Actually, I can’t solve the problem or explain the solution because
you haven’t uploaded any image — and even if you had, I currently cannot view or process images.
The text you pasted appears to be a
math worksheet titled “Subtraction by Partial Differences Method”, with 15 problems and their answers already filled in. It’s likely from abcteach.com (as shown by the watermark), and it’s designed to teach subtraction using the “partial differences” strategy — which involves breaking numbers into place values (hundreds, tens, ones) and subtracting each part separately before combining the results.
---
✔ What is the “Partial Differences Method”?
This is an alternative subtraction algorithm that avoids borrowing/regrouping. Instead, you:
1. Subtract each place value column *separately* (starting from left to right — hundreds, then tens, then ones).
2. Keep track of whether each partial difference is positive or negative.
3. Add all the partial differences together to get the final answer.
---
🔍 Example from the Worksheet: Problem #1
Problem:
682 – 281
Step-by-step using Partial Differences:
- Hundreds: 600 – 200 =
+400
- Tens: 80 – 80 =
0
- Ones: 2 – 1 =
+1
→ Total: 400 + 0 + 1 =
401 ✔
---
📌 Why This Method Is Useful
- Helps students understand place value deeply.
- Avoids confusion with borrowing.
- Encourages mental math and flexible thinking.
---
❗ Important Note About the Worksheet
Looking at the answers provided, some are
incorrect according to standard arithmetic — for example:
>
Problem #10: 423 – 311 = 111?
But 423 – 311 =
112, not 111.
(400–300=100, 20–10=10, 3–1=2 → 100+10+2=112)
Similarly,
Problem #15: 4548 – 386 = 4162?
Actual answer: 4548 – 386 =
4162 → That one is correct.
So while most answers are correct,
at least Problem #10 has a typo.
---
💡 How to Use This Worksheet
If you’re learning or teaching this method:
1. Cover the answers.
2. Solve each problem using partial differences.
3. Check your work against the key.
4. If you find discrepancies (like #10), discuss why — maybe it’s a teaching moment about checking your work!
---
✔ Final Answer Summary:
- The worksheet teaches subtraction via the
partial differences method.
- You subtract place values individually and sum the results.
- Most answers are correct, but
Problem #10 (423 – 311) should be 112, not 111.
- This method builds number sense and avoids regrouping.
Let me know if you’d like me to walk through any specific problem step by step!
Parent Tip: Review the logic above to help your child master the concept of partial differences worksheet.
