Long subtraction calculator
5,003 - 1,278 = 3,725 by long subtraction, borrowing across both zeros to make 13 in the ones column.
Difference
- Regrouping
- borrowed 10 in the ones, tens and hundreds
- Check
- 3,725 + 1,278 = 5,003
| Column | Top digit | After regrouping | Bottom digit | Difference |
|---|---|---|---|---|
| ones | 3 | 3 + 10 = 13 | 8 | 13 - 8 = 5 |
| tens | 0 | 0 - 1 + 10 = 9 | 7 | 9 - 7 = 2 |
| hundreds | 0 | 0 - 1 + 10 = 9 | 2 | 9 - 2 = 7 |
| thousands | 5 | 5 - 1 = 4 | 1 | 4 - 1 = 3 |
- "- 1" is the 1 a column lent to the column on its right; "+ 10" is the 10 it borrowed from the column on its left. Across a zero that reads 0 - 1 + 10 = 9.
How the Long Multiplication Calculator works
Long subtraction lines the numbers up by place value and subtracts one column at a time from the right. When the top digit is smaller than the bottom one, regroup: borrow 1 from the column to the left, which is worth 10 in the current column. Math textbooks call this subtraction with regrouping; older ones call it borrowing.
Worked example: 5,003 - 1,278.
Ones: 3 is smaller than 8. The tens and hundreds are both 0, so the borrow comes from the thousands. The 5 thousands become 4, the hundreds become 10 and then 9, the tens become 10 and then 9, and the ones become 13. 13 - 8 = 5. Tens: 9 - 7 = 2. Hundreds: 9 - 2 = 7. Thousands: 4 - 1 = 3.
The difference is 3,725.
Taken one column at a time, the same borrowing reads: a column that lent 1 to its right is 1 less, and a column that is then too small adds 10 borrowed from its left. Across a zero that is 0 - 1 + 10 = 9, the 9 written above each zero by hand.
Decimals line up on the decimal point, with zeros filling the empty places: 20 - 4.35 is 20.00 - 4.35 = 15.65.
Check a difference by adding it back: 3,725 + 1,278 = 5,003.
Long Multiplication Calculator FAQ
What does regrouping mean in subtraction?
Exchanging 1 of one place for 10 of the place to its right, so a column has enough to subtract from. 1 ten becomes 10 ones; the number keeps its value and is only written differently.
What if the bottom number is bigger than the top?
Subtract the smaller from the larger and make the answer negative: 1,278 - 5,003 = -(5,003 - 1,278) = -3,725.
How do I borrow from a zero?
Go left to the first digit that is not zero and take 1 from it; every zero passed on the way becomes 9. In 5,003 - 1,278 the 5 becomes 4, both zeros become 9, and the 3 becomes 13.