( \frac{22}{15} > \frac{6}{15} \). This statement is false.
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\( \frac{11}{3} \cdot \frac{2}{3} > \frac{11}{3} \):
- Calculate \( \frac{11}{3} \cdot \frac{2}{3} = \frac{22}{9} \).
- Compare \( \frac{22}{9} \) with \( \frac{11}{3} \).
- Convert \( \frac{11}{3} \) to a fraction with a denominator of 9: \( \frac{11}{3} = \frac{33}{9} \).
- Thus, \( \frac{22}{9} < \frac{33}{9} \). This statement is false.
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\( \frac{7}{3} \cdot \frac{1}{3} > \frac{7}{3} \):
- Calculate \( \frac{7}{3} \cdot \frac{1}{3} = \frac{7}{9} \).
- Compare \( \frac{7}{9} \) with \( \frac{7}{3} \).
- Convert \( \frac{7}{3} \) to a fraction with a denominator of 9: \( \frac{7}{3} = \frac{21}{9} \).
- Thus, \( \frac{7}{9} < \frac{21}{9} \). This statement is false.
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\( \frac{7}{3} \cdot \frac{1}{3} < \frac{7}{3} \):
- We already calculated \( \frac{7}{3} \cdot \frac{1}{3} = \frac{7}{9} \).
- Compare \( \frac{7}{9} \) with \( \frac{7}{3} \) (as calculated previously).
- Thus, \( \frac{7}{9} < \frac{21}{9} \). This statement is true.
Conclusion: The true statement is \( \frac{7}{3} \cdot \frac{1}{3} < \frac{7}{3} \).
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