Math worksheet for practicing order of operations with parentheses, brackets, and braces.

Let's solve each expression step by step, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right), and carefully handling parentheses, brackets, and braces.

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1) $[-5 \times (2 - (-6)) + (-1 + 4)] \times 3$

Step-by-step:

- Simplify inside parentheses:
- $2 - (-6) = 2 + 6 = 8$
- $-1 + 4 = 3$
- Now substitute:
- $[-5 \times 8 + 3] \times 3$
- Multiply:
- $-5 \times 8 = -40$
- So: $[-40 + 3] \times 3 = [-37] \times 3$
- Multiply:
- $-37 \times 3 = -111$

✔ Answer: $-111$

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2) $48 \div [8 - (17 - 13)] + 1$

Step-by-step:

- Simplify inner parentheses:
- $17 - 13 = 4$
- Then:
- $8 - 4 = 4$
- Now:
- $48 \div 4 + 1 = 12 + 1 = 13$

✔ Answer: $13$

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3) $37 - |(14 - 2) \times (5 + 7)|$

Step-by-step:

- Simplify inside parentheses:
- $14 - 2 = 12$
- $5 + 7 = 12$
- Multiply:
- $12 \times 12 = 144$
- Absolute value:
- $|144| = 144$
- Subtract:
- $37 - 144 = -107$

✔ Answer: $-107$

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4) $2 \times ([32 - 1 + (-11 + 2)] + 11)$

Step-by-step:

- Simplify inside inner parentheses:
- $-11 + 2 = -9$
- Now simplify inside brackets:
- $32 - 1 + (-9) = 31 - 9 = 22$
- Add 11:
- $22 + 11 = 33$
- Multiply:
- $2 \times 33 = 66$

✔ Answer: $66$

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5) $45 - [3 \times ((10 + 6) \div 8 + (16 - 8))]$

Step-by-step:

- Simplify inner parentheses:
- $10 + 6 = 16$
- $16 - 8 = 8$
- Divide:
- $16 \div 8 = 2$
- Add:
- $2 + 8 = 10$
- Multiply:
- $3 \times 10 = 30$
- Subtract:
- $45 - 30 = 15$

✔ Answer: $15$

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6) $[9 + 44 - (5 \times 18)] \div 4$

Step-by-step:

- Multiply:
- $5 \times 18 = 90$
- Simplify inside brackets:
- $9 + 44 = 53$
- $53 - 90 = -37$
- Divide:
- $-37 \div 4 = -9.25$

✔ Answer: $-9.25$ or $-\frac{37}{4}$

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7) $5 \times [24 + (3 \times 12)] + 12] \div 6$

Wait — there’s a mismatch in parentheses. Let's check:

Original:
$5 \times [24 + (3 \times 12)] + 12] \div 6$

This has an extra closing bracket. Likely meant to be:

> $5 \times [24 + (3 \times 12) + 12] \div 6$

Assuming that’s correct:

Step-by-step:

- $3 \times 12 = 36$
- $24 + 36 + 12 = 72$
- $5 \times 72 = 360$
- $360 \div 6 = 60$

✔ Answer: $60$

*(Note: If original was different, please clarify. But this is most logical interpretation.)*

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8) $(27 + [-34 + (45 - 49) - 2]) + 18$

Step-by-step:

- $45 - 49 = -4$
- $-34 + (-4) = -38$
- $-38 - 2 = -40$
- $27 + (-40) = -13$
- $-13 + 18 = 5$

✔ Answer: $5$

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9) $[(7 \times 7) - 17] \div (-7 + 15)$

Step-by-step:

- $7 \times 7 = 49$
- $49 - 17 = 32$
- $-7 + 15 = 8$
- $32 \div 8 = 4$

✔ Answer: $4$

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10) $46 - |[(25 \times 4) + 50] - 11|$

Step-by-step:

- $25 \times 4 = 100$
- $100 + 50 = 150$
- $150 - 11 = 139$
- $|139| = 139$
- $46 - 139 = -93$

✔ Answer: $-93$

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✔ Final Answers:

1) $-111$
2) $13$
3) $-107$
4) $66$
5) $15$
6) $-9.25$ or $-\frac{37}{4}$
7) $60$ *(assuming corrected expression)*
8) $5$
9) $4$
10) $-93$

Let me know if you'd like these formatted for printing or with steps in a table!