Subtract whole numbers (written strategies) - Across zeros
Theory
To subtract from a number with zeros, borrow across them. A zero cannot lend, so the borrow moves left; each zero it passes becomes a 9, and the last becomes 10.
Subtracting from a number with zeros still uses borrowing, but a zero has nothing to lend.
The borrow moves left until it reaches a digit that can give. Each zero it passes through becomes a 9, and the last one becomes 10 for the column that needed it.
So \(500\) is regrouped as \(4\) hundreds, \(9\) tens and \(10\) ones before you subtract.
When the borrow reaches a zero it cannot stop there, so it keeps moving left. Every zero it passes turns into a \(9\).
| Number | Regrouped as |
|---|---|
| \(500\) | \(4\) – \(9\) – \(10\) |
| \(1000\) | \(0\) – \(9\) – \(9\) – \(10\) |
| \(3000\) | \(2\) – \(9\) – \(9\) – \(10\) |
How to subtract across zeros
- Move the borrow left past each zero until you reach a digit that can give.
- Change that digit down by one, turn each zero passed into a \(9\), and make the last one \(10\).
- Subtract each column as usual.
\(500\) becomes \(4\), \(9\), \(10\).
| \(500 - 236\) | \(=\) | \(264\) |
\(1000\) becomes \(0\), \(9\), \(9\), \(10\).
| \(1000 - 457\) | \(=\) | \(543\) |
| \(3000 - 1234\) | \(=\) | \(1766\) |
Count back \(7\) from \(9000\).
| \(9000 - 7\) | \(=\) | \(8993\) |
Common pitfalls
Frequently asked questions
How do you subtract across zeros?
Borrow from the first non-zero digit to the left. Each zero passed becomes a \(9\) and the last becomes \(10\). \(500-236=264\).
Why does a zero become 9 when you borrow?
The borrow takes one from further left and passes it along. Each zero lends ten and keeps one less than ten, which is \(9\).
How do you work out 1000 minus a number?
Regroup \(1000\) as \(0\), \(9\), \(9\), \(10\) and subtract each column. For example \(1000-457=543\).
How can you check a subtraction?
Add your answer to the number you took away. If it gives the number you started with, the subtraction is correct.