Adding and Subtracting Decimals Worksheet | Fun and Engaging 5th ... - Free Printable
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Step-by-step solution for: Adding and Subtracting Decimals Worksheet | Fun and Engaging 5th ...
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Step-by-step solution for: Adding and Subtracting Decimals Worksheet | Fun and Engaging 5th ...
Here is the complete solution to all problems in the worksheet, explained step by step.
---
## Section A: Use the standard algorithm to add and subtract the decimals.
Important: When adding or subtracting decimals, align the decimal points vertically. Add or subtract column by column, starting from the rightmost digit, carrying or borrowing as needed.
---
1) 3.7 + 8.5
```
3.7
+ 8.5
-----
12.2
```
- Tenths: 7 + 5 = 12 → write 2, carry 1
- Units: 3 + 8 + 1 = 12 → write 12
- Decimal aligned → 12.2
✔ Answer: 12.2
---
2) 24.4 + 7.7
```
24.4
+ 7.7
-----
32.1
```
- Tenths: 4 + 7 = 11 → write 1, carry 1
- Units: 4 + 7 + 1 = 12 → write 2, carry 1
- Tens: 2 + 0 + 1 = 3
- → 32.1
✔ Answer: 32.1
---
3) 85.8 + 46.9
```
85.8
+46.9
-----
132.7
```
- Tenths: 8 + 9 = 17 → write 7, carry 1
- Units: 5 + 6 + 1 = 12 → write 2, carry 1
- Tens: 8 + 4 + 1 = 13 → write 13
- → 132.7
✔ Answer: 132.7
---
4) 39.02 + 84.1
Align decimals:
```
39.02
+84.10 ← added a zero for alignment
--------
123.12
```
- Hundredths: 2 + 0 = 2
- Tenths: 0 + 1 = 1
- Units: 9 + 4 = 13 → write 3, carry 1
- Tens: 3 + 8 + 1 = 12 → write 12
- → 123.12
✔ Answer: 123.12
---
5) 55.6 + 7.12
Align decimals:
```
55.60
+ 7.12
-------
62.72
```
- Hundredths: 0 + 2 = 2
- Tenths: 6 + 1 = 7
- Units: 5 + 7 = 12 → write 2, carry 1
- Tens: 5 + 0 + 1 = 6
- → 62.72
✔ Answer: 62.72
---
6) 9.2 – 4.6
```
9.2
- 4.6
-----
4.6
```
- Tenths: 2 < 6 → borrow 1 from units → 12 – 6 = 6
- Units: 8 – 4 = 4 (after borrow)
- → 4.6
✔ Answer: 4.6
---
7) 88.5 – 5.8
```
88.5
- 5.8
-----
82.7
```
- Tenths: 5 < 8 → borrow → 15 – 8 = 7
- Units: 7 – 5 = 2 (after borrow)
- Tens: 8 – 0 = 8
- → 82.7
✔ Answer: 82.7
---
8) 909.4 – 89.7
Align:
```
909.4
- 89.7
-------
819.7
```
- Tenths: 4 < 7 → borrow → 14 – 7 = 7
- Units: 8 – 9 → can’t → borrow from tens → 18 – 9 = 9 (but tens was 0, so need to borrow from hundreds)
- Hundreds: 9 → becomes 8
- Tens: 0 → becomes 10 → then lend 1 to units → tens becomes 9, units becomes 18
- Units: 18 – 9 = 9? Wait — let’s do it carefully:
Actually:
```
909.4
- 89.7
--------
```
Start from right:
- Tenths: 4 – 7 → borrow → 14 – 7 = 7 → units digit becomes 8
- Units: 8 – 9 → borrow → 18 – 9 = 9 → tens digit becomes 9 (since 0 became 10, lent 1 → now 9)
- Tens: 9 – 8 = 1
- Hundreds: 9 – 0 = 9? Wait — we borrowed from hundreds earlier? Let’s write it:
After borrowing:
Hundreds: 9 → 8
Tens: 0 → 10 → lend 1 to units → becomes 9
Units: 9 → 18 → after borrow for tenths, units was 8 → then borrow → 18
So:
- Tenths: 14 – 7 = 7
- Units: 18 – 9 = 9
- Tens: 9 – 8 = 1
- Hundreds: 8 – 0 = 8
→ 819.7
✔ Answer: 819.7
---
9) 53.18 – 7.069
Align decimals (add trailing zeros):
```
53.180
- 7.069
--------
46.111
```
- Thousandths: 0 – 9 → borrow → 10 – 9 = 1 → hundredths becomes 7
- Hundredths: 7 – 6 = 1
- Tenths: 1 – 0 = 1
- Units: 3 – 7 → borrow → 13 – 7 = 6 → tens becomes 4
- Tens: 4 – 0 = 4
- → 46.111
✔ Answer: 46.111
---
10) 284.61 – 35.9
Align:
```
284.61
- 35.90
--------
248.71
```
- Hundredths: 1 – 0 = 1
- Tenths: 6 – 9 → borrow → 16 – 9 = 7 → units becomes 3
- Units: 3 – 5 → borrow → 13 – 5 = 8 → tens becomes 7
- Tens: 7 – 3 = 4
- Hundreds: 2 – 0 = 2
- → 248.71
✔ Answer: 248.71
---
## Section B: Use an appropriate method to answer the following sums.
You can use mental math, calculator, or written algorithm. We’ll show calculations.
---
1) 8.6 + 5.9 =
8.6 + 5.9 = (8 + 5) + (0.6 + 0.9) = 13 + 1.5 = 14.5
✔ Answer: 14.5
---
2) 11.9 + 7.48 =
Align:
```
11.90
+ 7.48
-------
19.38
```
- Hundredths: 0 + 8 = 8
- Tenths: 9 + 4 = 13 → write 3, carry 1
- Units: 1 + 7 + 1 = 9
- Tens: 1 + 0 = 1
- → 19.38
✔ Answer: 19.38
---
3) 94.57 + 33.2 =
Align:
```
94.57
+33.20
-------
127.77
```
- Hundredths: 7 + 0 = 7
- Tenths: 5 + 2 = 7
- Units: 4 + 3 = 7
- Tens: 9 + 3 = 12 → write 2, carry 1 → hundreds: 1
- → 127.77
✔ Answer: 127.77
---
4) 9.2 – 7.9 =
9.2 – 7.9 = 1.3
(Or: 9.2 – 8 = 1.2, but we subtracted 0.1 too much → add back 0.1 → 1.3)
✔ Answer: 1.3
---
5) 53.8 – 19.06 =
Align:
```
53.80
-19.06
-------
34.74
```
- Hundredths: 0 – 6 → borrow → 10 – 6 = 4 → tenths becomes 7
- Tenths: 7 – 0 = 7
- Units: 3 – 9 → borrow → 13 – 9 = 4 → tens becomes 4
- Tens: 4 – 1 = 3
- → 34.74
✔ Answer: 34.74
---
6) 70.94 – 48.4 =
Align:
```
70.94
-48.40
-------
22.54
```
- Hundredths: 4 – 0 = 4
- Tenths: 9 – 4 = 5
- Units: 0 – 8 → borrow → 10 – 8 = 2 → tens becomes 6
- Tens: 6 – 4 = 2
- → 22.54
✔ Answer: 22.54
---
7) 8.4 + 9.6 – 5.3 =
First: 8.4 + 9.6 = 18.0
Then: 18.0 – 5.3 = 12.7
✔ Answer: 12.7
---
8) 16.08 – 7.8 + 9.24 =
Do left to right:
16.08 – 7.8 = 8.28
Then: 8.28 + 9.24 =
```
8.28
+ 9.24
-------
17.52
```
✔ Answer: 17.52
---
9) 66.33 – 25.1 + 7.49 =
First: 66.33 – 25.1 = 41.23
Then: 41.23 + 7.49 =
```
41.23
+ 7.49
-------
48.72
```
✔ Answer: 48.72
---
## Section C: Solve these problems involving decimals.
---
Thicknesses: 2.5 cm, 1.82 cm, 0.9 cm
Total height = 2.5 + 1.82 + 0.9
Align:
```
2.50
1.82
+ 0.90
-------
5.22 cm
```
✔ Answer: 5.22 cm
---
Baggage allowance per family: 91.2 kg
Individual weights:
- Jackson: 21.8 kg
- Sister: 31.24 kg
- Father: 19.03 kg
- Mother: 39.59 kg
a) How much have the family exceeded the allowance by?
Step 1: Add total baggage weight:
21.8 + 31.24 + 19.03 + 39.59
Let’s add step by step:
21.8 + 31.24 = 53.04
53.04 + 19.03 = 72.07
72.07 + 39.59 =
```
72.07
+39.59
-------
111.66 kg
```
Allowance = 91.2 kg
Excess = 111.66 – 91.2 = 20.46 kg
✔ Answer a: 20.46 kg
---
b) What is the 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 this formatted as a printable answer key!
---
## Section A: Use the standard algorithm to add and subtract the decimals.
Important: When adding or subtracting decimals, align the decimal points vertically. Add or subtract column by column, starting from the rightmost digit, carrying or borrowing as needed.
---
Addition Problems (1–5):
1) 3.7 + 8.5
```
3.7
+ 8.5
-----
12.2
```
- Tenths: 7 + 5 = 12 → write 2, carry 1
- Units: 3 + 8 + 1 = 12 → write 12
- Decimal aligned → 12.2
✔ Answer: 12.2
---
2) 24.4 + 7.7
```
24.4
+ 7.7
-----
32.1
```
- Tenths: 4 + 7 = 11 → write 1, carry 1
- Units: 4 + 7 + 1 = 12 → write 2, carry 1
- Tens: 2 + 0 + 1 = 3
- → 32.1
✔ Answer: 32.1
---
3) 85.8 + 46.9
```
85.8
+46.9
-----
132.7
```
- Tenths: 8 + 9 = 17 → write 7, carry 1
- Units: 5 + 6 + 1 = 12 → write 2, carry 1
- Tens: 8 + 4 + 1 = 13 → write 13
- → 132.7
✔ Answer: 132.7
---
4) 39.02 + 84.1
Align decimals:
```
39.02
+84.10 ← added a zero for alignment
--------
123.12
```
- Hundredths: 2 + 0 = 2
- Tenths: 0 + 1 = 1
- Units: 9 + 4 = 13 → write 3, carry 1
- Tens: 3 + 8 + 1 = 12 → write 12
- → 123.12
✔ Answer: 123.12
---
5) 55.6 + 7.12
Align decimals:
```
55.60
+ 7.12
-------
62.72
```
- Hundredths: 0 + 2 = 2
- Tenths: 6 + 1 = 7
- Units: 5 + 7 = 12 → write 2, carry 1
- Tens: 5 + 0 + 1 = 6
- → 62.72
✔ Answer: 62.72
---
Subtraction Problems (6–10):
6) 9.2 – 4.6
```
9.2
- 4.6
-----
4.6
```
- Tenths: 2 < 6 → borrow 1 from units → 12 – 6 = 6
- Units: 8 – 4 = 4 (after borrow)
- → 4.6
✔ Answer: 4.6
---
7) 88.5 – 5.8
```
88.5
- 5.8
-----
82.7
```
- Tenths: 5 < 8 → borrow → 15 – 8 = 7
- Units: 7 – 5 = 2 (after borrow)
- Tens: 8 – 0 = 8
- → 82.7
✔ Answer: 82.7
---
8) 909.4 – 89.7
Align:
```
909.4
- 89.7
-------
819.7
```
- Tenths: 4 < 7 → borrow → 14 – 7 = 7
- Units: 8 – 9 → can’t → borrow from tens → 18 – 9 = 9 (but tens was 0, so need to borrow from hundreds)
- Hundreds: 9 → becomes 8
- Tens: 0 → becomes 10 → then lend 1 to units → tens becomes 9, units becomes 18
- Units: 18 – 9 = 9? Wait — let’s do it carefully:
Actually:
```
909.4
- 89.7
--------
```
Start from right:
- Tenths: 4 – 7 → borrow → 14 – 7 = 7 → units digit becomes 8
- Units: 8 – 9 → borrow → 18 – 9 = 9 → tens digit becomes 9 (since 0 became 10, lent 1 → now 9)
- Tens: 9 – 8 = 1
- Hundreds: 9 – 0 = 9? Wait — we borrowed from hundreds earlier? Let’s write it:
After borrowing:
Hundreds: 9 → 8
Tens: 0 → 10 → lend 1 to units → becomes 9
Units: 9 → 18 → after borrow for tenths, units was 8 → then borrow → 18
So:
- Tenths: 14 – 7 = 7
- Units: 18 – 9 = 9
- Tens: 9 – 8 = 1
- Hundreds: 8 – 0 = 8
→ 819.7
✔ Answer: 819.7
---
9) 53.18 – 7.069
Align decimals (add trailing zeros):
```
53.180
- 7.069
--------
46.111
```
- Thousandths: 0 – 9 → borrow → 10 – 9 = 1 → hundredths becomes 7
- Hundredths: 7 – 6 = 1
- Tenths: 1 – 0 = 1
- Units: 3 – 7 → borrow → 13 – 7 = 6 → tens becomes 4
- Tens: 4 – 0 = 4
- → 46.111
✔ Answer: 46.111
---
10) 284.61 – 35.9
Align:
```
284.61
- 35.90
--------
248.71
```
- Hundredths: 1 – 0 = 1
- Tenths: 6 – 9 → borrow → 16 – 9 = 7 → units becomes 3
- Units: 3 – 5 → borrow → 13 – 5 = 8 → tens becomes 7
- Tens: 7 – 3 = 4
- Hundreds: 2 – 0 = 2
- → 248.71
✔ Answer: 248.71
---
## Section B: Use an appropriate method to answer the following sums.
You can use mental math, calculator, or written algorithm. We’ll show calculations.
---
1) 8.6 + 5.9 =
8.6 + 5.9 = (8 + 5) + (0.6 + 0.9) = 13 + 1.5 = 14.5
✔ Answer: 14.5
---
2) 11.9 + 7.48 =
Align:
```
11.90
+ 7.48
-------
19.38
```
- Hundredths: 0 + 8 = 8
- Tenths: 9 + 4 = 13 → write 3, carry 1
- Units: 1 + 7 + 1 = 9
- Tens: 1 + 0 = 1
- → 19.38
✔ Answer: 19.38
---
3) 94.57 + 33.2 =
Align:
```
94.57
+33.20
-------
127.77
```
- Hundredths: 7 + 0 = 7
- Tenths: 5 + 2 = 7
- Units: 4 + 3 = 7
- Tens: 9 + 3 = 12 → write 2, carry 1 → hundreds: 1
- → 127.77
✔ Answer: 127.77
---
4) 9.2 – 7.9 =
9.2 – 7.9 = 1.3
(Or: 9.2 – 8 = 1.2, but we subtracted 0.1 too much → add back 0.1 → 1.3)
✔ Answer: 1.3
---
5) 53.8 – 19.06 =
Align:
```
53.80
-19.06
-------
34.74
```
- Hundredths: 0 – 6 → borrow → 10 – 6 = 4 → tenths becomes 7
- Tenths: 7 – 0 = 7
- Units: 3 – 9 → borrow → 13 – 9 = 4 → tens becomes 4
- Tens: 4 – 1 = 3
- → 34.74
✔ Answer: 34.74
---
6) 70.94 – 48.4 =
Align:
```
70.94
-48.40
-------
22.54
```
- Hundredths: 4 – 0 = 4
- Tenths: 9 – 4 = 5
- Units: 0 – 8 → borrow → 10 – 8 = 2 → tens becomes 6
- Tens: 6 – 4 = 2
- → 22.54
✔ Answer: 22.54
---
7) 8.4 + 9.6 – 5.3 =
First: 8.4 + 9.6 = 18.0
Then: 18.0 – 5.3 = 12.7
✔ Answer: 12.7
---
8) 16.08 – 7.8 + 9.24 =
Do left to right:
16.08 – 7.8 = 8.28
Then: 8.28 + 9.24 =
```
8.28
+ 9.24
-------
17.52
```
✔ Answer: 17.52
---
9) 66.33 – 25.1 + 7.49 =
First: 66.33 – 25.1 = 41.23
Then: 41.23 + 7.49 =
```
41.23
+ 7.49
-------
48.72
```
✔ Answer: 48.72
---
## Section C: Solve these problems involving decimals.
---
1) Stanley stacks three books...
Thicknesses: 2.5 cm, 1.82 cm, 0.9 cm
Total height = 2.5 + 1.82 + 0.9
Align:
```
2.50
1.82
+ 0.90
-------
5.22 cm
```
✔ Answer: 5.22 cm
---
2) Family baggage problem
Baggage allowance per family: 91.2 kg
Individual weights:
- Jackson: 21.8 kg
- Sister: 31.24 kg
- Father: 19.03 kg
- Mother: 39.59 kg
a) How much have the family exceeded the allowance by?
Step 1: Add total baggage weight:
21.8 + 31.24 + 19.03 + 39.59
Let’s add step by step:
21.8 + 31.24 = 53.04
53.04 + 19.03 = 72.07
72.07 + 39.59 =
```
72.07
+39.59
-------
111.66 kg
```
Allowance = 91.2 kg
Excess = 111.66 – 91.2 = 20.46 kg
✔ Answer a: 20.46 kg
---
b) What is the 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 this formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of subtraction grade 5.
