Concept 4 of 7
Take It Away: Borrowing
Today's big idea
When the top digit is too small, borrow one from the column to its left.
Borrowing splits a ten into ten ones, so the column can finally cope.
How it works
👀 What's going on?
Taking 9 away from 3 is not something you can do yet. But 6,235 minus 1,584 asks exactly that in the tens column, and 7,000 minus 2,463 asks it in every column at once. A short column has to get help from somewhere.
💡 Here's the trick
Look at the sum above. When the top digit is smaller than the one below it, the column borrows 1 from its neighbour on the left. That 1 arrives worth 10, because the next column along is ten times bigger. A 3 becomes 13, and now the subtraction works. The same trick works all the way up to thousands.
🪄 How to do it
- 1.Start at the ones, the way the sum above starts.
- 2.If the top digit is too small, take 1 from the column on its left and add 10 to yours.
- 3.Cross out the column you borrowed from and write it one lower, then carry on left.
✍️ Try it
Work out 6,235 − 1,584. Then try 7,000 − 2,463, where three zeros mean the borrow has to travel a long way.
For the first, 5 − 4 = 1. The tens need 3 − 8, so borrow: 13 − 8 = 5. The hundreds are now 1, so borrow again: 11 − 5 = 6. The thousands are now 5, and 5 − 1 = 4, giving 4,651. For the second, the borrow starts at the ones and travels all the way from the 7, leaving 4,537.
⚠️ Watch out
You might be thinking you can add the 10 and leave the neighbour alone. You cannot. Whatever your column gains, the column you borrowed from has to lose. Skip that half and you have quietly invented an extra ten.
🌟 Why this matters
Working out change, or how many days are left, or how much further you have to walk, all run on this. It is the half of subtraction that actually needs care.
Exam tip: Write the crossings-out rather than holding them in your head; that is where the marks go.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Subtract: 432 − 187”
- 1
Start at ones
2 − 7. The 2 is too small! 🚨 Time to borrow.
- 2
Borrow from the tens
Tens is 3 → cross it out, make it 2. Ones becomes 12. Now: 12 − 7 = 5.
- 3
Tens column
2 − 8. Too small again! Borrow from hundreds. 4 → 3, tens becomes 12. 12 − 8 = 4.
- 4
Hundreds ✓
3 − 1 = 2. 432 − 187 = 245
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Blue rods are tens, yellow squares are ones. If there aren't enough ones to take away, break 1 ten into 10 ones first.
52 − 27
ROUND 1 OF 2We must take away 7 ones, but there are only 2. Not enough!
Quick check
✅ VERIFICATION
What is 5,003 − 2,687?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Missing Numbers
Start at the output and reverse each step.