Let's analyze each comparison:
### First Comparison:
1. [tex]\(\frac{1}{15} \times \frac{3}{11}\)[/tex] [tex]$\square$[/tex] [tex]\(\frac{3}{11}\)[/tex]
Let's compare the left-hand side with the right-hand side:
- [tex]\(\frac{1}{15} \times \frac{3}{11}\)[/tex] is approximately equal to [tex]\(0.01818181818181818\)[/tex].
- [tex]\(\frac{3}{11}\)[/tex] is approximately equal to [tex]\(0.2727272727272727\)[/tex].
Clearly, [tex]\(0.01818181818181818 < 0.2727272727272727\)[/tex].
Thus, the inequality is:
[tex]\[
\frac{1}{15} \times \frac{3}{11} \quad < \quad \frac{3}{11}
\][/tex]
### Second Comparison:
2. [tex]\(\frac{1}{12} \times \frac{12}{5}\)[/tex] [tex]$\square$[/tex] [tex]\(\frac{1}{12}\)[/tex]
Compare the left-hand side with the right-hand side:
- [tex]\(\frac{1}{12} \times \frac{12}{5}\)[/tex] is approximately equal to [tex]\(0.19999999999999998\)[/tex].
- [tex]\(\frac{1}{12}\)[/tex] is approximately equal to [tex]\(0.08333333333333333\)[/tex].
Clearly, [tex]\(0.19999999999999998 > 0.08333333333333333\)[/tex].
Thus, the inequality is:
[tex]\[
\frac{1}{12} \times \frac{12}{5} \quad > \quad \frac{1}{12}
\][/tex]
### Third Comparison:
3. [tex]\(\frac{11}{2} \times \frac{12}{5}\)[/tex] [tex]$\square$[/tex] [tex]\(\frac{12}{5}\)[/tex]
Compare the left-hand side with the right-hand side:
- [tex]\(\frac{11}{2} \times \frac{12}{5}\)[/tex] is equal to [tex]\(13.2\)[/tex].
- [tex]\(\frac{12}{5}\)[/tex] is equal to [tex]\(2.4\)[/tex].
Clearly, [tex]\(13.2 > 2.4\)[/tex].
Thus, the inequality is:
[tex]\[
\frac{11}{2} \times \frac{12}{5} \quad > \quad \frac{12}{5}
\][/tex]
So, the filled blanks in the inequalities are:
1. [tex]\[
\frac{1}{15} \times \frac{3}{11} \quad < \quad \frac{3}{11}
\][/tex]
2. [tex]\[
\frac{1}{12} \times \frac{12}{5} \quad > \quad \frac{1}{12}
\][/tex]
3. [tex]\[
\frac{11}{2} \times \frac{12}{5} \quad > \quad \frac{12}{5}
\][/tex]
