To solve the comparison [tex]\(\frac{9}{12}<\frac{3}{2}\)[/tex] and determine whether it is true or false, we will follow these steps:
1. Simplify the fractions (if possible):
- Simplify [tex]\(\frac{9}{12}\)[/tex]:
[tex]\[
\frac{9}{12} = \frac{9 \div 3}{12 \div 3} = \frac{3}{4}
\][/tex]
- Simplify [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\frac{3}{2} = \text{This fraction is already in its simplest form.}
\][/tex]
2. Convert the fractions to decimal form:
- Convert [tex]\(\frac{3}{4}\)[/tex] to a decimal:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
- Convert [tex]\(\frac{3}{2}\)[/tex] to a decimal:
[tex]\[
\frac{3}{2} = 1.5
\][/tex]
3. Compare the decimal values:
- Compare [tex]\(0.75\)[/tex] and [tex]\(1.5\)[/tex]:
[tex]\[
0.75 < 1.5
\][/tex]
Since [tex]\(0.75\)[/tex] is less than [tex]\(1.5\)[/tex], the comparison [tex]\(\frac{9}{12}<\frac{3}{2}\)[/tex] is true.
So, the detailed solution to the problem is:
[tex]\[
\boxed{(0.75, 1.5, \text{True})}
\][/tex]
Thus, the value of the benchmark is not directly required here, and we have:
[tex]\[
\frac{9}{12} < \frac{3}{2} \quad \text{is} \quad \text{True}
\][/tex]
