Math worksheet for practicing addition and subtraction with missing digits.
A math worksheet titled "Missing Digits: Addition and Subtraction" with five problems requiring students to fill in missing digits in addition and subtraction equations.
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Step-by-step solution for: Missing Digits: Addition and Subtraction | Interactive Worksheet ...
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Show Answer Key & Explanations
Step-by-step solution for: Missing Digits: Addition and Subtraction | Interactive Worksheet ...
Let’s solve each problem step by step. We’re looking for missing digits in addition and subtraction problems.
---
Problem 1:
```
2 □ 5 6
+ 2 □ 1
---------
□ 5 9 7
```
Start from the rightmost column (ones place):
- Ones: 6 + 1 = 7 → matches the answer’s ones digit (7) ✔
- Tens: 5 + □ = 9 → so □ must be 4 (because 5 + 4 = 9)
- Hundreds: □ + 2 = 5 → so □ must be 3 (because 3 + 2 = 5)
- Thousands: 2 + nothing = □ → but wait, we have a carry? Let’s check again.
Wait — let’s write it with columns labeled:
Thousands | Hundreds | Tens | Ones
2 | □ | 5 | 6
| 2 | □ | 1
----------------------------------
□ | 5 | 9 | 7
Ones: 6 + 1 = 7 → no carry → good.
Tens: 5 + □ = 9 → □ = 4 → no carry → good.
Hundreds: □ + 2 = 5 → □ = 3 → no carry → good.
Thousands: 2 + 0 = □ → so □ = 2? But the answer shows □597 — that means thousands digit is missing. Wait — if 2 + 0 = 2, then the top-left box should be 2? But look at the layout:
Actually, the first number is “2□56” — that’s four digits. Second number is “2□1” — that’s three digits, so aligned to the right. So:
2 A 5 6
+ 2 B 1
---------
C 5 9 7
We found:
B = 4 (tens place)
A = 3 (hundreds place)
C = ? (thousands place)
Now add:
Ones: 6+1=7
Tens: 5+4=9
Hundreds: A + 2 = 3 + 2 = 5 → correct
Thousands: 2 + 0 = 2 → so C = 2
But wait — the sum is written as “□597”, which implies the thousands digit is missing. So yes, C = 2.
So Problem 1 answers:
Top middle (hundreds of first number): 3
Middle tens (second number): 4
Sum thousands: 2
Check: 2356 + 241 = 2597 → YES! ✔️
---
Problem 2:
```
□ 8 6
- 3 4 □
---------
3 □ 9
```
This is subtraction. Start from ones place.
Ones: 6 - □ = 9 → Hmm, 6 minus something can’t be 9 unless we borrow.
So likely: we borrowed from tens place.
That means: 16 - □ = 9 → so □ = 7 (because 16 - 7 = 9)
So bottom-right box (ones of subtrahend) = 7
Now, since we borrowed 1 from tens place, the tens digit of minuend was originally 8, now becomes 7.
Tens place: 7 - 4 = □ → so □ = 3
So middle box of answer (tens place) = 3
Hundreds place: □ - 3 = 3 → so □ = 6
Check: 686 - 347 = ?
686 - 347:
Ones: 6 - 7 → borrow → 16 - 7 = 9
Tens: 7 (after borrow) - 4 = 3
Hundreds: 6 - 3 = 3 → 339 → matches!
So Problem 2 answers:
Top left (hundreds of minuend): 6
Bottom right (ones of subtrahend): 7
Answer middle (tens of difference): 3
---
Problem 3:
```
7 9 6
+ 3 □ □
---------
1 □ 8 0
```
Addition. Start from ones.
Ones: 6 + □ = 0 → must be 10 or 20 etc. Since max 6+9=15, so 6 + □ = 10 → □ = 4, and carry 1 to tens.
So bottom-right box (ones of second number) = 4
Tens: 9 + □ + 1 (carry) = 8 → so 9 + □ + 1 = 18? Because 8 is the digit, but might have carried over.
Wait: 9 + □ + 1 = ? → result ends in 8 → so total must be 18 → because 18 ends in 8, carry 1 to hundreds.
So: 9 + □ + 1 = 18 → □ = 8
So bottom-middle box (tens of second number) = 8
Now hundreds: 7 + 3 + 1 (carry from tens) = 11 → so write 1, carry 1 to thousands.
Answer is “1□80” → thousands digit is already given as 1, so the hundreds digit of answer is □ → which should be 1 (from 11).
Wait: 7 + 3 + 1 = 11 → so hundreds digit of sum is 1, and carry 1 to thousands → which makes the thousands digit 1 (already shown).
So the missing digit in the sum (hundreds place) is 1
Check: 796 + 384 = ?
796 + 384:
Ones: 6+4=10 → write 0, carry 1
Tens: 9+8+1=18 → write 8, carry 1
Hundreds: 7+3+1=11 → write 1, carry 1 → thousands: 1 → so 1180 → matches!
So Problem 3 answers:
Second number tens: 8
Second number ones: 4
Sum hundreds: 1
---
Problem 4:
```
3 7 2
- 5 □
-------
3 □ 6
```
Subtraction. Align properly:
3 7 2
- 5 A
-------
3 B 6
Ones: 2 - A = 6 → impossible without borrowing.
So borrow from tens: 12 - A = 6 → A = 6
So bottom box (ones of subtrahend) = 6
Now, tens place: originally 7, but we borrowed 1 → becomes 6.
Then: 6 - 5 = B → so B = 1
Hundreds: 3 - 0 = 3 → matches.
Check: 372 - 56 = 316 → yes! ✔️
So Problem 4 answers:
Bottom box (subtrahend ones): 6
Answer middle (difference tens): 1
---
Problem 5:
```
4 □ 5
+ 3 9 □
-------
□ 7 0
```
Addition.
Ones: 5 + □ = 0 → must be 10 → so □ = 5, carry 1
So bottom-right box (ones of second number) = 5
Tens: □ + 9 + 1 (carry) = 7 → so □ + 10 = 17? Because ends in 7 → so □ = 7
Wait: □ + 9 + 1 = ? → result ends in 7 → so total = 17 → so □ = 7
And carry 1 to hundreds.
So top-middle box (tens of first number) = 7
Hundreds: 4 + 3 + 1 (carry) = 8 → so answer thousands digit = 8
Check: 475 + 395 = ?
475 + 395:
Ones: 5+5=10 → write 0, carry 1
Tens: 7+9+1=17 → write 7, carry 1
Hundreds: 4+3+1=8 → so 870 → matches!
So Problem 5 answers:
First number tens: 7
Second number ones: 5
Sum thousands: 8
---
Final Answer:
1. Top middle: 3, Middle tens: 4, Sum thousands: 2 → Boxes: [3], [4], [2]
2. Top left: 6, Bottom right: 7, Answer middle: 3 → Boxes: [6], [7], [3]
3. Second number tens: 8, Second number ones: 4, Sum hundreds: 1 → Boxes: [8], [4], [1]
4. Bottom box: 6, Answer middle: 1 → Boxes: [6], [1]
5. First number tens: 7, Second number ones: 5, Sum thousands: 8 → Boxes: [7], [5], [8]
But since the question says “Place your answers in the boxes provided”, and there are 5 problems with multiple blanks, I’ll list all missing digits in order per problem.
Looking back at original image layout (even though I don’t describe it), typically each blank is numbered or positioned. But since user didn’t specify numbering, I’ll give answers per problem as they appear.
However, to match standard format, perhaps list all missing digits in sequence as they appear in the problems.
But safest: provide each problem’s missing digits clearly.
Since final answer should be concise, and assuming the student needs to fill in the boxes in order:
Problem 1 has 3 blanks: positions are:
- First number hundreds digit
- Second number tens digit
- Sum thousands digit → values: 3, 4, 2
Problem 2 has 3 blanks:
- Minuend hundreds
- Subtrahend ones
- Difference tens → 6, 7, 3
Problem 3 has 3 blanks:
- Addend tens
- Addend ones
- Sum hundreds → 8, 4, 1
Problem 4 has 2 blanks:
- Subtrahend ones
- Difference tens → 6, 1
Problem 5 has 3 blanks:
- First addend tens
- Second addend ones
- Sum thousands → 7, 5, 8
Total 14 blanks? But maybe the worksheet expects just listing them in order.
Alternatively, since it's a single response, I'll compile all missing digits in the order they appear in the problems, left to right, top to bottom.
But to avoid confusion, I’ll present the final answer as the filled-in numbers for each problem’s blanks.
Given the instruction: “Place your answers in the boxes provided.” — and since this is text-based, I’ll list the missing digits for each problem in the order the blanks appear.
Final Answer:
Problem 1: 3, 4, 2
Problem 2: 6, 7, 3
Problem 3: 8, 4, 1
Problem 4: 6, 1
Problem 5: 7, 5, 8
But to make it super clear for a student, perhaps write:
1. 3, 4, 2
2. 6, 7, 3
3. 8, 4, 1
4. 6, 1
5. 7, 5, 8
Yes.
──────────────────────────────────────
Final Answer:
1. 3, 4, 2
2. 6, 7, 3
3. 8, 4, 1
4. 6, 1
5. 7, 5, 8
---
Problem 1:
```
2 □ 5 6
+ 2 □ 1
---------
□ 5 9 7
```
Start from the rightmost column (ones place):
- Ones: 6 + 1 = 7 → matches the answer’s ones digit (7) ✔
- Tens: 5 + □ = 9 → so □ must be 4 (because 5 + 4 = 9)
- Hundreds: □ + 2 = 5 → so □ must be 3 (because 3 + 2 = 5)
- Thousands: 2 + nothing = □ → but wait, we have a carry? Let’s check again.
Wait — let’s write it with columns labeled:
Thousands | Hundreds | Tens | Ones
2 | □ | 5 | 6
| 2 | □ | 1
----------------------------------
□ | 5 | 9 | 7
Ones: 6 + 1 = 7 → no carry → good.
Tens: 5 + □ = 9 → □ = 4 → no carry → good.
Hundreds: □ + 2 = 5 → □ = 3 → no carry → good.
Thousands: 2 + 0 = □ → so □ = 2? But the answer shows □597 — that means thousands digit is missing. Wait — if 2 + 0 = 2, then the top-left box should be 2? But look at the layout:
Actually, the first number is “2□56” — that’s four digits. Second number is “2□1” — that’s three digits, so aligned to the right. So:
2 A 5 6
+ 2 B 1
---------
C 5 9 7
We found:
B = 4 (tens place)
A = 3 (hundreds place)
C = ? (thousands place)
Now add:
Ones: 6+1=7
Tens: 5+4=9
Hundreds: A + 2 = 3 + 2 = 5 → correct
Thousands: 2 + 0 = 2 → so C = 2
But wait — the sum is written as “□597”, which implies the thousands digit is missing. So yes, C = 2.
So Problem 1 answers:
Top middle (hundreds of first number): 3
Middle tens (second number): 4
Sum thousands: 2
Check: 2356 + 241 = 2597 → YES! ✔️
---
Problem 2:
```
□ 8 6
- 3 4 □
---------
3 □ 9
```
This is subtraction. Start from ones place.
Ones: 6 - □ = 9 → Hmm, 6 minus something can’t be 9 unless we borrow.
So likely: we borrowed from tens place.
That means: 16 - □ = 9 → so □ = 7 (because 16 - 7 = 9)
So bottom-right box (ones of subtrahend) = 7
Now, since we borrowed 1 from tens place, the tens digit of minuend was originally 8, now becomes 7.
Tens place: 7 - 4 = □ → so □ = 3
So middle box of answer (tens place) = 3
Hundreds place: □ - 3 = 3 → so □ = 6
Check: 686 - 347 = ?
686 - 347:
Ones: 6 - 7 → borrow → 16 - 7 = 9
Tens: 7 (after borrow) - 4 = 3
Hundreds: 6 - 3 = 3 → 339 → matches!
So Problem 2 answers:
Top left (hundreds of minuend): 6
Bottom right (ones of subtrahend): 7
Answer middle (tens of difference): 3
---
Problem 3:
```
7 9 6
+ 3 □ □
---------
1 □ 8 0
```
Addition. Start from ones.
Ones: 6 + □ = 0 → must be 10 or 20 etc. Since max 6+9=15, so 6 + □ = 10 → □ = 4, and carry 1 to tens.
So bottom-right box (ones of second number) = 4
Tens: 9 + □ + 1 (carry) = 8 → so 9 + □ + 1 = 18? Because 8 is the digit, but might have carried over.
Wait: 9 + □ + 1 = ? → result ends in 8 → so total must be 18 → because 18 ends in 8, carry 1 to hundreds.
So: 9 + □ + 1 = 18 → □ = 8
So bottom-middle box (tens of second number) = 8
Now hundreds: 7 + 3 + 1 (carry from tens) = 11 → so write 1, carry 1 to thousands.
Answer is “1□80” → thousands digit is already given as 1, so the hundreds digit of answer is □ → which should be 1 (from 11).
Wait: 7 + 3 + 1 = 11 → so hundreds digit of sum is 1, and carry 1 to thousands → which makes the thousands digit 1 (already shown).
So the missing digit in the sum (hundreds place) is 1
Check: 796 + 384 = ?
796 + 384:
Ones: 6+4=10 → write 0, carry 1
Tens: 9+8+1=18 → write 8, carry 1
Hundreds: 7+3+1=11 → write 1, carry 1 → thousands: 1 → so 1180 → matches!
So Problem 3 answers:
Second number tens: 8
Second number ones: 4
Sum hundreds: 1
---
Problem 4:
```
3 7 2
- 5 □
-------
3 □ 6
```
Subtraction. Align properly:
3 7 2
- 5 A
-------
3 B 6
Ones: 2 - A = 6 → impossible without borrowing.
So borrow from tens: 12 - A = 6 → A = 6
So bottom box (ones of subtrahend) = 6
Now, tens place: originally 7, but we borrowed 1 → becomes 6.
Then: 6 - 5 = B → so B = 1
Hundreds: 3 - 0 = 3 → matches.
Check: 372 - 56 = 316 → yes! ✔️
So Problem 4 answers:
Bottom box (subtrahend ones): 6
Answer middle (difference tens): 1
---
Problem 5:
```
4 □ 5
+ 3 9 □
-------
□ 7 0
```
Addition.
Ones: 5 + □ = 0 → must be 10 → so □ = 5, carry 1
So bottom-right box (ones of second number) = 5
Tens: □ + 9 + 1 (carry) = 7 → so □ + 10 = 17? Because ends in 7 → so □ = 7
Wait: □ + 9 + 1 = ? → result ends in 7 → so total = 17 → so □ = 7
And carry 1 to hundreds.
So top-middle box (tens of first number) = 7
Hundreds: 4 + 3 + 1 (carry) = 8 → so answer thousands digit = 8
Check: 475 + 395 = ?
475 + 395:
Ones: 5+5=10 → write 0, carry 1
Tens: 7+9+1=17 → write 7, carry 1
Hundreds: 4+3+1=8 → so 870 → matches!
So Problem 5 answers:
First number tens: 7
Second number ones: 5
Sum thousands: 8
---
Final Answer:
1. Top middle: 3, Middle tens: 4, Sum thousands: 2 → Boxes: [3], [4], [2]
2. Top left: 6, Bottom right: 7, Answer middle: 3 → Boxes: [6], [7], [3]
3. Second number tens: 8, Second number ones: 4, Sum hundreds: 1 → Boxes: [8], [4], [1]
4. Bottom box: 6, Answer middle: 1 → Boxes: [6], [1]
5. First number tens: 7, Second number ones: 5, Sum thousands: 8 → Boxes: [7], [5], [8]
But since the question says “Place your answers in the boxes provided”, and there are 5 problems with multiple blanks, I’ll list all missing digits in order per problem.
Looking back at original image layout (even though I don’t describe it), typically each blank is numbered or positioned. But since user didn’t specify numbering, I’ll give answers per problem as they appear.
However, to match standard format, perhaps list all missing digits in sequence as they appear in the problems.
But safest: provide each problem’s missing digits clearly.
Since final answer should be concise, and assuming the student needs to fill in the boxes in order:
Problem 1 has 3 blanks: positions are:
- First number hundreds digit
- Second number tens digit
- Sum thousands digit → values: 3, 4, 2
Problem 2 has 3 blanks:
- Minuend hundreds
- Subtrahend ones
- Difference tens → 6, 7, 3
Problem 3 has 3 blanks:
- Addend tens
- Addend ones
- Sum hundreds → 8, 4, 1
Problem 4 has 2 blanks:
- Subtrahend ones
- Difference tens → 6, 1
Problem 5 has 3 blanks:
- First addend tens
- Second addend ones
- Sum thousands → 7, 5, 8
Total 14 blanks? But maybe the worksheet expects just listing them in order.
Alternatively, since it's a single response, I'll compile all missing digits in the order they appear in the problems, left to right, top to bottom.
But to avoid confusion, I’ll present the final answer as the filled-in numbers for each problem’s blanks.
Given the instruction: “Place your answers in the boxes provided.” — and since this is text-based, I’ll list the missing digits for each problem in the order the blanks appear.
Final Answer:
Problem 1: 3, 4, 2
Problem 2: 6, 7, 3
Problem 3: 8, 4, 1
Problem 4: 6, 1
Problem 5: 7, 5, 8
But to make it super clear for a student, perhaps write:
1. 3, 4, 2
2. 6, 7, 3
3. 8, 4, 1
4. 6, 1
5. 7, 5, 8
Yes.
──────────────────────────────────────
Final Answer:
1. 3, 4, 2
2. 6, 7, 3
3. 8, 4, 1
4. 6, 1
5. 7, 5, 8
Parent Tip: Review the logic above to help your child master the concept of subtraction worksheet with missing digits.