Maths Library

Vertical Subtraction Algorithm: Year 4 maths

This topic covers the formal vertical algorithm for subtraction with decomposition and exchanging across columns. Pupils practise structured layout, exchanging from tens, hundreds, and thousands, and dealing with interior zeros.

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What this covers

Vertical Subtraction Algorithm is taught in Year 4 (age 9 to 10) as a topic to introduce. It sits in the Number strand.

Worked example

Calculate: 503 - 267 using column subtraction.

  1. Align digits: 3 - 7 requires an exchange. Tens column has 0, so exchange from hundreds: 5 becomes 4, tens becomes 10.
  2. Exchange 1 ten to ones: tens becomes 9, ones becomes 13.
  3. Subtract ones: 13 - 7 = 6; tens: 9 - 6 = 3; hundreds: 4 - 2 = 2. Total is 236.

Answer: 236

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. 2-digit numbers without decomposition
  2. 3-digit numbers with single exchange from tens to ones
  3. 3-digit numbers with exchanges across tens and hundreds
  4. 4-digit numbers with borrowing across interior zeros (e.g., 4005 - 1268)
  5. 5-digit numbers with multiple chained decompositions

Common mistakes

  • Subtracting the top number from the bottom number when top digit is smaller
  • Failing to reduce the lending digit by 1 when decomposing across a zero

Curriculum links

Indicative matches to Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M4N02 Add and subtract whole numbers fluently using written column methods.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Vertical Subtraction Algorithm

Year 4 maths

Qs
6
Marks
24
NameDateScore / 24
1.
793 085 − 648 461 =
[4]
2.
884 303 − 521 664 =
[4]
3.
863 716 − 461 890 =
[4]
4.
631 921 − 457 655 =
[4]
5.
722 058 − 342 778 =
[4]
6.
308 778 − 241 856 =
[4]

Answer key

  1. 144 624Subtract column by column, exchanging when the top digit is smaller; 793 085 − 648 461 = 144 624
  2. 362 639Subtract column by column, exchanging when the top digit is smaller; 884 303 − 521 664 = 362 639
  3. 401 826Subtract column by column, exchanging when the top digit is smaller; 863 716 − 461 890 = 401 826
  4. 174 266Subtract column by column, exchanging when the top digit is smaller; 631 921 − 457 655 = 174 266
  5. 379 280Subtract column by column, exchanging when the top digit is smaller; 722 058 − 342 778 = 379 280
  6. 66 922Subtract column by column, exchanging when the top digit is smaller; 308 778 − 241 856 = 66 922