Evaluating Expressions with Nested Parentheses Worksheets - Free Printable

Let's evaluate 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), especially paying attention to nested parentheses.

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1) $ 29 + (14 \times (9 - 4)) + 7 - 5 $

- First, innermost parentheses:
$ 9 - 4 = 5 $
- Then multiplication:
$ 14 \times 5 = 70 $
- Now substitute:
$ 29 + 70 + 7 - 5 $
- Left to right:
$ 29 + 70 = 99 $
$ 99 + 7 = 106 $
$ 106 - 5 = 101 $

✔ Answer: 101

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2) $ 13 \times 8 + ((55 - 7) + 12) $

- Inner parentheses:
$ 55 - 7 = 48 $
- Then:
$ 48 + 12 = 60 $
- Now:
$ 13 \times 8 = 104 $
- Then:
$ 104 + 60 = 164 $

✔ Answer: 164

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3) $ (2 \times (51 + 3)) - 54 + 3 $

- Inside parentheses:
$ 51 + 3 = 54 $
- Multiply:
$ 2 \times 54 = 108 $
- Now:
$ 108 - 54 + 3 $
- Left to right:
$ 108 - 54 = 54 $
$ 54 + 3 = 57 $

✔ Answer: 57

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4) $ 19 - 61 + ((3 \times 12) + 9) - 14 $

- Inner:
$ 3 \times 12 = 36 $
- Then:
$ 36 + 9 = 45 $
- Now:
$ 19 - 61 + 45 - 14 $
- Left to right:
$ 19 - 61 = -42 $
$ -42 + 45 = 3 $
$ 3 - 14 = -11 $

✔ Answer: -11

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5) $ 35 - ((27 + 3) + 11) \times 3 + 10 $

- Inner parentheses:
$ 27 + 3 = 30 $
- Then:
$ 30 + 11 = 41 $
- Multiply:
$ 41 \times 3 = 123 $
- Now:
$ 35 - 123 + 10 $
- Left to right:
$ 35 - 123 = -88 $
$ -88 + 10 = -78 $

✔ Answer: -78

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6) $ 120 + (15 \times (39 + 13)) - 43 $

- Inner:
$ 39 + 13 = 52 $
- Multiply:
$ 15 \times 52 = 780 $
- Now:
$ 120 + 780 - 43 $
- $ 120 + 780 = 900 $
$ 900 - 43 = 857 $

✔ Answer: 857

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7) $ 19 \times 65 + (2 + (1 - 16)) $

- Innermost:
$ 1 - 16 = -15 $
- Then:
$ 2 + (-15) = -13 $
- Now:
$ 19 \times 65 = 1235 $
- Then:
$ 1235 + (-13) = 1235 - 13 = 1222 $

✔ Answer: 1222

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8) $ ((4 \times 15) + 27) + 3 - 90 + 2 $

- Inner:
$ 4 \times 15 = 60 $
- Then:
$ 60 + 27 = 87 $
- Now:
$ 87 + 3 = 90 $
$ 90 - 90 = 0 $
$ 0 + 2 = 2 $

✔ Answer: 2

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9) $ 180 + ((7 + 3) \times 2) - 1 + 8 $

- Inner:
$ 7 + 3 = 10 $
- Multiply:
$ 10 \times 2 = 20 $
- Now:
$ 180 + 20 - 1 + 8 $
- Left to right:
$ 180 + 20 = 200 $
$ 200 - 1 = 199 $
$ 199 + 8 = 207 $

✔ Answer: 207

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10) $ (50 + (35 + 7)) - 2 \times 4 $

- Inner:
$ 35 + 7 = 42 $
- Then:
$ 50 + 42 = 92 $
- Now:
$ 2 \times 4 = 8 $
- Then:
$ 92 - 8 = 84 $

✔ Answer: 84

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✔ Final Answers:

1. 101
2. 164
3. 57
4. -11
5. -78
6. 857
7. 1222
8. 2
9. 207
10. 84

Let me know if you'd like these explained in a different format or with visual steps!