Solve: `345678 xx 999999`

Options

A. `345677653422`
B. `354677654322`
C. `345677654322`
D. `346577564322`

Answer

To solve the multiplication of `345678` by `999999`, we can use a mathematical trick that simplifies the calculation.

### Step-by-Step Solution:

1. **Recognize the Pattern**:
The number `999999` can be expressed as `1000000 - 1`. This means that multiplying any number by `999999` is the same as multiplying it by `1000000` and then subtracting the original number.

2. **Multiply by 1000000**:
First, we multiply `345678` by `1000000`:
\[ 345678 \times 1000000 = 345678000000 \]

3. **Subtract the Original Number**:
Now, subtract `345678` from the result obtained in the previous step:
\[ 345678000000 - 345678 = 345678000000 - 000345678 \]

4. **Perform the Subtraction**:
Align the numbers for subtraction:
\[ 345678000000 - 000000345678 \]
Performing the subtraction:
- Start from the rightmost digit:
- 0 - 8 = 2 (borrow 1)
- 0 - 7 = 3 (borrow 1)
- 0 - 6 = 4 (borrow 1)
- 0 - 5 = 5 (borrow 1)
- 0 - 4 = 6 (borrow 1)
- 0 - 3 = 7 (borrow 1)
- 0 - 2 = 8 (borrow 1)
- 0 - 1 = 9 (borrow 1)
- 5 - 0 = 5
- 4 - 0 = 4
- 3 - 0 = 3
Thus, the result is:
\[ 345677654322 \]

5. **Final Result**:
Therefore, the product of `345678` and `999999` is:
\[ 345677654322 \]