The problem asks us to identify all the fractions from the list $\frac{1}{20}$, $\frac{1}{3}$, $\frac{5}{7}$, $\frac{1}{100}$, and $\frac{1}{5}$ that are smaller than $\frac{1}{7}$.

1. Problem Description

The problem asks us to identify all the fractions from the list $\frac{1}{20}$, $\frac{1}{3}$, $\frac{5}{7}$, $\frac{1}{100}$, and $\frac{1}{5}$ that are smaller than $\frac{1}{7}$.

2. Solution Steps

We need to compare each fraction in the list to $\frac{1}{7}$.

* Compare $\frac{1}{20}$ and $\frac{1}{7}$. Since $20 > 7$, we have $\frac{1}{20} < \frac{1}{7}$.

* Compare $\frac{1}{3}$ and $\frac{1}{7}$. Since $3 < 7$, we have $\frac{1}{3} > \frac{1}{7}$.

* Compare $\frac{5}{7}$ and $\frac{1}{7}$. Since $5 > 1$, we have $\frac{5}{7} > \frac{1}{7}$.

* Compare $\frac{1}{100}$ and $\frac{1}{7}$. Since $100 > 7$, we have $\frac{1}{100} < \frac{1}{7}$.

* Compare $\frac{1}{5}$ and $\frac{1}{7}$. Since $5 < 7$, we have $\frac{1}{5} > \frac{1}{7}$.

So, the fractions smaller than $\frac{1}{7}$ are $\frac{1}{20}$ and $\frac{1}{100}$.

3. Final Answer

$\frac{1}{20}$, $\frac{1}{100}$