To determine the product of each expression and see if it is less than, greater than, or equal to \( \frac{3}{4} \), we can calculate the products of the given expressions.
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\( \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \)
- Since \( \frac{9}{16} \) is approximately \( 0.5625 \), this is less than \( \frac{3}{4} \).
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\( \frac{5}{2} \times \frac{3}{4} = \frac{15}{8} \)
- Since \( \frac{15}{8} \) is \( 1.875 \), this is greater than \( \frac{3}{4} \).
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\( \frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4} \)
- Since \( \frac{1}{4} \) is \( 0.25 \), this is less than \( \frac{3}{4} \).
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\( \frac{7}{7} \times \frac{3}{4} = 1 \times \frac{3}{4} = \frac{3}{4} \)
- This is equal to \( \frac{3}{4} \).
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\( \frac{5}{5} \times \frac{3}{4} = 1 \times \frac{3}{4} = \frac{3}{4} \)
- This is also equal to \( \frac{3}{4} \).
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\( \frac{9}{7} \times \frac{3}{4} = \frac{27}{28} \)
- Since \( \frac{27}{28} \) is approximately \( 0.9643 \), this is greater than \( \frac{3}{4} \).
Now, we can organize them in the table:
| Category | Expression | |---------------------|----------------------------------| | Less than \( \frac{3}{4} \) | \( \frac{3}{4} \times \frac{3}{4} \) ( \( \frac{9}{16} \) ) | | | \( \frac{1}{3} \times \frac{3}{4} \) ( \( \frac{1}{4} \) ) | | Greater than \( \frac{3}{4} \) | \( \frac{5}{2} \times \frac{3}{4} \) ( \( \frac{15}{8} \) ) | | | \( \frac{9}{7} \times \frac{3}{4} \) ( \( \frac{27}{28} \) ) | | Equal to \( \frac{3}{4} \) | \( \frac{7}{7} \times \frac{3}{4} \) ( \( \frac{3}{4} \) ) | | | \( \frac{5}{5} \times \frac{3}{4} \) ( \( \frac{3}{4} \) ) |
Hope that helps!