You cannot borrow from nothing: subtraction
The Short Answer
Subtraction at this level turns on exchanging across zeros. When the column next door is empty you cannot take from it, so you keep travelling left until you find a column with something in it, and let the exchange ripple back. Decimals must be padded to the same length first, exactly as in addition.
What do subtraction questions test at this level?
The same thing addition does — setting out — with one extra difficulty that has its own name in our lessons: working down through a row of zeros.
You cannot borrow from nothing
50 000 − 23 847
Look at the units. Nought take away seven will not go. So we borrow from next door — and next door is a nought as well. So is the one after that.
You cannot borrow from nothing. So keep travelling left until you find a column with something in it. Here that is the 5 in the ten thousands.
Exchange one ten thousand, and let it ripple back: the thousands become nine, the hundreds become nine, the tens become nine, and the units finally have ten to work with.
Can you show me a worked example?
Counting up, as an alternative
Worth knowing, because some children find exchanging fragile and counting up robust.
From 23 847 to 24 000 is 153. From 24 000 to 50 000 is 26 000. Add them: 26 153.
Same answer, no exchanging, and no row of zeros to negotiate. It is particularly good when the number being subtracted from is round, which on this topic it very often is.
Decimals: pad first
Exactly as in addition, and slightly more urgent. Write 40 as 40.00 before subtracting 12.65, so there is a column for every digit to sit in.
A missing column at the end of a subtraction is where the exchanging goes wrong, and the zero costs nothing to write.
Where do pupils lose marks?
Getting lost in the ripple and turning one zero into a nine but not the next.
Skipping the estimate, so an answer that is out by ten thousand goes unnoticed.
Forgetting to pad decimals, which addition punishes and subtraction punishes harder.
Try it yourself
Estimate first. Where you meet a row of zeros, travel left to the first column with something in it.
- 50 000 − 23 847
- Estimate that first. What should the answer be near?
- 20.05 − 7.4
- In 50 000 − 23 847, why do the zeros become nines?
- A tank holds 40 litres and 12.65 litres are used. How much is left?
- 26 153. Units: 0 take 7 will not go, and the next two columns are zeros as well. Travel left to the 5 in the ten thousands, exchange one, and let it ripple back.
- About 26 000. Round to 50 000 − 24 000. An answer of 36 153 or 2 615 is then visibly wrong.
- 12.65. Pad the second number to 7.40 first, then subtract as usual.
- Because each zero borrows from the column to its left and immediately lends to the column on its right. It ends up holding nine — ten received, one passed on. Saying that aloud is better than teaching it as a trick, because it keeps working when the numbers change.
- 27.35 litres. Write 40 as 40.00 so the places match, then subtract. Padding matters as much here as in addition.
How much practice does this type need at home?
Short and specific. Practise subtracting from round numbers — 30 000, 5 000, 200 — because that is where the zeros are and that is where the marks are.
And try both methods on the same question, then ask your child which they found easier. Children who know they have a second route are much calmer when the first one goes wrong in the middle.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
What is actually happening when we exchange across zeros?
Each zero borrows ten from its left and immediately lends one to its right, which leaves it holding nine. That is why a row of zeros turns into a row of nines. Teaching it as 'the zeros become nines' works and is a rule to remember; teaching what is happening means your child can rebuild it when they forget, which under pressure they will.
My child gets this right at home and wrong in a test. Why?
Usually because at home they are doing one calculation and in a test they are doing it fifth, quickly, after four others. The defence is the estimate. A child who has said 'about 26 000' before starting will notice an answer of 36 153; a child who has not will write it down and move on.
Do decimals need padding for subtraction too?
Yes, and more urgently than for addition, because a missing column at the end of a subtraction is where the exchanging goes wrong. Write 40 as 40.00 before subtracting 12.65. It is the same habit as in addition and it should be automatic before either becomes fast.
Is a mental method ever better here?
For subtractions near a round number, yes — 50 000 − 23 847 can be done by counting up from 23 847 to 24 000, then to 50 000, which some children find far easier than exchanging. It is worth showing both, because counting up avoids the row of zeros entirely and children who find exchanging fragile often find counting up robust.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
We Teach This Method Every Week in Winslow
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