Column addition and subtraction
Maths · Key Stage 2 · The School
Line up the places, not the ends
Columns work because each one holds a single place value. Line up ones under ones and tens under tens — with whole numbers that means lining up the right-hand ends, but with decimals it means lining up the decimal points, which is the same rule stated properly. Adding 12.5 and 3.75 by their right-hand ends gives a badly wrong answer.
Carrying is exchanging
When a column comes to ten or more, you cannot write two digits in one place, so you exchange: ten ones become one ten, carried into the next column. Subtraction runs the same trade backwards — if you cannot take 7 from 3, exchange one ten from next door into ten ones, making 13. Saying "exchange" rather than "borrow" is worth the effort, because nothing is borrowed and nothing is given back.
Estimate first, then check
Before calculating, round and get roughly the answer: 4,213 + 2,897 is about 4,000 + 3,000 = 7,000. Now if the column method produces 1,110 or 71,110 you know instantly something went wrong. This single habit catches almost every misaligned column and missed carry, and it takes about five seconds.
Write 45 with the 7 under the 5, in the ones column: 5 + 7 = 12, so write 2 and carry 1 ten. 4 + 1 = 5. Answer 52. Now write it lined up on the LEFT instead, with the 7 under the 4: you would add 4 + 7 in the tens column and get 115. The digits were identical; only the alignment changed, and it changed the answer by 63. That is why the rule is places, not edges — and why decimals line up on the point.