How do you multiply two whole numbers?

To multiply two whole numbers, you can use a method that involves breaking down the multiplication into smaller steps, focusing on place value, and using the concept of carrying over. This method is outlined in a video titled "Multiplication | How to Multiply Whole Numbers - YouTube" and involves these core steps:

Step-by-Step Multiplication Process:

1. Set up the problem: Write the two numbers one above the other, aligning the ones, tens, hundreds, etc. Place the multiplication symbol (x) to the left of the bottom number.

   • For example:

      23
     x 4
     ----

2. Multiply by the ones digit: Start by multiplying the ones digit of the bottom number by each digit of the top number, from right to left. Write the result below the line, aligning the ones digit of the product with the ones digit of the numbers you are multiplying.

   • In our example, 4 times 3 is 12. Write down 2 and carry over 1.

        1
      23
     x 4
     ----
       2

3. Handle the Carry-over: If the result of a multiplication is a two-digit number, write the ones digit of the product and carry over the tens digit to the next multiplication step.

   • In our example we carried over 1. Next multiply 4 times 2 which is 8. Then add the carry-over 1: 8+1 =9. Write down 9.

        1
      23
     x 4
     ----
     92

4. Repeat for other digits: If the bottom number has more than one digit, repeat the process by starting with the tens digit of the bottom number. Before starting, put a zero as placeholder below the first result before you start multiplying. Write each resulting line below, shifted one place to the left to account for place value.

   • Let's consider multiplying 23 by 14

          1
        23
      x 14
      ----
         92    
        230  (1x23)
      ----

5. Add the Results: Finally, add all the partial products to get the final answer (the "product").

   • In our example, 92 + 230 = 322.

           1
         23
       x 14
       ----
          92    
         230 
       ----
        322

Example from the provided reference:

• The video example shows multiplying 56 by 4.
• 4 x 6 is 24. You write down 4 and carry over 2.
• Then 4 x 5 is 20, plus the carried 2, which is 22.
• The final product, the answer to the multiplication problem, is 224.

Key concepts:

• Product: The result of multiplying two numbers is called the product.
• Carry-over: When the result of multiplying two digits is a two-digit number, the tens digit is carried over to be added to the next product.
• Place Value: Understanding the place value of each digit is essential for setting up the problem and shifting the partial products to the left when there is more than one digit in the multiplier.