Multiplication with Regrouping

Multiplication with regrouping, also known as carrying, is a fundamental concept in mathematics that allows students to multiply multi-digit numbers accurately. This method involves breaking down numbers into more manageable parts, multiplying them, and regrouping any value over ten to the next place value.

Let us understand this way - When performing multiplication, if the product of two digits exceeds 9, we carry over the extra value to the next column. This process of carrying over is called regrouping. It is necessary to ensure that place values are correctly aligned in multi-digit multiplication.

In this article, we will discuss this method in detail.

Why is Regrouping Important?

In multiplication, if the multiplication of two-digit figures exceeds 9, then we add the excess to the next number column. This process of carrying over is termed as regrouping. There is a need to pay a lot of attention to the formation of place values while solving multi-digit multiplication problems.

Steps for Multiplication with Regrouping

Let’s understand the process of multiplication with regrouping using examples:

Example 1: Multiply 34 × 26.

Solution:

Step 1: Multiply the ones in place

• Multiply 6 (ones place of 26) by 4 (ones place of 34).
• 6 × 4 = 24. Write 4 in the ones column and carry over 2 to the tens place.

Step 2: Multiply the tens place

• Multiply 6 by 3 (tens place of 34).
• 6 × 3 = 18. Add the carried 2, giving 20. Write 20 below the line.

Step 3: Multiply the next row

• Multiply 2 (tens place of 26) by 4. Write the result in the second row, starting from the tens column.
• Multiply 2 by 3. Add the results.

Step 4: Add both rows

• After multiplying and regrouping, add the two results to get the final answer.

Thus, 34 × 26 = 884.

This can represented as the following illustration:

👁 34x26

Example 2: Multiply 56 × 42.

Solution:

• Multiply 6 × 2 = 12. Write 2, carry over 1.
• Multiply 5 × 2 = 10. Add the carried 1 = 11.
• Multiply 6 × 4 = 24. Write 4 in the tens column.
• Multiply 5 × 4 = 20. Add the results to get 2352.

This can represented as the following illustration:

👁 56x42

Example 3: Multiply 123 × 45.

Solution:

• Multiply 5 × 3 = 15. Write 5, carry over 1.
• Multiply 5 × 2 = 10. Add the carried 1 = 11.
• Multiply 5 × 1 = 5. Write 6 (with carried 1).
• Multiply 4 × 123 (shifted by one column), then add to the first row.

This can represented as the following illustration:

👁 123x45

Example 4: Multiply 87 × 56.

Solution:

Step 1: Multiply 6 by 7 = 42. Write 2, carry over 4.

Step 2: Multiply 6 by 8 = 48. Add the carried 4 = 52. Write 52.

Step 3: Multiply 5 (in the tens place) by 87 (shift one column to the left).

• Multiply 5 by 7 = 35. Write 5, carry over 3.
• Multiply 5 by 8 = 40. Add the carried 3 = 43. Write 43.

Step 4: Add both rows (522 and 4350) to get 4872.

This can represented as the following illustration:

👁 87x54

Example 5: Multiply 245 × 32.

Solution:

Step 1: Multiply 2 by 245:

• 2 × 5 = 10. Write 0, carry over 1.
• 2 × 4 = 8. Add the carried 1 = 9.
• 2 × 2 = 4. Write 490.

Step 2: Multiply 3 (tens place) by 245 (shift one column to the left):

• 3 × 5 = 15. Write 5, carry over 1.
• 3 × 4 = 12. Add the carried 1 = 13.
• 3 × 2 = 6. Add the carried 1 to get 7. Write 735.

Step 3: Add both rows (490 and 7350) to get 7840.

This can represented as the following illustration:

👁 245x32

Example 6: Multiply 134 × 67.

Solution:

Step 1: Multiply 7 by 134:

• 7 × 4 = 28. Write 8, carry over 2.
• 7 × 3 = 21. Add the carried 2 = 23. Write 3, carry over 2.
• 7 × 1 = 7. Add the carried 2 = 9. Write 938.

Step 2: Multiply 6 (tens place) by 134 (shift one column to the left):

• 6 × 4 = 24. Write 4, carry over 2.
• 6 × 3 = 18. Add the carried 2 = 20. Write 0, carry over 2.
• 6 × 1 = 6. Add the carried 2 to get 8. Write 8040.

Step 3: Add both rows (938 and 8040) to get 8978.

This can represented as the following illustration:

👁 137x67

Example 7: Multiply 532 × 48

Solution:

Step 1: Multiply 8 by 532:

• 8 × 2 = 16. Write 6, carry over 1.
• 8 × 3 = 24. Add the carried 1 = 25. Write 5, carry over 2.
• 8 × 5 = 40. Add the carried 2 = 42. Write 4256.

Step 2: Multiply 4 (tens place) by 532 (shift one column to the left):

• 4 × 2 = 8. Write 8.
• 4 × 3 = 12. Write 2, carry over 1.
• 4 × 5 = 20. Add the carried 1 = 21. Write 21280.

Step 3: Add both rows (4256 and 21280) to get 25536.

This can represented as the following illustration:

👁 532x48

Multiplication with Regrouping Worksheet -

You can download this worksheet with answer key from following:

Conclusion

In conclusion, multiplication with regrouping helps us handle larger numbers by breaking the process into simpler steps. When multiplying, if a product in a column is more than 9, we regroup by carrying over the extra value to the next column.

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