To find the product of \( \frac{3}{4} \times \frac{5}{4} \), we multiply the numerators and the denominators:
\[ \frac{3 \times 5}{4 \times 4} = \frac{15}{16} \]
Now we can compare \( \frac{15}{16} \) to \( \frac{3}{4} \) and \( \frac{5}{3} \).
-
Converting \( \frac{3}{4} \) to a fraction with a denominator of 16: \[ \frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16} \] Now, \( \frac{15}{16} \) is greater than \( \frac{3}{4} \).
-
Converting \( \frac{5}{3} \) to a fraction with a denominator of 16: \[ \frac{5}{3} \approx 1.6667 \quad \text{(Equivalent fraction: } \frac{5 \times 16}{3 \times 16} = \frac{80}{48}) \] In simpler terms, \( \frac{5}{3} \) is approximately \( 1.6667 \) which is greater than \( 1 \). Thus, when we compare \( \frac{15}{16} \) with \( \frac{5}{3} \), \( \frac{15}{16} \) is less than \( \frac{5}{3} \).
In conclusion, the statements can be filled in as follows:
The product will be greater than \( \frac{3}{4} \) and less than \( \frac{5}{3} \).
Final answer: The product will be greater than \( \frac{3}{4} \) and less than \( \frac{5}{3} \).