Partial Difference Subtraction (upper elem) Clip Art - Free Printable
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Step-by-step solution for: Partial Difference Subtraction (upper elem) Clip Art
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Show Answer Key & Explanations
Step-by-step solution for: Partial Difference Subtraction (upper elem) Clip Art
You’ve uploaded a worksheet titled “Subtraction: Partial Differences Method” from abcteach.com. The task is to solve the 15 subtraction problems using the Partial Differences Method.
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## ✔ What is the Partial Differences Method?
This is an alternative subtraction strategy that breaks numbers into their place values (hundreds, tens, ones) and subtracts each place value separately — without borrowing or regrouping. You then add up the partial differences to get the final answer.
> Important: If the top digit is smaller than the bottom digit in a column, you still subtract (top - bottom), which gives a *negative* partial difference. You’ll handle the negative number when adding all partial differences.
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## 🧮 Let’s Solve Each Problem Step-by-Step
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Break down by place value:
- Hundreds: 600 – 200 = 400
- Tens: 50 – 80 = –30
- Ones: 2 – 1 = +1
Add partial differences:
400 + (–30) + 1 = 371
✔ Answer: 371
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- Hundreds: 800 – 500 = 300
- Tens: 60 – 60 = 0
- Ones: 9 – 7 = +2
Total: 300 + 0 + 2 = 302
✔ Answer: 302
---
- Hundreds: 600 – 100 = 500
- Tens: 10 – 30 = –20
- Ones: 2 – 1 = +1
Total: 500 – 20 + 1 = 481
✔ Answer: 481
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- Hundreds: 300 – 100 = 200
- Tens: 60 – 50 = +10
- Ones: 8 – 6 = +2
Total: 200 + 10 + 2 = 212
✔ Answer: 212
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- Hundreds: 500 – 400 = 100
- Tens: 40 – 10 = +30
- Ones: 7 – 8 = –1
Total: 100 + 30 – 1 = 129
✔ Answer: 129
---
- Hundreds: 200 – 100 = 100
- Tens: 60 – 30 = +30
- Ones: 9 – 8 = +1
Total: 100 + 30 + 1 = 131
✔ Answer: 131
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- Hundreds: 300 – 200 = 100
- Tens: 20 – 80 = –60
- Ones: 6 – 4 = +2
Total: 100 – 60 + 2 = 42
✔ Answer: 42
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- Hundreds: 700 – 600 = 100
- Tens: 50 – 90 = –40
- Ones: 0 – 8 = –8
Total: 100 – 40 – 8 = 52
✔ Answer: 52
---
- Hundreds: 500 – 100 = 400
- Tens: 10 – 40 = –30
- Ones: 8 – 6 = +2
Total: 400 – 30 + 2 = 372
✔ Answer: 372
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- Hundreds: 400 – 300 = 100
- Tens: 20 – 10 = +10
- Ones: 3 – 2 = +1
Total: 100 + 10 + 1 = 111
✔ Answer: 111
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*(Now we have 4-digit numbers — same method!)*
- Thousands: 2000 – 1000 = 1000
- Hundreds: 400 – 200 = +200
- Tens: 60 – 0 = +60
- Ones: 3 – 9 = –6
Total: 1000 + 200 + 60 – 6 = 1254
✔ Answer: 1254
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- Thousands: 4000 – 1000 = 3000
- Hundreds: 700 – 500 = +200
- Tens: 40 – 60 = –20
- Ones: 8 – 2 = +6
Total: 3000 + 200 – 20 + 6 = 3186
✔ Answer: 3186
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- Thousands: 9000 – 1000 = 8000
- Hundreds: 800 – 600 = +200
- Tens: 40 – 30 = +10
- Ones: 2 – 7 = –5
Total: 8000 + 200 + 10 – 5 = 8205
✔ Answer: 8205
---
- Thousands: 7000 – 2000 = 5000
- Hundreds: 600 – 900 = –300
- Tens: 0 – 20 = –20
- Ones: 5 – 7 = –2
Total: 5000 – 300 – 20 – 2 = 4678
✔ Answer: 4678
---
*(Note: 336 is a 3-digit number — align it to the right!)*
Think of 336 as 0336 for alignment.
- Thousands: 4000 – 0 = 4000
- Hundreds: 500 – 300 = +200
- Tens: 40 – 30 = +10
- Ones: 8 – 6 = +2
Total: 4000 + 200 + 10 + 2 = 4212
✔ Answer: 4212
---
## 📋 Final Answers Summary:
1. 371
2. 302
3. 481
4. 212
5. 129
6. 131
7. 42
8. 52
9. 372
10. 111
11. 1254
12. 3186
13. 8205
14. 4678
15. 4212
---
## 💡 Why Use This Method?
- Helps students understand place value deeply.
- Avoids confusion with borrowing/regrouping.
- Encourages mental math and flexible thinking.
- Great for building number sense before moving to traditional algorithms.
---
Let me know if you’d like a printable version or visual diagrams for any problem! 😊
---
## ✔ What is the Partial Differences Method?
This is an alternative subtraction strategy that breaks numbers into their place values (hundreds, tens, ones) and subtracts each place value separately — without borrowing or regrouping. You then add up the partial differences to get the final answer.
> Important: If the top digit is smaller than the bottom digit in a column, you still subtract (top - bottom), which gives a *negative* partial difference. You’ll handle the negative number when adding all partial differences.
---
## 🧮 Let’s Solve Each Problem Step-by-Step
---
Problem 1: 652 – 281
Break down by place value:
- Hundreds: 600 – 200 = 400
- Tens: 50 – 80 = –30
- Ones: 2 – 1 = +1
Add partial differences:
400 + (–30) + 1 = 371
✔ Answer: 371
---
Problem 2: 869 – 567
- Hundreds: 800 – 500 = 300
- Tens: 60 – 60 = 0
- Ones: 9 – 7 = +2
Total: 300 + 0 + 2 = 302
✔ Answer: 302
---
Problem 3: 612 – 131
- Hundreds: 600 – 100 = 500
- Tens: 10 – 30 = –20
- Ones: 2 – 1 = +1
Total: 500 – 20 + 1 = 481
✔ Answer: 481
---
Problem 4: 368 – 156
- Hundreds: 300 – 100 = 200
- Tens: 60 – 50 = +10
- Ones: 8 – 6 = +2
Total: 200 + 10 + 2 = 212
✔ Answer: 212
---
Problem 5: 547 – 418
- Hundreds: 500 – 400 = 100
- Tens: 40 – 10 = +30
- Ones: 7 – 8 = –1
Total: 100 + 30 – 1 = 129
✔ Answer: 129
---
Problem 6: 269 – 138
- Hundreds: 200 – 100 = 100
- Tens: 60 – 30 = +30
- Ones: 9 – 8 = +1
Total: 100 + 30 + 1 = 131
✔ Answer: 131
---
Problem 7: 326 – 284
- Hundreds: 300 – 200 = 100
- Tens: 20 – 80 = –60
- Ones: 6 – 4 = +2
Total: 100 – 60 + 2 = 42
✔ Answer: 42
---
Problem 8: 750 – 698
- Hundreds: 700 – 600 = 100
- Tens: 50 – 90 = –40
- Ones: 0 – 8 = –8
Total: 100 – 40 – 8 = 52
✔ Answer: 52
---
Problem 9: 518 – 146
- Hundreds: 500 – 100 = 400
- Tens: 10 – 40 = –30
- Ones: 8 – 6 = +2
Total: 400 – 30 + 2 = 372
✔ Answer: 372
---
Problem 10: 423 – 312
- Hundreds: 400 – 300 = 100
- Tens: 20 – 10 = +10
- Ones: 3 – 2 = +1
Total: 100 + 10 + 1 = 111
✔ Answer: 111
---
Problem 11: 2463 – 1209
*(Now we have 4-digit numbers — same method!)*
- Thousands: 2000 – 1000 = 1000
- Hundreds: 400 – 200 = +200
- Tens: 60 – 0 = +60
- Ones: 3 – 9 = –6
Total: 1000 + 200 + 60 – 6 = 1254
✔ Answer: 1254
---
Problem 12: 4748 – 1562
- Thousands: 4000 – 1000 = 3000
- Hundreds: 700 – 500 = +200
- Tens: 40 – 60 = –20
- Ones: 8 – 2 = +6
Total: 3000 + 200 – 20 + 6 = 3186
✔ Answer: 3186
---
Problem 13: 9842 – 1637
- Thousands: 9000 – 1000 = 8000
- Hundreds: 800 – 600 = +200
- Tens: 40 – 30 = +10
- Ones: 2 – 7 = –5
Total: 8000 + 200 + 10 – 5 = 8205
✔ Answer: 8205
---
Problem 14: 7605 – 2927
- Thousands: 7000 – 2000 = 5000
- Hundreds: 600 – 900 = –300
- Tens: 0 – 20 = –20
- Ones: 5 – 7 = –2
Total: 5000 – 300 – 20 – 2 = 4678
✔ Answer: 4678
---
Problem 15: 4548 – 336
*(Note: 336 is a 3-digit number — align it to the right!)*
Think of 336 as 0336 for alignment.
- Thousands: 4000 – 0 = 4000
- Hundreds: 500 – 300 = +200
- Tens: 40 – 30 = +10
- Ones: 8 – 6 = +2
Total: 4000 + 200 + 10 + 2 = 4212
✔ Answer: 4212
---
## 📋 Final Answers Summary:
1. 371
2. 302
3. 481
4. 212
5. 129
6. 131
7. 42
8. 52
9. 372
10. 111
11. 1254
12. 3186
13. 8205
14. 4678
15. 4212
---
## 💡 Why Use This Method?
- Helps students understand place value deeply.
- Avoids confusion with borrowing/regrouping.
- Encourages mental math and flexible thinking.
- Great for building number sense before moving to traditional algorithms.
---
Let me know if you’d like a printable version or visual diagrams for any problem! 😊
Parent Tip: Review the logic above to help your child master the concept of partial differences worksheet.
