Which of the following statements is true?(1 point)

Question

Responses

5/6⋅3/4>5/6
Start Fraction 5 over 6 End Fraction times Start Fraction 3 over 4 End Fraction greater than Start Fraction 5 over 6 End Fraction

5/2⋅7/6>5/2
Start Fraction 5 over 2 End Fraction times Start Fraction 7 over 6 End Fraction greater than Start Fraction 5 over 2 End Fraction

13/8⋅4/7>13/8
Start Fraction 13 over 8 End Fraction times Start Fraction 4 over 7 End Fraction greater than Start Fraction 13 over 8 End Fraction

5/2⋅7/6<5/2

Answer 1

Let's analyze each statement to determine whether it is true or false.

1. \( \frac{5}{6} \cdot \frac{3}{4} > \frac{5}{6} \):

   • Calculate \( \frac{5}{6} \cdot \frac{3}{4} = \frac{5 \times 3}{6 \times 4} = \frac{15}{24} = \frac{5}{8} \).
   • Since \( \frac{5}{8} < \frac{5}{6} \), this statement is false.

2. \( \frac{5}{2} \cdot \frac{7}{6} > \frac{5}{2} \):

   • Calculate \( \frac{5}{2} \cdot \frac{7}{6} = \frac{5 \times 7}{2 \times 6} = \frac{35}{12} \).
   • Since \( \frac{35}{12} > \frac{5}{2} = \frac{30}{12} \), this statement is true.

3. \( \frac{13}{8} \cdot \frac{4}{7} > \frac{13}{8} \):

   • Calculate \( \frac{13}{8} \cdot \frac{4}{7} = \frac{13 \times 4}{8 \times 7} = \frac{52}{56} = \frac{13}{14} \).
   • Since \( \frac{13}{14} < \frac{13}{8} \) (because \( \frac{13}{8} = \frac{26}{16} > \frac{13}{14} = \frac{26}{28} \)), this statement is false.

4. \( \frac{5}{2} \cdot \frac{7}{6} < \frac{5}{2} \):

   • We already calculated \( \frac{5}{2} \cdot \frac{7}{6} = \frac{35}{12} \) and found it greater than \( \frac{5}{2} \).
   • Thus, this statement is false.

Based on the analysis, the true statement is: \( \frac{5}{2} \cdot \frac{7}{6} > \frac{5}{2} \).