PEMDAS Problems Worksheets 5th Grade - Free Printable

Let's solve each problem step by step using the order of operations (PEMDAS), which stands for:

- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)

We'll also pay close attention to nested parentheses, meaning parentheses inside other parentheses. We solve from the innermost set outward.

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1) $ 6^2 - (32 - 29)^2 = $

- First, evaluate exponents and parentheses:
- $ 6^2 = 36 $
- $ (32 - 29) = 3 $, so $ 3^2 = 9 $
- Now: $ 36 - 9 = 27 $

✔ Answer: 27

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2) $ [(21 - 17) \times (14 - 9)]^2 = $

- Inner parentheses:
- $ 21 - 17 = 4 $
- $ 14 - 9 = 5 $
- Multiply: $ 4 \times 5 = 20 $
- Now square: $ 20^2 = 400 $

✔ Answer: 400

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3) $ 11^2 - 3 \times 8 - 5^2 - 19 = $

- Exponents:
- $ 11^2 = 121 $
- $ 5^2 = 25 $
- Now: $ 121 - 3 \times 8 - 25 - 19 $
- Multiplication: $ 3 \times 8 = 24 $
- Now: $ 121 - 24 - 25 - 19 $
- Left to right:
- $ 121 - 24 = 97 $
- $ 97 - 25 = 72 $
- $ 72 - 19 = 53 $

✔ Answer: 53

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4) $ 11^2 - (3 \times [8 - (5^2 - 19)]) = $

- Start with innermost parentheses:
- $ 5^2 = 25 $
- $ 25 - 19 = 6 $
- Then: $ 8 - 6 = 2 $
- Then: $ 3 \times 2 = 6 $
- Now: $ 11^2 = 121 $
- So: $ 121 - 6 = 115 $

✔ Answer: 115

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5) $ 11^2 - [3 \times (8 - 5)^2] - 19 = $

- $ 11^2 = 121 $
- $ 8 - 5 = 3 $
- $ 3^2 = 9 $
- $ 3 \times 9 = 27 $
- Now: $ 121 - 27 - 19 $
- $ 121 - 27 = 94 $
- $ 94 - 19 = 75 $

✔ Answer: 75

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6) $ 12 \times (3 + 11 + 6) - 2^3 = $

- Parentheses: $ 3 + 11 + 6 = 20 $
- $ 12 \times 20 = 240 $
- $ 2^3 = 8 $
- $ 240 - 8 = 232 $

✔ Answer: 232

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7) $ 4^2 + 2^4 \times [40 - (31 - 29)^2] = $

- Exponents:
- $ 4^2 = 16 $
- $ 2^4 = 16 $
- Inside brackets:
- $ 31 - 29 = 2 $
- $ 2^2 = 4 $
- $ 40 - 4 = 36 $
- Now: $ 16 + 16 \times 36 $
- Multiplication first: $ 16 \times 36 = 576 $
- $ 16 + 576 = 592 $

✔ Answer: 592

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8) $ 1^3 \times [((9 - 21 + 7) - (2^4 - 5))] = $

- $ 1^3 = 1 $
- Inside first parentheses: $ 9 - 21 + 7 = -5 $
- $ 2^4 = 16 $
- $ 16 - 5 = 11 $
- Now: $ (-5) - 11 = -16 $
- Multiply by 1: $ 1 \times (-16) = -16 $

✔ Answer: -16

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9) $ 10^2 \times 9 - (4^3 - 4 \times 10) = $

- $ 10^2 = 100 $
- $ 4^3 = 64 $
- $ 4 \times 10 = 40 $
- $ 64 - 40 = 24 $
- Now: $ 100 \times 9 = 900 $
- $ 900 - 24 = 876 $

✔ Answer: 876

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10) $ 4^2 + 5^2 - [2 \times (11 + 9 + 13)] = $

- $ 4^2 = 16 $
- $ 5^2 = 25 $
- $ 11 + 9 + 13 = 33 $
- $ 2 \times 33 = 66 $
- Now: $ 16 + 25 = 41 $
- $ 41 - 66 = -25 $

✔ Answer: -25

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✔ Final Answers:

1) 27
2) 400
3) 53
4) 115
5) 75
6) 232
7) 592
8) -16
9) 876
10) -25

Let me know if you'd like a printable version or explanation in a different format!