Long (column) subtraction
Column subtraction with regrouping (‘borrowing’) when the top digit is smaller than the bottom.
Year 3 starts with two-digit subtraction without crossing tens; by Year 5 children handle five-digit subtraction with multiple regroups. The UK convention is ‘exchange’ (rather than the older ‘borrow’) but both terms appear.
Worked examples
523 - 178 = 345. Exchange a ten to do 13-8=5; exchange a hundred to do 11-7=4 (after the previous exchange); 4-1=3.
1000 - 327 = 673. Multi-step exchange because of the zeros.
Decimals: 5.6 - 1.84 = 3.76. Pad with zeros: 5.60 - 1.84.
Frequently asked questions
Why ‘exchange’ not ‘borrow’?
‘Borrow’ suggests it gets returned, which is misleading. ‘Exchange’ reflects what you're really doing: a 10 from the next column becomes 10 ones.
My answer is bigger than the start — what went wrong?
Almost always a column was added instead of subtracted somewhere. Check each column.