Long Subtraction Calculator (with Borrowing)
Subtract numbers in columns with borrowing and regrouping, shown step by step — including chained borrows across zeros and a built-in addition check.
What is long subtraction?
Long subtraction stacks two numbers so matching place values line up, then subtracts one column at a time from right to left. When a top digit is smaller than the digit below it, you borrow (regroup) 1 from the next column to the left.
The steps
- Stack the numbers, ones under ones, tens under tens.
- Subtract each column from the right.
- If the top digit is smaller, borrow 1 from the left column, adding 10 to the current one.
- Check by adding the difference back to the number you subtracted.
Worked example: 245 − 147
- Ones: 5 is less than 7, so borrow — 15 − 7 = 8. The tens 4 becomes 3.
- Tens: now 3 is less than 4, so borrow — 13 − 4 = 9. The hundreds 2 becomes 1.
- Hundreds: 1 − 1 = 0.
So 245 − 147 = 98. Check: 98 + 147 = 245.
Borrowing across a zero: 300 − 148
The ones column needs to borrow, but the tens digit is 0 and cannot lend. The chain reaches the hundreds:
- Hundreds 3 becomes 2, lending to the tens.
- Tens 0 becomes 10, then lends 1 to the ones and is left as 9.
- Ones become 10: 10 − 8 = 2. Tens: 9 − 4 = 5. Hundreds: 2 − 1 = 1.
So 300 − 148 = 152. The same chain turns 1000 − 1 into 999.
Subtracting decimals: 82.5 − 17.75
Line up the decimal points and pad: 82.50 − 17.75. Borrow through the columns to get 64.75.
When the answer is negative: 147 − 245
The top number is smaller, so subtract the other way and add a sign: 245 − 147 = 98, giving 147 − 245 = −98.
Common mistakes
- Forgetting to reduce the column you borrowed from.
- Stopping the borrow chain too early when passing zeros.
- Not lining up decimal points before subtracting.
Long subtraction is the mirror of long addition: addition carries, subtraction borrows.
Frequently asked questions
- What is borrowing in subtraction?
- Borrowing (also called regrouping) happens when the top digit in a column is smaller than the bottom digit. You take 1 from the next column to the left, which adds 10 to the current column so the subtraction can be done. For example, to do 5 minus 7 you borrow to make it 15 minus 7.
- How do you borrow across a zero?
- When the column you want to borrow from is a 0, it cannot give 1 directly. It borrows from the next column to its left first, becoming 10, then lends 1 and is left as 9. This chain continues past every 0. In 300 minus 148 the tens 0 becomes 9 and the hundreds 3 becomes 2.
- How do I check a subtraction answer?
- Add the difference to the number you subtracted. If the result equals the number you started from, the subtraction is correct. For 245 minus 147 equals 98, check that 98 plus 147 equals 245.
- What if the top number is smaller than the bottom number?
- The difference is negative. This calculator subtracts the smaller value from the larger one and attaches a minus sign, so 147 minus 245 gives negative 98.
- How do I subtract decimals in columns?
- Line up the decimal points so tenths sit under tenths and hundredths under hundredths, pad the shorter number with trailing zeros, then subtract column by column exactly like whole numbers.
- What is the difference between carrying and borrowing?
- Carrying is used in addition when a column total is more than 9. Borrowing is the reverse move in subtraction when a column cannot subtract without help. Addition carries left to right of the overflow, subtraction borrows from the left.
- Is regrouping the same as borrowing?
- Yes. Regrouping and borrowing name the same step — trading one unit of a larger place for ten units of the next smaller place so a column can be subtracted.