Decimals Worksheets - Math Monks - Free Printable

Let's solve each part of the worksheet step by step.

---

Addition

#### (a) \( 34.67 + 27.85 \)
1. Align the decimal points:
```
34.67
+ 27.85
```
2. Add column by column from right to left:
- Hundredths: \( 7 + 5 = 12 \) → Write 2, carry 1.
- Tenths: \( 6 + 8 + 1 = 15 \) → Write 5, carry 1.
- Ones: \( 4 + 7 + 1 = 12 \) → Write 2, carry 1.
- Tens: \( 3 + 2 + 1 = 6 \).

Result: \( 62.52 \)

Answer: \( \boxed{62.52} \)

#### (b) \( 237.66 + 39.10 \)
1. Align the decimal points:
```
237.66
+ 39.10
```
2. Add column by column from right to left:
- Hundredths: \( 6 + 0 = 6 \).
- Tenths: \( 6 + 1 = 7 \).
- Ones: \( 7 + 9 = 16 \) → Write 6, carry 1.
- Tens: \( 3 + 3 + 1 = 7 \).
- Hundreds: \( 2 \).

Result: \( 276.76 \)

Answer: \( \boxed{276.76} \)

#### (c) \( 88.49 + 70.40 \)
1. Align the decimal points:
```
88.49
+ 70.40
```
2. Add column by column from right to left:
- Hundredths: \( 9 + 0 = 9 \).
- Tenths: \( 4 + 4 = 8 \).
- Ones: \( 8 + 0 = 8 \).
- Tens: \( 8 + 7 = 15 \) → Write 5, carry 1.
- Hundreds: \( 0 + 1 = 1 \).

Result: \( 158.89 \)

Answer: \( \boxed{158.89} \)

---

Subtraction

#### (a) \( 45.63 - 30.12 \)
1. Align the decimal points:
```
45.63
- 30.12
```
2. Subtract column by column from right to left:
- Hundredths: \( 3 - 2 = 1 \).
- Tenths: \( 6 - 1 = 5 \).
- Ones: \( 5 - 0 = 5 \).
- Tens: \( 4 - 3 = 1 \).

Result: \( 15.51 \)

Answer: \( \boxed{15.51} \)

#### (b) \( 94.609 - 78.517 \)
1. Align the decimal points:
```
94.609
- 78.517
```
2. Subtract column by column from right to left:
- Thousandths: \( 9 - 7 = 2 \).
- Hundredths: \( 0 - 1 \) → Borrow 1 from tenths (0 becomes 10, 6 becomes 5): \( 10 - 1 = 9 \).
- Tenths: \( 5 - 5 = 0 \).
- Ones: \( 4 - 8 \) → Borrow 1 from tens (4 becomes 14, 9 becomes 8): \( 14 - 8 = 6 \).
- Tens: \( 8 - 7 = 1 \).

Result: \( 16.092 \)

Answer: \( \boxed{16.092} \)

#### (c) \( 6.97 - 5.03 \)
1. Align the decimal points:
```
6.97
- 5.03
```
2. Subtract column by column from right to left:
- Hundredths: \( 7 - 3 = 4 \).
- Tenths: \( 9 - 0 = 9 \).
- Ones: \( 6 - 5 = 1 \).

Result: \( 1.94 \)

Answer: \( \boxed{1.94} \)

---

Multiplication

#### (a) \( 6.72 \times 12 \)
1. Multiply as if they are whole numbers:
```
672
x 12
------
1344 (672 × 2)
672 (672 × 1, shifted one place to the left)
------
8064
```
2. Count the total number of decimal places in the factors: \( 6.72 \) has 2 decimal places, and \( 12 \) has 0 decimal places. Total: 2 decimal places.
3. Place the decimal point in the product: \( 80.64 \).

Answer: \( \boxed{80.64} \)

#### (b) \( 97.304 \times 67.3 \)
1. Multiply as if they are whole numbers:
```
97304
x 673
--------
291912 (97304 × 3)
681128 (97304 × 7, shifted one place to the left)
583824 (97304 × 6, shifted two places to the left)
--------
65420432
```
2. Count the total number of decimal places in the factors: \( 97.304 \) has 3 decimal places, and \( 67.3 \) has 1 decimal place. Total: 4 decimal places.
3. Place the decimal point in the product: \( 6542.0432 \).

Answer: \( \boxed{6542.0432} \)

#### (c) \( 13.79 \times 9.36 \)
1. Multiply as if they are whole numbers:
```
1379
x 936
------
8274 (1379 × 6)
4137 (1379 × 3, shifted one place to the left)
12411 (1379 × 9, shifted two places to the left)
------
1290864
```
2. Count the total number of decimal places in the factors: \( 13.79 \) has 2 decimal places, and \( 9.36 \) has 2 decimal places. Total: 4 decimal places.
3. Place the decimal point in the product: \( 129.0864 \).

Answer: \( \boxed{129.0864} \)

---

Division

#### (a) \( 99.67 \div 7 \)
1. Perform long division:
- \( 7 \) goes into \( 9 \) once (write 1, remainder 2).
- Bring down 9: \( 29 \div 7 = 4 \) (write 4, remainder 1).
- Bring down 6: \( 16 \div 7 = 2 \) (write 2, remainder 2).
- Bring down 7: \( 27 \div 7 = 3 \) (write 3, remainder 6).
- Add a decimal point and bring down 0: \( 60 \div 7 = 8 \) (write 8, remainder 4).
- Bring down 0: \( 40 \div 7 = 5 \) (write 5, remainder 5).

Result: \( 14.23857\ldots \) (repeating).

Answer: \( \boxed{14.2386} \) (rounded to 4 decimal places)

#### (b) \( 89.76 \div 4 \)
1. Perform long division:
- \( 4 \) goes into \( 8 \) twice (write 2, no remainder).
- Bring down 9: \( 9 \div 4 = 2 \) (write 2, remainder 1).
- Bring down 7: \( 17 \div 4 = 4 \) (write 4, remainder 1).
- Bring down 6: \( 16 \div 4 = 4 \) (write 4, no remainder).

Result: \( 22.44 \).

Answer: \( \boxed{22.44} \)

#### (c) \( 60.57 \div 9 \)
1. Perform long division:
- \( 9 \) goes into \( 60 \) six times (write 6, remainder 6).
- Bring down 5: \( 65 \div 9 = 7 \) (write 7, remainder 2).
- Bring down 7: \( 27 \div 9 = 3 \) (write 3, no remainder).

Result: \( 6.73 \).

Answer: \( \boxed{6.73} \)

---

Final Answers

1. Addition:
- (a) \( \boxed{62.52} \)
- (b) \( \boxed{276.76} \)
- (c) \( \boxed{158.89} \)

2. Subtraction:
- (a) \( \boxed{15.51} \)
- (b) \( \boxed{16.092} \)
- (c) \( \boxed{1.94} \)

3. Multiplication:
- (a) \( \boxed{80.64} \)
- (b) \( \boxed{6542.0432} \)
- (c) \( \boxed{129.0864} \)

4. Division:
- (a) \( \boxed{14.2386} \)
- (b) \( \boxed{22.44} \)
- (c) \( \boxed{6.73} \)