Expressions with Parentheses, Brackets, and Braces Worksheets - Free Printable

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 1: Simplify inside parentheses:
- $2 - (-6) = 2 + 6 = 8$
- $-1 + 4 = 3$

Now substitute:
$$
[-5 \times 8 + 3] \times 3
$$

Step 2: Multiply:
- $-5 \times 8 = -40$

So:
$$
[-40 + 3] \times 3 = [-37] \times 3 = -111
$$

✔ Answer: -111

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

Step 1: Simplify inside parentheses:
- $17 - 13 = 4$

Now:
$$
48 \div [8 - 4] + 1 = 48 \div 4 + 1
$$

Step 2: Divide:
- $48 \div 4 = 12$

Then add:
- $12 + 1 = 13$

✔ Answer: 13

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

Step 1: Simplify inside parentheses:
- $14 - 2 = 12$
- $5 + 7 = 12$

Now:
$$
37 - |12 \times 12| = 37 - |144|
$$

Absolute value:
- $|144| = 144$

So:
$$
37 - 144 = -107
$$

✔ Answer: -107

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

Step 1: Simplify innermost parentheses:
- $-11 + 2 = -9$

Now:
$$
[32 - 1 + (-9)] + 11 = [31 - 9] + 11 = 22 + 11 = 33
$$

Now multiply:
$$
2 \times 33 = 66
$$

✔ Answer: 66

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

Step 1: Simplify inside parentheses:
- $10 + 6 = 16$
- $16 - 8 = 8$

Now:
$$
45 - [3 \times 16 \div 8 + 8]
$$

Step 2: Do multiplication and division from left to right:
- $3 \times 16 = 48$
- $48 \div 8 = 6$

Now:
$$
45 - [6 + 8] = 45 - 14 = 31
$$

✔ Answer: 31

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

Step 1: Multiply:
- $5 \times 18 = 90$

Now:
$$
[9 + 44 - 90] \div 4 = [53 - 90] \div 4 = [-37] \div 4 = -9.25
$$

But let’s keep as fraction:
- $-37/4 = -9\frac{1}{4}$ or $-9.25$

✔ Answer: -9.25 (or $-\frac{37}{4}$)

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

Step 1: Simplify inside parentheses:
- $3 \times 12 = 36$

Now:
$$
5 \times [24 + 36] + 12 \div 6 = 5 \times 60 + 2
$$

Because $12 \div 6 = 2$

Now:
- $5 \times 60 = 300$
- $300 + 2 = 302$

✔ Answer: 302

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

Step 1: Simplify innermost:
- $45 - 49 = -4$

Now:
$$
[-34 + (-4) - 2] = -34 - 4 - 2 = -40
$$

Now:
$$
(27 + (-40)) + 18 = (-13) + 18 = 5
$$

✔ Answer: 5

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

Step 1: Simplify:
- $7 \times 7 = 49$
- $-7 + 15 = 8$

Now:
$$
(49 - 17) \div 8 = 32 \div 8 = 4
$$

✔ Answer: 4

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

Step 1: Multiply:
- $25 \times 4 = 100$

Now:
$$
[(100 + 50) - 11] = [150 - 11] = 139
$$

Take absolute value:
- $|139| = 139$

Now:
$$
46 - 139 = -93
$$

✔ Answer: -93

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✔ Final Answers:

1) -111
2) 13
3) -107
4) 66
5) 31
6) -9.25 (or $-\frac{37}{4}$)
7) 302
8) 5
9) 4
10) -93

Let me know if you'd like these steps formatted for a worksheet or explained further!