Mastering 2-Digit Multiplication with Regrouping

Understanding 2-Digit Multiplication with Regrouping

Two-digit multiplication is an important skill to master as it lays the foundation for more complex mathematical operations. Regrouping, or carrying over, is often necessary when the product of digits exceeds 9. Let’s break down the process step by step:

Example Problem: Multiply 24 by 36

1. Set Up the Problem: Write the numbers one above the other, aligning them to the right:

    24
   × 36

2. Multiply the Ones Place: Start by multiplying the bottom number’s ones place (6) by each digit of the top number (24):

   • 6 × 4 = 24. Write down 4 and carry over 2.
   • 6 × 2 = 12, now add the carried 2: 12 + 2 = 14. Write down 14 next to 4.

   Your work should look like this:

    24
   × 36
   ──────
    144  (6 × 24 = 144)

3. Multiply the Tens Place: Now multiply the tens place (3) by the entire top number (24). Since 3 represents 30, you will actually be multiplying by 30:

   • 3 × 4 = 12. Write down 2 (and carry over 1).
   • 3 × 2 = 6, then add the carried 1: 6 + 1 = 7.

   Since we are in the tens place, we need to add a zero to the end of this product (the result of 30 times 24):

   Your work should look like this:

    24
   × 36
   ──────
    144  
   +720  (3 × 24 = 72, written as 720)

4. Add the Results: Now, add the numbers you calculated:

    144
   +720 
   ──────
    864

So, 24 multiplied by 36 equals 864.

Helpful Tips:

• Always align your numbers by place value (ones under ones, tens under tens).
• Remember to carry over if your product is 10 or greater—this is essential in regrouping.
• Practice with different two-digit numbers to become confident in this technique.
• Use grid paper or draw lines to help keep your numbers neat and organized.
• Encourage yourself to double-check your addition at the end to ensure accuracy.