Column Addition and Subtraction Explained for Parents

Column addition and subtraction is largely how most adults learned to add and subtract multi-digit numbers too — but the specific language schools now use around it (particularly for subtraction "borrowing") has changed, which can make homework help feel unfamiliar even when the underlying method is the same.

Column addition, step by step

Numbers are stacked with matching place values aligned (units under units, tens under tens). Starting from the right (units column), add each column, writing any "carry" into the next column left. Example: 347 + 265 — units: 7+5=12, write 2, carry 1. Tens: 4+6+1(carried)=11, write 1, carry 1. Hundreds: 3+2+1=6. Answer: 612.

Column subtraction, step by step

Same alignment, but working right to left, subtracting the bottom digit from the top. When the top digit is smaller, you "exchange" (the modern term for what used to be called "borrowing") from the column to its left. Example: 523 - 178 — units: 3-8 isn't possible, exchange from tens, making it 13-8=5. Tens: now 1 (after exchange) - 7 isn't possible, exchange from hundreds, making it 11-7=4. Hundreds: 4-1=3. Answer: 345.

Why "exchange" rather than "borrowing"

The newer terminology reflects a genuine shift in how the concept is explained — rather than a vague sense of "borrowing" something that gets paid back, "exchanging" ten units for one ten (or ten tens for one hundred) makes the actual place-value mechanics explicit, which better supports genuine understanding rather than a memorised procedure.

Where children commonly go wrong

• Misaligning columns, especially with numbers of different lengths
• Forgetting to carry or exchange, especially across several columns in a row
• Subtracting the smaller digit from the larger regardless of position, rather than exchanging correctly

Helping without confusing things further

If you learned a different method at school, it's worth asking your child to show you exactly how their teacher does it, rather than teaching your own version — mixing methods at this stage often causes more confusion than it resolves, even when both methods are mathematically valid.