Subtraction with Regrouping up to 1000

When you subtract two 3-digit numbers, sometimes a digit on top is smaller than the digit directly below it in the same column. You cannot subtract a bigger digit from a smaller one and get a positive whole number in that column, so you need to borrow, or regroup, from the column to its left. Regrouping means breaking apart one group of ten from the next place value so the column you're working on has enough to subtract from.

This builds directly on subtracting with digits up to 1000, where every column already had enough to subtract without any borrowing. Once numbers stop lining up so neatly, regrouping is the tool that keeps the column method working for any pair of numbers up to 1000.

Work from right to left: ones, then tens, then hundreds.

• Look at the ones column. If the top digit is smaller than the bottom digit, borrow 1 ten from the tens column. That ten becomes 10 extra ones, so the top ones digit increases by 10, and the tens digit on top decreases by 1.
• Move to the tens column. If it's now too small to subtract, borrow 1 hundred from the hundreds column the same way: add 10 to the tens digit, and subtract 1 from the hundreds digit.
• Finally subtract in the hundreds column as usual.

Subtract \( 325 - 148 \).

Ones column: \( 5 \) is smaller than \( 8 \), so borrow 1 ten from the tens column. The tens digit \( 2 \) becomes \( 1 \), and the ones digit \( 5 \) becomes \( 15 \). Now \( 15 - 8 = 7 \).

Tens column: after borrowing, the tens digit is \( 1 \), and \( 1 - 4 \) is still not possible, so this problem actually needs a second borrow (shown in the diagram below).

Reading the diagram: the hundreds digit \( 3 \) lends 1 hundred to the tens column, becoming \( 2 \), and the tens digit becomes \( 11 \), so \( 11 - 4 = 7 \). The hundreds column finishes with \( 2 - 1 = 1 \). Putting the columns together gives \( 325 - 148 = 177 \).

Subtract \( 500 - 267 \). Here the tens and ones digits of \( 500 \) are both \( 0 \), which forces regrouping to ripple through more than one column.

Ones column: \( 0 \) is smaller than \( 7 \), so borrow from the tens column. But the tens digit is also \( 0 \), so first borrow 1 hundred from the hundreds column, turning the tens digit into \( 10 \). Then borrow 1 of those tens into the ones column, turning the ones digit into \( 10 \) and leaving \( 9 \) tens. Now \( 10 - 7 = 3 \) in the ones column, \( 9 - 6 = 3 \) in the tens column, and \( 4 - 2 = 2 \) in the hundreds column, since 1 hundred was already borrowed away. The result is \( 500 - 267 = 233 \).

This chain of borrows is exactly what you'll see in identifying the missing digits in subtraction, where knowing how borrowing changes each digit helps you work backward to fill in a hidden number.

Two quick checks help catch mistakes in a regrouping problem. First, add the answer back to the number you subtracted: \( 233 + 267 \) should return \( 500 \). Second, estimate before you start by rounding both numbers, which is covered in subtraction using estimation; a rough answer near \( 200 \) or \( 300 \) tells you whether your exact column answer is reasonable.

• Always compare the top and bottom digit in a column before deciding whether to borrow.
• Cross out the digit you borrow from and write the new, smaller value just above it, the same way the diagram shows.
• Add exactly 10 to the column that needed help, never more and never less.
• Work one column at a time, left-over borrows can force a second borrow, as in the \( 500 - 267 \) example.

Related lessons

• Math 3