Add and Subtract Decimals: Missing Digits - Math Worksheets - Free Printable
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Step-by-step solution for: Add and Subtract Decimals: Missing Digits - Math Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Add and Subtract Decimals: Missing Digits - Math Worksheets
Absolutely! Let’s solve each section of the worksheet step by step, explaining the methods used.
---
## Section A: Column Addition and Subtraction
We align decimals by their decimal points and add/subtract column by column, carrying or borrowing as needed.
---
1) 3.7 + 8.5
```
3.7
+ 8.5
-----
12.2
```
→ 7 + 5 = 12 → write 2, carry 1
→ 3 + 8 + 1 = 12 → write 12
→ Answer: 12.2
---
2) 24.4 + 7.7
```
24.4
+ 7.7
-----
32.1
```
→ 4 + 7 = 11 → write 1, carry 1
→ 4 + 7 + 1 = 12 → write 2, carry 1
→ 2 + 0 + 1 = 3
→ Answer: 32.1
---
3) 85.8 + 46.9
```
85.8
+46.9
-----
132.7
```
→ 8 + 9 = 17 → write 7, carry 1
→ 5 + 6 + 1 = 12 → write 2, carry 1
→ 8 + 4 + 1 = 13 → write 13
→ Answer: 132.7
---
4) 39.02 + 84.1
Write 84.1 as 84.10 to match decimal places:
```
39.02
+84.10
------
123.12
```
→ 2 + 0 = 2
→ 0 + 1 = 1
→ 9 + 4 = 13 → write 3, carry 1
→ 3 + 8 + 1 = 12 → write 12
→ Answer: 123.12
---
5) 55.6 + 7.12
Write 55.6 as 55.60:
```
55.60
+ 7.12
------
62.72
```
→ 0 + 2 = 2
→ 6 + 1 = 7
→ 5 + 7 = 12 → write 2, carry 1
→ 5 + 0 + 1 = 6
→ Answer: 62.72
---
6) 9.2 - 4.6
```
9.2
- 4.6
-----
4.6
```
→ 2 - 6 → borrow 1 → 12 - 6 = 6
→ 8 - 4 = 4 (since we borrowed)
→ Answer: 4.6
---
7) 88.5 - 5.8
```
88.5
- 5.8
-----
82.7
```
→ 5 - 8 → borrow → 15 - 8 = 7
→ 7 - 5 = 2 (after borrow)
→ 8 - 0 = 8
→ Answer: 82.7
---
8) 909.4 - 89.7
```
909.4
- 89.7
-------
819.7
```
→ 4 - 7 → borrow → 14 - 7 = 7
→ 8 - 9 → borrow → 18 - 9 = 9 (but 0 became 9 after borrow)
→ 8 - 8 = 0? Wait — let's do it carefully:
Actually:
- Units place: 9 → becomes 8 after borrow → 8 - 8 = 0? No — better to write:
```
909.4
- 89.7
--------
```
Align:
```
909.4
- 89.7
--------
```
Start from right:
→ 4 - 7 → borrow → 14 - 7 = 7 → tenths
→ 8 (was 9, borrowed) - 9 → can’t → borrow from hundreds → 18 - 9 = 9 → units
→ 0 (was 9, borrowed) → now 9 → 9 - 8 = 1 → tens
→ 8 (hundreds) remains → 8
Wait — actually:
Hundreds: 9 → borrow → becomes 8
Tens: 0 → becomes 10 → but we need to borrow for units → so tens become 9, units become 19? Let’s do it properly:
Easier way:
909.4 - 89.7 = ?
Think: 909.4 - 90 + 0.3 = 819.4 + 0.3 = 819.7
Or calculate:
```
909.4
- 89.7
---------
819.7
```
✔ Answer: 819.7
---
9) 53.18 - 7.069
Write 53.18 as 53.180
```
53.180
- 7.069
--------
46.111
```
→ 0 - 9 → borrow → 10 - 9 = 1
→ 7 - 6 = 1 (after borrow)
→ 1 - 0 = 1
→ 3 - 7 → borrow → 13 - 7 = 6
→ 4 (after borrow) - 0 = 4
→ Answer: 46.111
---
10) 284.61 - 35.9
Write 35.9 as 35.90
```
284.61
- 35.90
--------
248.71
```
→ 1 - 0 = 1
→ 6 - 9 → borrow → 16 - 9 = 7
→ 3 (after borrow) - 5 → borrow → 13 - 5 = 8
→ 7 (after borrow) - 3 = 4
→ 2 - 0 = 2
→ Answer: 248.71
---
## ✔ Section A Answers:
1) 12.2
2) 32.1
3) 132.7
4) 123.12
5) 62.72
6) 4.6
7) 82.7
8) 819.7
9) 46.111
10) 248.71
---
## Section B: Use an appropriate method
You can use mental math, column method, or calculator — but since this is foundation level, we’ll show clear steps.
---
1) 8.6 + 5.9
= 8.6 + 6 - 0.1 = 14.6 - 0.1 = 14.5
Or:
```
8.6
+ 5.9
-----
14.5
```
✔ 14.5
---
2) 11.9 + 7.48
Write 11.9 as 11.90
```
11.90
+ 7.48
------
19.38
```
✔ 19.38
---
3) 94.57 + 33.2
Write 33.2 as 33.20
```
94.57
+33.20
------
127.77
```
✔ 127.77
---
4) 9.2 - 7.9
= 9.2 - 8 + 0.1 = 1.2 + 0.1 = 1.3
Or:
```
9.2
- 7.9
-----
1.3
```
✔ 1.3
---
5) 53.8 - 19.06
Write 53.8 as 53.80
```
53.80
-19.06
------
34.74
```
✔ 34.74
---
6) 70.94 - 48.4
Write 48.4 as 48.40
```
70.94
-48.40
------
22.54
```
✔ 22.54
---
7) 8.4 + 9.6 - 5.3
First: 8.4 + 9.6 = 18.0
Then: 18.0 - 5.3 = 12.7
✔ 12.7
---
8) 16.08 - 7.8 + 9.24
Do left to right:
16.08 - 7.8 = 8.28
8.28 + 9.24 = 17.52
✔ 17.52
---
9) 66.33 - 25.1 + 7.49
66.33 - 25.1 = 41.23
41.23 + 7.49 = 48.72
✔ 48.72
---
## ✔ Section B Answers:
1) 14.5
2) 19.38
3) 127.77
4) 1.3
5) 34.74
6) 22.54
7) 12.7
8) 17.52
9) 48.72
---
## Section C: Word Problems
---
Books: 2.5 cm, 1.82 cm, 0.9 cm
Total height = 2.5 + 1.82 + 0.9
First, 2.5 + 1.82 = 4.32
Then, 4.32 + 0.9 = 5.22 cm
✔ Answer: 5.22 cm
---
Family allowance: 91.2 kg
Baggage weights:
- Jackson: 21.8 kg
- Sister: 31.24 kg
- Father: 19.03 kg
- Mother: 39.59 kg
a) How much have they exceeded the allowance by?
First, total baggage weight:
21.8 + 31.24 = 53.04
53.04 + 19.03 = 72.07
72.07 + 39.59 = 111.66 kg
Excess = 111.66 - 91.2 = 20.46 kg
✔ Answer a: 20.46 kg
---
b) Total baggage allowance for 5 families
One family: 91.2 kg
Five families: 91.2 × 5
91.2 × 5 = (90 × 5) + (1.2 × 5) = 450 + 6 = 456 kg
✔ Answer b: 456 kg
---
## ✔ Final Answers Summary:
---
1) 12.2
2) 32.1
3) 132.7
4) 123.12
5) 62.72
6) 4.6
7) 82.7
8) 819.7
9) 46.111
10) 248.71
---
1) 14.5
2) 19.38
3) 127.77
4) 1.3
5) 34.74
6) 22.54
7) 12.7
8) 17.52
9) 48.72
---
1) 5.22 cm
2a) 20.46 kg
2b) 456 kg
---
Let me know if you’d like these written out in a printable format or with visual column layouts!
---
## Section A: Column Addition and Subtraction
We align decimals by their decimal points and add/subtract column by column, carrying or borrowing as needed.
---
Addition Problems
1) 3.7 + 8.5
```
3.7
+ 8.5
-----
12.2
```
→ 7 + 5 = 12 → write 2, carry 1
→ 3 + 8 + 1 = 12 → write 12
→ Answer: 12.2
---
2) 24.4 + 7.7
```
24.4
+ 7.7
-----
32.1
```
→ 4 + 7 = 11 → write 1, carry 1
→ 4 + 7 + 1 = 12 → write 2, carry 1
→ 2 + 0 + 1 = 3
→ Answer: 32.1
---
3) 85.8 + 46.9
```
85.8
+46.9
-----
132.7
```
→ 8 + 9 = 17 → write 7, carry 1
→ 5 + 6 + 1 = 12 → write 2, carry 1
→ 8 + 4 + 1 = 13 → write 13
→ Answer: 132.7
---
4) 39.02 + 84.1
Write 84.1 as 84.10 to match decimal places:
```
39.02
+84.10
------
123.12
```
→ 2 + 0 = 2
→ 0 + 1 = 1
→ 9 + 4 = 13 → write 3, carry 1
→ 3 + 8 + 1 = 12 → write 12
→ Answer: 123.12
---
5) 55.6 + 7.12
Write 55.6 as 55.60:
```
55.60
+ 7.12
------
62.72
```
→ 0 + 2 = 2
→ 6 + 1 = 7
→ 5 + 7 = 12 → write 2, carry 1
→ 5 + 0 + 1 = 6
→ Answer: 62.72
---
Subtraction Problems
6) 9.2 - 4.6
```
9.2
- 4.6
-----
4.6
```
→ 2 - 6 → borrow 1 → 12 - 6 = 6
→ 8 - 4 = 4 (since we borrowed)
→ Answer: 4.6
---
7) 88.5 - 5.8
```
88.5
- 5.8
-----
82.7
```
→ 5 - 8 → borrow → 15 - 8 = 7
→ 7 - 5 = 2 (after borrow)
→ 8 - 0 = 8
→ Answer: 82.7
---
8) 909.4 - 89.7
```
909.4
- 89.7
-------
819.7
```
→ 4 - 7 → borrow → 14 - 7 = 7
→ 8 - 9 → borrow → 18 - 9 = 9 (but 0 became 9 after borrow)
→ 8 - 8 = 0? Wait — let's do it carefully:
Actually:
- Units place: 9 → becomes 8 after borrow → 8 - 8 = 0? No — better to write:
```
909.4
- 89.7
--------
```
Align:
```
909.4
- 89.7
--------
```
Start from right:
→ 4 - 7 → borrow → 14 - 7 = 7 → tenths
→ 8 (was 9, borrowed) - 9 → can’t → borrow from hundreds → 18 - 9 = 9 → units
→ 0 (was 9, borrowed) → now 9 → 9 - 8 = 1 → tens
→ 8 (hundreds) remains → 8
Wait — actually:
Hundreds: 9 → borrow → becomes 8
Tens: 0 → becomes 10 → but we need to borrow for units → so tens become 9, units become 19? Let’s do it properly:
Easier way:
909.4 - 89.7 = ?
Think: 909.4 - 90 + 0.3 = 819.4 + 0.3 = 819.7
Or calculate:
```
909.4
- 89.7
---------
819.7
```
✔ Answer: 819.7
---
9) 53.18 - 7.069
Write 53.18 as 53.180
```
53.180
- 7.069
--------
46.111
```
→ 0 - 9 → borrow → 10 - 9 = 1
→ 7 - 6 = 1 (after borrow)
→ 1 - 0 = 1
→ 3 - 7 → borrow → 13 - 7 = 6
→ 4 (after borrow) - 0 = 4
→ Answer: 46.111
---
10) 284.61 - 35.9
Write 35.9 as 35.90
```
284.61
- 35.90
--------
248.71
```
→ 1 - 0 = 1
→ 6 - 9 → borrow → 16 - 9 = 7
→ 3 (after borrow) - 5 → borrow → 13 - 5 = 8
→ 7 (after borrow) - 3 = 4
→ 2 - 0 = 2
→ Answer: 248.71
---
## ✔ Section A Answers:
1) 12.2
2) 32.1
3) 132.7
4) 123.12
5) 62.72
6) 4.6
7) 82.7
8) 819.7
9) 46.111
10) 248.71
---
## Section B: Use an appropriate method
You can use mental math, column method, or calculator — but since this is foundation level, we’ll show clear steps.
---
1) 8.6 + 5.9
= 8.6 + 6 - 0.1 = 14.6 - 0.1 = 14.5
Or:
```
8.6
+ 5.9
-----
14.5
```
✔ 14.5
---
2) 11.9 + 7.48
Write 11.9 as 11.90
```
11.90
+ 7.48
------
19.38
```
✔ 19.38
---
3) 94.57 + 33.2
Write 33.2 as 33.20
```
94.57
+33.20
------
127.77
```
✔ 127.77
---
4) 9.2 - 7.9
= 9.2 - 8 + 0.1 = 1.2 + 0.1 = 1.3
Or:
```
9.2
- 7.9
-----
1.3
```
✔ 1.3
---
5) 53.8 - 19.06
Write 53.8 as 53.80
```
53.80
-19.06
------
34.74
```
✔ 34.74
---
6) 70.94 - 48.4
Write 48.4 as 48.40
```
70.94
-48.40
------
22.54
```
✔ 22.54
---
7) 8.4 + 9.6 - 5.3
First: 8.4 + 9.6 = 18.0
Then: 18.0 - 5.3 = 12.7
✔ 12.7
---
8) 16.08 - 7.8 + 9.24
Do left to right:
16.08 - 7.8 = 8.28
8.28 + 9.24 = 17.52
✔ 17.52
---
9) 66.33 - 25.1 + 7.49
66.33 - 25.1 = 41.23
41.23 + 7.49 = 48.72
✔ 48.72
---
## ✔ Section B Answers:
1) 14.5
2) 19.38
3) 127.77
4) 1.3
5) 34.74
6) 22.54
7) 12.7
8) 17.52
9) 48.72
---
## Section C: Word Problems
---
1) Book Stack Height
Books: 2.5 cm, 1.82 cm, 0.9 cm
Total height = 2.5 + 1.82 + 0.9
First, 2.5 + 1.82 = 4.32
Then, 4.32 + 0.9 = 5.22 cm
✔ Answer: 5.22 cm
---
2) Family Baggage Allowance
Family allowance: 91.2 kg
Baggage weights:
- Jackson: 21.8 kg
- Sister: 31.24 kg
- Father: 19.03 kg
- Mother: 39.59 kg
a) How much have they exceeded the allowance by?
First, total baggage weight:
21.8 + 31.24 = 53.04
53.04 + 19.03 = 72.07
72.07 + 39.59 = 111.66 kg
Excess = 111.66 - 91.2 = 20.46 kg
✔ Answer a: 20.46 kg
---
b) Total baggage allowance for 5 families
One family: 91.2 kg
Five families: 91.2 × 5
91.2 × 5 = (90 × 5) + (1.2 × 5) = 450 + 6 = 456 kg
✔ Answer b: 456 kg
---
## ✔ Final Answers Summary:
---
Section A
1) 12.2
2) 32.1
3) 132.7
4) 123.12
5) 62.72
6) 4.6
7) 82.7
8) 819.7
9) 46.111
10) 248.71
---
Section B
1) 14.5
2) 19.38
3) 127.77
4) 1.3
5) 34.74
6) 22.54
7) 12.7
8) 17.52
9) 48.72
---
Section C
1) 5.22 cm
2a) 20.46 kg
2b) 456 kg
---
Let me know if you’d like these written out in a printable format or with visual column layouts!
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting decimals worksheets.
