Column Subtraction with Borrowing

What is column subtraction?

Column subtraction is a tidy way to take one number away from another by stacking them and working column by column. Like column addition, it relies on place value, so it helps to be confident with ones, tens and hundreds — see Place Value to Thousands if you need a refresher.

Setting up: line up the place values

Write the bigger number on top and the number you are taking away underneath. Line up the digits by place:

• ones under ones
• tens under tens
• hundreds under hundreds

Then draw a line for the answer and start from the right.

  52
- 27
----

When subtraction is easy — and when it is not

Sometimes every top digit is bigger than the one below it, and you just subtract straight away. But often a top digit is too small. For example, in the ones column you might need 2 − 7. You cannot take 7 from 2.

That is when you borrow (also called exchanging or regrouping).

The rule for borrowing

If the top digit is too small, borrow one from the next column to the left. That one is worth ten in the current column.

Borrowing does not change the value of the number. You are simply regrouping: one ten becomes ten ones. The total stays the same; only how it is grouped changes.

Worked example 1: two-digit numbers

Work out 52 − 27.

  4 12
   5 2
 - 2 7
 ----
   2 5

1. Ones column: you need 2 − 7, but 2 is too small. Borrow 1 ten from the tens column. The 2 ones become 12 ones, and the 5 tens drop to 4 tens.
2. Now subtract the ones: 12 − 7 = 5.
3. Tens column: the 5 is now 4. So 4 − 2 = 2.
4. Read the answer: 25.

Why it works: 52 is 5 tens and 2 ones. We changed it to 4 tens and 12 ones — still 52, just grouped differently. Now there are enough ones to subtract.

Worked example 2: three-digit numbers

Work out 624 − 158.

  5 11 14
   6  2  4
 - 1  5  8
 -------
   4  6  6

1. Ones: 4 − 8 is too small. Borrow 1 ten → ones become 14, tens drop from 2 to 1. Now 14 − 8 = 6.
2. Tens: the tens digit is now 1. 1 − 5 is too small. Borrow 1 hundred → tens become 11, hundreds drop from 6 to 5. Now 11 − 5 = 6.
3. Hundreds: 5 − 1 = 4.
4. Read the answer: 466.

This sum needed two borrows, one after the other. Take them one column at a time and it stays simple.

Worked example 3: borrowing across a zero

Work out 403 − 158.

A zero in the middle makes borrowing trickier, because you cannot borrow from an empty column. You must borrow from further left first.

  3 10 13
   4  0  3
 - 1  5  8
 -------
   2  4  5

1. Ones: 3 − 8 is too small. We need to borrow, but the tens digit is 0 — nothing to borrow yet. So first borrow from the hundreds: the 4 hundreds become 3, and the 0 tens become 10.
2. Now borrow 1 of those tens for the ones: tens drop from 10 to 9, ones become 13. Then 13 − 8 = 5.
3. Tens: the tens are now 9. 9 − 5 = 4.
4. Hundreds: 3 − 1 = 2.
5. Read the answer: 245.

Checking by adding back

The best way to check subtraction is to add your answer back. If it returns the number you started with, you are correct.

Subtraction	Answer	Check (answer + amount taken)	Correct?
52 − 27	25	25 + 27 = 52	Yes
624 − 158	466	466 + 158 = 624	Yes
403 − 158	245	245 + 158 = 403	Yes

If the check does not match, look back for a borrow you missed. This is the reverse of the carrying you learned in Column Addition with Carrying.

Try it yourself

Set these out in columns and subtract, borrowing where needed. Then check each by adding back.

• 71 − 38 (Answer: 33)
• 500 − 246 (Answer: 254)
• 832 − 567 (Answer: 265)

The middle one needs you to borrow across two zeros — work patiently from the hundreds.

Great job!

You can now subtract big numbers using column subtraction, and you understand why borrowing keeps the value the same. Together with addition, this lets you handle almost any number problem.

Practise quick takeaways in Mental Math Strategies, or revisit Addition and Subtraction Made Easy for more examples.