Subtract whole numbers (written strategies) - With regrouping
Theory
When a top digit is smaller than the digit below it, you trade (regroup): take one from the next column to the left and turn it into ten in the column you are working on. This Year 5 maths page shows how to subtract with trading in one or more columns, check the answer by adding, find missing numbers and avoid the common mistakes.
Trading (regrouping or decomposition) happens when a top digit is smaller than the bottom digit. Take \(1\) from the next column to the left; it is worth ten in the column you are working on.
One ten becomes ten ones, one hundred becomes ten tens, one thousand becomes ten hundreds. The top number is renamed, not changed: \(632\) is the same as \(6\) hundreds, \(2\) tens and \(12\) ones.
After trading, the column you traded from is one less. Cross out the old digit and write the new one above it.
In the working, O, T, H, Th, TTh, HTh and M stand for ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions.
Trading renames the top number without changing it:
How to subtract with trading
- Line up the numbers, larger on top, and start with the ones.
- If the top digit is too small, take \(1\) from the next column left and add ten to this column.
- Subtract the column, then move left. Remember the column you traded from is now one less.
- Check by adding the answer to the bottom number.
| \(\text{O: }13 - 8\) | \(=\) | \(5\) |
| \(\text{T: }6 - 3\) | \(=\) | \(3\) |
The answer is \(35\).
| \(\text{O: }12 - 5\) | \(=\) | \(7\) |
| \(\text{T: }12 - 7\) | \(=\) | \(5\) |
| \(\text{H: }5 - 3\) | \(=\) | \(2\) |
The answer is \(257\).
| \(\text{O: }13 - 8\) | \(=\) | \(5\) |
| \(\text{T: }13 - 6\) | \(=\) | \(7\) |
| \(\text{H: }11 - 8\) | \(=\) | \(3\) |
| \(\text{Th: }4 - 1\) | \(=\) | \(3\) |
The answer is \(3375\).
| \(\text{O: }12 - 6\) | \(=\) | \(6\) |
| \(\text{T: }14 - 7\) | \(=\) | \(7\) |
| \(\text{H: }12 - 4\) | \(=\) | \(8\) |
| \(\text{Th: }10 - 8\) | \(=\) | \(2\) |
| \(\text{TTh: }6 - 3\) | \(=\) | \(3\) |
The answer is \(32\,876\).
| \(\text{O: }5 + 8\) | \(=\) | \(13\ (\text{carry } 1)\) |
| \(\text{T: }7 + 6 + 1\) | \(=\) | \(14\ (\text{carry } 1)\) |
| \(\text{H: }3 + 8 + 1\) | \(=\) | \(12\ (\text{carry } 1)\) |
| \(\text{Th: }3 + 1 + 1\) | \(=\) | \(5\) |
The sum is the top number, \(5243\), so the subtraction is correct.
| \(\text{O: }14 - 7\) | \(=\) | \(7\) |
| \(\text{T: }12 - 6\) | \(=\) | \(6\) |
| \(\text{H: }6 - 4\) | \(=\) | \(2\) |
The missing number is \(267\). Check: \(734 - 267 = 467\).
| \(\text{O: }12 - 5\) | \(=\) | \(7\) |
| \(\text{T: }13 - 7\) | \(=\) | \(6\) |
| \(\text{H: }5 - 3\) | \(=\) | \(2\) |
Zara should have traded in the ones and the tens. The answer is \(267\). Check: \(267 + 375 = 642\).
Common pitfalls
Frequently asked questions
What is trading in subtraction?
Trading, or regrouping, is taking \(1\) from the next column to the left and turning it into ten in the column you are working on, because the top digit is too small.
When do you need to trade?
When the top digit in a column is smaller than the bottom digit, such as \(2 - 5\) in the ones of \(632 - 375\).
Why does the next digit go down by one?
You took one ten (or hundred, or thousand) from it. \(632\) becomes \(6\) hundreds, \(2\) tens and \(12\) ones, then \(5\) hundreds, \(12\) tens and \(12\) ones.
How do you check a subtraction with trading?
Add your answer to the number you subtracted. \(257 + 375 = 632\), so \(632 - 375 = 257\) is right.
Can you trade in more than one column?
Yes. \(5243 - 1868\) needs a trade in the ones, tens and hundreds.