Long Subtraction Calculator (column subtraction with borrowing, step by step)

Understanding the long subtraction calculator — concept and principle

This calculator subtracts whole numbers in columns with borrowing, explaining every column, including borrowing across zeros, and checks the answer by adding back. It also counts the borrows. Use it to check homework, teach regrouping or verify a written subtraction.

How it is calculated

1. Line the numbers up by place value.
2. Subtract column by column, starting with the ones.
3. If the top digit is smaller than the bottom digit, borrow: take 1 from the next column to the left and add 10 to the current top digit.
4. When the next column is 0, it must borrow from the column beyond it first.

• Check: difference + subtracted number = top number.

The principle

Borrowing is regrouping in the other direction from carrying: one ten is exchanged for ten ones, one hundred for ten tens. The value of the top number does not change, only how it is split among the columns, so that every column can be subtracted without going negative. With zeros, the exchange simply passes along: 5,003 becomes 4 thousands, 9 hundreds, 9 tens and 13 ones.

Worked example

Default inputs: 5,003 − 2,647.

1. Ones place: (3 + 10) − 7 = 6, borrow 1 from the next place.
2. Tens place: ((0 − 1) + 10) − 4 = 5, borrow 1 from the next place.
3. Hundreds place: ((0 − 1) + 10) − 6 = 3, borrow 1 from the next place.
4. Thousands place: (5 − 1) − 2 = 2.
5. Difference: 2,356, with 3 borrows; check 2,356 + 2,647 = 5,003.

How to read the result

Adding the difference back to the subtracted number must give the top number; that is the quickest check. An estimate also helps: 5,000 − 2,650 ≈ 2,350.

Common mistakes

• Subtracting the smaller digit from the larger in each column regardless of which is on top.
• Forgetting that a column you borrowed from is now 1 less.
• Mishandling borrowing across several zeros.
• Putting the smaller number on top.

Frequently asked questions

How do you subtract across zeros?

Borrow from the first non-zero digit to the left; each zero in between becomes 9.

What is 5,003 − 2,647?

2,356.

How do I check a subtraction?

Add the answer to the number you subtracted; you should get the top number.

Sources: OpenStax, Prealgebra 2e (2020), §1.3 Subtract Whole Numbers