Math worksheet for subtracting thousandths with regrouping, ideal for classroom or home learning.
A math worksheet titled "Subtract Thousandths less than 100 with Regrouping" featuring 12 subtraction problems involving decimal numbers, designed for educational practice.
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Step-by-step solution for: Subtract Thousandths less than 100 with Regrouping: Vertical ...
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Show Answer Key & Explanations
Step-by-step solution for: Subtract Thousandths less than 100 with Regrouping: Vertical ...
To solve these subtraction problems, we need to subtract the bottom number from the top number. Since these are decimals, it's important to line up the decimal points and make sure each place value (tenths, hundredths, thousandths) is aligned correctly. We’ll go one problem at a time.
---
Problem 1: 98.330 - 0.150
Align decimals:
```
98.330
- 0.150
--------
```
Subtract thousandths: 0 - 0 = 0
Hundredths: 3 - 5 → can’t do, borrow from tenths → 13 - 5 = 8
Tenths: after borrowing, 2 - 1 = 1
Ones: 8 - 0 = 8
Tens: 9 - 0 = 9
→ 98.180
---
Problem 2: 49.082 - 8.276
Align:
```
49.082
- 8.276
--------
```
Thousandths: 2 - 6 → borrow → 12 - 6 = 6
Hundredths: 7 (after borrow) - 7 = 0
Tenths: 9 (after borrow) - 2 = 7? Wait — let’s redo carefully.
Actually:
Start from right:
Thousandths: 2 < 6 → borrow from hundredths → but hundredths is 8 → becomes 7, thousandths becomes 12 → 12 - 6 = 6
Hundredths: 7 - 7 = 0
Tenths: 0 < 2 → borrow from ones → ones is 9 → becomes 8, tenths becomes 10 → 10 - 2 = 8
Ones: 8 - 8 = 0
Tens: 4 - 0 = 4
Wait — actually, 49.082 minus 8.276:
Let me write it with placeholders:
```
49.082
- 8.276
---------
```
From right:
Thousandths: 2 - 6 → borrow → 12 - 6 = 6 (hundredths digit was 8, now 7)
Hundredths: 7 - 7 = 0
Tenths: 0 - 2 → can't, so borrow from ones → ones is 9 → becomes 8, tenths becomes 10 → 10 - 2 = 8
Ones: 8 - 8 = 0
Tens: 4 - 0 = 4
So result: 40.806
Check: 40.806 + 8.276 = 49.082 → yes!
---
Problem 3: 83.593 - 54.458
```
83.593
- 54.458
--------
```
Thousandths: 3 - 8 → borrow → 13 - 8 = 5 (hundredths 9→8)
Hundredths: 8 - 5 = 3
Tenths: 5 - 4 = 1
Ones: 3 - 4 → can't → borrow from tens → 13 - 4 = 9 (tens 8→7)
Tens: 7 - 5 = 2
→ 29.135
Check: 29.135 + 54.458 = 83.593 → correct.
---
Problem 4: 87.230 - 0.160
```
87.230
- 0.160
--------
```
Thousandths: 0 - 0 = 0
Hundredths: 3 - 6 → borrow → 13 - 6 = 7 (tenths 2→1)
Tenths: 1 - 1 = 0
Ones: 7 - 0 = 7
Tens: 8 - 0 = 8
→ 87.070
---
Problem 5: 60.024 - 8.317
```
60.024
- 8.317
--------
```
Thousandths: 4 - 7 → borrow → 14 - 7 = 7 (hundredths 2→1)
Hundredths: 1 - 1 = 0
Tenths: 0 - 3 → can't → borrow from ones → ones is 0 → can't → borrow from tens → tens 6→5, ones become 10, then borrow for tenths → ones 10→9, tenths become 10 → 10 - 3 = 7
Ones: 9 - 8 = 1
Tens: 5 - 0 = 5
→ 51.707
Check: 51.707 + 8.317 = 60.024 → yes.
---
Problem 6: 93.693 - 56.458
```
93.693
- 56.458
--------
```
Thousandths: 3 - 8 → borrow → 13 - 8 = 5 (hundredths 9→8)
Hundredths: 8 - 5 = 3
Tenths: 6 - 4 = 2
Ones: 3 - 6 → borrow → 13 - 6 = 7 (tens 9→8)
Tens: 8 - 5 = 3
→ 37.235
Check: 37.235 + 56.458 = 93.693 → correct.
---
Problem 7: 15.949 - 0.995
```
15.949
- 0.995
--------
```
Thousandths: 9 - 5 = 4
Hundredths: 4 - 9 → borrow → 14 - 9 = 5 (tenths 9→8)
Tenths: 8 - 9 → borrow → 18 - 9 = 9 (ones 5→4)
Ones: 4 - 0 = 4
Tens: 1 - 0 = 1
→ 14.954
Check: 14.954 + 0.995 = 15.949 → yes.
---
Problem 8: 44.295 - 6.609
```
44.295
- 6.609
--------
```
Thousandths: 5 - 9 → borrow → 15 - 9 = 6 (hundredths 9→8)
Hundredths: 8 - 0 = 8
Tenths: 2 - 6 → borrow → 12 - 6 = 6 (ones 4→3)
Ones: 3 - 6 → borrow → 13 - 6 = 7 (tens 4→3)
Tens: 3 - 0 = 3
→ 37.686
Check: 37.686 + 6.609 = 44.295 → yes.
---
Problem 9: 71.900 - 68.402
```
71.900
- 68.402
--------
```
Thousandths: 0 - 2 → borrow → 10 - 2 = 8 (hundredths 0→9, but wait — hundredths is 0, so need to borrow from tenths)
Better step-by-step:
Thousandths: 0 - 2 → borrow from hundredths → but hundredths is 0 → borrow from tenths → tenths is 9 → becomes 8, hundredths becomes 10, then borrow for thousandths → hundredths 10→9, thousandths becomes 10 → 10 - 2 = 8
Hundredths: 9 - 0 = 9
Tenths: 8 - 4 = 4
Ones: 1 - 8 → can't → borrow from tens → 11 - 8 = 3 (tens 7→6)
Tens: 6 - 6 = 0
→ 3.498
Check: 3.498 + 68.402 = 71.900 → yes.
---
Problem 10: 47.193 - 6.466
```
47.193
- 6.466
--------
```
Thousandths: 3 - 6 → borrow → 13 - 6 = 7 (hundredths 9→8)
Hundredths: 8 - 6 = 2
Tenths: 1 - 4 → borrow → 11 - 4 = 7 (ones 7→6)
Ones: 6 - 6 = 0
Tens: 4 - 0 = 4
→ 40.727
Check: 40.727 + 6.466 = 47.193 → yes.
---
Problem 11: 70.073 - 1.866
```
70.073
- 1.866
--------
```
Thousandths: 3 - 6 → borrow → 13 - 6 = 7 (hundredths 7→6)
Hundredths: 6 - 6 = 0
Tenths: 0 - 8 → can't → borrow from ones → ones is 0 → borrow from tens → tens 7→6, ones become 10, then borrow for tenths → ones 10→9, tenths become 10 → 10 - 8 = 2
Ones: 9 - 1 = 8
Tens: 6 - 0 = 6
→ 68.207
Check: 68.207 + 1.866 = 70.073 → yes.
---
Problem 12: 93.920 - 45.678
```
93.920
- 45.678
--------
```
Thousandths: 0 - 8 → borrow → 10 - 8 = 2 (hundredths 2→1)
Hundredths: 1 - 7 → borrow → 11 - 7 = 4 (tenths 9→8)
Tenths: 8 - 6 = 2
Ones: 3 - 5 → borrow → 13 - 5 = 8 (tens 9→8)
Tens: 8 - 4 = 4
→ 48.242
Check: 48.242 + 45.678 = 93.920 → yes.
---
Final Answers:
1. 98.180
2. 40.806
3. 29.135
4. 87.070
5. 51.707
6. 37.235
7. 14.954
8. 37.686
9. 3.498
10. 40.727
11. 68.207
12. 48.242
Final Answer:
[98.180, 40.806, 29.135, 87.070, 51.707, 37.235, 14.954, 37.686, 3.498, 40.727, 68.207, 48.242]
---
Problem 1: 98.330 - 0.150
Align decimals:
```
98.330
- 0.150
--------
```
Subtract thousandths: 0 - 0 = 0
Hundredths: 3 - 5 → can’t do, borrow from tenths → 13 - 5 = 8
Tenths: after borrowing, 2 - 1 = 1
Ones: 8 - 0 = 8
Tens: 9 - 0 = 9
→ 98.180
---
Problem 2: 49.082 - 8.276
Align:
```
49.082
- 8.276
--------
```
Thousandths: 2 - 6 → borrow → 12 - 6 = 6
Hundredths: 7 (after borrow) - 7 = 0
Tenths: 9 (after borrow) - 2 = 7? Wait — let’s redo carefully.
Actually:
Start from right:
Thousandths: 2 < 6 → borrow from hundredths → but hundredths is 8 → becomes 7, thousandths becomes 12 → 12 - 6 = 6
Hundredths: 7 - 7 = 0
Tenths: 0 < 2 → borrow from ones → ones is 9 → becomes 8, tenths becomes 10 → 10 - 2 = 8
Ones: 8 - 8 = 0
Tens: 4 - 0 = 4
Wait — actually, 49.082 minus 8.276:
Let me write it with placeholders:
```
49.082
- 8.276
---------
```
From right:
Thousandths: 2 - 6 → borrow → 12 - 6 = 6 (hundredths digit was 8, now 7)
Hundredths: 7 - 7 = 0
Tenths: 0 - 2 → can't, so borrow from ones → ones is 9 → becomes 8, tenths becomes 10 → 10 - 2 = 8
Ones: 8 - 8 = 0
Tens: 4 - 0 = 4
So result: 40.806
Check: 40.806 + 8.276 = 49.082 → yes!
---
Problem 3: 83.593 - 54.458
```
83.593
- 54.458
--------
```
Thousandths: 3 - 8 → borrow → 13 - 8 = 5 (hundredths 9→8)
Hundredths: 8 - 5 = 3
Tenths: 5 - 4 = 1
Ones: 3 - 4 → can't → borrow from tens → 13 - 4 = 9 (tens 8→7)
Tens: 7 - 5 = 2
→ 29.135
Check: 29.135 + 54.458 = 83.593 → correct.
---
Problem 4: 87.230 - 0.160
```
87.230
- 0.160
--------
```
Thousandths: 0 - 0 = 0
Hundredths: 3 - 6 → borrow → 13 - 6 = 7 (tenths 2→1)
Tenths: 1 - 1 = 0
Ones: 7 - 0 = 7
Tens: 8 - 0 = 8
→ 87.070
---
Problem 5: 60.024 - 8.317
```
60.024
- 8.317
--------
```
Thousandths: 4 - 7 → borrow → 14 - 7 = 7 (hundredths 2→1)
Hundredths: 1 - 1 = 0
Tenths: 0 - 3 → can't → borrow from ones → ones is 0 → can't → borrow from tens → tens 6→5, ones become 10, then borrow for tenths → ones 10→9, tenths become 10 → 10 - 3 = 7
Ones: 9 - 8 = 1
Tens: 5 - 0 = 5
→ 51.707
Check: 51.707 + 8.317 = 60.024 → yes.
---
Problem 6: 93.693 - 56.458
```
93.693
- 56.458
--------
```
Thousandths: 3 - 8 → borrow → 13 - 8 = 5 (hundredths 9→8)
Hundredths: 8 - 5 = 3
Tenths: 6 - 4 = 2
Ones: 3 - 6 → borrow → 13 - 6 = 7 (tens 9→8)
Tens: 8 - 5 = 3
→ 37.235
Check: 37.235 + 56.458 = 93.693 → correct.
---
Problem 7: 15.949 - 0.995
```
15.949
- 0.995
--------
```
Thousandths: 9 - 5 = 4
Hundredths: 4 - 9 → borrow → 14 - 9 = 5 (tenths 9→8)
Tenths: 8 - 9 → borrow → 18 - 9 = 9 (ones 5→4)
Ones: 4 - 0 = 4
Tens: 1 - 0 = 1
→ 14.954
Check: 14.954 + 0.995 = 15.949 → yes.
---
Problem 8: 44.295 - 6.609
```
44.295
- 6.609
--------
```
Thousandths: 5 - 9 → borrow → 15 - 9 = 6 (hundredths 9→8)
Hundredths: 8 - 0 = 8
Tenths: 2 - 6 → borrow → 12 - 6 = 6 (ones 4→3)
Ones: 3 - 6 → borrow → 13 - 6 = 7 (tens 4→3)
Tens: 3 - 0 = 3
→ 37.686
Check: 37.686 + 6.609 = 44.295 → yes.
---
Problem 9: 71.900 - 68.402
```
71.900
- 68.402
--------
```
Thousandths: 0 - 2 → borrow → 10 - 2 = 8 (hundredths 0→9, but wait — hundredths is 0, so need to borrow from tenths)
Better step-by-step:
Thousandths: 0 - 2 → borrow from hundredths → but hundredths is 0 → borrow from tenths → tenths is 9 → becomes 8, hundredths becomes 10, then borrow for thousandths → hundredths 10→9, thousandths becomes 10 → 10 - 2 = 8
Hundredths: 9 - 0 = 9
Tenths: 8 - 4 = 4
Ones: 1 - 8 → can't → borrow from tens → 11 - 8 = 3 (tens 7→6)
Tens: 6 - 6 = 0
→ 3.498
Check: 3.498 + 68.402 = 71.900 → yes.
---
Problem 10: 47.193 - 6.466
```
47.193
- 6.466
--------
```
Thousandths: 3 - 6 → borrow → 13 - 6 = 7 (hundredths 9→8)
Hundredths: 8 - 6 = 2
Tenths: 1 - 4 → borrow → 11 - 4 = 7 (ones 7→6)
Ones: 6 - 6 = 0
Tens: 4 - 0 = 4
→ 40.727
Check: 40.727 + 6.466 = 47.193 → yes.
---
Problem 11: 70.073 - 1.866
```
70.073
- 1.866
--------
```
Thousandths: 3 - 6 → borrow → 13 - 6 = 7 (hundredths 7→6)
Hundredths: 6 - 6 = 0
Tenths: 0 - 8 → can't → borrow from ones → ones is 0 → borrow from tens → tens 7→6, ones become 10, then borrow for tenths → ones 10→9, tenths become 10 → 10 - 8 = 2
Ones: 9 - 1 = 8
Tens: 6 - 0 = 6
→ 68.207
Check: 68.207 + 1.866 = 70.073 → yes.
---
Problem 12: 93.920 - 45.678
```
93.920
- 45.678
--------
```
Thousandths: 0 - 8 → borrow → 10 - 8 = 2 (hundredths 2→1)
Hundredths: 1 - 7 → borrow → 11 - 7 = 4 (tenths 9→8)
Tenths: 8 - 6 = 2
Ones: 3 - 5 → borrow → 13 - 5 = 8 (tens 9→8)
Tens: 8 - 4 = 4
→ 48.242
Check: 48.242 + 45.678 = 93.920 → yes.
---
Final Answers:
1. 98.180
2. 40.806
3. 29.135
4. 87.070
5. 51.707
6. 37.235
7. 14.954
8. 37.686
9. 3.498
10. 40.727
11. 68.207
12. 48.242
Final Answer:
[98.180, 40.806, 29.135, 87.070, 51.707, 37.235, 14.954, 37.686, 3.498, 40.727, 68.207, 48.242]
Parent Tip: Review the logic above to help your child master the concept of subtraction worksheet with thousands.