Decimal Operations Mixed Exercise Worksheet | Printable PDF ... - Free Printable

Let's solve each part of this Decimal Operations Mixed Exercise step by step and explain the solutions clearly.

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Section A: Additions and Subtractions

We need to align decimals correctly and perform addition/subtraction.

1) $ 2.4 + 4.7 = $

$$
\begin{array}{r}
2.4 \\
+ 4.7 \\
\hline
7.1 \\
\end{array}
$$

✔ Answer: 7.1

2) $ 45.36 + 27.9 = $

First, write 27.9 as 27.90 to match decimal places:

$$
\begin{array}{r}
45.36 \\
+ 27.90 \\
\hline
73.26 \\
\end{array}
$$

✔ Answer: 73.26

3) $ 151.6 + 67.82 = $

Write 151.6 as 151.60:

$$
\begin{array}{r}
151.60 \\
+ 67.82 \\
\hline
219.42 \\
\end{array}
$$

✔ Answer: 219.42

4) $ 70 - 23.19 = $

Write 70 as 70.00:

$$
\begin{array}{r}
70.00 \\
- 23.19 \\
\hline
46.81 \\
\end{array}
$$

✔ Answer: 46.81

5) $ 88.051 - 27.34 = $

Write 27.34 as 27.340:

$$
\begin{array}{r}
88.051 \\
- 27.340 \\
\hline
60.711 \\
\end{array}
$$

✔ Answer: 60.711

6) $ 413.75 - 59.118 = $

Write 413.75 as 413.750:

$$
\begin{array}{r}
413.750 \\
- 59.118 \\
\hline
354.632 \\
\end{array}
$$

✔ Answer: 354.632

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Section B: Multiplications and Divisions

#### Multiplication: Multiply as if whole numbers, then count decimal places.

1) $ 0.7 \times 0.4 = $

$ 7 \times 4 = 28 $. Two decimal places total → 0.28

✔ Answer: 0.28

2) $ 0.08 \times 0.9 = $

$ 8 \times 9 = 72 $. Three decimal places (two in 0.08, one in 0.9) → 0.072

✔ Answer: 0.072

3) $ 1.2 \times 0.11 = $

$ 12 \times 11 = 132 $. Three decimal places → 0.132

✔ Answer: 0.132

4) $ 2.5 \times 3.2 = $

$ 25 \times 32 = 800 $. Two decimal places → 8.00 → 8.0

✔ Answer: 8.0

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#### Division: Use multiplication or move decimal points.

5) $ 84 \div 0.7 = $

Multiply numerator and denominator by 10 to eliminate decimal:

$ \frac{84}{0.7} = \frac{840}{7} = 120 $

✔ Answer: 120

6) $ 96 \div 1.2 = $

Multiply numerator and denominator by 10:

$ \frac{96}{1.2} = \frac{960}{12} = 80 $

✔ Answer: 80

7) $ 5.4 \div 0.09 = $

Multiply numerator and denominator by 100:

$ \frac{5.4}{0.09} = \frac{540}{9} = 60 $

✔ Answer: 60

8) $ 21 \div 0.015 = $

Multiply numerator and denominator by 1000:

$ \frac{21}{0.015} = \frac{21000}{15} = 1400 $

✔ Answer: 1400

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Section C: Word Problems Involving Decimals

#### 1) Find the mean average of the 5 numbers:

Numbers:
0.72, 1.04, 0.3, 0.93, 1.51

Add them:

$$
0.72 + 1.04 = 1.76 \\
1.76 + 0.3 = 2.06 \\
2.06 + 0.93 = 2.99 \\
2.99 + 1.51 = 4.50
$$

Sum = 4.50

Now divide by 5:

$$
4.50 \div 5 = 0.90
$$

✔ Answer: 0.90

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#### 2) Convert 56.8 km to miles

Given: Divide km by 1.6 to get miles

$$
56.8 \div 1.6 = ?
$$

To make it easier, multiply numerator and denominator by 10:

$$
\frac{568}{16} = 35.5
$$

✔ Answer: 35.5 miles

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#### 3) Area of a circle with radius 4.8 cm

Formula: $ \text{Area} = \pi r^2 \approx 3.14 \times r^2 $

So:

$ r = 4.8 $

$ r^2 = 4.8 \times 4.8 = 23.04 $

Now:

$ 3.14 \times 23.04 $

Break it down:

$ 3 \times 23.04 = 69.12 $
$ 0.14 \times 23.04 = ? $

Calculate:

$ 0.1 \times 23.04 = 2.304 $
$ 0.04 \times 23.04 = 0.9216 $
Add: $ 2.304 + 0.9216 = 3.2256 $

Now total area:

$ 69.12 + 3.2256 = 72.3456 $

✔ Answer: 72.3456 cm²

(You can round to 2 decimal places: 72.35 cm², but exact is fine.)

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✔ Final Answers Summary:

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Section A

1) 7.1
2) 73.26
3) 219.42
4) 46.81
5) 60.711
6) 354.632

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Section B

1) 0.28
2) 0.072
3) 0.132
4) 8.0
5) 120
6) 80
7) 60
8) 1400

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Section C

1) Mean = 0.90
2) 56.8 km = 35.5 miles
3) Area = 72.3456 cm² (or ≈ 72.35 cm²)

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