What is Long Multiplication?

Long multiplication is a method to multiply two numbers together, especially when they have multiple digits. Let's break it down step by step.

Step-by-Step Guide to Long Multiplication

Step 1: Write Down the Numbers

Start by writing the larger number on top and the smaller number beneath it, aligning the numbers to the right. For example, if we want to multiply 34 by 6, write it like this:

    34
  x  6

Step 2: Multiply the Digits

Start with the rightmost digit of the bottom number. Multiply this digit by each digit of the top number, starting from the right. In our example:

• 6 (from 6) x 4 (from 34) = 24
• Write down 4 and carry over 2 to the next multiplication.
• 6 (from 6) x 3 (from 34) = 18, then add the carry-over 2. So, 18 + 2 = 20.

Now we write it down:

    34
  x  6
  -----
    204

Step 3: Add Any Carry-Over

If you have a carry-over from your multiplications, ensure you add them before finalizing your answer. In this example, we already added the carry-over, so there’s nothing more to add.

More Complex Example

Let’s look at a more complex example: multiplying 234 by 12.

    234
  x  12

• First, multiply 234 by 2 (the rightmost digit of 12):
• 2 x 4 = 8
• 2 x 3 = 6
• 2 x 2 = 4

So, you write:

    234
  x  12
  -----
    468  (This is 234 x 2)

• Next, multiply 234 by 1 (the next digit of 12). Remember, this is actually 10, so we need to add a zero at the end:
• 1 x 4 = 4
• 1 x 3 = 3
• 1 x 2 = 2

So, write this down as:

    234
  x  12
  -----
    468
 +2340  (This is 234 x 10, shifted one place to the left)

Step 4: Add the Results Together

Now, we need to add the two products we found:

    468
  +2340
  -----
   2808

Conclusion

So, 234 multiplied by 12 equals 2808. Long multiplication can take some practice, but with these steps, you’ll get the hang of it quickly! Try practicing with different numbers to improve your skills.