Question: Multiply $34 \times 27$ using the Russian peasant method.
Fill in the Russian peasant columns.
$34 \quad 27$
Determine which rows to remove, then use the remaining rows to write an expression for the desired sum.
1. **State the problem:** We want to multiply $34$ by $27$ using the Russian peasant multiplication method.
2. **Explain the method:** This method involves repeatedly halving the first number and doubling the second number, discarding rows where the first number is even, then summing the remaining second numbers.
3. **Create the columns:**
\begin{align*}
\text{First column} & \quad \text{Second column} \\
34 & 27 \\
17 & 54 \\
8 & 108 \\
4 & 216 \\
2 & 432 \\
1 & 864
\end{align*}
4. **Remove rows where the first number is even:**
Remove rows with $34$, $8$, $4$, and $2$ because they are even.
Remaining rows:
\begin{align*}
17 & 54 \\
1 & 864
\end{align*}
5. **Sum the second column of remaining rows:**
$$54 + 864 = 918$$
6. **Final answer:**
$$34 \times 27 = 918$$