Printable math worksheet for practicing decimal addition and subtraction with regrouping.
Worksheet titled "Add and Subtract Decimals with Regrouping" featuring nine decimal arithmetic problems, including addition and subtraction with regrouping, designed for educational practice.
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Step-by-step solution for: Add and Subtract Decimals with Regrouping: Vertical - Math ...
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Show Answer Key & Explanations
Step-by-step solution for: Add and Subtract Decimals with Regrouping: Vertical - Math ...
Let's solve each of the decimal addition and subtraction problems step by step, with regrouping where necessary.
---
```
1.5
+ 7.7
-----
9.2
```
Explanation:
Add the tenths: 5 + 7 = 12 → write down 2, carry over 1 to the ones place.
Add the ones: 1 + 7 = 8, plus the carried 1 = 9.
Result: 9.2
---
Align decimals:
```
13.90
+ 51.58
-------
65.48
```
Explanation:
Convert 13.9 to 13.90 for easier alignment.
Add hundredths: 0 + 8 = 8
Tenths: 9 + 5 = 14 → write 4, carry 1
Ones: 3 + 1 = 4, plus carry = 5
Tens: 1 + 5 = 6
Result: 65.48
---
Align decimals (add a zero):
```
49.680
- 28.689
--------
20.991
```
Explanation:
Borrow from the left when needed.
Start from right:
- 0 - 9 → can't do → borrow → 10 - 9 = 1, but next digit is 8 → becomes 7 after borrowing.
- 7 - 8 → can't → borrow → 17 - 8 = 9, previous becomes 5.
- 5 - 6 → can't → borrow → 15 - 6 = 9, previous becomes 8.
- 8 - 8 = 0
- 9 - 2 = 7? Wait — let's go step by step.
Actually, better:
```
49.680
- 28.689
--------
```
From right:
- 0 - 9 → borrow → 10 - 9 = 1, 8 becomes 7
- 7 - 8 → borrow → 17 - 8 = 9, 6 becomes 5
- 5 - 6 → borrow → 15 - 6 = 9, 9 becomes 8
- 8 - 8 = 0
- 4 - 2 = 2
Wait — tens: 4 (from 49) minus 2 (from 28) = 2
But we had 49.680 → 4 tens, 9 ones
After borrowing:
- Ones: 9 → became 8 after borrow
- So: 8 - 8 = 0
- Tens: 4 - 2 = 2
So result: 20.991
✔ Correct.
---
```
2.6
+ 5.7
-----
8.3
```
Explanation:
6 + 7 = 13 → write 3, carry 1
2 + 5 = 7, plus carry = 8
Result: 8.3
---
Align:
```
74.80
+ 10.57
-------
85.37
```
Explanation:
Hundredths: 0 + 7 = 7
Tenths: 8 + 5 = 13 → write 3, carry 1
Ones: 4 + 0 = 4, plus carry = 5
Tens: 7 + 1 = 8
Result: 85.37
---
```
36.831
- 29.266
--------
7.565
```
Step-by-step:
- Thousandths: 1 - 6 → borrow → 11 - 6 = 5, 3 becomes 2
- Hundredths: 2 - 6 → borrow → 12 - 6 = 6, 8 becomes 7
- Tenths: 7 - 2 = 5
- Ones: 6 - 9 → borrow → 16 - 9 = 7, 3 becomes 2
- Tens: 2 - 2 = 0
Wait: original number is 36.831 → so tens digit is 3, ones is 6
After borrowing:
- Ones: 6 → becomes 5 after borrow? Let's recheck:
Better:
```
36.831
-29.266
-------
```
Start from right:
- 1 - 6 → borrow → 11 - 6 = 5 → 3 becomes 2
- 2 - 6 → borrow → 12 - 6 = 6 → 8 becomes 7
- 7 - 2 = 5
- 6 - 9 → borrow → 16 - 9 = 7 → 3 becomes 2
- 2 - 2 = 0
So result: 7.565
✔ Yes.
---
```
1.49
+ 4.78
------
6.27
```
Explanation:
- 9 + 8 = 17 → write 7, carry 1
- 4 + 7 = 11, plus carry = 12 → write 2, carry 1
- 1 + 4 = 5, plus carry = 6
Result: 6.27
---
Align:
```
93.100
- 12.401
--------
80.699
```
Step-by-step:
- Thousandths: 0 - 1 → borrow → 10 - 1 = 9 → 0 becomes 9 after borrow?
Wait:
```
93.100
- 12.401
--------
```
Rightmost:
- 0 - 1 → borrow → 10 - 1 = 9 → 0 becomes 9 (but borrowed from left)
- But next digit is 0 → need to keep borrowing.
So:
- Thousandths: 0 - 1 → borrow → 10 - 1 = 9 → now 0 becomes 9, but it was already 0 → must go further.
Breakdown:
- Start from thousandths: 0 - 1 → can’t → borrow from hundredths
- But hundredths is 0 → so go to tenths: 1 → becomes 0, then hundredths gets 10
- Then hundredths gives 1 to thousandths → so thousandths becomes 10
- Now: 10 - 1 = 9
- Hundredths: now 9 (after giving 1), but subtract 0 → 9 - 0 = 9
- Tenths: 0 (after lending) - 4 → can’t → borrow from ones
- Ones: 3 → becomes 2, tenths get 10 → 10 - 4 = 6
- Ones: 2 - 2 = 0
- Tens: 9 - 1 = 8
Wait — original number: 93.100 → tens: 9, ones: 3
After:
- Tens: 9 - 1 = 8
- Ones: 3 → lent to tenths → becomes 2, then subtract 2 → 2 - 2 = 0
- Tenths: 1 → became 0, then got 10 → 10 - 4 = 6
- Hundredths: 0 → got 10, gave 1 → 9 - 0 = 9
- Thousandths: 10 - 1 = 9
So result: 80.699
✔ Correct.
---
```
41.933
- 27.958
--------
13.975
```
Step-by-step:
- Thousandths: 3 - 8 → borrow → 13 - 8 = 5 → 3 becomes 2
- Hundredths: 2 - 5 → borrow → 12 - 5 = 7 → 9 becomes 8
- Tenths: 8 - 9 → borrow → 18 - 9 = 9 → 1 becomes 0
- Ones: 0 - 7 → borrow → 10 - 7 = 3 → 4 becomes 3
- Tens: 3 - 2 = 1
Wait: original tens: 4 (from 41), ones: 1
After:
- Tens: 4 → becomes 3 after borrow
- Ones: 1 → becomes 10 after borrow, then 10 - 7 = 3? No — we are subtracting 7 from ones?
Wait: subtracting 27.958 → so ones digit is 7
But after borrowing:
- Ones: 1 → becomes 0 after lending to tenths
- Then we need to borrow from tens → tens: 4 → becomes 3
- Ones: 10 → then subtract 7 → 3
Tenths: 9 → became 8 after lending to hundredths → then 8 - 9 → need to borrow → 18 - 9 = 9
Hundredths: 3 → became 2 after lending → then 2 - 5 → borrow → 12 - 5 = 7
Thousandths: 3 - 8 → borrow → 13 - 8 = 5
So final:
- Tens: 3 - 2 = 1
- Ones: 3
- Tenths: 9
- Hundredths: 7
- Thousandths: 5
→ 13.975
✔ Correct.
---
```
1.57
+ 2.65
------
4.22
```
- 7 + 5 = 12 → write 2, carry 1
- 5 + 6 = 11, plus carry = 12 → write 2, carry 1
- 1 + 2 = 3, plus carry = 4
Result: 4.22
---
Align:
```
68.610
- 45.752
--------
22.858
```
Step-by-step:
- Thousandths: 0 - 2 → borrow → 10 - 2 = 8 → 1 becomes 0
- Hundredths: 0 - 5 → borrow → 10 - 5 = 5 → 6 becomes 5
- Tenths: 5 - 7 → borrow → 15 - 7 = 8 → 8 becomes 7
- Ones: 7 - 5 = 2 → wait: original ones: 8 → became 7 after borrow → 7 - 5 = 2
- Tens: 6 - 4 = 2
Wait:
- Original: 68.610 → tens: 6, ones: 8
- After borrowing:
- Tenths: 6 → became 5 after lending to hundredths
- But we need to subtract 7 in tenths → so 5 → borrow from ones
- Ones: 8 → becomes 7
- Tenths: 15 - 7 = 8
- Then hundredths: 1 → became 0 after lending → now 0 - 5 → borrow → 10 - 5 = 5 → 6 becomes 5
- Thousandths: 0 → became 10 → 10 - 2 = 8
So:
- Tens: 6 - 4 = 2
- Ones: 7 - 5 = 2
- Tenths: 8
- Hundredths: 5
- Thousandths: 8
→ 22.858
✔ Correct.
---
```
80.915
- 78.398
--------
2.517
```
Step-by-step:
- Thousandths: 5 - 8 → borrow → 15 - 8 = 7 → 1 becomes 0
- Hundredths: 0 - 9 → borrow → 10 - 9 = 1 → 9 becomes 8
- Tenths: 8 - 3 = 5
- Ones: 0 - 8 → can't → borrow from tens
- Tens: 8 → becomes 7, ones: 10 → 10 - 8 = 2
- Tens: 7 - 7 = 0
So:
- Tens: 0
- Ones: 2
- Tenths: 5
- Hundredths: 1
- Thousandths: 7
→ 2.517
✔ Correct.
---
## ✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1.5 + 7.7 | 9.2 |
| 13.9 + 51.58 | 65.48 |
| 49.68 - 28.689 | 20.991 |
| 2.6 + 5.7 | 8.3 |
| 74.8 + 10.57 | 85.37 |
| 36.831 - 29.266 | 7.565 |
| 1.49 + 4.78 | 6.27 |
| 93.10 - 12.401 | 80.699 |
| 41.933 - 27.958 | 13.975 |
| 1.57 + 2.65 | 4.22 |
| 68.61 - 45.752 | 22.858 |
| 80.915 - 78.398 | 2.517 |
---
Let me know if you'd like this formatted as a printable answer sheet!
---
1. 1.5 + 7.7
```
1.5
+ 7.7
-----
9.2
```
Explanation:
Add the tenths: 5 + 7 = 12 → write down 2, carry over 1 to the ones place.
Add the ones: 1 + 7 = 8, plus the carried 1 = 9.
Result: 9.2
---
2. 13.9 + 51.58
Align decimals:
```
13.90
+ 51.58
-------
65.48
```
Explanation:
Convert 13.9 to 13.90 for easier alignment.
Add hundredths: 0 + 8 = 8
Tenths: 9 + 5 = 14 → write 4, carry 1
Ones: 3 + 1 = 4, plus carry = 5
Tens: 1 + 5 = 6
Result: 65.48
---
3. 49.68 - 28.689
Align decimals (add a zero):
```
49.680
- 28.689
--------
20.991
```
Explanation:
Borrow from the left when needed.
Start from right:
- 0 - 9 → can't do → borrow → 10 - 9 = 1, but next digit is 8 → becomes 7 after borrowing.
- 7 - 8 → can't → borrow → 17 - 8 = 9, previous becomes 5.
- 5 - 6 → can't → borrow → 15 - 6 = 9, previous becomes 8.
- 8 - 8 = 0
- 9 - 2 = 7? Wait — let's go step by step.
Actually, better:
```
49.680
- 28.689
--------
```
From right:
- 0 - 9 → borrow → 10 - 9 = 1, 8 becomes 7
- 7 - 8 → borrow → 17 - 8 = 9, 6 becomes 5
- 5 - 6 → borrow → 15 - 6 = 9, 9 becomes 8
- 8 - 8 = 0
- 4 - 2 = 2
Wait — tens: 4 (from 49) minus 2 (from 28) = 2
But we had 49.680 → 4 tens, 9 ones
After borrowing:
- Ones: 9 → became 8 after borrow
- So: 8 - 8 = 0
- Tens: 4 - 2 = 2
So result: 20.991
✔ Correct.
---
4. 2.6 + 5.7
```
2.6
+ 5.7
-----
8.3
```
Explanation:
6 + 7 = 13 → write 3, carry 1
2 + 5 = 7, plus carry = 8
Result: 8.3
---
5. 74.8 + 10.57
Align:
```
74.80
+ 10.57
-------
85.37
```
Explanation:
Hundredths: 0 + 7 = 7
Tenths: 8 + 5 = 13 → write 3, carry 1
Ones: 4 + 0 = 4, plus carry = 5
Tens: 7 + 1 = 8
Result: 85.37
---
6. 36.831 - 29.266
```
36.831
- 29.266
--------
7.565
```
Step-by-step:
- Thousandths: 1 - 6 → borrow → 11 - 6 = 5, 3 becomes 2
- Hundredths: 2 - 6 → borrow → 12 - 6 = 6, 8 becomes 7
- Tenths: 7 - 2 = 5
- Ones: 6 - 9 → borrow → 16 - 9 = 7, 3 becomes 2
- Tens: 2 - 2 = 0
Wait: original number is 36.831 → so tens digit is 3, ones is 6
After borrowing:
- Ones: 6 → becomes 5 after borrow? Let's recheck:
Better:
```
36.831
-29.266
-------
```
Start from right:
- 1 - 6 → borrow → 11 - 6 = 5 → 3 becomes 2
- 2 - 6 → borrow → 12 - 6 = 6 → 8 becomes 7
- 7 - 2 = 5
- 6 - 9 → borrow → 16 - 9 = 7 → 3 becomes 2
- 2 - 2 = 0
So result: 7.565
✔ Yes.
---
7. 1.49 + 4.78
```
1.49
+ 4.78
------
6.27
```
Explanation:
- 9 + 8 = 17 → write 7, carry 1
- 4 + 7 = 11, plus carry = 12 → write 2, carry 1
- 1 + 4 = 5, plus carry = 6
Result: 6.27
---
8. 93.10 - 12.401
Align:
```
93.100
- 12.401
--------
80.699
```
Step-by-step:
- Thousandths: 0 - 1 → borrow → 10 - 1 = 9 → 0 becomes 9 after borrow?
Wait:
```
93.100
- 12.401
--------
```
Rightmost:
- 0 - 1 → borrow → 10 - 1 = 9 → 0 becomes 9 (but borrowed from left)
- But next digit is 0 → need to keep borrowing.
So:
- Thousandths: 0 - 1 → borrow → 10 - 1 = 9 → now 0 becomes 9, but it was already 0 → must go further.
Breakdown:
- Start from thousandths: 0 - 1 → can’t → borrow from hundredths
- But hundredths is 0 → so go to tenths: 1 → becomes 0, then hundredths gets 10
- Then hundredths gives 1 to thousandths → so thousandths becomes 10
- Now: 10 - 1 = 9
- Hundredths: now 9 (after giving 1), but subtract 0 → 9 - 0 = 9
- Tenths: 0 (after lending) - 4 → can’t → borrow from ones
- Ones: 3 → becomes 2, tenths get 10 → 10 - 4 = 6
- Ones: 2 - 2 = 0
- Tens: 9 - 1 = 8
Wait — original number: 93.100 → tens: 9, ones: 3
After:
- Tens: 9 - 1 = 8
- Ones: 3 → lent to tenths → becomes 2, then subtract 2 → 2 - 2 = 0
- Tenths: 1 → became 0, then got 10 → 10 - 4 = 6
- Hundredths: 0 → got 10, gave 1 → 9 - 0 = 9
- Thousandths: 10 - 1 = 9
So result: 80.699
✔ Correct.
---
9. 41.933 - 27.958
```
41.933
- 27.958
--------
13.975
```
Step-by-step:
- Thousandths: 3 - 8 → borrow → 13 - 8 = 5 → 3 becomes 2
- Hundredths: 2 - 5 → borrow → 12 - 5 = 7 → 9 becomes 8
- Tenths: 8 - 9 → borrow → 18 - 9 = 9 → 1 becomes 0
- Ones: 0 - 7 → borrow → 10 - 7 = 3 → 4 becomes 3
- Tens: 3 - 2 = 1
Wait: original tens: 4 (from 41), ones: 1
After:
- Tens: 4 → becomes 3 after borrow
- Ones: 1 → becomes 10 after borrow, then 10 - 7 = 3? No — we are subtracting 7 from ones?
Wait: subtracting 27.958 → so ones digit is 7
But after borrowing:
- Ones: 1 → becomes 0 after lending to tenths
- Then we need to borrow from tens → tens: 4 → becomes 3
- Ones: 10 → then subtract 7 → 3
Tenths: 9 → became 8 after lending to hundredths → then 8 - 9 → need to borrow → 18 - 9 = 9
Hundredths: 3 → became 2 after lending → then 2 - 5 → borrow → 12 - 5 = 7
Thousandths: 3 - 8 → borrow → 13 - 8 = 5
So final:
- Tens: 3 - 2 = 1
- Ones: 3
- Tenths: 9
- Hundredths: 7
- Thousandths: 5
→ 13.975
✔ Correct.
---
10. 1.57 + 2.65
```
1.57
+ 2.65
------
4.22
```
- 7 + 5 = 12 → write 2, carry 1
- 5 + 6 = 11, plus carry = 12 → write 2, carry 1
- 1 + 2 = 3, plus carry = 4
Result: 4.22
---
11. 68.61 - 45.752
Align:
```
68.610
- 45.752
--------
22.858
```
Step-by-step:
- Thousandths: 0 - 2 → borrow → 10 - 2 = 8 → 1 becomes 0
- Hundredths: 0 - 5 → borrow → 10 - 5 = 5 → 6 becomes 5
- Tenths: 5 - 7 → borrow → 15 - 7 = 8 → 8 becomes 7
- Ones: 7 - 5 = 2 → wait: original ones: 8 → became 7 after borrow → 7 - 5 = 2
- Tens: 6 - 4 = 2
Wait:
- Original: 68.610 → tens: 6, ones: 8
- After borrowing:
- Tenths: 6 → became 5 after lending to hundredths
- But we need to subtract 7 in tenths → so 5 → borrow from ones
- Ones: 8 → becomes 7
- Tenths: 15 - 7 = 8
- Then hundredths: 1 → became 0 after lending → now 0 - 5 → borrow → 10 - 5 = 5 → 6 becomes 5
- Thousandths: 0 → became 10 → 10 - 2 = 8
So:
- Tens: 6 - 4 = 2
- Ones: 7 - 5 = 2
- Tenths: 8
- Hundredths: 5
- Thousandths: 8
→ 22.858
✔ Correct.
---
12. 80.915 - 78.398
```
80.915
- 78.398
--------
2.517
```
Step-by-step:
- Thousandths: 5 - 8 → borrow → 15 - 8 = 7 → 1 becomes 0
- Hundredths: 0 - 9 → borrow → 10 - 9 = 1 → 9 becomes 8
- Tenths: 8 - 3 = 5
- Ones: 0 - 8 → can't → borrow from tens
- Tens: 8 → becomes 7, ones: 10 → 10 - 8 = 2
- Tens: 7 - 7 = 0
So:
- Tens: 0
- Ones: 2
- Tenths: 5
- Hundredths: 1
- Thousandths: 7
→ 2.517
✔ Correct.
---
## ✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1.5 + 7.7 | 9.2 |
| 13.9 + 51.58 | 65.48 |
| 49.68 - 28.689 | 20.991 |
| 2.6 + 5.7 | 8.3 |
| 74.8 + 10.57 | 85.37 |
| 36.831 - 29.266 | 7.565 |
| 1.49 + 4.78 | 6.27 |
| 93.10 - 12.401 | 80.699 |
| 41.933 - 27.958 | 13.975 |
| 1.57 + 2.65 | 4.22 |
| 68.61 - 45.752 | 22.858 |
| 80.915 - 78.398 | 2.517 |
---
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of adding subtracting decimals worksheet.