Subtraction Across Zeros (A) math worksheet featuring problems that require borrowing across zeros.

You've uploaded a worksheet titled “Subtraction Across Zeros (A)”, which contains 25 subtraction problems where the minuend (top number) often contains one or more zeros — making borrowing across multiple place values necessary. This is a common and important skill in elementary arithmetic.

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## ✔ GOAL:
Calculate each difference (i.e., solve each subtraction problem).

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## 🧠 STRATEGY FOR “SUBTRACTION ACROSS ZEROS”:

When subtracting and you encounter a zero in the minuend that needs to borrow, you must “borrow across zeros.” Here’s how:

1. Look at the rightmost digit.
2. If the top digit is smaller than the bottom digit, borrow from the left.
3. If the digit to the left is 0, keep moving left until you find a non-zero digit.
4. Borrow 1 from that digit, turning it into one less, and each zero you passed becomes 9 — except the last one, which becomes 10.
5. Then proceed with subtraction.

> Example:
> `70008`
> `-46275`
> → You need to borrow from the 7 (ten-thousands place). The 7 becomes 6, and the three zeros become 9s, and the last 8 becomes 18.
> So: 6 9 9 9 18
> Now subtract normally.

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## ✏️ SOLUTIONS (with step-by-step for first few, then all answers)

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🔹 Problem 1:

70008 – 46275

```
70008
– 46275
-------
```

→ Borrow across zeros:
7 becomes 6, next three digits become 9, last digit becomes 18.

```
6 9 9 9 18
– 4 6 2 7 5
------------
2 3 7 3 3
```

✔ Answer: 23733

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🔹 Problem 2:

90008 – 81632

Borrow: 9 → 8, next three digits become 9, last digit 8 → 18

```
8 9 9 9 18
– 8 1 6 3 2
------------
0 8 3 7 6 → 8376
```

✔ Answer: 8376

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🔹 Problem 3:

40005 – 21610

Borrow: 4 → 3, next three digits become 9, last digit 5 → 15

```
3 9 9 9 15
– 2 1 6 1 0
------------
1 8 3 9 5
```

✔ Answer: 18395

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🔹 Problem 4:

30004 – 23037

Borrow: 3 → 2, next three digits become 9, last digit 4 → 14

```
2 9 9 9 14
– 2 3 0 3 7
------------
0 6 9 6 7 → 6967
```

✔ Answer: 6967

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🔹 Problem 5:

80007 – 60271

Borrow: 8 → 7, next three digits become 9, last digit 7 → 17

```
7 9 9 9 17
– 6 0 2 7 1
------------
1 9 7 3 6
```

✔ Answer: 19736

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## ✔ ALL ANSWERS (in order):

Here are the solutions for all 25 problems:

1. 70008 – 46275 = 23733
2. 90008 – 81632 = 8376
3. 40005 – 21610 = 18395
4. 30004 – 23037 = 6967
5. 80007 – 60271 = 19736

6. 50004 – 21677 = 28327
7. 70002 – 46573 = 23429
8. 80006 – 62264 = 17742
9. 30004 – 21840 = 8164
10. 60005 – 46144 = 13861

11. 40001 – 18330 = 21671
12. 20006 – 16001 = 4005
13. 40003 – 19291 = 20712
14. 80004 – 24789 = 55215
15. 30000 – 13608 = 16392

16. 80008 – 14484 = 65524
17. 80000 – 56696 = 23304
18. 70008 – 42826 = 27182
19. 70001 – 49175 = 20826
20. 60001 – 55516 = 4485

21. 80000 – 74646 = 5354
22. 50001 – 32645 = 17356
23. 80005 – 58407 = 21598
24. 20003 – 19416 = 587
25. 70000 – 40101 = 29899

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## 📝 FINAL NOTES:

- These problems reinforce regrouping (borrowing) across multiple zeros — a critical skill before moving to larger numbers or decimals.
- Always double-check your borrowing steps — it’s easy to miscount when crossing several zeros.
- Encourage students to write out the borrowed form (like 6 9 9 9 18) if needed for clarity.

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✔ All problems solved! Let me know if you’d like a printable answer key or step-by-step breakdowns for any specific problem.