Question: Multiply $34 \times 27$ using the Russian peasant method.
11 34
8 108
4 216
2 432
1 864
Determine which rows to remove, then use the remaining rows to write an expression for the desired sum.
The sum is ____. (Do not simplify.)
$34 \times 27 = ____$
1. **State the problem:** We want to multiply $34$ by $27$ using the Russian peasant method.
2. **Explain the method:** The Russian peasant method involves repeatedly halving one number and doubling the other, discarding rows where the halved number is even, and summing the remaining doubled numbers.
3. **Given table:**
| Halved Number | Doubled Number |
|---------------|---------------|
| 11 | 34 |
| 8 | 108 |
| 4 | 216 |
| 2 | 432 |
| 1 | 864 |
4. **Identify rows to keep:** Keep rows where the halved number is odd: $11$, $1$.
5. **Write the sum expression:**
$$34 \times 27 = 34 + 864$$
6. **Note:** The problem asks not to simplify, so the final answer is the sum expression above.