Solve using short cut methods: `64xx125`

Answer

To solve the multiplication of \(64 \times 125\) using shortcut methods, we can follow these steps:

### Step-by-Step Solution

1. **Rewrite the Multiplication**:
We can rewrite \(64 \times 125\) as \(125 \times 64\).

2. **Break Down the Calculation**:
We can break down the multiplication into smaller parts. Start with the last digit of \(125\) which is \(5\):
\[ 5 \times 4 = 20 \]
Write down \(0\) and carry over \(2\).

3. **Cross Multiply**:
Now, we will cross-multiply the remaining digits:
- Multiply the first two digits of \(64\) (which are \(6\) and \(4\)) with the last digit of \(125\) (which is \(5\)):
\[ 2 \times 4 + 6 \times 5 + \text{carry} = 2 \times 4 + 30 + 2 = 8 + 30 + 2 = 40 \]
Write down \(0\) and carry over \(4\).

4. **Multiply the Last Two Digits**:
Now, we multiply the last two digits of \(125\) (which are \(12\)) with \(64\):
\[ 4 \times 1 + 6 \times 2 + \text{carry} = 4 + 12 + 4 = 20 \]
Write down \(0\) and carry over \(2\).

5. **Final Multiplication**:
Finally, multiply the first digit of \(125\) (which is \(1\)) with \(64\):
\[ 1 \times 6 + \text{carry} = 6 + 2 = 8 \]

6. **Combine the Results**:
Now, we combine all the parts we calculated:
- From step 2: \(0\)
- From step 3: \(0\)
- From step 4: \(0\)
- From step 5: \(8\)

This gives us \(8000\).

### Final Answer:
Thus, \(64 \times 125 = 8000\).