Multiply 23857 by 9999.

Answer

To solve the multiplication of 23857 by 9999, we can use a shortcut method by rewriting 9999 in a more manageable form. Here’s the step-by-step solution:

### Step 1: Rewrite 9999
We can express 9999 as:
\[ 9999 = 10000 - 1 \]

### Step 2: Set up the multiplication
Now, we can rewrite the multiplication:
\[ 23857 \times 9999 = 23857 \times (10000 - 1) \]

### Step 3: Distribute the multiplication
Using the distributive property, we can expand this:
\[ 23857 \times 9999 = 23857 \times 10000 - 23857 \times 1 \]

### Step 4: Calculate each part
Now, we calculate each part:
1. \( 23857 \times 10000 = 238570000 \)
2. \( 23857 \times 1 = 23857 \)

### Step 5: Subtract the second part from the first
Now we subtract the two results:
\[ 238570000 - 23857 = 238546143 \]

### Final Answer
Thus, the product of 23857 and 9999 is:
\[ \boxed{238546143} \]

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