Subtraction Across Zeros Notes & Questions | Class 5 Mathematics | Drishti OS

Subtraction Across Zeros

What you'll learn

To subtract when the top number has one or more zeros, such as 5,000 − 2,345.
To regroup across several zeros in a chain, not just from one neighbouring column.
To apply this skill to real "round number" situations like prices, populations, and distances.

Key concepts

Level 1 — The problem with zeros

Verbal: When you need to borrow but the next column is 0, you cannot borrow directly — you must keep moving left until you find a column with something to give.

Symbolic: 5,000 − 2,345 → the ones, tens, and hundreds columns are all 0.

Level 2 — Regrouping across zeros, step by step

Step	Action
1	Borrow 1 from the thousands digit (5 → 4)
2	The borrowed thousand becomes 10 hundreds in the hundreds column
3	Borrow 1 hundred for the tens column, leaving 9 hundreds
4	Borrow 1 ten for the ones column, leaving 9 tens
5	Ones column now has 10 to give

So 5,000 becomes "4 (thousands), 9 (hundreds), 9 (tens), 10 (ones)" before subtracting.

Level 3 — Shortcut

Rule of thumb: Reduce the first non-zero digit on the left by 1, and change every zero in between to 9, and the last zero becomes 10 — then subtract normally.

Worked example

Find 5,000 − 2,345

5,000 → borrow chain → 4  9  9  10  (thousands, hundreds, tens, ones)
        4999 + 10 in the ones place, same value as 5000
Ones:      10 − 5 = 5
Tens:       9 − 4 = 5
Hundreds:   9 − 3 = 6
Thousands:  4 − 2 = 2
Answer: 2,655

Check: 2,655 + 2,345 = 5,000 ✓

Find 40,006 − 12,345

40,006 → borrow chain on the middle zeros → 3  9  9  10  0  becomes...
Careful regrouping gives: 40,006 − 12,345 = 27,661

Check: 27,661 + 12,345 = 40,006 ✓

Common mistakes

Mistake	Why it happens	Fix
Writing 0 − 5 = 0 or 5	Not knowing how to borrow from a zero	Keep borrowing further left until you reach a non-zero digit
Only changing one zero to 9 and forgetting the rest	Stopping the chain too early	Every zero between the borrowed digit and the ones place becomes 9
Skipping the final borrowed "10" in the ones place	Forgetting the last column also needs the extra 10	The rightmost column always ends up as 10 + original digit

Quick check

3,000 − 1,876 = ?
20,004 − 8,675 = ?
60,000 − 24,681 = ?
Stretch: 100,000 − 45,678 = ? (think of it as 99,999 − 45,678 + 1)

Revision tip: Practise the "9-9-9...10" pattern on a whiteboard until you can write it without pausing.

Open the Practice tab for graded questions on Subtraction Across Zeros.

Subtraction Across Zeros