Math worksheet for practicing complex calculations using parentheses, featuring 24 problems and a calculator challenge section.

Problem: Solve the calculations and order the expressions from smallest to largest.

#### Part 1: Work out these complex calculations

We will solve each calculation step by step, following the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

---

1. \( (4 + 7) \times 3 \)

\[
(4 + 7) \times 3 = 11 \times 3 = 33
\]

---

2. \( 12 - (2 \times 5) \)

\[
12 - (2 \times 5) = 12 - 10 = 2
\]

---

3. \( (60 \div 10) - 8 \)

\[
(60 \div 10) - 8 = 6 - 8 = -2
\]

---

4. \( 25 + (3 \times 8) \)

\[
25 + (3 \times 8) = 25 + 24 = 49
\]

---

5. \( 10 \div (17 - 15) \)

\[
10 \div (17 - 15) = 10 \div 2 = 5
\]

---

6. \( 3 \times (12 - 4) \)

\[
3 \times (12 - 4) = 3 \times 8 = 24
\]

---

7. \( 9 - (2 \times 7) \)

\[
9 - (2 \times 7) = 9 - 14 = -5
\]

---

8. \( (24 \div 6) - 10 \)

\[
(24 \div 6) - 10 = 4 - 10 = -6
\]

---

9. \( \frac{1}{2} \times (20 - 4) \)

\[
\frac{1}{2} \times (20 - 4) = \frac{1}{2} \times 16 = 8
\]

---

10. \( (9 \times 6) - 42 \)

\[
(9 \times 6) - 42 = 54 - 42 = 12
\]

---

11. \( 50 - (4 \times 9) \)

\[
50 - (4 \times 9) = 50 - 36 = 14
\]

---

12. \( 27 \div (81 \div 9) \)

\[
27 \div (81 \div 9) = 27 \div 9 = 3
\]

---

13. \( (5 \times 11) - (3 \times 20) \)

\[
(5 \times 11) - (3 \times 20) = 55 - 60 = -5
\]

---

14. \( (30 - 12) \times (20 \div 10) \)

\[
(30 - 12) \times (20 \div 10) = 18 \times 2 = 36
\]

---

15. \( (16 + 11) - (5 \times 6) \)

\[
(16 + 11) - (5 \times 6) = 27 - 30 = -3
\]

---

16. \( (8 \times 6) \div (1.5 + 2.5) \)

\[
(8 \times 6) \div (1.5 + 2.5) = 48 \div 4 = 12
\]

---

Part 2: Calculator Challenges

These calculations involve more decimal numbers and larger values. We will solve them step by step.

---

17. \( 67.5 - (2.7 \times 9) \)

\[
2.7 \times 9 = 24.3
\]
\[
67.5 - 24.3 = 43.2
\]

---

18. \( (17.8 + 27.4) \times 19 \)

\[
17.8 + 27.4 = 45.2
\]
\[
45.2 \times 19 = 858.8
\]

---

19. \( 6000 - (172.95 \times 12) \)

\[
172.95 \times 12 = 2075.4
\]
\[
6000 - 2075.4 = 3924.6
\]

---

20. \( (5250 \div 25) - 190.9 \)

\[
5250 \div 25 = 210
\]
\[
210 - 190.9 = 19.1
\]

---

21. \( 3728 + (165.75 \times 4) \)

\[
165.75 \times 4 = 663
\]
\[
3728 + 663 = 4391
\]

---

22. \( 3750 - (872.4 \times 4) \)

\[
872.4 \times 4 = 3489.6
\]
\[
3750 - 3489.6 = 260.4
\]

---

23. \( (28 \times 37) - (65 \times 16) \)

\[
28 \times 37 = 1036
\]
\[
65 \times 16 = 1040
\]
\[
1036 - 1040 = -4
\]

---

24. \( (6720 \div 100) + (17.5 \times 8) \)

\[
6720 \div 100 = 67.2
\]
\[
17.5 \times 8 = 140
\]
\[
67.2 + 140 = 207.2
\]

---

Part 3: Order these expressions from smallest to largest

The expressions are:
1. \( 1.75 - (8.2 \div 4) \)
2. \( (0.35 \times 5) - (3.5 \div 5) \)
3. \( 8 - (1.63 \times 6) \)

#### Expression 1: \( 1.75 - (8.2 \div 4) \)
\[
8.2 \div 4 = 2.05
\]
\[
1.75 - 2.05 = -0.3
\]

#### Expression 2: \( (0.35 \times 5) - (3.5 \div 5) \)
\[
0.35 \times 5 = 1.75
\]
\[
3.5 \div 5 = 0.7
\]
\[
1.75 - 0.7 = 1.05
\]

#### Expression 3: \( 8 - (1.63 \times 6) \)
\[
1.63 \times 6 = 9.78
\]
\[
8 - 9.78 = -1.78
\]

#### Ordering the results:
- Expression 3: \( -1.78 \)
- Expression 1: \( -0.3 \)
- Expression 2: \( 1.05 \)

So, the order from smallest to largest is:
\[
-1.78, -0.3, 1.05
\]

---

Final Answers:

#### Part 1: Complex Calculations
\[
\boxed{
\begin{array}{lll}
1) & 33 & 2) & 2 & 3) & -2 \\
4) & 49 & 5) & 5 & 6) & 24 \\
7) & -5 & 8) & -6 & 9) & 8 \\
10) & 12 & 11) & 14 & 12) & 3 \\
13) & -5 & 14) & 36 & 15) & -3 \\
16) & 12 & & &
\end{array}
}
\]

#### Part 2: Calculator Challenges
\[
\boxed{
\begin{array}{ll}
17) & 43.2 \\
18) & 858.8 \\
19) & 3924.6 \\
20) & 19.1 \\
21) & 4391 \\
22) & 260.4 \\
23) & -4 \\
24) & 207.2 \\
\end{array}
}
\]

#### Part 3: Ordering Expressions
\[
\boxed{-1.78, -0.3, 1.05}
\]