Method of Regrouping in addition and subtraction

The Method of Regrouping, also known as “carrying” in addition or “borrowing” in subtraction, is a technique used to handle numbers when performing these operations, especially with multi-digit numbers.

Regrouping helps manage numbers across different place values, such as ones, tens, hundreds, etc., during addition and subtraction.

Let’s break down both addition and subtraction using this method with detailed steps and examples.

Regrouping in Addition

When the sum of digits in a particular place value column (like ones, tens, etc.) is greater than 9, we regroup by carrying over the extra value to the next higher place value.

Step-by-Step Process:

1. Align the Numbers: Write the numbers vertically, aligning them by place value (ones, tens, hundreds, etc.).
2. Start from the Right: Begin adding the digits from the rightmost column (ones) to the leftmost column.
3. Add the Digits: If the sum of the digits in any column is 10 or more, regroup.
4. Carry Over: Write down the rightmost digit of the sum in that column and carry over the leftmost digit to the next column to the left.

Example:

Let’s add 487 + 356.

1. Align the Numbers:

      487
   +  356

2. Start from the Right (Ones Column):

• 7 (from 487) + 6 (from 356) = 13.
• Write down 3 and carry over 1.

2. Tens Column:

• 8 + 5 + 1 (carried over) = 14.
• Write down 4 and carry over 1.

2. Hundreds Column:

• 4 + 3 + 1 (carried over) = 8.
• Write down 8.

2. Final Answer:

      487
   +  356
   ------
      843

Regrouping in Subtraction

Regrouping in subtraction is often called borrowing. When we subtract and the digit in the minuend (top number) is smaller than the digit in the subtrahend (bottom number) in a particular place value, we need to borrow from the next higher place value.

Step-by-Step Process:

1. Align the Numbers: Write the larger number on top and the smaller number directly underneath it, aligning by place value.
2. Start from the Right: Begin subtracting from the rightmost column.
3. Check for Borrowing: If the digit in the top number is smaller than the bottom number in any column, you need to borrow.
4. Borrowing: Decrease the next left digit by 1 and add 10 to the current digit.

Example:

Let’s subtract 352 – 178.

1. Align the Numbers:

      352
   -  178

2. Start from the Right (Ones Column):

• 2 – 8: cannot subtract, so borrow 1 from the tens column.
• The 5 becomes 4, and the 2 becomes 12.
• Now, 12 – 8 = 4.

2. Tens Column:

• Now, we have 4 (from borrowing) – 7: cannot subtract again, so borrow from the hundreds.
• The 3 becomes 2, and the 4 becomes 14.
• Now, 14 – 7 = 7.

2. Hundreds Column:

• 2 – 1 = 1.

2. Final Answer:

      352
   -  178
   ------
      174

Summary

• In addition, regrouping involves carrying over when a sum is 10 or more.
• In subtraction, regrouping involves borrowing when the top digit is smaller than the bottom digit.

This method is essential for accurately performing arithmetic operations with larger numbers.