Add Two 4-Digit Numbers with Regrouping: Missing Digits - Practice worksheet for math skills.

Let’s solve each problem step by step. We’re adding two 4-digit numbers, and some digits are missing. We’ll use regrouping (carrying) when needed.

---

Problem 1:
```
40□9
+ 2□19
------
637□
```

Start from the right (ones place):

- Ones: 9 + 9 = 18 → write 8, carry 1
→ So last digit of answer is 8

Tens place: □ + 1 + 1 (carry) = 7
→ □ + 2 = 7 → □ = 5

Hundreds place: 0 + □ = 3? Wait — we might have a carry from tens? No, tens was 5+1+1=7, no carry to hundreds.

Wait — let’s recheck:

Actually, in tens place: first number has □, second has 1, plus carry 1 → total = 7
So: □ + 1 + 1 = 7 → □ = 5 → correct.

Now hundreds: 0 (from top) + □ (bottom) = 3? But wait — look at the sum: 6378

Top: 40□9 → so hundreds digit is □? Wait no — let's label positions:

Number 1: thousands=4, hundreds=0, tens=□, ones=9
Number 2: thousands=2, hundreds=□, tens=1, ones=9
Sum: thousands=6, hundreds=3, tens=7, ones=8

Ones: 9+9=18 → write 8, carry 1 ✔️
Tens: □ + 1 + 1 = 7 → □ = 5 ✔️
Hundreds: 0 + □ = 3? But 0 + ? = 3 → must be 3? But wait — is there a carry from tens? Tens gave us 7, which is less than 10 → no carry to hundreds.

So hundreds: 0 + □ = 3 → □ = 3

Thousands: 4 + 2 = 6 ✔️

So missing digits:
First number tens: 5
Second number hundreds: 3
Answer ones: 8

Check: 4059 + 2319 = ?

4059
+2319
= 6378 ✔️

✔ Problem 1 solved: missing digits are 5, 3, 8

---

Problem 2:
```
5□49
+ 10□2
------
676□
```

Ones: 9 + 2 = 11 → write 1, carry 1

Tens: 4 + □ + 1 = 6 → 5 + □ = 6 → □ = 1

Hundreds: □ + 0 = 7? Wait — check:

Top: 5□49 → hundreds digit is □
Bottom: 10□2 → hundreds digit is 0? Wait — 10□2 means thousands=1, hundreds=0, tens=□, ones=2

Sum: 676□

Ones: 9+2=11 → write 1, carry 1 → so answer ends with 1

Tens: 4 + □ + 1 = 6 → □ + 5 = 6 → □ = 1

Hundreds: □ (top) + 0 (bottom) = 7? But wait — did we get a carry from tens? Tens: 4+1+1=6 → no carry → so □ + 0 = 7 → □ = 7

Thousands: 5 + 1 = 6 ✔️

Check: 5749 + 1012 = ?

5749
+1012
= 6761 ✔️

Missing digits: top hundreds=7, bottom tens=1, answer ones=1

✔ Problem 2: 7, 1, 1

---

Problem 3:
```
421□
+ 36□5
------
7□30
```

Ones: □ + 5 = 0 or 10? Since result ends in 0 → must be 10 → so □ = 5, carry 1

Tens: 1 + □ + 1 = 3 → 2 + □ = 3 → □ = 1

Hundreds: 2 + 6 = 8? But sum shows □ in hundreds place → wait, sum is 7□30 → thousands=7, hundreds=?, tens=3, ones=0

We have:

Ones: □ + 5 = 10 → □ = 5, carry 1 ✔️
Tens: 1 + □ + 1 = 3 → □ = 1 ✔️
Hundreds: 2 + 6 = 8 → but sum has □ here → should be 8? But wait — is there a carry from tens? Tens: 1+1+1=3 → no carry → so hundreds = 2+6=8

But sum is 7□30 → so hundreds digit is 8? Then thousands: 4+3=7 ✔️

So sum is 7830

Check: 4215 + 3615 = ?

4215
+3615
= 7830 ✔️

Missing digits: top ones=5, bottom tens=1, sum hundreds=8

✔ Problem 3: 5, 1, 8

---

Problem 4:
```
306□
+ □435
------
9□00
```

Ones: □ + 5 = 0 or 10? Ends in 0 → must be 10 → □ = 5, carry 1

Tens: 6 + 3 + 1 = 10 → write 0, carry 1 ✔️ matches sum tens=0

Hundreds: 0 + 4 + 1 = 5 → but sum has □ in hundreds → should be 5? Sum is 9□00 → so hundreds digit is 5?

Thousands: 3 + □ = 9? But we may have carry from hundreds.

Hundreds: 0 + 4 + 1 (carry from tens) = 5 → no carry to thousands? 5 < 10 → no carry

Then thousands: 3 + □ = 9 → □ = 6

Check: 3065 + 6435 = ?

3065
+6435
= 9500 ✔️

Sum is 9500 → so hundreds digit is 5

Missing digits: top ones=5, bottom thousands=6, sum hundreds=5

✔ Problem 4: 5, 6, 5

---

Problem 5:
```
□457
+ 2□44
------
46□1
```

Ones: 7 + 4 = 11 → write 1, carry 1 ✔️ matches sum ones=1

Tens: 5 + 4 + 1 = 10 → write 0, carry 1 → so sum tens digit is 0? But sum is 46□1 → tens is □ → so □ = 0

Hundreds: 4 + □ + 1 = 6 → 5 + □ = 6 → □ = 1

Thousands: □ + 2 = 4? But we had carry from hundreds? Hundreds: 4+1+1=6 → no carry → so □ + 2 = 4 → □ = 2

Check: 2457 + 2144 = ?

2457
+2144
= 4601 ✔️

Missing digits: top thousands=2, bottom hundreds=1, sum tens=0

✔ Problem 5: 2, 1, 0

---

Problem 6:
```
□297
+ 2□79
------
74□6
```

Ones: 7 + 9 = 16 → write 6, carry 1 ✔️

Tens: 9 + 7 + 1 = 17 → write 7, carry 1 → but sum tens is □ → should be 7? Sum is 74□6 → tens digit is □ → so □ = 7

Hundreds: 2 + □ + 1 = 4 → 3 + □ = 4 → □ = 1

Thousands: □ + 2 = 7? But we had carry from hundreds? Hundreds: 2+1+1=4 → no carry → so □ + 2 = 7 → □ = 5

Check: 5297 + 2179 = ?

5297
+2179
= 7476 ✔️

Missing digits: top thousands=5, bottom hundreds=1, sum tens=7

✔ Problem 6: 5, 1, 7

---

Problem 7:
```
1□98
+ 48□5
------
618□
```

Ones: 8 + 5 = 13 → write 3, carry 1 → so answer ends with 3

Tens: 9 + □ + 1 = 8? That can’t be — 9 + something +1 = 8? Must be 18 → because 9+□+1 ≥ 10 → so write 8, carry 1

So: 9 + □ + 1 = 18 → □ + 10 = 18 → □ = 8

Hundreds: □ + 8 + 1 = 1? Again, probably 11 → write 1, carry 1

So: □ + 8 + 1 = 11 → □ + 9 = 11 → □ = 2

Thousands: 1 + 4 + 1 = 6 ✔️

Check: 1298 + 4885 = ?

1298
+4885
= 6183 ✔️

Missing digits: top hundreds=2, bottom tens=8, answer ones=3

✔ Problem 7: 2, 8, 3

---

Problem 8:
```
27□8
+ □595
------
6□93
```

Ones: 8 + 5 = 13 → write 3, carry 1 ✔️

Tens: □ + 9 + 1 = 9? → □ + 10 = 9? Impossible → must be 19 → write 9, carry 1

So: □ + 9 + 1 = 19 → □ + 10 = 19 → □ = 9

Hundreds: 7 + 5 + 1 = 13 → write 3, carry 1 → but sum hundreds is □ → should be 3? Sum is 6□93 → hundreds digit is □ → so □ = 3

Thousands: 2 + □ + 1 = 6 → 3 + □ = 6 → □ = 3

Check: 2798 + 3595 = ?

2798
+3595
= 6393 ✔️

Missing digits: top tens=9, bottom thousands=3, sum hundreds=3

✔ Problem 8: 9, 3, 3

---

Problem 9:
```
□488
+ 17□3
------
428□
```

Ones: 8 + 3 = 11 → write 1, carry 1 → so answer ends with 1

Tens: 8 + □ + 1 = 8 → 9 + □ = 8? Impossible → must be 18 → write 8, carry 1

So: 8 + □ + 1 = 18 → □ + 9 = 18 → □ = 9

Hundreds: 4 + 7 + 1 = 12 → write 2, carry 1 ✔️ matches sum hundreds=2

Thousands: □ + 1 + 1 = 4 → □ + 2 = 4 → □ = 2

Check: 2488 + 1793 = ?

2488
+1793
= 4281 ✔️

Missing digits: top thousands=2, bottom tens=9, answer ones=1

✔ Problem 9: 2, 9, 1

---

Now, compiling all answers in order as they appear on the worksheet (left to right, top to bottom):

Row 1:
1. 40□9 + 2□19 = 637□ → missing: 5, 3, 8
2. 5□49 + 10□2 = 676□ → missing: 7, 1, 1
3. 421□ + 36□5 = 7□30 → missing: 5, 1, 8

Row 2:
4. 306□ + □435 = 9□00 → missing: 5, 6, 5
5. □457 + 2□44 = 46□1 → missing: 2, 1, 0
6. □297 + 2□79 = 74□6 → missing: 5, 1, 7

Row 3:
7. 1□98 + 48□5 = 618□ → missing: 2, 8, 3
8. 27□8 + □595 = 6□93 → missing: 9, 3, 3
9. □488 + 17□3 = 428□ → missing: 2, 9, 1

Final Answer:
The missing digits for each problem, in order, are:

Problem 1: 5, 3, 8
Problem 2: 7, 1, 1
Problem 3: 5, 1, 8
Problem 4: 5, 6, 5
Problem 5: 2, 1, 0
Problem 6: 5, 1, 7
Problem 7: 2, 8, 3
Problem 8: 9, 3, 3
Problem 9: 2, 9, 1