Add & subtract decimals (with money notation) worksheets | Worsheets library - Free Printable

Let's solve each problem step by step, filling in the missing digits in the decimal addition and subtraction problems. We'll work through each one carefully.

---

1.

```
21.5
+ 51.□
-------
□2.5
```

We know:
- 21.5 + 51.□ = □2.5

Let’s add:
- Tenths place: 5 + □ → ends in .5 → so tenths digit must be 0 (since 5 + 0 = 5)
- So missing digit in 51.□ is 0, making it 51.0
- Now: 21.5 + 51.0 = 72.5 → so the sum is 72.5

So:
- Missing digit in second number: 0
- Missing digit in sum: 7

✔ Answer:
```
21.5
+ 51.0
-------
72.5
```

---

2.

```
10.0
+ □5.0
-------
3□.0
```

Add:
- 10.0 + □5.0 = 3□.0

Let’s suppose the missing digit in the second number is x, so it’s x5.0
Then: 10.0 + x5.0 = (10 + x5) = 3□.0

Try x = 2 → 10.0 + 25.0 = 35.0 → matches!

So:
- Missing digit in second number: 2
- Sum is 35.0 → missing digit: 5

✔ Answer:
```
10.0
+ 25.0
-------
35.0
```

---

3.

```
1.0
+ 5□.0
-------
54.0
```

So: 1.0 + 5□.0 = 54.0

Subtract: 54.0 - 1.0 = 53.0 → so second number is 53.0

So missing digit is 3

✔ Answer:
```
1.0
+ 53.0
-------
54.0
```

---

4.

```
3□.0
+ 29.0
-------
□9.0
```

Let’s denote:
- First number: 3x.0
- Sum: y9.0

So: 3x.0 + 29.0 = y9.0

Try to find x such that:
- 3x.0 + 29.0 = y9.0

Try x = 0 → 30.0 + 29.0 = 59.0 → ends with 9 → good!
→ sum is 59.0 → y = 5

So:
- Missing digit in first number: 0
- Missing digit in sum: 5

✔ Answer:
```
30.0
+ 29.0
-------
59.0
```

---

5.

```
33.6□
+ 3□.00
-------
□7.65
```

Let’s write clearly:
- 33.6□ + 3□.00 = □7.65

Let’s look at hundredths place:
- 6□ + 00 → result is 65 → so tenths digit of first number must be 5 → 33.65

Now:
- 33.65 + 3□.00 = □7.65

Subtract 33.65 from both sides:
- 3□.00 = □7.65 - 33.65 = ?

Compute: □7.65 - 33.65 = (□7 - 33).00 → need this to be a number ending in 00? No — but we’re adding 3□.00

Wait: Let’s just try values.

We have:
- 33.65 + 3x.00 = y7.65

So: 33.65 + 3x.00 = y7.65

Subtract 33.65:
→ 3x.00 = y7.65 - 33.65 = (y7 - 33).00 → no, better:

Do actual addition:

Tenths: 6 + 0 = 6 → OK

Hundredths: 5 + 0 = 5 → OK

Units: 3 + x → must give 7 or carry over?

But result has units digit 7 → so 3 + x = 7 → x = 4? But then:
- 33.65 + 34.00 = 67.65 → yes! Sum is 67.65

So:
- First number: 33.65 → missing digit: 5
- Second number: 34.00 → missing digit: 4
- Sum: 67.65 → missing digit: 6

✔ Answer:
```
33.65
+ 34.00
-------
67.65
```

---

6.

```
□1.82
+ 6□.69
-------
133.□□
```

Let’s call:
- First number: x1.82
- Second: 6y.69
- Sum: 133.zw

Let’s add:

Start from right:
- Hundredths: 2 + 9 = 11 → write 1, carry 1
- Tenths: 8 + 6 = 14 + carry 1 = 15 → write 5, carry 1
- Units: 1 + y + carry 1 = ? → must end with 3 in tens and units?
Sum is 133.zw → so total is around 133

So: x1.82 + 6y.69 = 133.zw

Try estimating:
- Max: 91.82 + 69.69 = ~161 → too big
- Min: 11.82 + 60.69 = ~72 → too small

Try x = 6 → 61.82 + 6y.69 = ?

61.82 + 60.69 = 122.51 → too low
61.82 + 69.69 = 131.51 → close
61.82 + 70.69 = 132.51 → still low
61.82 + 71.69 = 133.51 → perfect!

So:
- First number: 61.82 → missing digit: 6
- Second number: 71.69 → missing digit: 1
- Sum: 133.51 → missing digits: 5 and 1

Check:
```
61.82
+ 71.69
-------
133.51
```
Yes!

✔ Answer:
```
61.82
+ 71.69
-------
133.51
```

---

7.

```
42.1□
+ 3□.80
-------
□1.94
```

Let’s denote:
- First: 42.1a
- Second: 3b.80
- Sum: c1.94

Work backwards:

Hundredths: a + 0 = 4 → so a = 4

So first number: 42.14

Tenths: 1 + 8 = 9 → OK

Units: 2 + b = 1? But 2 + b can’t be 1 unless carry-over

Wait: sum is c1.94 → units digit is 1

But 2 + b = 1 → only possible if there's carry-over from tenths? But tenths: 1 + 8 = 9 → no carry

So 2 + b = 1 → impossible unless b negative

Wait — maybe carry from tenths? But 1 + 8 = 9 → no carry

Wait — perhaps I made a mistake.

Wait: sum is c1.94 → so units digit is 1

But 2 + b = 1 → not possible unless carry from tenths → but tenths are 1 + 8 = 9 → no carry

Unless b is such that 2 + b = 11 → then carry 1 → units digit 1

So 2 + b = 11 → b = 9

Then carry 1 to tens

Tens: 4 + 3 + 1 = 8 → so sum should be 81.94

But sum is written as □1.94 → so tens digit is 8 → c = 8

So:
- First number: 42.14 → missing digit: 4
- Second number: 39.80 → missing digit: 9
- Sum: 81.94 → missing digit: 8

Check:
```
42.14
+ 39.80
-------
81.94
```
Yes!

✔ Answer:
```
42.14
+ 39.80
-------
81.94
```

---

8.

```
□.78
+ 51.9□
-------
56.□0
```

Let’s denote:
- First: a.78
- Second: 51.9b
- Sum: 56.c0

Hundredths: 8 + b → ends in 0 → so 8 + b = 10 → b = 2 → carry 1

Tenths: 7 + 9 = 16 + carry 1 = 17 → write 7, carry 1

Units: a + 1 + carry 1 = 6 → a + 2 = 6 → a = 4

Tens: 0 + 5 + carry 1 = 6 → OK

So:
- First number: 4.78 → missing digit: 4
- Second number: 51.92 → missing digit: 2
- Sum: 56.70 → missing digit: 7

Check:
```
4.78
+ 51.92
-------
56.70
```
Yes!

✔ Answer:
```
4.78
+ 51.92
-------
56.70
```

---

9.

```
97.□
- 3□.2
-------
62.7
```

Let’s denote:
- 97.x - 3y.2 = 62.7

We can rearrange:
- 97.x - 62.7 = 3y.2

Compute: 97.x - 62.7 = 34.3 + x

Better: let’s do subtraction.

Start from tenths:
- x - 2 = 7 → but x < 2 → borrow needed

So: (10 + x) - 2 = 7 → 10 + x = 9 → x = -1 → impossible

Wait: actually, if we borrow:
- Tenths: x - 2 → need to borrow → becomes (10 + x) - 2 = 7 → 10 + x = 9 → x = -1 → invalid

Wait — maybe the minuend is 97.x → units digit is 7, subtract 3y.2

Let’s try:
- 97.x - 3y.2 = 62.7

Try solving:
- 97.x = 62.7 + 3y.2 = (62 + 3y) + (0.7 + 0.2) = (62 + 3y) + 0.9

So 97.x = (62 + 3y) + 0.9

So 97.x ≈ 62 + 3y + 0.9 → 97 - 0.9 = 96.1 = 62 + 3y → 3y = 34.1 → not integer

Wait — try concrete values.

Try y = 4 → 3y.2 = 34.2 → 97.x - 34.2 = 62.7 → 97.x = 62.7 + 34.2 = 96.9 → so x = 9

So:
- 97.9 - 34.2 = 63.7 → not 62.7 → too high

Try y = 5 → 35.2 → 62.7 + 35.2 = 97.9 → so 97.9 - 35.2 = 62.7 → YES!

So:
- First number: 97.9 → missing digit: 9
- Second number: 35.2 → missing digit: 5
- Result: 62.7 → already given

✔ Answer:
```
97.9
- 35.2
-------
62.7
```

---

10.

```
7□.7
- 57.7
-------
22.□
```

Let’s denote:
- 7x.7 - 57.7 = 22.y

So: 7x.7 = 22.y + 57.7 = (22 + 57) + (y + 0.7) = 79 + y + 0.7

So 7x.7 = 79 + y + 0.7 → so 7x.7 ≈ 79. something

So x = 9 → 79.7

Then: 79.7 - 57.7 = 22.0 → so y = 0

So:
- First number: 79.7 → missing digit: 9
- Result: 22.0 → missing digit: 0

✔ Answer:
```
79.7
- 57.7
-------
22.0
```

---

11.

```
□8.9
- 35.5
-------
6□.4
```

Let’s denote:
- x8.9 - 35.5 = 6y.4

So: x8.9 = 6y.4 + 35.5 = (6y + 35) + (0.4 + 0.5) = (6y + 35) + 0.9

So x8.9 = 6y + 35.9

Try y = 3 → 63.4 → 63.4 + 35.5 = 98.9 → so x8.9 = 98.9 → x = 9

So:
- First number: 98.9 → missing digit: 9
- Result: 63.4 → missing digit: 3

Check: 98.9 - 35.5 = 63.4 → YES!

✔ Answer:
```
98.9
- 35.5
-------
63.4
```

---

12.

```
4□.6
- 42.□
-------
4.2
```

Let’s denote:
- 4x.6 - 42.y = 4.2

So: 4x.6 = 4.2 + 42.y = 46.2 + y

So 4x.6 = 46.2 + y → so x must be 6 → 46.6

Then: 46.6 - 42.y = 4.2 → 46.6 - 4.2 = 42.4 → so y = 4

So:
- First number: 46.6 → missing digit: 6
- Second number: 42.4 → missing digit: 4

Check: 46.6 - 42.4 = 4.2 → YES!

✔ Answer:
```
46.6
- 42.4
-------
4.2
```

---

13.

```
2□.99
- 15.7□
-------
9.□5
```

Let’s denote:
- 2x.99 - 15.7y = 9.z5

Start from right:

Hundredths: 9 - y = 5 → so y = 4 (no borrow)

Tenths: 9 - 7 = 2 → but result is z → wait, result tenths digit is z, but we have 9 - 7 = 2 → so z = 2?

But check:

Wait: 2x.99 - 15.74 = 9.25?

Try x = 5 → 25.99 - 15.74 = 10.25 → too big

Try x = 4 → 24.99 - 15.74 = 9.25 → YES!

So:
- First number: 24.99 → missing digit: 4
- Second number: 15.74 → missing digit: 4
- Result: 9.25 → missing digit: 2

✔ Answer:
```
24.99
- 15.74
-------
9.25
```

---

14.

```
□1.58
- 3□.90
-------
27.6□
```

Let’s denote:
- x1.58 - 3y.90 = 27.6z

Try to compute:

Start from right:
- Hundredths: 8 - 0 = 8 → z = 8

Tenths: 5 - 9 → can't do → borrow → 15 - 9 = 6 → OK

Units: 1 - y → but we borrowed → so 0 - y → need to borrow again

Tens: x - 3 → but we’ll see

Let’s try to solve:

Let’s suppose:
- x1.58 - 3y.90 = 27.68

Try y = 3 → 33.90 → x1.58 = 27.68 + 33.90 = 61.58 → so x = 6

So:
- First number: 61.58
- Second: 33.90
- Check: 61.58 - 33.90 = 27.68 → YES!

So:
- First number: 61.58 → missing digit: 6
- Second number: 33.90 → missing digit: 3
- Result: 27.68 → missing digit: 8

✔ Answer:
```
61.58
- 33.90
-------
27.68
```

---

15.

```
92.8□
- 84.□7
-------
□.45
```

Let’s denote:
- 92.8a - 84.b7 = c.45

Hundredths: a - 7 = 5 → so a = 2 (if no borrow), or a + 10 - 7 = 5 → a = 2 → no borrow

Tenths: 8 - b = 4 → b = 4

Units: 2 - 4 → can't do → borrow → 12 - 4 = 8 → but we need to borrow from tens

Tens: 9 - 8 = 1 → but we borrowed → 8 - 8 = 0 → so c = 0?

Wait:

Let’s do full subtraction:

Assume a = 2 → 92.82
b = 4 → 84.47

Then: 92.82 - 84.47 = ?

92.82 - 84.47 = 8.35 → but we want c.45 → not matching

Wait — we want result to be c.45 → tenths digit 4

But 8.35 → tenths digit is 3 → not 4

Try different.

We had:
- Hundredths: a - 7 = 5 → so a = 2 → no borrow → 2 - 7 → no, 2 < 7 → must borrow

So: 12 - 7 = 5 → so a + 10 - 7 = 5 → a = 2 → yes

So a = 2 → 92.82

Tenths: 8 - b → but we borrowed → so 7 - b = 4 → b = 3

Now: 92.82 - 84.37 = ?

92.82 - 84.37 = 8.45 → YES!

So:
- First number: 92.82 → missing digit: 2
- Second number: 84.37 → missing digit: 3
- Result: 8.45 → missing digit: 8

✔ Answer:
```
92.82
- 84.37
-------
8.45
```

---

16.

```
47.7□
- 25.□7
-------
□2.08
```

Let’s denote:
- 47.7a - 25.b7 = c2.08

Hundredths: a - 7 = 8 → can’t → so borrow → (10 + a) - 7 = 8 → 10 + a = 15 → a = 5

So a = 5 → 47.75

Tenths: 7 - b → but we borrowed → so 6 - b = 0 → b = 6

Now: 47.75 - 25.67 = ?

47.75 - 25.67 = 22.08 → YES!

So:
- First number: 47.75 → missing digit: 5
- Second number: 25.67 → missing digit: 6
- Result: 22.08 → missing digit: 2

✔ Answer:
```
47.75
- 25.67
-------
22.08
```

---

## ✔ Final Answers:

| Problem | Solution |
|--------|----------|
| 1 | `21.5 + 51.0 = 72.5` |
| 2 | `10.0 + 25.0 = 35.0` |
| 3 | `1.0 + 53.0 = 54.0` |
| 4 | `30.0 + 29.0 = 59.0` |
| 5 | `33.65 + 34.00 = 67.65` |
| 6 | `61.82 + 71.69 = 133.51` |
| 7 | `42.14 + 39.80 = 81.94` |
| 8 | `4.78 + 51.92 = 56.70` |
| 9 | `97.9 - 35.2 = 62.7` |
| 10 | `79.7 - 57.7 = 22.0` |
| 11 | `98.9 - 35.5 = 63.4` |
| 12 | `46.6 - 42.4 = 4.2` |
| 13 | `24.99 - 15.74 = 9.25` |
| 14 | `61.58 - 33.90 = 27.68` |
| 15 | `92.82 - 84.37 = 8.45` |
| 16 | `47.75 - 25.67 = 22.08` |

All solved! Let me know if you'd like a printable version or explanation for any specific one.