Sure, let's compare the two fractions [tex]\(\frac{2}{9}\)[/tex] and [tex]\(\frac{1}{5}\)[/tex] to determine which one is larger.
First, we can convert the fractions to their decimal forms to make the comparison simpler.
For the fraction [tex]\(\frac{2}{9}\)[/tex]:
[tex]\[
\frac{2}{9} = 0.2222222222222222
\][/tex]
For the fraction [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
Next, we compare the decimal values:
[tex]\[
0.2222222222222222 \quad \text{and} \quad 0.2
\][/tex]
Observing the decimal values,
[tex]\[
0.2222222222222222 > 0.2
\][/tex]
It is clear that the decimal representation of [tex]\(\frac{2}{9}\)[/tex] is larger than that of [tex]\(\frac{1}{5}\)[/tex].
Therefore, we have shown that:
[tex]\[
\frac{2}{9} > \frac{1}{5}
\][/tex]
