Subtraction with Regrouping

In this lesson, we will learn how to perform subtraction when we need to regroup. This occurs when the top number in a column is smaller than the bottom number.

Steps for Subtraction with Regrouping:

1. Align the numbers vertically by place value (ones, tens, hundreds, etc.).
2. Start from the rightmost column (the ones). If the top number is smaller, regroup from the next column.
3. Subtract the numbers in each column, moving left.

Example:

Let's solve the problem: 53 - 28.

1. Align the numbers:

   $$\begin{array}{rr} & 5 & 3 \\ - & 2 & 8 \\ \end{array}$$

2. Start from the rightmost column:

   • In the ones column, we have 3 - 8. Since 3 is smaller than 8, we need to regroup from the tens column.
   • Borrow 1 from the 5 in the tens place, making it 4 (5 - 1 = 4). This gives us 13 in the ones place (10 + 3).

3. Now perform the subtraction:

   • In the ones column: 13 - 8 = 5.
   • In the tens column: 4 - 2 = 2.

So, we find:

$$53 - 28 = 25$$

Key Questions:

• What do you do if the top number is smaller than the bottom number in a column?
• How do you know when to regroup?
• Can you explain why we have to borrow when regrouping?

Keywords:

• Regrouping
• Borrowing
• Subtraction
• Place Value
• Ones
• Tens